Edited by
Igor Medintz
Niko Hildebrandt
FRET - Förster Resonance
Energy Transfer
(also available in digital formats)
Balzani, V., Ceroni, P., Juris, A.
Sauer, M., Hofkens, J., Enderlein, J.
Photochemistry and
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Handbook of Fluorescence
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Concepts, Research Topics, Applications
From Single Molecules to Ensembles
2014
ISBN: 978-3-527-33479-7
2011
ISBN: 978-3-527-31669-4
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FRET - Förster Resonance Energy Transfer
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Edited by Igor Medintz and Niko Hildebrandt
Dr. Igor Medintz
U.S. Naval Research Laboratory
Center for Bio/Molecular Science and
Engineering
4555 Overlook Avenue, SW
Washington D.C. 20375
United States
Dr. Niko Hildebrandt
Universite Paris-Sud
Institut d’Electronique Fondamentale
NanoBioPhotonics
Bâtiment 220
91405 Orsay Cedex
France
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Editors
Contents
Preface XV
List of Contributors XIX
Part One
Background, Theory, and Concepts 1
1
How I Remember Theodor F€
orster 3
Herbert Dreeskamp
2
Remembering Robert Clegg and Elizabeth Jares-Erijman and Their
Contributions to FRET 9
Thomas M. Jovin
Biographical Sketch of Bob Clegg 10
Biographical Sketch of Eli Jares-Erijman 11
The Pervasive Influence of Gregorio Weber 12
Contributions by Bob Clegg to FRET 12
Contributions by Eli Jares-Erijman to FRET 16
A Final Thought 18
References 19
2.1
2.2
2.3
2.4
2.5
2.6
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
F€
orster Theory 23
B. Wieb van der Meer
Introduction 23
Pre-F€orster 23
Bottom Line 25
9000-Form, 9-Form, and Practical Expressions of the R06 Equation 26
Overlap Integral 28
Zones 31
Transfer Mechanisms 33
Kappa-Squared Basics 34
Ideal Dipole Approximation 35
Resonance as an All-or-Nothing Effect 36
Details About the All-or-Nothing Approximation of Resonance 39
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jV
j Contents
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
5
5.1
5.2
5.3
5.4
5.4.1
5.4.2
5.4.2.1
5.4.2.2
5.4.2.3
5.4.2.4
5.4.2.5
5.4.3
Classical Theory Completed 41
Oscillator Strength–Emission Spectrum Relation
for the Donor 42
Oscillator Strength–Absorption Spectrum Relation
for the Acceptor 43
Quantum Mechanical Theory 44
Transfer in a Random System 47
Details for Transfer in a Random System 48
Concentration Depolarization 51
FRET Theory 1965–2012 52
References 59
Optimizing the Orientation Factor Kappa-Squared for More Accurate
FRET Measurements 63
B. Wieb van der Meer, Daniel M. van der Meer, and Steven S. Vogel
Two-Thirds or Not Two-Thirds? 63
Relevant Questions 65
How to Visualize Kappa-Squared? 65
Kappa-Squared Can Be Measured in At Least One Case 68
Averaging Regimes 70
Dynamic Averaging Regime 72
What Is the Most Probable Value for Kappa-Squared in the
Dynamic Regime? 76
Optimistic, Conservative, and Practical Approaches 83
Comparison with Experimental Results 85
Smart Simulations Are Superior 90
Static Kappa-Squared 92
Beyond Regimes 101
Conclusions 102
References 103
How to Apply FRET: From Experimental Design to Data Analysis 105
Niko Hildebrandt
Introduction: FRET – More Than a Four-Letter Word! 105
FRET: Let’s get started! 106
FRET: The Basic Concept 107
FRET: Inevitable Mathematics 112
F€orster Distance (or F€orster Radius) 112
FRET Efficiency 113
Determination by Donor Quenching 113
Determination by Acceptor Sensitization 113
Determination by Donor Quenching and Acceptor Sensitization 114
Determination by Donor Photobleaching 115
Determination by Acceptor Photobleaching 115
FRET with Multiple Donors and/or Acceptors 116
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VI
5.5
5.5.1
5.5.2
5.5.3
5.5.3.1
5.5.3.2
5.5.3.3
5.6
5.6.1
5.6.1.1
5.6.2
5.6.3
5.6.4
5.6.4.1
5.6.4.2
5.6.4.3
5.6.4.4
5.7
6
6.1
6.2
6.3
6.3.1
6.3.2
6.3.3
6.3.4
6.3.5
6.3.6
6.3.7
6.4
6.4.1
6.4.2
6.4.3
6.4.4
6.4.5
6.4.6
6.4.7
FRET: The Experiment 118
The Donor–Acceptor FRET Pair 118
F€orster Distance Determination 119
The Main FRET Experiment 122
Steady-State FRET Measurements 123
Time-Resolved FRET Measurements 130
Interpretation of Time-Resolved FRET Data 133
FRET beyond F€orster 139
Time-Resolved FRET with Lanthanide-Based Donors 140
Terbium to Quantum Dot FRET Using Time-Resolved Donor
Quenching and Acceptor Sensitization Analysis 141
BRET and CRET 147
Energy Transfer to Metal Nanoparticles (FRET, NSET, DMPET,
NPILM, etc.) 148
Other Transfer Mechanisms 150
Electron Exchange Energy Transfer (Dexter Transfer) 151
Charge Transfer (Marcus Theory) 152
Plasmon Coupling 153
Singlet Oxygen Diffusion 154
Summary and Outlook 155
References 156
Materials for FRET Analysis: Beyond Traditional Dye–Dye
Combinations 165
Kim E. Sapsford, Bridget Wildt, Angela Mariani, Andrew B. Yeatts,
and Igor Medintz
Introduction 165
Bioconjugation 166
Organic Materials 171
Ultraviolet, Visible, and Near-Infrared
Emitting Dyes 171
Quencher Molecules 173
Environmentally Sensitive Fluorophores 175
Dye-Modified Microspheres/Nanomaterials 179
Dendrimers and Polymer Macromolecules 180
Photochromic Dyes 182
Carbon Nanomaterials 186
Biological Materials 188
Natural Fluorophores 188
Nonnatural Amino Acids 190
Green Fluorescent Protein and Derivatives 192
Light-Harvesting Proteins 200
DNA-Based Macrostructures/Nanotechnology 201
Enzyme-Generated Bioluminescence 201
Enzyme-Generated Chemiluminescence 209
jVII
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Contents
j Contents
6.5
6.5.1
6.5.2
6.5.3
6.5.4
6.5.5
6.6
6.7
Inorganic Materials 211
Luminescent Lanthanide Complexes and Doped Nano-/
Microparticles 212
Luminescent Transition Metal Complexes 217
Noble Metal Nanomaterials (Gold, Silver, and Copper) 219
Silicon-Based Materials 222
Semiconductor Nanocrystals 223
Multi-FRET Systems 231
Summary and Outlook 236
References 236
Part Two
Common FRET Techniques/Applications 269
7
In Vitro FRET Sensing, Diagnostics, and Personalized Medicine 271
Samantha Spindel, Jessica Granek, and Kim E. Sapsford
Introduction 271
Small Organic Molecules and Synthetic Organic
Polymers 272
Carbohydrate–Lipid 273
The Biotin–Avidin Interaction 273
Proteins and Peptides 275
Binding Proteins 275
Antigens and Epitope-Based Peptide Sequences 277
Peptide Sequences for Enzymatic Sensing 279
Antibodies 282
Nucleic Acid (DNA/RNA) 287
Molecular Beacons 288
Polymerase Chain Reaction and FRET 289
FRET Hybridization Probes 290
TaqMan 291
Scorpion Assay 292
Others 294
Isothermal Amplification Reactions and FRET 294
Clinical Applications of Nucleic Acid Detection
Using FRET 295
Detection of Pathogens 295
Prognostic and Diagnostic Applications 296
Pharmacogenomics and Personalized Medicine 298
Aptamers 299
High-Throughput and Point-of-Care Devices 302
PoC Technology Advances 302
PoC Material Advances 304
Conclusions 305
References 305
7.1
7.2
7.3
7.4
7.5
7.5.1
7.5.2
7.5.3
7.6
7.7
7.7.1
7.7.2
7.7.2.1
7.7.2.2
7.7.2.3
7.7.2.4
7.7.3
7.7.4
7.7.4.1
7.7.4.2
7.7.4.3
7.8
7.9
7.9.1
7.9.2
7.10
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VIII
8
8.1
8.2
8.2.1
8.2.1.1
8.2.1.2
8.2.1.3
8.2.2
8.2.3
8.2.4
8.3
8.3.1
8.3.2
8.3.3
8.3.3.1
8.3.3.2
8.4
8.4.1
8.4.2
8.5
9
9.1
9.2
9.3
9.3.1
9.3.2
9.4
9.4.1
9.4.2
9.5
9.6
9.6.1
9.6.2
9.7
9.7.1
9.7.2
9.8
9.9
Single-Molecule Applications 323
Thomas Pons
Introduction 323
Single-Molecule FRET of Immobilized Molecules 324
Experimental Setup 324
Molecule Immobilization 324
Fluorophore Photostability 325
Optical Setup 326
Data Analysis 326
Applications 329
Analyzing Complex FRET Trajectories 334
Single-Molecule FRET of Freely Diffusing Molecules 336
Experimental Setup 336
Applications 337
Advanced Solution smFRET Methods 343
Alternate Laser Excitation 343
Multiparameter Fluorescence Detection 344
Single-Molecule FRET Studies Involving Multiple FRET Partners 346
Multistep FRET 347
Multi-Acceptor and Multi-Donor Systems 348
Conclusions and Perspectives 351
References 353
Implementation of FRET Technologies for Studying the Folding and
Conformational Changes in Biological Structures 357
Philip J. Robinson and Cheryl A. Woolhead
Introduction to Using FRET in Biological Systems 357
F€orster Formalism in the Determination of Biological Structures 358
FRET Experiments in Complex Biological Systems 360
The Importance of Experimental Design 360
Site-Specific Labeling and Choosing the Most Effective FRET Pair 361
Biological Model System 1: The Ribosome 362
Intersubunit Rotation within the Ribosome 363
Dynamic Intrasubunit Movement Within the Ribosome 365
Biological System 2: Nascent Polypeptide Structure 365
Biological System 3: Chaperone-Mediated Protein Folding 368
Signal Recognition Particle 368
Trigger Factor 369
Biological System 4: Mature Protein Folding Intermediates 371
Unfolding Kinetics of Monellin 372
Intermediate Folding State of the Src Homology 3 Domain 374
Biological System 5: Intersubunit Distance in Multimeric Protein
Complexes 375
Biological System 6: Protein–Protein Interactions in the Assembly of
Protein Polymers 378
jIX
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Contents
9.9.1
9.9.2
9.10
9.10.1
9.10.2
9.10.3
10
10.1
10.2
10.2.1
10.2.2
10.3
10.3.1
10.3.2
10.4
10.4.1
10.4.2
10.4.3
10.4.4
10.5
Part Three
11
11.1
11.1.1
11.1.1.1
11.1.1.2
11.1.1.3
11.1.2
11.1.2.1
11.1.2.2
11.1.2.3
11.1.2.4
11.1.2.5
FtsZ Assembly and Subunit Exchange 379
Defining the Molecular Link in Serpin Polymers 380
Biological System 7: FRET in Nucleic Acid Systems 385
Determining the Structure and Configuration
of DNA Junctions 386
Measuring the Opening and Closing of a
Nanoscale DNA Box 388
FRET Between a DNA Polymerase and Its Substrate 390
References 392
FRET-Based Cellular Sensing with Genetically Encoded Fluorescent
Indicators 397
Jonathan C. Claussen, Niko Hildebrandt, and Igor Medintz
Introduction 397
Enzymes 399
Kinase Activity/Phosphorylation 399
Protease Activity 403
Metabolites 407
Sugars 407
Glutamate 410
Second Messengers 412
cAMP 412
cGMP 415
Nitric Oxide 417
Calcium 419
Conclusions 421
References 423
FRET with Recently Developed Materials 431
FRET with Fluorescent Proteins 433
Hiofan Hoi, Yidan Ding, and Robert E. Campbell
Introduction to FPs 433
Wild-Type FPs 433
Natural Sources 433
Structure 434
Chromophore Formation 436
Engineered FPs for FRET Applications 438
Overview 438
Blue–Green FRET Pairs 440
Cyan–Yellow FRET Pairs 441
FRET with Orange, Red, and Far-Red FPs 443
Atypical FPs Useful for FRET Applications 445
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j Contents
X
11.1.3
11.2
11.2.1
11.2.1.1
11.2.1.2
11.2.1.3
11.2.2
11.2.2.1
11.2.2.2
11.2.2.3
11.2.3
11.2.3.1
11.2.3.2
11.2.3.3
11.2.3.4
11.2.4
11.2.4.1
11.2.4.2
11.2.4.3
11.3
Why Use FPs for FRET? 446
Using FPs for FRET Imaging 446
Photophysical Properties and Typical F€
orster Radii 446
Overview 446
Spectral Overlap 447
Orientation Factors 449
Potential Sources of Artifacts During FRET Imaging 450
Photobleaching 450
Photoconversion 451
pH Dependence 452
Biochemical and Structural Considerations 453
General Considerations when Labeling Proteins with FPs 453
Labeling Proteins for Intermolecular FRET Experiments 454
Labeling Proteins for Intramolecular FRET Experiments 454
FP Oligomerization and FRET Efficiency 455
Applications and Examples 458
Overview 458
FRET Biosensor Case Study 459
FRET between FPs and Other Donor or Acceptor Materials 460
Conclusions 462
References 463
12
Semiconductor Quantum Dots and FRET 475
W. Russ Algar, Melissa Massey, and Ulrich J. Krull
Introduction 475
A Quick Review of FRET 476
Quantum Dots 477
A Brief History 478
The Structure of Quantum Dots: The Core 478
The Optical Properties of Quantum Dots 480
Overcoming the Limitations of Molecular Fluorophores 482
The Structure of Quantum Dots: The Shell 483
Quantum Confinement 485
Quantum Dot Photophysics 488
Quantum Dot Synthesis 491
Quantum Dot Coatings 493
Quantum Dot Bioconjugation 496
Quantum Dot Nomenclature in This Chapter 499
Quantum Dots and FRET 499
Quantum Dots as Donors 499
Applicability of the F€orster Formalism 502
QDs as Acceptors 504
The Importance of Bioconjugate Chemistry 506
Quantum Dots as Donors in Biological Applications 508
Association and Dissociation to Modulate QD-FRET 508
12.1
12.2
12.3
12.3.1
12.3.2
12.3.3
12.3.4
12.3.5
12.3.6
12.3.7
12.3.8
12.3.9
12.3.10
12.3.11
12.4
12.4.1
12.4.2
12.4.3
12.4.4
12.5
12.5.1
jXI
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Contents
j Contents
12.5.1.1
12.5.1.2
12.5.1.3
12.5.1.4
12.5.1.5
12.5.1.6
12.5.2
12.5.3
12.5.4
12.5.5
12.5.6
12.5.6.1
12.5.6.2
12.5.6.3
12.5.6.4
12.5.6.5
12.5.7
12.6
12.6.1
12.6.2
12.6.3
12.6.4
12.7
12.7.1
12.7.2
12.7.2.1
12.7.2.2
12.8
12.8.1
12.8.2
12.9
13
13.1
13.2
13.2.1
13.2.2
13.2.3
13.3
13.4
13.4.1
13.4.2
Bioanalysis of Carbohydrates 509
Homogeneous Immunoassays 510
Hybridization Assays 511
Bioanalyses Using Aptamers and DNAzymes 516
Bioanalysis of Hydrolytic Enzymes 519
Gene Delivery 524
Changes in Distance to Modulate QD-FRET 524
Conformational Insights from QD-FRET 528
Dynamic Modulation of the Spectral Overlap Integral
and QD-FRET 530
Single-Pair QD-FRET 534
Solid-Phase QD-FRET 540
Biomolecular Surface Tethers 542
Chemical Conjugation to an Interface 544
Interfacial Ligand Exchange 545
Electrostatic Immobilization 547
Advantages of Immobilized QDs 548
Photodynamic Therapy 549
Quantum Dots as Acceptors in Biological Applications 552
Chemiluminescence Resonance Energy Transfer (CRET) 553
Bioluminescence Resonance Energy Transfer (BRET) 555
Lanthanide Donors 560
Quantum Dot Donors (for Quantum Dot Acceptors) 565
Energy Transfer between Quantum Dots and Other
Nanomaterials 569
Gold Nanoparticles 569
Carbon Nanomaterials 575
Graphene and Graphene Oxide 575
Carbon Nanotubes 577
Nonbiological Applications of Quantum Dots and FRET 578
Photovoltaic Cells 580
Light-Emitting Diodes (LEDs) 582
Summary 583
References 584
Multistep FRET and Nanotechnology 607
Bo Albinsson and Jonas K. Hannestad
Introduction 607
Fundamentals of Multistep FRET 608
Hetero-FRET 609
Multicolor FRET and Alternating-Laser Excitation 611
Homo-FRET 612
Energy Transfer in Photosynthesis 615
Photonic Wires and Multistep FRET in Nanotechnology 617
Photonic Wires 617
Beyond Wires 628
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XII
13.4.3
13.4.4
13.4.5
13.4.6
13.5
13.6
Light Harvesting 632
Functional Control 638
Quantum Dots in Multistep FRET 641
Potential Outputs and Uses for Channeled Excitation Energy 643
Summary 647
Note Added in Proof 648
References 648
Part Four
Supporting Information and Conclusions 655
14
Data 657
Alice G. Byrne, Matthew M. Byrne, George Coker III, Kelly B. Gemmill,
Christopher Spillmann, Igor Medintz, Seth L. Sloan,
and B. Wieb van der Meer
Tables before 1987 658
Introduction to the Table of Traditional Chromophores 658
F€orster Distances and Other FRET Data before 1994 703
F€orster Distances for Traditional Probes More Recent Than 1993 703
FRET Data on Fluorescent Proteins 703
FRET Data on Quantum Dots 742
Donor–Acceptor Pairs with a F€orster Distance in a Given Range 742
Table–Reference Directory 744
References 745
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
Outlook on FRET: The Future of Resonance Energy Transfer 757
A Rosy Crystal Ball View of FRET 757
Thomas M. Jovin
Do Not Ask What FRET Can Do for You, Ask What You Can Do for
FRET 757
B. Wieb van der Meer
FRET: Future Research with an Exciting Technology 758
Niko Hildebrandt
Future of FRET 760
Kim E. Sapsford
Outlook on Single-Molecule FRET 760
Thomas Pons
Outlook on FRET with fluorescent proteins 761
Robert E. Campbell
Luminescent Nanoparticles: Scaffolds for Assembling “Smarter” FRET
Probes 762
W. Russ Algar
References 764
Index 767
jXIII
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Contents
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Preface
Several factors over the last few years have come together to contribute to the origin
and development of this book. First and foremost is the incredible expansion in the
application of FRET and its derivative techniques, especially in the biological
sciences. Web of Science (www.thomsonreuters.com) provides more than 12,000
items using the search term FRET as a unique topic, while PubMed (www.ncbi.nlm
.nih.gov/pubmed) provides almost 6000 items. The latter site also allows tracking of
these items over time with 0 hits shown for 1979 and >1000 predicted for 2013 – an
impressive and eye-opening increase. This stands in stark contrast to the years
1970–1990 that have less than 20 publications in total. This is not to say that nothing
significant happened during this time period, but rather it reflects how specialized
the field was and reminding us also of how poor the performance of journal citation
and referencing tools were before the 1990s. In terms of just citations alone,
F€orster’s original 1948 paper in Annalen der Physik has to its credit a remarkable
5000 citations, although it is safe to say that only a minority of those who cite this
article have read it (especially in the original German). Indeed, some scientists
consider this to be one of the most cited papers that has never been actually read.
Development of and access to a wide range of versatile fluorescent materials in
conjunction with improved, easy-to-use and yet incredibly sophisticated microscopes and fluorometers have coincided with, helped drive, and also increased FRET
usage. Fluorophores that are utilized in FRET now commonly encompass organic
dyes, fluorescent proteins, semiconductor quantum dots, metal chelates, various
noble metal and other nanoparticles, intrinsically fluorescent amino acids, biological
cofactors, and polymers, to name but a few members of this growing library. Hand
in hand with materials development is the growing availability of numerous reactive
and bioorthogonal chemistries to site–specifically attach such fluorophores to all
types of biological molecules ranging from proteins to DNA. This, in conjunction
with FRETs unique ability to consistently provide nanoscale inter- and intramolecular separation distances, has meant that its utility is also rapidly growing
in structural studies of biomolecules and biological complexes. We have also seen
the implementation of intracellularly expressed fluorescent protein-based FRET
sensors expand so rapidly over the past 15 years that it is now not uncommon to
encounter students who do not know where this technology originated from (Roger
Tsien, University of California San Diego). Perhaps this is the ultimate form of a
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jXV
j Preface
compliment in science – when something becomes so commonplace and widely
accepted that people forget who invented it. Concomitant with this rapid development of materials, commercial microscope systems combined with sophisticated
analytical software are now widely available providing direct access to many different
FRET techniques and their derivatives. Another proof that FRET techniques have
come of age is the recent meeting entitled “F€
orster Resonance Energy Transfer in the
Life Sciences” held at the Max Planck Institute for Biophysical Chemistry in
G€ottingen, Germany, in March 2011. This relaxed and wonderfully stimulating
discussion meeting organized by Donna Arndt-Jovin, Stefan Hell, Thomas Jovin,
Claus Seidel, and J€
urgen Troe focused on all the different aspects of FRET from
analytical techniques and microscopy to new materials. That FRET could be the
stand-alone subject of an international scientific meeting speaks volumes to its
growing utility. In addition, not many people realize that the genomics revolution of
the past 15–20 years owes a large debt to the use of FRET. Richard Mathies and Alex
Glazer at the University of California Berkeley were among the first to realize that
use of a dye-based FRET system could drastically simplify the instrumental requirements for DNA sequencing. By linking a single donor dye with four different
acceptors (representing the four DNA bases), they were able to provide a set of four
common DNA primers. These constructs used FRET to create four spectrally wellseparated windows that could be excited by a single laser wavelength in any
electrophoretic system instead of requiring two or three separate lasers. This
strategy quickly became the workhorse of DNA analysis and, as is typical for any
successful and proprietary technology, this also became the subject of considerable
litigation. Similar FRET systems form the basis for numerous genotyping tests such
as the Taqman assay that have also contributed quite considerably to genomics. A
variety of other FRET assay formats for monitoring enzymatic activity and the like
have also become quite commonplace in biosensing, biological research, and drug
discovery.
Niko and I both come from laboratories that are very interested in understanding
how newer materials such as quantum dots and/or long-lifetime rare-earth chelates
engage in FRET and other forms of energy transfer. These materials provide for
fascinating energy transfer configurations that were not described or even considered in F€orster’s seminal treatise. For example, can FRET occur when the acceptor is
as well excited as a donor while manifesting a much longer excited state lifetime as
in the case of pairing an organic dye donor such as fluorescein with a red-emitting
quantum dot. With questions such as this in mind, one of the main FRET resources
that is almost invariably consulted first in the pursuit of appropriate background is
Lakowicz’s excellent primer – Principles of Fluorescence Spectroscopy (Springer).
Although still one of the most readable textbooks ever published, this resource
provides only a limited amount of data and discussion on the intricacies of FRET.
Van Der Meer’s Resonance Energy Transfer Theory and Data (Wiley-VCH Verlag
GmbH) is far more detailed about FRET mechanics and is another well-cited
reference in this area; however, this has unfortunately fallen out of print and is
quite hard to find. Thus, it was that we both found ourselves lamenting the lack of an
up-to-date and detailed resource/primer on all aspects of FRET when Wiley-VCH
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XVI
graciously approached us about undertaking a book on an important scientific area
of our choice. It did not take us long to decide the subject that we were going to
propose.
The authors who contributed the individual chapters in this book reflect not only
some of the principal experts in the field but also the wide diversity of FRET
application itself. We very much appreciate the support of leaders in this field,
including Robert E. Campbell, Bo Albinsson, and Jonas Hannestad. We were also
overjoyed when Wieb van Der Meer agreed to make several major contributions to
this project. The book is divided into four major parts. Part One provides some
background, theory, and key concepts. This part begins with a personal remembrance of Theodor F€orster by one of his former students and colleagues Herbert
Dreeskamp (Chapter 1). Thomas Jovin then notes the recent passing of Robert Clegg
and Elizabeth Jares-Erijman by describing their important contributions to FRET
(Chapter 2). Wieb van der Meer then takes us in detail through the F€
orster theory
and tackles the always important yet continually vexing issue of kappa-squared
(Chapters 3 and 4). Niko Hildebrandt then provides a detailed primer on how to
apply FRET – from experimental design to data analysis (Chapter 5). Finally, Kim
Sapsford updates a previous 2006 paper that describes the ever-growing FRET
toolbox of diverse fluorophores (Chapter 6). Part Two of the book focuses on some
common FRET techniques and applications. Kim Sapsford and her colleagues from
the U.S. Food and Drug Administration again contribute with a discussion of FRET
application for in vitro sensing and diagnostics (Chapter 7). Thomas Pons then
reviews single-molecule FRET applications, which represent another rapidly growing and important area (Chapter 8). Cheryl Woolhead provides a description of FRET
utility in the determination of protein, peptide, and other biological structures
(Chapter 9). This part ends with a contribution from Jonathan Claussen on FRETbased cellular biosensing with genetically encoded fluorescent indicators (Chapter 10). Part Three looks at recent developments starting with the use of fluorescent
proteins from Robert Campbell (Chapter 11). This is followed by a review of FRET
usage with semiconductor quantum dots from W. Russ Algar and colleagues
(Chapter 12) along with an overview of the growing area of multistep FRET
from Bo Albinsson and Jonas Hannestad (Chapter 13). The concluding Part
Four includes a detailed and vastly updated series of supporting tables on FRET
pairs and F€orster distances collected and collated by Wieb van der Meer (Chapter 14).
These tables were so useful in his previous book that we could not let this
opportunity to update them go unused. Finally, some of the authors provide their
own outlook on and perspectives of FRET (Chapter 15).
We want to thank all of the authors for not only their time and contributions but
also for their incredible patience with us as this book slowly came together. The same
is true for our coworkers at Wiley, including Eva-Stina M€
uller and Heike N€
othe. We
have tried to focus on the important aspects that will both help the FRET novice and
reinforce the understanding of a seasoned FRET user. Given the details and growth
of this technology, we realize that we could not include everything we wanted and
our apologies are further extended for any and all omissions along with any errors.
We admit that we were rather naïve and a little overly hopeful in some of our initial
jXVII
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Preface
j Preface
ideas and desires for this book. A detailed historical accounting of F€
orster’s life and
work is still missing from the literature and although we tried repeatedly, we could
not bring this to fruition for the current book. We also wanted a dedicated Web site to
accompany this book where FRET data, especially on newer donor–acceptor pairs,
could be continuously updated along with providing a forum for discussion and
solicitation of experimental advice. Alas, such a home is not to be found as of yet.
Finally, although he tried quite valiantly, Niko could not convince any television
producers or comic book publishers to introduce a new superhero for children (and
scientists), namely, Captain FRET who solves complicated situations with the
application of resonance energy transfer while carefully explaining the subsequent
photophysical analysis for the layman. If there is ever an update to this book, we will
redouble our efforts to bring these additional ideas to reality.
In the preface to Resonance Energy Transfer Theory and Data, Wieb van Der Meer
outlines how most scientists with interest in energy transfer can be subdivided into
two groups: those interested in homotransfer, the homotransferites (primarily
biochemists), and those interested in heterotransfer, the heterotransferites (primarily physical chemists). In the same manner as him, this book is written for all and
not just one group. However, in adhering to the culture of our times and rather than
differentiating between groups, we would like to add a new all-inclusive description
to the FRET user anthology; if you are able to utilize FRET successfully (in any form),
then you should be considered and referred to as a “FRET jock” and this should be a
moniker of distinction and pride among your scientific colleagues. It is our fervent
hope that well-worn copies of this book find their way onto your office and laboratory
shelves.
Niko Hildebrandt
Igor L. Medintz
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XVIII
List of Contributors
Bo Albinsson
Chalmers University of Technology
Department of Chemistry and
Biotechnology/Physical Chemistry
41296 Gothenburg
Sweden
W. Russ Algar
University of British Columbia
Department of Chemistry
2036 Main Mall
Vancouver
British Columbia
V6T 1Z1
Canada
Alice G. Byrne
Western Kentucky University
Department of Physics and
Astronomy
1906 College Heights Blvd
Bowling Green
KY 42101
USA
Matthew M. Byrne
Western Kentucky University
Department of Physics and
Astronomy
1906 College Heights Blvd
Bowling Green
KY 42101
USA
Robert E. Campbell
University of Alberta
Department of Chemistry
11227 Saskatchewan Drive
Edmonton
Alberta
T6G 2G2
Canada
Jonathan C. Claussen
U.S. Naval Research Laboratory
Center for Bio/Molecular Science
and Engineering
Code 6900
4555 Overlook Avenue, SW
Washington
DC 20375
USA
and
George Mason University
College of Science
Fairfax
VA 22030
USA
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jXIX
George Coker, III
Western Kentucky University
Department of Physics and
Astronomy
1906 College Heights Blvd
Bowling Green
KY 42101
USA
Yidan Ding
University of Alberta
Department of Chemistry
11227 Saskatchewan Drive
Edmonton
Alberta
T6G 2G2
Canada
Herbert Dreeskamp
Technische Universit€at
Braunschweig
Germany
Kelly B. Gemmill
U.S. Naval Research Laboratory
Center for Bio/Molecular Science
and Engineering
Code 6900
4555 Overlook Avenue, SW
Washington
DC 20375
USA
Jessica Granek
U.S. Food and Drug Administration
CDRH/OSEL/DB
WO64 RM3028 HFZ-110
10903 New Hampshire Avenue
Silver Spring
MD 20993
USA
Jonas K. Hannestad
Chalmers University of Technology
Department of Chemistry and
Biotechnology/Physical Chemistry
41296 Gothenburg
Sweden
Niko Hildebrandt
Universite Paris-Sud
Institut d’Electronique Fondamentale
NanoBioPhotonics
Bâtiment 220
91405 Orsay Cedex
France
Hiofan Hoi
University of Alberta
Department of Chemistry
11227 Saskatchewan Drive
Edmonton
Alberta
T6G 2G2
Canada
Thomas M. Jovin
Max Planck Institute for Biophysical
Chemistry
Laboratory of Cellular Dynamics
37077 G€
ottingen
Germany
Ulrich J. Krull
University of Toronto Mississauga
Department of Chemical and
Physical Sciences
3359 Mississauga Rd. North
Mississauga
Ontario
L5L 1C6
Canada
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j List of Contributors
XX
Angela Mariani
U.S. Food and Drug Administration
CDRH/OSEL/DB
WO64 RM3028 HFZ-110
10903 New Hampshire Avenue
Silver Spring
MD 20993
USA
Melissa Massey
University of Toronto Mississauga
Department of Chemical and
Physical Sciences
3359 Mississauga Rd. North
Mississauga
Ontario
L5L 1C6
Canada
Igor Medintz
U.S. Naval Research Laboratory
Center for Bio/Molecular Science
and Engineering
Code 6900
4555 Overlook Avenue, SW
Washington
DC 20375
USA
Thomas Pons
ESPCI–CNRS–UPMC (UMR8213)
Laboratoire de Physique et d’Etude
des Materiaux
10, rue Vauquelin
75005 Paris
France
Philip J. Robinson
University of Glasgow
College of Medical, Veterinary and
Life Sciences
Institute of Molecular, Cell and
Systems Biology
Glasgow
Lanarkshire G12 8QQ
Great Britain
Kim E. Sapsford
U.S. Food and Drug Administration
CDRH/OSEL/DB
WO64 RM3028 HFZ-110
10903 New Hampshire Avenue
Silver Spring
MD 20993
USA
Seth L. Sloan
Western Kentucky University
Department of Physics and
Astronomy
1906 College Heights Blvd
Bowling Green
KY 42101
USA
Christopher Spillmann
U.S. Naval Research Laboratory
Center for Bio/Molecular Science
and Engineering
Code 6900
4555 Overlook Avenue, SW
Washington
DC 20375
USA
jXXI
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List of Contributors
j List of Contributors
Samantha Spindel
U.S. Food and Drug Administration
CDRH/OSEL/DB
WO64 RM3028 HFZ-110
10903 New Hampshire Avenue
Silver Spring
MD 20993
USA
Bridget Wildt
U.S. Food and Drug Administration
CDRH/OSEL/DB
WO64 RM3028 HFZ-110
10903 New Hampshire Avenue
Silver Spring
MD 20993
USA
B. Wieb van der Meer
Western Kentucky University
Department of Physics and
Astronomy
1906 College Heights Blvd
Bowling Green
KY 42101
USA
Cheryl A. Woolhead
University of Glasgow
College of Medical, Veterinary and
Life Sciences
Institute of Molecular, Cell and
Systems Biology
Glasgow
Lanarkshire G12 8QQ
Great Britain
Daniel M. van der Meer
TelaPoint
9500 Ormsby Station Road, Suite 402
Louisville
KY 40223
USA
Steven S. Vogel
National Institutes of Health
National Institute on Alcohol Abuse
and Alcoholism
Laboratory of Molecular Physiology
5625 Fishers Lane
Bethesda
MD 20892
USA
Andrew B. Yeatts
U.S. Food and Drug Administration
CDRH/OSEL/DB
WO64 RM3028 HFZ-110
10903 New Hampshire Avenue
Silver Spring
MD 20993
USA
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XXII
Part One
Background, Theory, and Concepts
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j1
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1
How I Remember Theodor F€
orster)
Herbert Dreeskamp
I first met Theodor F€orster in 1959, after my postdoctoral years in the United States,
at a conference on fast reactions organized by Manfred Eigen in the Harz Mountains. Very prominent scientists attended, such as Eyring, Noyes, and the three men
seen in Figure 1.1 (from left to right) George Porter, Theodor F€
orster, and Albert
Weller.
Half a century ago “fast reaction” meant flash photolysis in the microsecond range
by Norrish and Porter or relaxation methods by Eigen. As I remember, it was F€
orster
who pointed out clearly that the term “fast” characterized our technical facilities at
that time rather than the scientific problem at hand. The time range of fast chemical
reactions may better be characterized by the rearrangement of electrons in the
1016 s range, the vibration of nuclei in the 1012 s range, or the deactivation of
electronically excited states in the 109 s range. Thus, if there are reactions of
electronically excited states – and after all, molecules do have characteristically
different properties in their different electronic states – you will be able to investigate
these reactions in the nanosecond range by just studying fluorescence, which is
emitted in competition to these photochemical reactions. And since F€
orster had, at
the beginning of his career, studied the absorption spectra of organic compounds,
that is, the electronic structure of their ground and excited states, he was able to find
the proteolytic reactions of aromatic compounds as the classical example of using
fluorescence to investigate fast chemical reactions. To me this example shows
clearly, in a nutshell, F€orster’s approach to the scientific problem and why he was so
extremely successful in opening new avenues in photochemistry.
Sometimes it was said that he was gifted by a remarkable intuition. I am sure his
intuition was the result of strict devotion to science, very hard work, his enormous
) This chapter is based on a talk given by the
author at the International Bunsen
Discussion Meeting on “Light Harvesting
and Solar Energy Conversion,” March 29,
2010, Stuttgart-Hohenheim,
commemorating the 100th birthday of
Theodor F€
orster (1910–1974). The author
studied physics in Bonn and Paris, spent
decisive years 1960–1970 with F€orster in
Stuttgart, and was professor of physical
chemistry at the Technische Universit€at
Braunschweig. He thanks Dr. Eberhard
F€orster, son of Theodor F€orster, for the
pictures used in this chapter.
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j3
j 1 How I Remember Theodor F€orster
Figure 1.1
knowledge of the literature, and his insistence to reach a complete understanding of
the problem at hand.
Theodor F€orster was a son of Frankfurt am Main, like Otto Hahn (as shown in
Figure 1.2, second from left, and F€orster is the first from right). He got a training
there as a theoretical physicist when both he and quantum mechanics were quite
young (Figure 1.3). As an assistant to Karl Friedrich Bonhoeffer in Leipzig, he came
under the influence of such eminent men – besides Bonhoeffer of course – as
Heisenberg, Kautsky, and, I think particularly, Peter Debye. Since those Leipzig days
there is the most remarkable and efficient interplay between theory and experiment
in the work of Theodor F€orster.
Figure 1.2
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4
Figure 1.3
His aim was to search for the most appropriate solution of the scientific problem, or
in his favorite words: “Die richtige Deutung einer Beobachtung” (The correct
interpretation of an observation). This included taking carefully all information
into account, separating the important from the trivial, designing a simple experiment, and arriving at the correct interpretation, if possible, without any too elaborate
computer analysis. For me, this picture (Figure 1.4) from the Posen or G€
ottingen
years – the 1940s – may illustrate what I tried to say: Brains seem to be more
important than fancy equipment or powerful computers.
Very often it was both a relief and a delight for all of us who were present, when
after a somewhat incomprehensible seminar talk he would stand up and quite
politely say, “If I understand you correctly, you meant to say this and that . . . ” and
he would give in a few words a lucid interpretation of the topic at hand.
I once asked F€orster how to grade a thesis paper, and he advised me to be not too
strict. But for him, Theodor F€orster, his scientific work had to meet the highest
standards. Things had to be correct, of course, but equally important: it had to
include the most concise analysis of the problem, a perfect logic of the solution, and
a clear statement on the significance of the results. He did not publish much, but the
things he did publish can be a source of inspiration still today.
j5
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1 How I Remember Theodor F€orster
j 1 How I Remember Theodor F€orster
Figure 1.4
You may know that the phenomenon of fluorescence depolarization was an
important step that ultimately led to an understanding of electronic excitation
energy transfer between molecules. After a large amount of empirical material had
been accumulated by others, F€orster, in a lucidly written review article, gave a
brilliant analysis of this effect and brought a long discussion ultimately to an end.
Thus, may I advice you, once in a while, to take your time off from the lab and go to
the library and study a paper of his, or better still his most admirable monograph
“Fluoreszenz organischer Verbindungen.” You may be rewarded by getting a hint on
how problems may be solved by putting them in the right perspective, a strategy in
which Theodor F€orster was a superb master.
My picture of F€orster would be incomplete without remembering how much he
enjoyed the company of colleagues, or of his students, for example, at a Christmas
party in the lab (Figure 1.5).
Very often prominent colleagues from abroad came to Stuttgart, gave a talk, and
certainly were invited by him and his wife Martha (Figure 1.6) to their home.
Regularly, younger members of the department were also invited to these evenings.
For me, certainly the most memorable of these meetings was when James Franck
visited Stuttgart, I think in 1964 (Figure 1.6). You all will know the fundamental work
in atomic physics done in Berlin and G€ottingen by Franck and Hertz in the 1920s, or
the direct proof of a radiationless energy transfer between atomic systems by Franck
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6
Figure 1.5
and Cario. But I think we should also remember that James Franck was the initiator
of the Franck Report of 1945.
In the last picture (Figure 1.7), you see James Franck and Theodor F€
orster many
years after the war, evidently discussing at a scientific conference. Also the topic of
their discussion was – I am pretty sure, – the phenomenon of light harvesting,
energy transfer, and photosynthesis, questions that fascinated both these men for
many years. Franck gave the first experimental proof that the electronic energy may
be exchanged radiationlessly among atoms, and F€
orster, some 25 years later, on the
basis of his deep understanding of quantum mechanics, gave us the theory of the
Figure 1.6
j7
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1 How I Remember Theodor F€orster
j 1 How I Remember Theodor F€orster
Figure 1.7
nontrivial transfer of electronic energy in molecular systems, the “F€
orster resonance
energy transfer” (FRET), which gave us a formula that has become extremely
important in biological sciences.
The contributions of Theodor F€orster to modern photochemistry are most
impressive, but equally fascinating to me is the way in which he elaborated these
things. If you have a look at his strategy, I am certain you will have a good chance to
profit also from this aspect of the work of Theodor F€
orster.
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8
2
Remembering Robert Clegg and Elizabeth Jares-Erijman
and Their Contributions to FRET
Thomas M. Jovin
Robert M. Clegg
Elizabeth A. Jares-Erijman
This is a rather personal account, yet not biographical, of a scientific “family” bound by
circumstances and a common pervasive scientific theme. It is perhaps the essential
nature of F€orster resonance energy transfer (FRET) – a near-field resonance phenomenon – that engenders “resonating” interactions between individuals. For Robert
(“Bob”) Clegg and Elizabeth (“Eli”) Jares-Erijman, as well as for the redactor of this
account, Thomas (“Tom”) Jovin, there were distinct circles of scientific and personal
influences that dictated how FRET entered their lives and careers. As in the case of
most scientists, the initial event was exposure to key literature. In the emerging FRET
field after World War II, a number of highly cited original papers and reviews
stimulated innumerable scientists to incorporate FRET into their conceptual and
experimental strategies. The reason lay with their authors, leading protagonists and
innovators, who in historical order included Theodor F€
orster [1], Gregorio Weber [2],
Izchak Steinberg [3], Lubert Stryer [4], and Ludwig (Lenny) Brand [5]. There are other
equally valuable sources; I cite these because they predominated in my case and were
also highly influential for Bob and Eli, ultimately leading to their own valuable
contributions.
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j9
j 2 Remembering Robert Clegg and Elizabeth Jares-Erijman and Their Contributions to FRET
2.1
Biographical Sketch of Bob Clegg
Robert MacDonald Clegg succumbed to cancer on October 15, 2012. His tragic death
represents an immense loss not only to the members of his immediate family (wife
Margitta, and sons Benjamin, Niels, and Robert), but also to his very extensive
“scientific family” of colleagues and friends.
Bob received his PhD in physical chemistry from Cornell University in 1974,
having worked with Elliot Elson on the theory and practice of rapid chemical
kinetics, specifically chemical relaxation following pressure perturbation. Elliot
was a product of the lab of Buzz Baldwin in the Stanford Biochemistry Department and his influence on Bob’s view of science and research cannot be overemphasized. As a postdoc (with me) in the Department of Molecular Biology at
the Max Planck Institute for Biophysical Chemistry, Bob quickly demonstrated his
depth of knowledge and unique leadership and innovative skills. He assumed the
position of Senior Staff Research Associate with an independent group in 1976.
Over the next two decades, he pursued numerous lines of research, devising and
applying quantitative thermodynamic, kinetic, and spectroscopic techniques,
particularly fluorescence – which he had not used previously – to studies of
macromolecular systems such as RNA polymerase. He became one of the best
expounders worldwide of the theory and practice of FRET (energy transfer) and
was involved in pioneering implementations and applications of fluorescence
lifetime imaging microscopy (FLIM). Bob is well remembered in G€
ottingen for
being “big and broad” in both science and physique, but also for his invariably
cheerful and gentle disposition. He was ever ready to offer help in the form of
advice or action. He was everybody’s friend.
During a sabbatical leave in 1996 at the University of Illinois (UIC) in Champaign,
Bob established a close working relationship with fluorescence pioneer Gregorio
Weber. Weber’s distinguished disciple Enrico Gratton induced Bob’s repatriation to
the United States (UIC) in 1998, with an appointment as professor in the Departments of Physics and Bioengineering and as a member of the faculty of the
Biophysics program (at the time of his death, Bob was its director and an affiliate
of the Institute for Genomic Biology). In this academic environment, Bob quickly
established himself as a leading researcher in numerous biophysical disciplines as
well as an extraordinarily dedicated and capable teacher.
Bob was both an excellent experimentalist and theoretician, and consistently
sought a fundamental understanding of the phenomena under investigation. In so
doing, he displayed a unique capacity for deciphering structure–function relationships in complex systems involving transitions in molecular conformation and
association of proteins and nucleic acids. His contributions to the expansion of
optical microscopy into new fields of biology and biotechnology were also numerous
and profound.
The breadth of Bob’s interests and associations was reflected in his membership
in the Biophysical Society, the American Physical Society, FASEB, the Optical
Society of America, and the American Chemical Society. In 2009, the Biophysical
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10
Society recognized his contributions to fluorescence with the Weber Award for
Excellence in Theory and Experiments in Fluorescence, Fluorescence Subgroup.
That same year, he received from the Society for Experimental Biology and Medicine
the Alan MacDiarmid Best Paper Award in the interdisciplinary research category.
The paper in question was “Engineering redox-sensitive linkers for genetically
encoded FRET-based biosensors,” a typical (for Bob) synthesis of biology, chemistry,
and physics.
2.2
Biographical Sketch of Eli Jares-Erijman
Elizabeth Andreas Jares-Erijman, professor in the Department of Organic Chemistry
at the University of Buenos Aires, Argentina, died of cancer on September 29, 2011.
She was 50 years old. As in the case of Bob Clegg, we, the scientific community, lost
an excellent, innovative scientist, a stimulating teacher, and a wonderful friend.
A chemist by training, Elizabeth Eli received her PhD from the University of
Buenos Aires in Argentina in 1989. After a postdoctoral period in the Department of
Chemistry at UIC, she was transferred to my lab in G€
ottingen in 1993, accompanied
by her husband Leonardo (Leo) – also a postdoc in the department – and her
daughter Paula (see more details later). Three years later, Eli returned to Argentina
and rejoined the Department of Organic Chemistry in the Faculty of Exact and
Natural Sciences. She advanced through the academic hierarchy and occupied a
pivotal role in the teaching and research activities of the department. Eli had her
second child, Florencia, in 1998.
In 2004, the Max Planck Institute for Biophysical Chemistry recognized her
seminal contributions and involvement with the research program of the institute
and proposed her for appointment as Head of a Max Planck Partner Group of the
institute. This came to pass after an evaluation by an outside commission. Hers was
the first partner group to be established in Argentina, in fact, the first in all of Latin
America.
Eli was one of the few individuals in Latin American science who crossed rigid
departmental lines in order to establish a comprehensive and systematic research effort
in what is currently designated as chemical and supramolecular biology. She established
a Laboratory of Nanotools and Bioimaging to promote the design and use of novel
organic probes and multifunctional nanoparticles as biosensors and “nanoactuators.”
New implementations of FRET, for example, exploiting the phenomenon of photochromism, were an important feature in many of these systems. However, the biological
applications were always at the research focus, as illustrated in recent publications
devoted to a-synuclein, the “amyloid” protein in Parkinson’s disease (PD).
Eli was an excellent citizen of her scientific community, serving in many
commissions, both at the local and at the national levels. By all indicators, she
was an inspired and very competent teacher. A significant indicator of her persuasive
and inspiring leadership is the quality and success of the people who worked with
her. She received numerous awards for her scientific achievements, which included
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2.2 Biographical Sketch of Eli Jares-Erijman
j 2 Remembering Robert Clegg and Elizabeth Jares-Erijman and Their Contributions to FRET
the prize Eduardo G. Gros and the prize Bernado A. Houssay (an Argentine Nobel
laureate), and was nominated in 2011 for the prestigious UNESCO-L’Oreal Award
for Women in Science. In 2012, the Argentine Foundation of Nanotechnology (FAN)
established a prize for Scientific Quality “Doctora Elizabeth Jares-Erijman,” and the
newly established CONICET Institute of Nanosciences bears her name.
2.3
The Pervasive Influence of Gregorio Weber
As has already been stated, Gregorio Weber plays a central role in this account, first of
all due to the preeminent position he occupied in the scientific world. He is
recognized as the person responsible for much of the theoretical and experimental
developments in/of modern fluorescence spectroscopy. In particular, he pioneered
the application of this technique in the biological sciences. In so doing and by virtue
of his extraordinary human qualities, he served as an inspirational teacher to
generations of spectroscopists and biophysicists working in basic science, biomedicine, and on industrial implementations of the numerous instrumentation and
techniques developed in his lab. His list of achievements is extensive and unique:
synthesis and application of small-molecule probes of hydrodynamic properties,
polarity, and microviscosity; theory of fluorescence polarization and FRET; intrinsic
fluorescence of the amino acids and of complexes of FAD and NADH; development
of frequency domain fluorimetry; and studies of protein structure under pressure.
In our work in G€ottingen, we were of course guided by the publications of this
illustrious “father of biological fluorescence,” and a more personal association
started in the 1970s. Gregorio and I shared an Argentine origin and thus it was not
by accident that in 1993, during a visit to UIC, he introduced me to the Argentine
husband–wife scientist pair Leo and Eli. Leo was Gregorio’s (last) postdoc and
Gregorio recommended that both he and Eli extend their postdoctoral experience
with a stint in our institute in G€ottingen, Germany. It was in this manner that Leo
came to work with Bob Clegg and Eli came to work with me. In the three ensuing
years, as well as thereafter, we kept “growing up with FRET” together, sharing our
admiration of Gregorio Weber with other celebrated postdoctoral “FRETists” (now
professors), such as Dorus Gadella Jr., Gerard Marriott, and Philippe Bastiaens. We
also benefited from Gregorio’s insight and advice offered during occasional visits to
the institute. Bob’s (and my) sentiments regarding Gregorio Weber are well
expressed in Figure 2.1, taken from one of his many lectures on fluorescence
and FRET, years later. Gregorio passed away, also of cancer, in 1997.
2.4
Contributions by Bob Clegg to FRET
It is perhaps appropriate to invoke at this stage a particular formulation of the
scientific method: (i) a scientific hypothesis can never be shown to be absolutely true,
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12
Figure 2.1 Bob Clegg’s expression of indebtedness to Gregorio Weber.
and must potentially be disprovable; (ii) the hypothesis must be useful until it is
disproved; and (iii) the simplest hypothesis must be favored, unless it can be shown
to be false (Ockham’s razor). Bob was meticulous about the application of these
precepts and his contributions accordingly took two forms: direct (offering new
insights) and indirect (providing inspiration to others). In his work he applied a keen
innate physical intuition and was highly social in the sense of exhibiting an
invariably pleasant, cheerful, and helpful disposition.
Bob’s research interests can be summarized as follows: (i) development and
applications of fluorescence lifetime-resolved imaging microscopy (FLI and
FLIM) and the development of unique dedicated software for analysis of such
data; (ii) development of instruments for rapid relaxation kinetics (T- and P-jump),
and microsecond rapid mixing; and (iii) applications of the advanced instrumentation to an exceedingly wide range of biological systems, animal and vegetal. The
underlying molecular mechanisms investigated included nucleic acid conformational equilibria and kinetics, and multisubunit functional proteins and photosynthetic systems. During his 21 years in Germany (1977–1998), Bob published
68 papers and contributions, most of which dealt with the structure of nucleic
acids. Nine were devoted to the theory and practice of FRET and another nine were
devoted to FLIM. Two FRET reviews had (and still have) a great impact on the field.
The first [6] was a detailed blueprint for the FRET practitioner. The underlying
theory was thoroughly presented as well as numerous techniques for the evaluation of population distributions and determinations of the FRET efficiency E:
sensitized emission, donor quenching, decrease in donor lifetime, and changes in
donor and acceptor anisotropy. In conclusion, Bob stated, “The measurements
cannot be better than the molecules that are being measured, so extreme care
j13
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2.4 Contributions by Bob Clegg to FRET
j 2 Remembering Robert Clegg and Elizabeth Jares-Erijman and Their Contributions to FRET
Figure 2.2 FRET strategy (geometrical model)
for determination of DNA helical parameters:
(a) the D–A vector R “swings around” the helix
as a function of separation N in the sequence
and axial displacement L of the fluorophores
relative to the bases to which they are attached,
(b) FRET efficiency as a function of N (in base
pair units). Inset: (ratio)A, a widely adopted
FRET measure introduced by Bob;
(ratio)A ¼ (acceptor emission sensitized by the
donor and excited directly at the donor
absorption band)/acceptor emission directly
excited at its absorption band. Adapted from
Ref. [9].
must be taken to ensure that the samples are well defined and pure. FRET with
specifically labeled nucleic acids will surely become more popular in the near
future; the method has the potential to distinguish many structural features and
symmetries ranging over molecular distances less than 100 A.” How true! The
second FRET review already dealt with FRET microscopy [7]. Bob contrasted in
detail and unique clarity a quantum mechanical and two classical derivations of
the FRET phenomenon, an issue he returned to repeatedly in later reviews and
historical accounts (see later).
A great deal of Bob’s research in Germany (and later, back in the United States)
was devoted to the study of DNA helices, junctions, bulges, and kinks, much of it
in close collaboration with David Lilley. FRET was an essential ingredient of this
research, as is well illustrated in three publications that received wide attention
[8–10]. One of these [9] featured the modulation of FRET according to the relative
geometric disposition of FRET donor and acceptor positioned around a DNA
helix (Figure 2.2).
The development of FLI instrumentation was a key and long-range element of
Bob’s research program, during both the German and subsequent US phases of his
career. The emphasis was always on maximal speed and multiparametric acquisition, a pioneering example being the PhD thesis work of Peter Schneider [11]. Our
extensive departmental involvement with FRET (flow cytometry and then imaging)
and FLIM in the years leading up to the fall of the Berlin Wall was greatly facilitated
by the participation of a large number of excellent colleagues from the Institute of
Biophysics in Debrecen, Hungary. This circumstance was brought about by the
farsighted efforts and perseverance of its director Sandor Damjanovich. Some of
these individuals are featured in the group photograph taken at the symposium in
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14
Figure 2.3 Bob Clegg (far left) and some former members of his group and other alumni of the
Department of Molecular Biology, Max Planck Institute for Biophysical Chemistry, who attended
the symposium honoring Theodor F€
orster in March 2011, G€
ottingen.
honor of Theodor F€orster (“F€orster resonance energy transfer in life sciences”) in
G€ottingen, March 2011, where some of us saw Bob for the last time (Figure 2.3). It
was on this occasion that Bob managed to track down the house where F€
orster
originated his theory and wrote his famous book Fluoreszenz organischer
Verbindungen.
Back in the United States (as of 1998) and established in an academic environment, Bob developed his capabilities to the full, including those as a gifted
“gadgeteer.” He shared responsibility for the celebrated nationally funded research
resource center, the LFD (Laboratory for Fluorescence Dynamics), established by
Enrico Gratton in 1986 at UIC and relocated in 2006 to the University of California,
Irvine. The LFD provided an excellent environment for cutting-edge technology
development. Thus, in the decade of 2000–2010, a real-time field FLIM instrument,
fully compatible with confocal optical configurations and with high contrast and
sensitivity, was devised, allowing the high-speed acquisition of three-dimensional
imaging and including spectral resolution. This instrumentation was applied to
process prostate biopsies in an attempt to facilitate diagnosis of prostate cancer. In
addition, the redistribution of a phototherapeutic/diagnostic compound (PpIX) in
live tumor cells was investigated, just one activity establishing FLIM as an important
technique in dermatology research [12]. A FRET redox biosensor was developed to
measure the oxidation–reduction potentials in fluids and cells [13]. In parallel, a
pressure-jump instrument was devised for studying photosynthetic plant systems,
including living organisms such as algae [14]. The same method was applicable to
kinetic studies of RNA/DNA conformational changes and binding of ligands. In
fact, numerous post-2000 publications, most using FRET but not cited here, were
dedicated to nucleic acid studies: four-way junctions (largely collaborations with
Taekjip Ha and David Lilley), hammerhead ribozymes, protein–DNA interactions,
j15
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2.4 Contributions by Bob Clegg to FRET
j 2 Remembering Robert Clegg and Elizabeth Jares-Erijman and Their Contributions to FRET
ribosomal intersubunit dynamics, and probe–DNA interactions; the latter studies
were conducted in the course of a very long-term collaboration with a close friend
and colleague, Frank Loontiens.
Data analysis was always a central issue for Bob in his work. As one example, the
FLIM polar plot analysis of frequency domain FLIM image data was established [15]
and extended by incorporating FRET-relevant spectral resolution [16] and newly
created image analysis algorithms for selecting important image locations via their
morphology using “wavelets” [17]. In addition, novel ways of “denoising” images
depending on the type of noise (Poissonian or Gaussian) were devised [18], dramatically increasing the accuracy of the FLI. The potential of lifetime-resolved imaging in
small organisms as well as live biological mammalian cells and photosynthesis (algae
as well as higher plants) was to be enhanced for 3-D imaging using sample excitation
single plane illumination microscopy (SPIM). Unfortunately, this work did not
proceed beyond the planning stage due to Bob’s sickness.
Bob did not neglect his dedication to the promotion of FRET history awareness
and the applications of the technique, almost invariably coupled with FLIM.
Accordingly, numerous reviews appeared (FRET [19–21] and FLIM [22–26]), which
complemented and extended the earlier publications. Bob’s service to the scientific
community was also evident in his many years as a member of the faculty of the
long-standing Annual Workshop on FRET Microscopy, organized by Ammasi
Periasamy, another prolific contributor to the FRET field and its literature.
2.5
Contributions by Eli Jares-Erijman to FRET
Eli arrived in our lab in 1993 after a postdoc at UIC working in the lab of Ken
Rinehart on the synthesis, isolation, and characterization of very complex natural
products. She was an accomplished organic chemist but had had little exposure to
fluorescence techniques, biophysical methods, and biomolecules. This situation
changed in a very short time, such that 3 years later, Eli would return to Argentina as
an accomplished biophysicist and an expert in fluorescence technology and probes.
In fact, the latter served as primary objectives and motivators of this development,
inasmuch as Eli displayed a keen ability to recognize the potential of new structural
motifs, scaffolds, and mechanisms in creating innovative probes of molecular states,
transitions, and localization. One of the first applications was in a study of
noncanonical DNA such as Z-DNA and so-called parallel-stranded DNA (psDNA),
using the FRET-based approach pioneered by Bob Clegg, while at the same time
extending it conceptually and experimentally (new ratio functions). The left-handed
character of Z-DNA was confirmed [27], but the helical sense of psDNA containing
AA and GG base pairs and also presumed to be left-handed was not published
because the extensive data posed (and still pose) problems of interpretation.
Eli’s chemical acumen became very evident in the next FRET-based studies of
photochromic compounds (diarylethenes) that provided a switchable acceptor
function by virtue of dual (“open” and “closed”) states interconvertible by cycles
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16
Figure 2.4 Photochromic FRET (pcFRET).
Exposure of the diarylethene (open form) to
near-UV light (250–320 nm) induces
photocyclization to the closed form. The latter
has an absorption band in the visible region
overlapping with the emission band of a (the)
donor, thus enabling FRET. Visible light leads to
cycloreversion. The bistable diarylethenes
exhibit little fatigue such that multiple cycles are
feasible.
of near-UV and visible light [28]. The distinctive absorption spectra of the closed and
open forms differ in the degree of superposition with the emission of an appropriately selected donor, thereby leading to a change in the overlap integral J, one of the
factors defining the F€orster transfer distance Ro. The mechanism of photochromic
FRET (pcFRET) is depicted in Figure 2.4; it was explored by systematic structural
modifications and careful thermodynamic and kinetic studies after Eli returned to
Argentina [28–30].
At this juncture, Eli was operating as a Partner Group of our Max Planck
Institute and was PI and co-PI on a number of nationally and internationally
funded programs. Her major focus was on the development and application of
smart sensors and devices combining luminescent, photochromic, and other
small molecules with nanostructures such as quantum dots (QDs). In about 1998,
QDs became commercially available through the auspices of Quantum Dot Corp.
(QDC). Eli was probably the first person to conduct FRET experiments utilizing
QDC QDs as donors and was instrumental in one of the first in-depth characterization of these new materials [31]. She readily perceived that emerging technologies based on a combination of chemistry, physics, and molecular biology were
creating demand for smart materials serving as reporters and sensors in microand nanosystems [32]. The pioneering study of epidermal growth factor receptor
(EGFR) activation and dynamics by microscopy of living cells using QD-EGF as
ligands [33] was one of the first responses to this challenge, and stimulated
numerous applications to other systems, including the insulin receptor [34,35].
Meanwhile, pcFRET was shown to operate at the level of a single particle [36] and
to offer a new means for conducting isothermal relaxation kinetic measurements
[37]. The pcFRET principle was extended to systems of core–shell QDs wrapped
with an amphiphilic polymer containing photochromic groups and, in some
j17
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2.5 Contributions by Eli Jares-Erijman to FRET
j 2 Remembering Robert Clegg and Elizabeth Jares-Erijman and Their Contributions to FRET
constructs, a second fluorophore [38–40]. Such nanoparticles are water dispersible
and can be reversibly modulated in fluorescence (quenched) by exercising the
photochromic cycle. Other “J-engineered” QDs for sensing pH were based on
FRET from the QD core to a shell of indicator molecules with pH-sensitive
absorption spectra [41].
A quite different endeavor featured the use of “nanodevices” to sense and control
the aggregation of amyloid proteins (specifically a-synuclein) in vitro and in the
cellular context, thereby contributing to a better understanding of the molecular
processes underlying the etiology of PD. This line of research led to the discovery of
novel supramolecular intermediates in the aggregation pathway of a-synuclein
preceding the formation of amyloid fibrils [42]. A prominent example is the “acuna”
(amyloid “cradle”), a submicrometer structure that may be (at least partially)
responsible for the toxicity and functional loss of dopaminergic neurons underlying
PD [42]. The effort required a very interdisciplinary approach, combining numerous
technologies such as organic synthesis, surface chemistry, physical and biophysical
analysis, and quantitative microscopy to develop the sensors and apply them in
context of cellular biology. Fluorogenic bisarsenical ligands [43], ratiometric [44]
and/or solvatochromic probes [45], and NIR cyanines [46] also provided potential
and actual novel FRET strategies for microscopy-based investigations of amyloid
proteins in vitro and in living cells [47–51]. Current efforts in Eli’s as yet functional
research group are also being directed at the design and synthesis of optimal
photoswitchable probes for the emerging superresolution microscopies.
As in the case of Bob Clegg, Eli published reviews on FRET imaging that have had
a wide acceptance [52–54]. They are somewhat unusual in presenting novel views of
photophysical phenomenon, such as the concept of a fluorophore as a photonic
“enzyme” [52], and in offering an open-ended classification scheme for FRET
methods. The latter include the donor and acceptor photobleaching techniques
that originated from our FRET community in G€
ottingen, largely inspired by the
unique publications, for example [55], of Tomas Hirschfeld, another illustrious
member of the pantheon of spectroscopists. In publications [50,53,54], and in fact
already in Ref. [27], it was proposed that in many FRET situations, calculations based
on the ratio kt =kf may be preferable to the classical kt =kd , such that one can “bid
farewell” to E and Ro . FRET is a moving target.
2.6
A Final Thought
People survive in our memories if we keep them there by willfully recalling their
personal qualities as well as their achievements. In Figure 2.5, we can appreciate that
Bob and Eli, despite their distinctive ways and views, were two of a kind. We miss
them both very much.
I am greatly indebted to Bob Clegg’s family and other colleagues for material that
made the writing of this chapter possible. Errors of commission and omission are
mine alone.
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18
Figure 2.5 Eli and Bob on the grounds of the riverside campus of the University of Buenos Aires
in 2010.
References
1 F€
orster, T. (2012) Energy migration and
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8 Clegg, R.M., Murchie, A.I., Zechel, A., and
Lilley, D.M. (1993) Observing the helical
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9 Gohlke F.C., Murchie, A.I., Lilley, D.M.,
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j 2 Remembering Robert Clegg and Elizabeth Jares-Erijman and Their Contributions to FRET
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Academy of Sciences of the United States of
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(1994) The solution structure of the fourway DNA junction at low-salt conditions: a
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analysis. Biophysical Journal, 66, 99–109.
Schneider, P.C. and Clegg, R.M. (1997)
Rapid acquisition, analysis, and display of
fluorescence lifetime-resolved images for
real-time applications. Review of Scientific
Instruments, 68, 4107–4119.
Hanson, K.M., Behne, M.J., Barry, N.P.,
Mauro, T.M., Gratton, E., and Clegg, R.M.
(2002) Two-photon fluorescence lifetime
imaging of the skin stratum corneum pH
gradient. Biophysical Journal, 83,
1682–1690.
Kolossov, V.L., Spring, B.Q., Clegg, R.M.,
Henry, J.J., Sokolowski, A., Kenis, P.J.,
and Gaskins, H.R. (2011) Development
of a high-dynamic range, GFP-based
FRET probe sensitive to oxidative
microenvironments. Experimental Biology
and Medicine (Maywood, NJ), 236, 681–691.
Holub, O., Seufferheld, M.J., Gohlke, C.,
Govindjee, and Clegg, R.M. (2000)
Fluorescence lifetime imaging (FLI) in
real-time: a new technique in
photosynthesis research. Photosynthetica,
38, 581–599.
Redford, G.I. and Clegg, R.M. (2005) Polar
plot representation for frequency-domain
analysis of fluorescence lifetimes. Journal
of Fluorine Chemistry, 15, 805–815.
Chen, Y.C. and Clegg, R.M. (2011) Spectral
resolution in conjunction with polar plots
improves the accuracy and reliability of
FLIM measurements and estimates of
FRET efficiency. Journal of Microscopy, 244,
21–37.
Buranachai, C., Kamiyama, D., Chiba, A.,
Williams, B.D., and Clegg, R.M. (2008)
Rapid frequency-domain FLIM spinning
disk confocal microscope: lifetime
resolution, image improvement, and
wavelet analysis. Journal of Fluorine
Chemistry, 18, 929–942.
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Image analysis for denoising full-field
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20
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Papageorgiou and Govindjee), Springer,
pp. 83–105.
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from conception through the labors of
birth, in Reviews in Fluorescence 2006 (eds
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pp. 1–45.
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energy transfer - FRET what is it, why do it,
and how it’s done, in FRET and FLIM
Techniques: Laboratory Techniques in
Biochemistry and Molecular Biology (ed. T.W.
J. Gadella), Elsevier.
Clegg, R.M., Holub, O., and Gohlke, C.
(2003) Fluorescence lifetime-resolved
imaging: measuring lifetimes in an image.
Methods in Enzymology, 360, 509–542.
Periasamy, A. and Clegg, R.M. (eds) (2009)
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Fluorescence lifetimes: fundamentals and
interpretations. Photosynthesis Research,
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Chen, Y.C. and Clegg, R.M. (2009)
Fluorescence lifetime-resolved imaging.
Photosynthesis Research, 102, 143–155.
Chen, Y.C., Spring, B.Q., and Clegg, R.M.
(2012) Fluorescence lifetime imaging
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Giordano, L., Macareno, J., Song, L., Jovin,
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(2000) Fluorescence resonance energy
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Grecco, H.E., Lidke, K.A., Heintzmann, R.,
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Ensemble and single particle photophysical
properties (two-photon excitation,
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169–179.
Jares-Erijman, E.A., Spagnuolo, C.,
Giordano, L., Etchehon, M., Kawior, J.,
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nalich-Arana, M., Bossi, M., Lidke, D.S.,
Post, J.N., Vermeij, R.J., Heintzmann, R.,
Lidke, K.A., Arndt-Jovin, D.J., and Jovin, T.
M. (2004) Novel (bio)chemical and (photo)
physical probes for imaging live cells, in
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8 (ed. G. Pifat-Mrzljak), Kluwer,
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Lidke, F.D.S., Nagy, P., Heintzmann, R.,
Arndt-Jovin, D.J., Post, J.N., Grecco, H.,
Jares-Erijman, E.A., and Jovin, T.M. (2004)
Quantum dot ligands provide new insights
into erbB/HER receptor-mediated signal
transduction. Nature Biotechnology, 22,
198–203.
Giudice, J., Jares-Erijman, E.A., and
Leskow, F.C. (2013) Endocytosis and
intracellular dissociation rates of human
insulin–insulin receptor complexes by
quantum dots in living cells. Bioconjugate
Chemistry, 24, 431–442.
Giudice, J., Barcos, L.S., Guaimas, F.F.,
Penas-Steinhardt, A., Giordano, L., JaresErijman, E.A., and Coluccio Leskow, F.
(2013) Insulin and insulin like growth
factor II endocytosis and signaling via
insulin receptor B. Cell Communication and
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Spagnuolo, C., Lidke, K.A., and Jovin, T.M.
(2005) Imaging quantum dots switched on
and off by photochromic Fluorescence
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Molecular Crystals and Liquid Crystals, 430,
257–265.
Jovin, T.M. and Jares-Erijman, E.A. (2005)
Photochromic relaxation kinetics
(pcRelKin). Molecular Crystals and Liquid
Crystals, 430, 281–286.
Díaz, S., Menendez, G., Etchehon, M.,
Giordano, L., Jovin, T.M., and JaresErijman, E.A. (2011) Photoswitchable
water-soluble quantum dots: pcFRET based
on amphiphilic photochromic polymer
coating. ACS Nano, 5, 2795–2805.
Díaz, S., Giordano, L., Jovin, T.M., and
Jares-Erijman, E.A. (2012) Modulation of a
photoswitchable dual-color quantum dot
containing a photochromic FRET acceptor
and an internal standard. Nano Letters, 12,
3537–3544.
Díaz, S.A., Giordano, L., Azcarate, J.C.,
Jovin, T.M., and Jares-Erijman, E.A. (2013)
Quantum dots as templates for selfassembly of photoswitchable polymers:
small, dual-color nanoparticles capable of
facile photomodulation. Journal of the
American Chemical Society, 135, 3208–3217.
Menendez, G., Roberti, M.J., Sigot, V.,
Etchehon, M., Jovin, T.M., and JaresErijman, E.A. (2009) Interplay of
multivalency and optical properties of
quantum dots: implications for sensing
and actuation in living cells. Proceedings of
SPIE, 7189, 71890-P1–71890-P9.
Fauerbach, J.A., Yushchenko, D.A.,
Shahmoradian, S.H., Chiu, W., Jovin, T.M.,
and Jares-Erijman, E.A. (2012)
Supramolecular non-amyloid
intermediates in the early stages of
a-synuclein aggregation. Biophysical
Journal, 102, 1127–1136.
Spagnuolo, C.C., Massad, W., Miskoski, S.,
Menendez, G.O., Garcia, N.A., and JaresErijman, E.A. (2009) Photostability and
spectral properties of fluorinated
fluoresceins and their biarsenical
derivatives: a combined experimental and
theoretical study. Photochemistry and
Photobiology, 85, 1082–1088.
Yushchenko, D.A., Fauerbach, J.A.,
Thirunavukkuarasu, S., Jares-Erijman, E.
A., and Jovin, T.M. (2010) Fluorescent
ratiometric MFC probe sensitive to the
early stages of a-synuclein aggregation.
j21
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optical properties and combination with
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22
3
F€
orster Theory
B. Wieb van der Meer
3.1
Introduction
Theory without experiment is like the sound of one hand clapping. F€
orster theory is
not like that at all. It is a thundering ovation linking theory and experiment by
explaining the relationship between spectral overlap, energy transfer, and proximity.
This chapter explains F€orster’s contributions to the theory of resonance energy
transfer. The readers of this chapter form, no doubt, a highly diverse group of
people. Most readers are probably only interested in the bottom line. Others may
want to know details. But which details? There are so many. To help students and
specialists find what they need, the chapter is presented as a sequence of a large
number of sections that are short and focused.
3.2
Pre-F€
orster
This section is based on some of the information in the most popular papers by
F€orster [1–5], Chapter 5 of Ref. [6], and Clegg’s history of FRET [7]. The emphasis
here is on the contributions of F€orster’s predecessors and contemporaries.
If you want to know who the scientists were who inspired F€
orster and what the
science was that motivated him, you should read his most important papers. His most
important, that is, his most cited papers are his papers published in 1946 [1] 1948 [2],
and 1949 [4] and reviews published in 1959 [3] and 1965 [5]. F€
orster’s papers are not
easy to understand. The language is not a problem because four of the five are in
English or translated into English. They are difficult because they use a lot of math and
complicated spectroscopic concepts. Nevertheless, if you are serious about FRET, you
should study them. Start with his 1946 paper [1] and the 1959 review [3]. These papers
are much more readable than F€orster’s most cited paper [2], because his 1946 paper
presents a very clear verbal description of the essential ideas on which the theory is
based and a thorough review of the experimental evidence of the importance of
resonance and his 1959 paper is designed to provide a conceptual understanding of the
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j23
j 3 F€orster Theory
FRET phenomenon with a minimum of equations, whereas his 1948 paper is a
rigorous treatment of the theory. In Ref. [3], he gives an overview of the then available
literature. For example, he mentions experiments proving that the observed transfer
mechanism could not be due to trivial reabsorption. His discussion of the various
transfer mechanism is very interesting. He compares, in Table 1 in Ref. [3], FRET,
reabsorption, donor–acceptor complex formation, and collisional quenching. This
table has been adopted in a slightly modified form in Section 3.7. In Refs [1,2], he
focuses on the theory of homotransfer, FRET between like molecules, whereas in Ref.
[4] (only available in German), he emphasizes heterotransfer, FRET between unlike
molecules. If one is interested in the fundamental aspects of the theory, refer to Refs
[1,2,5]. Reference [5] is a review. In this paper, he does more than just rehash his FRET
theory. Of the 10 sections, only the last one is about FRET. In his 1965 paper, he also
discusses exciton theory, strong coupling, weak coupling, and very weak coupling (very
weak coupling is the basis for FRET). His 1965 paper introduces an extension of his
theory put forward in his 1948 paper. This extension allows a description of the time
dependence of the donor fluorescence and the relation between the quantum yield of
the donor and the acceptor concentration (see Sections 3.16 and 3.17).
Newton said, “If I have seen further it is only by standing on the shoulders of
giants” [8]. Who were the giants for F€orster? J. Perrin and F. Perrin, Cario, Franck,
Kallmann, and London. In the late 1940s when F€
orster started his work on energy
transfer, the phenomenon of sensitized fluorescence was well established [2–5,7].
Cario had shown in 1922 that transfer of energy had taken place from excited
mercury atoms to thallium atoms in a mercury–thallium vapor mixture [9]. Cario
and Franck had presented similar results in a mercury–hydrogen system [10]. Many
other experimentalists had presented evidence for sensitized fluorescence from the
vapors of silver, cadmium, lead, zinc, and indium in the presence of mercury vapor
[7,9,10]. The starting point for a theoretical framework showing the role of resonance
in energy transfer was Franck’s principle: If effective energy transfer is to take place
from initially excited molecules to quenching molecules, the excited states of the
quenchers must be in energy resonance with the primarily excited states [11].
Kallmann and London [7,12] proposed a theory of energy transfer that can be
considered to be a precursor of F€orster’s theory in that it is based on the idea of
resonance and has the correct distance dependence of the transfer efficiency.
However, unrealistically sharp spectra were assumed and the link between the
distance dependence and spectra had limited significance. J. Perrin [13,14] introduced a classical theory modeling the fluorophores as electrical dipoles oscillating at
a single frequency with a rate of transfer proportional to the inverse of the distance to
the third power, not the sixth power as F€orster later found. As a result, the predicted
distance over which energy transfer would take place is much too large [7]. F. Perrin
[15,16] designed a quantum mechanical version of this theory extending the work by
Kallmann and London to transfer in solutions. The molecules are assumed to have
two states, a ground state and an excited state, so that the spectra would show sharp
peaks. F. Perrin found the same distance dependence as J. Perrin did. However, F.
Perrin did invoke collision broadening of the spectra by the solvent, decreasing the
predicted range of transfer, but it was still too large [7]. An interesting overview of the
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24
contributions of J. Perrin and F. Perrin, father and son, is available [17]. Oppenheimer and Arnold [7,18,19] pointed out that the phenomenon of resonance energy
transfer is very similar to internal conversion in radioactivity where an excited
nucleus transfers energy without radiation to one of the orbital electrons resulting in
ejection of this electron. Using this similarity, they derived an expression of the rate
of energy transfer for the case where the acceptors are randomly distributed around
a donor. Clegg showed that modifying their expression for the rate of transfer from
one dominant frequency to a spectrum of frequencies leads to F€
orster’s famous
equation for the donor–acceptor distance at which the rate of transfer equals that of
donor emission [7] (see the equation forR0 in Section 3.3). However, the fact is that
Oppenheimer and Arnold did not make these modifications. They did not come up
with the idea to incorporate experimentally obtained spectra into their theory.
F€orster did [1–5]. This is what sets F€orster apart from his predecessors and
contemporaries. They all assumed one dominant frequency and ignored experimental data on spectra. F€orster’s most important innovation was to incorporate
experimentally obtained parameters such as spectra, quantum yield, and lifetimes
into his theory, making it refutable, accessible, and extremely useful.
3.3
Bottom Line
To observe FRET, the following conditions must be met:
1) Donor and acceptor must have strong electronic transitions in the UV, visible, or IR.
2) Spectral overlap must exist between donor emission and acceptor absorbance
(see Section 3.5).
3) Donor and acceptor must be close, but not too close (see Sections 3.6 and 3.7).
4) The orientation factor should not be too small (see Section 3.8).
5) The donor emission should have a reasonably high quantum yield (see Equation 3.3 and also data in Chapter 14).
The following are the key quantities in F€orster’s theory:
kT ¼ rate of energy transfer (see Equation 3.2).
tD ¼ lifetime of the donor excited state in the absence of acceptor (see Equations 3.1 and 3.2).
r DA ¼ distance between donor and acceptor.
R0 ¼ F€orster distance, that is, the donor–acceptor distance at which kT ¼ 1=tD , so that
at that particular distance, the probability of the excited donor to fluoresce is equal to the
probability of transfer of energy to the acceptor (see Equations 3.3 and 3.3a–3.3c).
E ¼ efficiency of transfer (see Equation 3.1).
J ¼ overlap integral (see Section 3.5 and Equation 3.4).
k2 ¼ orientation factor (see Section 3.8 and Equation 3.3).
WD ¼ quantum yield of the donor fluorescence in the absence of acceptor (see
Equation 3.3).
n ¼ refractive index of the medium (see Equation 3.3).
j25
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3.3 Bottom Line
j 3 F€orster Theory
Constants in F€orster’s theory are as follows:
p ¼ 3:141592654;
ln 10 ¼ 2:302585093;
orster used N 0
N A ¼ 6:0221415 1023 per mole ðactually; F€
¼ 6:0221415 1020 per millimoleÞ:
The conclusion of F€orster’s theory can be conveniently written as the following set
of three equations:
kT
R6
¼ 6 06 :
kT þ 1=tD R0 þ r DA
1 R60
:
kT ¼
tD r 6DA
E¼
R60 ¼
9ðln 10Þk2 WD J
:
128p5 n4 N A
ð3:1Þ
ð3:2Þ
ð3:3Þ
For a derivation of these equations from classical theory, see Sections 3.5–3.14
(Sections 3.5–3.7 introduce basic ideas, the derivation starts in Section 3.8), and
from quantum mechanical theory, see Section 3.15. Note that the second equation
follows from the first (and the first from the second). An alternative expression for
the rate of transfer kT is
2 k
1
CDA ;
kT ¼ 6
ð3:2aÞ
n4
r DA
with
CDA ¼
9ðln 10ÞWD J
:
128p5 tD N A
ð3:2bÞ
This formulation, which is often used in photosynthesis, establishes a clear
separation between spectral properties (CDA ), geometric properties (k2 =r 6DA ), and
environmental factors (n) [20]. When r DA is in nanometers and kT is in inverse
picoseconds, C DA is expressed in nm6/ps.
Figure 3.1 illustrates the relations between efficiency and donor–acceptor distance
and F€orster distance and between F€orster distance and kappa-squared, overlap
integral, refractive index, and quantum yield.
3.4
9000-Form, 9-Form, and Practical Expressions of the R60 Equation
F€orster used N 0 instead of N A in Ref. [2], but used N A with 9000 instead of 9 in Ref.
[3]. However, N 0 ¼ N A as both have a unit and represent the same amount of
particles per mole: N 0 ¼ 6:02 1020 mmol1 ¼ 6:02 1023 mol1 ¼ N A . Braslavsky et al. pointed out that the frequently quoted 9000-form of Equation 3.3 (with a
factor of 9000 instead of 9) is incorrect [21]. Simplifying Equation 3.3 by substituting
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26
Figure 3.1 (a) The transfer efficiency E versus
the donor–acceptor distance r DA between 0 and
2 times the F€
orster distance. (b) The transfer
efficiency E versus the F€
orster distance R0
between 0 and 2 times the donor–acceptor
distance. (c) The relative F€
orster distance
versus the orientation factor, k2 , which varies
orster distance
between 0 and 4. R0 [2/3] is the F€
orster distance
at k2 ¼ 2=3. (d) The relative F€
R0/R0(J/J1) versus the relative overlap integral
J/J1, where J is the overlap integral and J1 is a
typical value of this integral, say 1 OLI.
orster distance that at J ¼ J1.
R0( J ¼ J1) is the F€
J-values vary over a wide range (see Chapter
14). (e) The relative F€
orster distance versus n,
the refractive index of the medium in which the
donor and acceptor are embedded. R0(n ¼ 1.4)
is the F€
orster distance for the refractive index
equal to 1.4. All refractive index values in the
literature are in the 1.33–1.6 range. The values
1.34 and 1.6 are the ones used most frequently.
(f) The relative F€
orster distance versus FD , the
quantum yield of the donor in the absence of
orster
the acceptor R0 (FD ¼ 0:5) is the F€
distance at FD ¼ 0:5. FD varies between 0 and
1 (see Chapter 14 for data).
j27
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3.4 9000-Form, 9-Form, and Practical Expressions of the R06 Equation
j 3 F€orster Theory
in the constants with units shown explicitly yields [21]
2
1=6
R0
k WD
Jl
:
¼ 0:02108
nm
n4
mol1 dm3 cm1 nm4
ð3:3aÞ
Equation 15 in Ref. [22] and the expressions given on page 16 of Ref. [6] are equally
valid, but the expression (3.3a) is preferable as it has the advantage that the choice of
units is absolutely clear, so that mistakes can be easily avoided. In practice, the OLI
(overlap–integral unit, introduced in Chapter 7 of Ref. [6]) is convenient. This unit is
defined as OLI ¼ 1014 mol1 dm3 cm1 nm4 ¼ 1014 mol1 dm3 cm3 , and is used
in Chapter 14. Alternative forms of (3.3a) using the OLI are as follows:
2
1=6
R0
k WD 100J l
:
¼ 2:108
nm
n4
OLI
ð3:3bÞ
2
1=6
R0
k WD J l
¼ 4:542
:
nm
n4
OLI
ð3:3cÞ
The following is a step-by-step derivation of Equation 3.3a from Equation 3.3:
1) Divide both sides of Equation 3.3 by nm6 and substitute in all the constants,
including the unit of Avogadro’s number, and Equation 3.3 thus becomes
(
)
R60
9ð2:302585Þ
k2 WD
J
:
¼
nm6
n4
nm6
128ð306:0197Þð6:022 1023 Þmol1
1
2) Move
to J and convert nm6 to dm3 cm1 nm4 using
17 mol
over
2
3
10 nm = dm cm1 ¼ 1.
2 17
k WD
J
10 nm2
:
n4
dm3 cm1
mol1 nm6
2 R6
k WD
J
3) Simplify yielding: 0 6 ¼ 87:8533 1012
:
nm
n4
mol1 dm3 cm1 nm4
R60
¼
nm6
9ð2:302585Þ
128ð306:0197Þð6:022 1023 Þ
4) Take the sixth root and arrive at Equation 3.3a.
3.5
Overlap Integral
The overlap integral can be calculated using wavelength (3.4), wave number (3.6), or
frequency (3.8). Most frequently, the wavelength form is used. This is often referred
to as J l and defined as:
ð
J l ¼ J ¼ f D ðlÞeA ðlÞl4 dl:
ð3:4Þ
The integral in Equation 3.4 extends over the region that encompasses the line
shapes of the relevant donor emission and acceptor absorption bands. Extending the
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28
Figure 3.2 (a) Donor emission spectrum (blue
curve) and acceptor extinction spectrum (red
curve) versus wavelength. The green area
indicates that there is overlap between the two
spectra. The green area is not the overlap
integral. (b) This schematic graph has three
different vertical scales, one in nm1 for the
blue curve (normalized donor fluorescence, the
area under this curve is one), another in M1
cm1 for the red curve (acceptor extinction),
and the third scale is in OLI/nanometer for the
green curve (overlap curve). The area under the
green curve is the overlap integral.
integrals from zero to infinity may add irrelevant addenda to the integrals when
other areas of overlap occur at very high and/or low wavelengths not relevant to the
specific energy transfer process of interest.1) The overlap integral J ¼ J l is conveniently expressed in OLIs, l is the wavelength of the light, most often expressed in
nanometers, eA ðlÞ is the molar extinction coefficient of the acceptor, usually in M1
cm1, and f D ðlÞ is the fluorescence spectrum of the donor normalized on the
wavelength scale:
f D ðlÞ ¼ Ð
F Dl ðlÞ
;
F Dl ðlÞdl
ð3:5Þ
where F Dl ðlÞ is the donor fluorescence per unit of wavelength interval and the
integral extends over the relevant donor emission band(s). A schematic illustration
of overlap is Figure 3.2.
The green area in Figure 3.2a is not the overlap integral. The green area only
shows that there is overlap and is certainly not a reliable measure for the magnitude
of the overlap integral. The donor emission f D ðlÞ (blue curve in Figure 3.2) is
usually expressed in 1/nm. The acceptor extinction eA ðlÞ (red curve) is in M1 cm1,
and the overlap curve (green) is in OLI/nm. The area under the green curve in
Figure 3.2b is the overlap integral. There are three different vertical scales in
Figure 3.2b. Therefore, by adjusting one scale with respect to the others, the
appearance of this figure can be adjusted. However, whatever scale adjustment
is made, Figure 3.2a can never be made to resemble Figure 3.2b, because the
1) Andrews, D.L. (2012) Private communication.
j29
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3.5 Overlap Integral
j 3 F€orster Theory
wavelength to the fourth factor will cause the peak of the overlap curve to be always at
a wavelength larger than the one where donor emission and acceptor extinction
intersect. The overlap integral in wave number form is
ð
f ð~nÞeA ð~nÞ
J¼ D 4
d~n:
ð3:6Þ
~n
Here, the integral extends over the region that encompasses the relevant donor
emission and acceptor absorption bands in terms of wave number, ~
n ¼ 1=l,
conveniently expressed in 1/nm, eA ð~nÞ is the molar extinction coefficient of the
acceptor, usually in M1 cm1, and f D ð~nÞ is the fluorescence spectrum of the donor
normalized on the wave number scale:
F D~n ð~nÞ
ð~nÞd~n;
f D ð~nÞ ¼ Ð
F D~n
ð3:7Þ
where F D~n ð~nÞ is the donor fluorescence per unit of wave number interval and the
integral extends over the relevant donor emission band(s).
The overlap integral in frequency form is the one appearing in F€
orster theory (see
Section 3.12):
ð
f ðnÞeA ðnÞ
J ¼ c4 D 4
dn:
ð3:8Þ
n
Here, the integral extends over the region that encompasses the relevant donor
emission and acceptor absorption bands in terms of frequency, n ¼ c=l, c is the
speed of light in vacuo, which is equal to about 3 108 m=s (more precisely
c ¼ 2:99792458 108 m=s). The frequency is conveniently expressed in hertz
(¼1/s), eA ðnÞ is the molar extinction coefficient of the acceptor, usually in M1
cm1, and f D ðnÞ is the fluorescence spectrum of the donor normalized on the
frequency scale:
f D ðnÞ ¼ Ð
F Dn ðnÞ
;
F Dn ðnÞdn
ð3:9Þ
where F Dn ðnÞ is the donor fluorescence per unit of frequency interval, and the
integral extends over the relevant donor emission band(s).
At first sight, the conversions from Equations 3.4–3.6, and to 3.8 look inconsistent
with the rules of calculus, but they are actually correct and follow from the “first law
of photophysics” (Chapter 2 of Ref. [6]):
F Dl dl ¼ F D~n d~n ¼ F Dn dn:
ð3:10Þ
The intensities are measured using monochromators or filters with a certain
resolution or bandwidth. The reading on the instrument is proportional to this
bandwidth if it is sufficiently small. The intensity is taken to be proportional to the
reading per wavelength or wave number or frequency. This proportionality is the
idea behind the first law of photophysics. Note that the extinction coefficient
transforms as eA ðlÞ ¼ eA ð~nÞ ¼ eA ðnÞ, because it is proportional to the logarithm
of a ratio of intensities.
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30
The overlap integral depends on both the absorption spectrum of the acceptor and
the emission spectrum of the donor. Absorption spectra vary as a rule relatively little
with change of solvent or temperature, but emission spectra may be very sensitive to
environment, a well-studied example being the fluorescence of indole derivatives
[23]. Analytical results for the overlap integral have been derived for bands of
Gaussian and log normal line shapes [24].
3.6
Zones
F€orster visualized a donor as a group of electrical oscillators close together. These
electrical oscillators produce an electrical field in the space around the donor. This
space consists of four zones: the contact zone or Dexter zone [25], the near zone or
the near field, the intermediate zone, and the far zone (also called the far-field or the
radiation zone). The concept of zones, illustrated in Figure 3.3, dates back to Hertz
[7] who actually considered three zones: the near, intermediate, and far, because he
set out to confirm Maxwell’s prediction of electromagnetic waves [7] and was not
interested in distances very close to the electrical oscillators.
The zones can be defined in terms of a distance b:
b¼
l
;
2pn
Figure 3.3 The space around a donor
fluorophore can be divided into four zones.
These zones are shown here on a logarithmic
scale with the outer radius of each ring being a
factor of 10 larger than the inner radius. The
donor occupies the center of the contact zone,
which extends up to about a nanometer or
more depending on the donor size (see
Table 3.1). Around this zone is the near field,
about 1–10 nm from the donor. The near field is
the only zone where F€
orster theory applies.
ð3:11Þ
Around the near field is the intermediate zone
from 10–1000 nm. Outside the intermediate
zone is the far field where electromagnetic
radiation takes place. If the acceptor
concentration is sufficiently small – so that the
probability of finding an acceptor in the contact
zone is very small – and the sample is not too
large – so that the probability of reabsorption is
small, FRET is the dominant mode of energy
transfer.
j31
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3.6 Zones
j 3 F€orster Theory
where l is the wavelength of the donor fluorescence that is usually in the 300–
800 nm range and n is the index of refraction of the medium in which the donor and
acceptor are embedded [26]. This index has values typically between 1.3 and 1.6. So, b
is about 100 nm or a little smaller. Properties of these zones are listed in Table 3.1.
FRET happens in the near field, that is, roughly in the 1–10 nm range. If it is less
than about 1 nm, F€orster theory does not apply for at least two reasons: First, the
complex formation may occur between donor and acceptor at such a proximity (see
also Section 3.7 and Refs [3,20,25]). Second, the F€
orster’s theory is based on the ideal
dipole approximation (IDA) and the IDA breaks down if the donor–acceptor distance
is on the order of 1 nm [28]. If the distance is larger than about 10 nm, contributions
to the electric field that are ignored in F€
orster’s theory become relevant. In the
radiation zone, the acceptor is capable of reabsorbing light emitted by the donor (see
Section 3.7).
Table 3.1 Zones around the donor.
Name
Alternative
name
Inner
radius
Outer
radius
Characteristics
Contact zone
Dexter
zone
0
0.01b
(1 nm)
Near-field
zone
Near field
0.01b
(1 nm)
0.1b
(10 nm)
0.1b
(10 nm)
10b
(1000 nm)
10b
Infinite
The ideal dipole approximation
breaks down [25]. An acceptor in
this zone may form a complex with
the donor [3]. F€orster theory does
not apply. For larger molecules
(chlorophyll and porphorin), the
outer radius is about 2–3 nm [27].
The distance dependence of transfer
is reviewed in Ref. [20]
F€orster theory is valid only in this
zone. The electric field due to
oscillating donor charges can be
considered as a sum of dipole terms
with a 1/distance3 dependence. The
inner radius may be bigger for
larger molecules (see above)
The electric field due to oscillating
donor charges has three terms with
different distance dependence,
none of which is dominant. F€orster
theory does not apply
Electromagnetic donor emission
takes place in this zone. The electric
field due to oscillating donor charges
has a 1/distance dependence. The
electric field lines are pinched off
and transverse waves are formed [7].
F€orster theory does not apply.
Reabsorption will occur
Intermediate
zone
Radiation
zone
Far field
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32
3.7
Transfer Mechanisms
F€orster was well aware of the fact that there are at least four different mechanisms by
which excitation energy can be transferred from a donor to an acceptor. These are
resonance energy transfer, reabsorption, complex formation, and collision quenching. Resonance energy transfer (also called FRET2)) [29], the main topic of this book,
is the radiationless transmission of an energy quantum from its site of absorption to
the site of its utilization in a molecule, or system of molecules, by resonance
interaction between chromophores, over distances considerably greater than interatomic without conversion to thermal energy and without the donor and acceptor
coming into kinetic collision. Reabsorption or “trivial reabsorption” is the emission
of a photon by the donor with the subsequent absorption of that photon by the
acceptor. Complex formation is the creation of an excited-state complex of a donor
and an acceptor that are in proximity, essentially in molecular contact with each
other. Collision quenching can occur when an excited molecule loses its excitation
energy to another molecule by colliding with it. As F€
orster pointed out, these four
transfer mechanisms have different characteristics and can, therefore, be distinguished experimentally [3]. Table 3.2, adopted with minor modifications, from one
of F€orster’s papers [3], summarizes these different characteristics. Quantum
Table 3.2 Characteristics of transfer mechanisms.
Sample volume: with increasing
volume, transfer exhibits
Viscosity: with increasing
viscosity, transfer exhibits
Donor lifetime: because of
transfer, the donor lifetime shows
Donor fluorescence spectrum:
comparing transfer and no
transfer. This spectrum is
Donor absorption spectrum:
comparing transfer and no
transfer. This spectrum is
Resonance
energy
transfer
Reabsorption
Complex
formation
Collision
quenching
No change
Increase
No change
No change
No change
No change
No change
Decrease
Decrease
No change
No change
Decrease
Unchanged
Changeda)
Unchanged
Unchanged
Unchanged
Unchanged
Changeda)
Unchanged
a) Changes only apply to the wavelength, not to the intensity.
2) There is general agreement about the
FRET acronym. However, there is no
consensus yet about the meaning of the
letters in FRET. Many authors read it as
“fluorescence resonance energy transfer,”
while many others as “F€orster resonance
energy transfer.” The author of this chapter
prefers “fluorescence with resonance
energy transfer.” “Fluorescence-detected
resonance energy transfer” was proposed
by Vanbeek et al. [29].
j33
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3.7 Transfer Mechanisms
j 3 F€orster Theory
electrodynamics teaches that all electric and magnetic interactions are mediated by
photons even in the near field. The photons in the near field are actually virtual
photons. As a result, FRET and trivial reabsorption can be interpreted as two
different aspects of the same phenomenon (see Section 3.19) [30].
3.8
Kappa-Squared Basics
The previous sections can be considered to provide an introduction to F€
orster theory.
This is the first of a group of sections (Section 3.8–3.14) forming F€
orster’s classical
derivation of his equations (Equations 3.1–3.3).
The orientation factor, kappa-squared, is the square of k, which is defined as
k ¼ cos qT 3cos qD cos qA :
ð3:12Þ
Here, qD is the angle between the donor emission transition moment and the
donor–acceptor connection line, qA is the angle between the acceptor absorption
transition moment and the donor–acceptor connection line, and qT is the angle
between the donor emission transition moment and the acceptor absorption
transition moment. Kappa-squared varies between 0 and 4 and is discussed, in
more detail, in Chapter 4. The relation between the F€
orster distance and the kappasquared is shown in Figure 3.1c. In F€orster theory, k appears in terms of dot products
^ ^a, and ^r , which are unit vectors: d^ along the donor dipole, ^
between d,
a along the
acceptor dipole, and ^r along the line from the donor to the acceptor. ^
d ^r ¼ cos qD ,
^a ^r ¼ cos qA , and d^ ^a ¼ cos qT . Kappa in terms of dot products is
k ¼ ^d ^a 3 ^d ^r ð^r ^aÞ:
ð3:13Þ
The angles and unit vectors are illustrated in Figure 3.4.
The amplitude of the donor dipole moment is qe DD (qe is the charge of an electron
d
and DD is the displacement of the charge, both shown below). It oscillates along the ^
direction at frequency nDONOR (in general, there is a distribution of frequencies) and
^ ^a, and ^r .
Figure 3.4 Illustration of the angles uD , uA , and uT and the unit vectors d,
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34
generates an electric field at the location of the acceptor. Donor and acceptor are
embedded in a medium with refractive index n, with a distance r DA between them.
At time t, the electric field generated by the donor dipole at the location of the
acceptor, in the near field, is given by
h
i
qe DD 3 ^d ^r ^r ^d cos ð2pnDONOR tÞ
~
E ¼
:
ð3:14Þ
4pe0 n2 r 3DA
The component of this field along the acceptor dipole is
q DD kcos ð2pnDONOR tÞ
~
E ^a ¼ e
:
4pe0 n2 r 3DA
ð3:15Þ
The mks unit system is used here. In the cgs system, the 4pe0 factor is replaced by 1.
3.9
Ideal Dipole Approximation
The donor is a group of oscillating charges. We can imagine a sphere drawn around
the center of the donor with radius RD containing all these charges. Similarly, the
acceptor is a group of oscillating charges contained in a sphere around its center
with radius RA . In the near field, the distance r DA between the center of the donor
and that of the acceptor is much larger than RD and also much larger than RA . As a
result, the ideal dipole approximation holds: The electromagnetic interaction
between donor and acceptor is a dipole–dipole interaction, and all interactions
due to higher multipoles can be ignored [31]. The ideal dipole approximation is
illustrated in Figure 3.5. It must be emphasized that the relevant donor and acceptor
dipoles are not permanent dipoles but oscillating dipoles; in quantum mechanical
terms, they are transition dipoles.
Consistent with this dominance of the dipole moment above all other multipoles,
F€orster visualized a donor or an acceptor molecule as a group of coupled electrical
oscillators [32]. Each electrical oscillator consists of an electron elastically bound to a
nucleus. The nucleus is stationary,3) but the electron can oscillate along a certain
direction (not along other directions). The charge of the electron is qe
(qe ¼ 1:60217646 1019 C) and its mass is me (me ¼ 9:10938188 1031 kg).
The values qe and me do not appear in the final results because they are taken
up by the spectral properties of the donor and the acceptor. The donor dipole is
^ a unit vector, and dipole
situated at the center of the donor and has a direction d,
moment~
p D ¼ qe DD ^d, where DD ^d is a vector sum of fluctuating vectors oscillating at
a range of frequencies. The vector DD ^d is from the center of all positive charges to
the center of all negative charges in the donor. Similarly, the acceptor dipole is
situated at the center of the acceptor and is along the unit vector ^
a and has dipole
moment~
p A ¼ qe DA ^a, where DA ^a is a vector sum of fluctuating vectors oscillating at
3) In reality the nuclei do oscillate, but at frequencies that are irrelevant for FRET.
j35
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3.9 Ideal Dipole Approximation
j 3 F€orster Theory
Figure 3.5 A cartoon of a donor molecule, on
the left, and an acceptor molecule, on the right.
In reality, both donor and acceptor contain
many charges, which vibrate and oscillate in
several directions and at a range of frequencies
on the order of 1 million GHz. When the size of
the donor is much smaller than the donor–
acceptor distance and the size of the acceptor is
also much smaller than this distance, the ideal
dipole approximation is valid.
a range of frequencies. It points from the center of all positive charges to the center
of all negative charges in the acceptor. We must realize that when a donor is excited
by an electromagnetic wave at a certain frequency, the donor will start oscillating at a
range of frequencies and not only at the frequency of the wave, because the
oscillators that make up the donor are coupled.
F€orster used the cgs unit system, which was the system of choice in the 1940s and
1950s. Today (2012) this system is hardly ever used, and in this presentation of F€
orster
theory, the mks system is used, which is also known as the SI system. In the cgs
system, the unit of charge is the statcoulomb (which is equal to the esu); but in the mks
system, the unit of charge is the coulomb (C ¼ A s). One statcoulomb is equal to
3.3356 1010 C [33]. A consequence of this difference in units is that many equations
in electromagnetism using the cgs system differ from the corresponding equations in
the mks system [33]. However, the final equations derived by F€
orster do not depend on
the system of units, but intermediate equations in the theory, for example, those for
energy, power, and intensity, have different forms in the two systems.
3.10
Resonance as an All-or-Nothing Effect
Resonance occurs when an oscillator capable of vibrating at a natural frequency
interacts with an external system that forces this oscillator to vibrate at an external
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36
frequency. The oscillator will pick up significant energy only if the external
frequency and the natural frequency are equal or nearly equal. Resonance is
everywhere: accomplished singers can break a wine glass by hitting the right note
[34], a sturdy bridge can collapse when jolted at the right frequency [35], and most
adults walk at a frequency of about 1 Hz because adult legs swing at a natural
frequency of about 1 Hz. The resonance phenomenon that concerns us here
occurs when acceptor charges oscillate in phase with donor charges at a distance.
In his classical theory of energy transfer [32], F€
orster visualized a donor or an
acceptor molecule as a group of coupled electrical oscillators. When the donor
oscillators are in an external electromagnetic field caused by light that can excite
the donor, the oscillators in the donor will oscillate and cause their own electromagnetic field. Acceptor oscillators often will not respond to the external electromagnetic field, but may be sensitive to the electric field from the donor oscillators.
Let us first focus on one electrical oscillator inside an acceptor responding to an
electric field generated by a donor at some distance away. We will call the direction
in which the acceptor oscillator can swing the acceptor direction. The natural
frequency of this oscillator is nACCEPTOR . The electric field is also along a certain
direction, the donor field direction, which is not necessarily the same as the
acceptor direction. However, this electric field must have a component along
the acceptor direction, otherwise there will be no response. The amplitude of
this component is E DF (which is equal to the amplitude of the donor field times
the cosine of the angle between the two directions). The frequency of the donor
field is nDONOR (which is also equal to the frequency of the donor oscillator). The
electric field starts at time 0 and lasts for a certain amount of time t, which can
vary. The energy W A that the acceptor dipole has at time t as a result of its
interaction with the donor field depends on the frequency difference
nACCEPTOR nDONOR . As a function of frequency, this energy has a strong maximum when this frequency difference is zero, but also has weak secondary maxima
at other values. F€orster made the approximation to replace this intricate resonance
behavior by a sharp rectangular peak. In other words, he assumed that either there
is resonance or there is nothing:
8
>
>
0;
>
>
>
< 2 2
qe E D
WA ¼
t2 ;
>
8me
>
>
>
>
: 0;
if
if
if
nDONOR nACCEPTOR <
1
;
2t
1
1
nDONOR nACCEPTOR ;
2t
2t
1
nDONOR nACCEPTOR > :
2t
ð3:16Þ
This approximation is schematically illustrated in Figure 3.6.
From Equation 3.16 we see that the value of this peak increases drastically with
time, but the width of the peak decreases with time. For example, doubling the time
yields a fourfold increase in the value at the peak, but leads to a reduction by a factor
of 2 in the width, as illustrated in Figure 3.7.
j37
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3.10 Resonance as an All-or-Nothing Effect
j 3 F€orster Theory
Figure 3.6 F€
orster replaced the resonance
curve by a rectangular peak. Vertically the
energy of the acceptor is plotted and
horizontally the frequency. The center of the
peak (for the curve as well as the rectangular
peak) corresponds to the donor frequency
being equal to the acceptor frequency.
Figure 3.7 The height of the resonance peak is proportional to time-squared, but the width is
proportional to the time. As a result, doubling the time yields a fourfold increase in the height of
the peak, but leads to a reduction by a factor of 2 in the width.
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38
3.11
Details About the All-or-Nothing Approximation of Resonance
The reader who has no problem accepting F€orster’s all-or-nothing approximation of
resonance and is not interested in the reasons why this approximation is good
should skip this section.
It turns out that F€orster’s all-or-nothing approximation of resonance is excellent. It
is not immediately obvious why. To prove that it is indeed very good, we must set up
an equation of motion for the acceptor oscillator, solve it, calculate the energy of the
acceptor, and compare this rigorous expression of the energy with the approximate
equation displayed in Equation 3.16.
Consider the forces acting on each acceptor oscillator. An electrical oscillator in
the acceptor can oscillate along a certain line, the acceptor direction, which we will
identify as the x-axis. The natural frequency of this oscillator is nACCEPTOR . This
frequency is related to the spring constant k and the mass of the oscillator me by
sffiffiffiffiffiffi
1
k
nACCEPTOR ¼
:
ð3:17Þ
2p me
The x-component of the electric field generated by a donor oscillator has
amplitude E D and frequency nDONOR and at time t is
x-component of the electric field generated by donor ¼ E D cos ð2pnDONOR tÞ:
ð3:18Þ
From Equation 3.15, we know E D is equal to
ED ¼
qe DD k
:
4pe0 n2 r 3DA
ð3:19Þ
According to Newton’s second law, the net force on the oscillating charge, the sum
of the elastic force kx and the electric force Q e E D cos ð2pnDONOR tÞ, equals the mass
times the acceleration:
me
d2
x ¼ kx þ qe DD cos ð2pnDONOR tÞ;
dt2
ð3:20Þ
where x is the displacement and qe is the charge of the oscillator. Substituting k ¼
4p2 me n2ACCEPTOR (from Equation 3.17) into (3.20), dividing by me, and utilizing the
abbreviations u ¼ 2pnACCEPTOR and w ¼ 2pnDONOR transform (3.20) into
d2
q DD
x ¼ u2 x þ e
cos ðwtÞ:
dt2
me
ð3:21Þ
The solution of Equation (3.21) for the case where the initial displacement and the
initial velocity are zero is
x¼
qe E D
ðcos ðwtÞ cos ðutÞÞ;
me ðu2 w 2 Þ
ð3:22Þ
j39
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3.11 Details About the All-or-Nothing Approximation of Resonance
j 3 F€orster Theory
so that the speed of the oscillator motion is
dx
uqe E D
w
sin ðutÞ sin ðwtÞ :
¼
dt me ðu2 w2 Þ
u
ð3:23Þ
The energy of the acceptor, W A , the sum of the potential energy,
ð1=2Þkx2 ¼ ð1=2Þme u2 x 2 , and the kinetic energy, ð1=2Þme ðdx=dtÞ2 , is
"
#
2
q2e E 2D
4u2
w
2
2
ð
cos
ð
wt
Þ
cos
ð
ut
Þ
Þ
:
WA ¼
t
þ
sin
ð
wt
Þ
sin
ð
ut
Þ
8me
u
ðw 2 u2 Þ2 t2
ð3:24Þ
2
For w ¼ u e with e p=t, the term in square brackets equals 1=ðetÞ and the term
in curly brackets equals ðetÞ2 . Therefore, at very small differences between the
donor and acceptor frequencies, this energy is equal to its maximum value ¼
W A;PEAK ¼ ½ðq2e E 2D Þ=8me t2 . Relevant values of t are on the order of the lifetime of
the excited state, so that 2p=t is on the order of 1–10 GHz, whereas u and w
correspond to frequencies in the UV or visible and are, therefore, on the order of a
million gigahertz. As a result, W A has a series of minima that are essentially equal to
zero for w ¼ u Np=t, where N is an even integer larger than 0. The case w ¼
u p=t corresponds to the border of the rectangular F€
orster peak. At that frequency,
the actual W A value is about 0:4 W A;PEAK . With w ¼ u Np=t where N is an odd
integer larger than 1, W A has secondary maxima equal to about 0:4 W A;PEAK =N 2 .
The width of the all-or-nothing peak equals 1=t. The width of the actual resonance
curve can be defined in terms of the area under the curve. The total area under the
all-or-nothing peak and that under the actual resonance curve turn out to be
essentially the same. Relevant intervals for the resonance curve are as follows:
Width of frequency
interval
Frequency interval in terms
of vACCEPTOR vDONOR
Approximate area under
the curve (% of total)
1/t
1/(2t) vACCEPTOR vDONOR 1/(2t)
77%
20/t
10/t vACCEPTOR vDONOR 10
99%
Most of the energy is transferred near the end of the lifetime of the excited state of
the donor, where t is on the order of nanoseconds, so that the width of the 99%
interval is about 20 GHz. However, the relevant frequency values in the spectra are
on the order of millions of gigahertz. This means that over 20 GHz, the spectra do
not vary at all. Since the all-or-nothing peak and the actual resonance peak have the
same area under the curve, the total amount of energy transferred in the all-ornothing approximation is equal to that transferred according to the actual resonance
curve when t is on the order of a nanosecond. The all-or-nothing approximation can
only fail if there is significant spectral variation over the 99% interval. Such variation
is expected when t is very small, less than a femtosecond. However, early in the
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40
process, the energy is extremely small because of the time-squared factor in the
magnitude of the peak (energy after a femtosecond ¼ 1012 energy after a nanosecond). We conclude, therefore, that F€orster’s all-or-nothing approximation, replacing Equation 3.24 by Equation 3.16, is excellent.
3.12
Classical Theory Completed
From Equation (3.16) we know that if one donor oscillator and one acceptor oscillator
have the exact same frequency n ¼ nDONOR, the acceptor has, due to a resonance
interaction with the donor, t s after the donor has started oscillating, an amount of
energy W A equal to
q2e E 2D t2
:
8me
WA ¼
ð3:25Þ
Expressing W A in terms of the donor–acceptor distance using Equation 3.19, we
find
q4e D2D k2 t2
WA ¼
8me ð4pe0 Þ2 n4 r 6DA
:
ð3:26Þ
D2D is proportional to W D , the energy of the donor oscillator, because
1
W D ¼ kD2D ¼ 2p2 me n2 D2D ;
2
ð3:27Þ
meaning that
D2D ¼
WD
:
2p2 me n2
ð3:28Þ
Substituting this into Equation 3.26 yields
WA ¼
q4e k2 W D t2
16p2 me n2 ð4pe0 Þ2 n4 r 6DA
:
ð3:29Þ
Now we must generalize this to the case where there is not just one frequency but
distributions of frequencies for donor and acceptor. Such distributions can be
described using oscillator strengths f eD ¼ f eD ðnÞ for the donor and f aA ¼ f aA ðnÞ for
the acceptor. Specifically,
f eD ¼ f eD ðnÞ ¼ probability to find a frequency between n and n þ dn:
ð3:30Þ
Remember that the width of the resonance peak, using F€
orster’s all-or-nothing
approximation, is 1=t (see Equation 3.16). Therefore, relating Equation 3.30 to the
corresponding acceptor frequency interval, we find
f aA ðnÞð1=tÞ ¼ acceptor frequencies resonating with donor:
ð3:31Þ
j41
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3.12 Classical Theory Completed
j 3 F€orster Theory
It follows, therefore, that we should multiply both sides of Equation 3.29 with
f eD ðnÞf aA ðnÞð1=tÞdn and integrate over all frequencies:
WA ¼
1
ð
q4e k2 W D t
16p2 me ð4pe0 Þ2 n4 r 6DA
0
f eD ðnÞf aA ðnÞdn
:
n2
ð3:32Þ
Differentiating this with respect to time gives us F€
orster’s rate equation:
dW A
¼ kT W D ;
dt
ð3:33Þ
with
kT ¼
1
ð
q4e k2
16p2 m2e ð4pe0 Þ2 n2 r 6DA
0
f eD ðnÞf aA ðnÞdn
:
n2
ð3:34Þ
Substituting Equations 3.42 and 3.46 into Equation 3.34 yields
kT ¼
9ðln 10Þk2 WD
128p5 N 0 tD r 6DA
1
ð
c4 f D ðnÞeA ðnÞdn
:
v4
ð3:35Þ
0
Using the definitions of the F€orster distance and the overlap integral, we find
R60 ¼
9ðln 10Þk2 WD J
;
128p5 n4 N 0
ð3:36Þ
and this equation is identical to Equation 3.3, because N 0 ¼ N A . In (3.36) J stands for
1
ð
J¼c
4
0
f D ðnÞeA ðnÞ
dn;
n4
which is Equation 3.8. And, we arrive at F€
orster’s equation:
6
1 R0
;
kT ¼
tD r 6DA
ð3:37Þ
ð3:38Þ
which is Equation 3.2. Note that in this section the integrals extend from zero to
infinite frequency as they are based on the theoretical model of coupled charged
oscillators. However, integrals based on experimentally obtained spectra should only
refer to the relevant part of the spectra as discussed in Section 3.5.
3.13
Oscillator Strength–Emission Spectrum Relation for the Donor
Consider a donor molecule capable of emitting light. The electromagnetic energy
this donor has is W D . If the quantum yield is WD , then the energy available
for fluorescence is WD W D . This can be emitted over a range of frequencies.
Ð1
The normalized fluorescence spectrum is f D ¼ f D ðnÞ, so that 0 f D ðnÞdn ¼ 1.
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42
The energy available for emission between n and n þ dn is equal to WD W D f D ðnÞdn.
The average lifetime of the excited state is tD . Therefore,
the rate of emission between n and n þ dn ¼
WD W D f D ðnÞdn
:
tD
ð3:39Þ
On the other hand, one electric oscillator having energy W D, mass me , charge qe ,
and frequency n, embedded in a medium with refractive index n, must radiate
energy in accordance with Maxwell’s theory of electromagnetism, at a following rate:
the rate of emission of one oscillator ¼
8p2 nn2 q2e W D
:
3ð4pe0 Þme c3
ð3:40Þ
We have a distribution of oscillators with a fraction of f eD ðnÞdn between n and
n þ dn. As a result, we have
the rate of emission between v and v þ dv ¼
8p2 nn2 q2e W D f eD ðnÞ
:
3ð4pe0 Þme c3
ð3:41Þ
Combining Equations 3.39 and 3.41 yields ½WD W D f D ðnÞ =tD ¼ ½8p2 nn2 q2e W D f eD ðnÞ =
½3ð4pe0 Þme c 3
Therefore, the relation between the donor oscillator strength and the donor
emission spectrum is
f eD ðnÞ ¼
3ð4pe0 Þme c3 WD f D ðnÞ
:
8p2 nn2 q2e tD
ð3:42Þ
3.14
Oscillator Strength–Absorption Spectrum Relation for the Acceptor
Imagine electromagnetic radiation falling upon 1 cm2 of a layer containing acceptor
molecules at a concentration c A moles=l. This layer has a very small thickness of ‘
cm. Consider the spectral energy density s ðnÞ, defined such that s ðnÞdn represents
the electromagnetic energy per unit of volume in the frequency range between n and
n þ dn. From the Lambert–Beer law, we find that the spectral energy density
absorbed in this layer is equal to the transmitted minus the incident spectral
density, that is, absorbed spectral energy density ¼ s ðnÞ 1 eeA cA ‘ , where eA ¼
eA ðnÞ is the molar extinction coefficient of the acceptor in units 1/(cm M). Because
‘ is very small, and therefore eA c A ‘ is very small, the following simplification is valid:
h
i
s ðnÞ 1 10eA cA ‘ ¼ s ðnÞ 1 eðln 10ÞeA cA ‘ ¼ s ðnÞ½1 f1 ðln 10ÞeA cA ‘g
¼ s ðnÞðln 10ÞeA cA ‘:
Here, ln 10 is the natural logarithm of 10 (see Section 3.3). Therefore,
ðln 10Þs ðnÞeA c A ‘ is the spectral energy density per unit of volume absorbed.
This energy is absorbed in an extremely short time. The speed at which this
radiation propagates in the medium is c=n (c is the speed of light in vacuo and n
j43
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3.14 Oscillator Strength–Absorption Spectrum Relation for the Acceptor
j 3 F€orster Theory
is the refractive index of the medium). Therefore, if we are interested in the energy
absorbed in 1 s, we must visualize a cylinder with a length of c=n and a crosssectional area of 1 cm2 just in front of the layer. The energy distributed over this
cylinder is the energy per second entering the layer. So, the energy per second
entering the layer is sðnÞ c=n, and the energy absorbed in it is
ðc=nÞðln 10Þs ðnÞeA cA ‘. This layer has a volume of ‘ 1 cm3 ¼ ‘ 1 ml. Since
the concentration of acceptor is c A moles=l, this volume contains
‘ cA millimoles, which is N 0 ‘cA acceptor molecules (N 0 is the number of molecules per millimole) (see Section 3.3). Thus,
energy absorbed per second and per molecule ¼
ðln 10ÞcsðnÞeA
:
nN 0
ð3:43Þ
On the other hand, from classical electromagnetic theory, we know that one electric
oscillator with mass me , charge qe , and frequency n, embedded in a medium with
refractive index n, where the spectral energy density is sðnÞ will absorb energy at a
predictable rate,
the energy absorbed per second by one oscillator ¼
pq2e sðnÞ
:
3n2 ð4pe0 Þme
ð3:44Þ
We have a distribution of oscillators with a fraction of f aA ðnÞdn between n and
n þ dn. As a result, we have
the energy absorbed per second per molecule ¼
pq2e sðnÞf aA ðnÞ
:
3n2 ð4pe0 Þme
ð3:45Þ
Combining Equations 3.43 and 3.45 yields
ðln 10ÞceA ðnÞs ðnÞ pq2e s ðnÞf aA ðnÞ
¼
:
nN 0
3n2 ð4pe0 Þme
Therefore, the relation between acceptor oscillator strength and acceptor extinction
spectrum is
f aA ðnÞ ¼
3ðln 10Þð4pe0 Þnme ceA ðnÞ
:
pN 0 q2e
ð3:46Þ
3.15
Quantum Mechanical Theory
When charges are bound to each other inside a molecule, the energies available to
them do not form a continuous spectrum, but the energy values are quantized.
Resonance energy transfer can, therefore, be understood as coupled transitions, as
shown in Figure 3.8. This diagram is essentially the same as the energy level
diagram introduced by F€orster in his 1959 paper [3].
According to quantum mechanics, a system can adopt a number of different
states. Considering a donor and an acceptor, it is clear that transfer may take place
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44
Figure 3.8 Simplified energy-level diagram of resonance energy transfer. D refers to the donor
and A to the acceptor; asterisks denote excited states. (Adapted from Ref. [2].)
from the state in which the donor is excited and the acceptor is not, jD Ai, to a state
in which the acceptor is excited and the donor is not, jDA i. The interaction
responsible for transfer at donor–acceptor distances larger than the sizes of the
charge distributions is the dipole–dipole interaction U, which is given by
U¼
1
½~
p A 3ð~
p D ^r Þð^r ~
p AÞ ;
p D ~
4pe0 n2 r 3DA
ð3:47Þ
where n is the refractive index of the medium, r DA denotes the distance between the
donor and the acceptor, ^r is a unit vector pointing from the donor to the acceptor,~
pD
and~
p A are the dipole moment vectors of the donor and acceptor charge distribution,
respectively, ~
p D ~
p A is the dot product of these two vectors, that is, the projection of
one on the other. According to the time-resolved perturbation theory, the rate of
transfer in the “very weak coupling” [5] limit is
ð
1
kT ðW D ; W A Þ ¼
ð3:48Þ
hD AjU jDA i2 dW;
h
where kT ðW D ; W A Þ is the rate of transfer from an excited donor molecule with
initial W D to an acceptor with initial energy W A, h is Planck’s constant, and the
integral is over all possible values of the transferred energy W. (The meaning of
“very weak”, “weak”, and “strong coupling” in this context is discussed by F€
orster [5],
Kasha [36], and Knox [20]. It is safe to assume that the Born–Oppenheimer
approximation is valid. This approximation states that the electronic motion and
j45
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3.15 Quantum Mechanical Theory
j 3 F€orster Theory
the nuclear motion in molecules can be separated, so that the wave function for the
molecule can be considered to be a product of an electronic wave function times a
nuclear wave function. As a result, the expectation value for the energy in Equa~ D and
tion 3.48 can be expressed in terms of electronic transition dipole moments m
~ A , of the donor and acceptor, respectively. These vectors can be written as
m
~ D ¼ jmD j^d and
m
~ A ¼ jmA j^a;
m
ð3:49Þ
where ^d and ^a are unit vectors in the direction of the donor and acceptor transition
moments, respectively, and, jmD j and jmA j represent the magnitudes of these
moments. In this approximation, the integrand in Equation 3.48 can be expressed
in terms of the electronic transition moments as follows:
hD AjU jDA i2 ¼
k2 m2D m2A
ð4pe0 Þ2 n4 r 6DA
S2D S2A ;
ð3:50Þ
where k2 is the orientation factor defined in Section 3.7 and m2D m2A is the square of
jmD jðjmA jÞ. The factors SD and SA represent vibrational overlap integrals: SD ¼
SD W D ; W D W is the overlap integral between the initial vibrational donor state
with energy W D and the final state with energy W D W, and SA ¼ SA W A ; W A þ W
is the overlap integral between the initial vibrational acceptor state with energy W A and
the final state with energy W A þ W. From the transfer rate kT ðW D ; W A Þ of Equation 14.2, we can obtain the total transfer rate of thermal equilibrium by introducing
suitable Boltzmann factors and integrating over all energies W D and W A . These
Boltzmann factors g W D for the excited donor and g ðW A Þ for the acceptor in the
ground state are continuous functions and are normalized on an energy scale. Therefore,
by multiplying both sides of Equation 3.48 by g W D dW D and g ðW A ÞdW A , integrating
over all W D and W A , and changing integration variable from energy to frequency: W to n,
we obtain the following expression for the total transfer rate kT :
kT ¼
with
and
k2
ð4pe0 Þ2 n4 h2 r 6DA
1
ð
M D ðnÞLA ðnÞdn;
ð3:51Þ
0
ð
MD ðnÞ ¼ m2D g W D S2D W D ; W D hn dW D
ð3:52aÞ
ð
LA ðnÞ ¼ m2A g ðW A ÞS2A ðW A ; W A þ hnÞdW A :
ð3:52bÞ
Analyses similar to that done in Sections 3.12 and 3.13 [32] show that M D ðnÞ is
related to the normalized fluorescence spectrum of the donor and LA ðnÞ is
proportional to the extinction spectrum of the acceptor:
MD ðnÞ ¼
ð4pe0 Þ3hWD c3 f D ðnÞ
:
32p3 ntD n3
ð3:53aÞ
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46
LA ðnÞ ¼
ð4pe0 Þ3ðln 10ÞnhceA ðnÞ
:
4p2 N 0 n
ð3:53bÞ
Substituting Equations 3.53a and 3.53b into Equation 3.51 yields F€
orster’s
equation for the rate of transfer:
kT ¼
9ðln 10Þk2 Q D
128p5 N 0 tD r 6DA
1
ð
c4 f D ðnÞeA ðnÞdn
:
v4
ð3:54Þ
0
This equation is the same as Equation 3.35. As noted in Section 3.12, the
theoretical integrals extend from zero to infinite frequency, but integrals based
on experimentally obtained spectra should only refer to the relevant part of the
spectra as discussed in Section 3.5.
3.16
Transfer in a Random System
Consider an ensemble of donor and acceptor molecules, belonging to different
species, for which the following assumptions hold:
1) The molecules are randomly distributed through three-dimensional space.
2) Resonance energy transfer is possible at an appreciable rate from donor to
acceptor, but transfer in the opposite direction is negligible.
3) Translational diffusion is slow compared to the rate of transfer, so that the
distances between donor–acceptor pairs do not change significantly during the
time transfer takes place.
F€orster has pointed out [3] that these conditions are approximately met in
solutions of moderated viscosity, in which case the Brownian rotational motion
for both donor and acceptor molecules is also much faster than the transfer and is
unrestricted, so that the orientation factor can be set equal to 2/3. However, in many
biological systems, these assumptions may not be correct (see Chapter 4). In a
system in which these assumptions apply, consider a donor molecule that is already
excited at time t ¼ 0. If no acceptor molecules had been present, it would lose its
excitation energy after an average lifetime tD through radiation or nonradiative
deactivation processes. Its natural rate of deactivation is, therefore, 1=tD . The
presence of an acceptor molecule at a distance r k provides another deactivation
pathway for the excited donor molecule. The rate of transfer from the donor to the
acceptor is, according to F€orster theory, ð1=tD ÞðR0 =r k Þ6 . Because of these two
competing processes, the probability r ¼ rðtÞ that the donor molecule is still excited
at time t is given by the following equation:
"
#
N d
1 X
R0 6
r;
ð3:55Þ
þ
r¼
dt
tD k¼1 r k
where the summation is over all N acceptor molecules in a spherical volume around
the excited donor molecule with a radius much larger than the F€
orster distance R0 .
j47
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3.16 Transfer in a Random System
j 3 F€orster Theory
The solution of this differential equation with the condition that rð0Þ ¼ 1 is
( "
# )
N 1 X
R0 6 t
:
ð3:56Þ
rðtÞ ¼ exp þ
tD k¼1 r k
tD
The donor fluorescence is proportional to the average of this quantity, hrðtÞi.
F€orster [4] showed that this average can be written as in Equation 3.57. The
derivation of Equation 3.57 is explained in Section 3.17, where other details about
transfer in a random system are also given:
pffiffi
rðtÞ ¼ exp s 2ðc=c0U Þ s ;
ð3:57Þ
where s ¼ t=tD and c 0U is the “critical concentration for heterotransfer,” which is
given by
3
3
c0U ¼ pffiffiffiffiffi 0 3 ¼ pffiffiffiffiffi
;
2 p3 N R0 2 p3 N A R30
ð3:58Þ
Note that there are two critical concentrations: c 0U and c 0L . c 0U is the critical
concentration for heterotransfer, that is, transfer between unlike molecules (U
stands for unlike), and c 0L is the critical concentration for homotransfer, that is,
transfer between like molecules (L stands for like), discussed in Section 3.17. The
efficiency E can also be calculated (see Section 3.17) and is given by
pffiffiffi
E ¼ px ðex Þ2 f1 erf ðx Þg; with x ¼ c=c0U ;
ð3:59Þ
where erf is the error function, which is defined below, in Equation 3.76. The
efficiency is plotted in Figure 3.9 versus x ¼ c=c 0U . It turns out that when c ¼ c 0U ,
the efficiency is equal to 76%.
3.17
Details for Transfer in a Random System
The average of rðtÞ, defined in Equation 3.56, plays a key role in F€
orster’s theory of
heterotransfer in a random system of donors and acceptors [4]. This average can be
written as
hrðtÞi ¼ et=tD ½HðtÞ N ;
ð3:60Þ
with
RðV
H ð tÞ ¼
6
eðR=R0 Þ
t=tD
w ðRÞdR;
ð3:61Þ
0
where RV is the radius of the sphere around the excited donor molecule that contains
the N acceptor molecules to which transfer can occur, w ðRÞdR represents the
probability for finding an acceptor molecule at a distance between R and R þ dR
from the excited donor molecule. The assumption of randomness (the first
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48
Figure 3.9 The efficiency versus concentration
for a system of random donors and acceptors
where the rotational diffusion is fast, but the
translational diffusion is slow compared to the
rate of transfer. Here, C is the acceptor
concentration and C0 is the critical
concentration for heterotransfer, C0 ¼ C0U,
defined in Equation 3.58. The graph follows
from Equation 3.59.
assumption in Section 3.15) implies that w ðRÞ is such that every point in the sphere
has equal probability for being occupied. Therefore, w ðRÞ must be equal to
w ðRÞ ¼ 3R2 =R3V :
ð3:62Þ
Substituting this into Equation 3.61 allows us to transform HðtÞ into
1 pffiffiffiffiffi
HðtÞ ¼
zV
2
1
ð
zV
ez
pffiffiffiffiffi dz;
z3
ð3:63Þ
where z and zV are defined as
6
R
t
z¼
;
R 0 tD
6
R0
t
:
zV ¼
RV tD
ð3:64Þ
ð3:65Þ
Through integration by parts, we obtain
1
ð
zV
ez
2ezV
pffiffiffiffiffi dz ¼ pffiffiffiffiffi 2
zV
z3
1
ð
0
ez
pffiffiffiffiffi dz þ 2
z3
zðV
0
ez
pffiffiffiffiffi dz:
z3
ð3:66Þ
Note that for all relevant values of the time t, zV is much smaller than 1, because
RV is assumed to be much larger than R0 . Therefore, it is a very good approximation
pffiffiffiffiffi
to expand the right-hand side of Equation 3.66 in powers of zV and to keep only the
j49
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3.17 Details for Transfer in a Random System
j 3 F€orster Theory
first two terms. Applying this approximation and substituting Equation 3.66 into
Equation 3.63 yields
pffiffiffiffiffiffiffiffi
pzV :
H ð tÞ ¼ 1 ð3:67Þ
As a result, the average of rðtÞ in Equation 3.60 can be rewritten as
hrðtÞi ¼ et=tD ð1 pffiffiffiffiffiffiffiffi N
pzV Þ :
ð3:68Þ
Because the number N can be assumed to be extremely large, Equation 3.68 can be
simplified to
N
pffiffiffiffiffiffi
1
pzV
¼ et=tD N pzV :
ð3:69Þ
hrðtÞi ¼ et=tD lim 1 N pffiffiffiffiffiffi
N!1
N
Employing the definition of zV and introducing x defined by
x¼
pffiffiffi 3
pNR0
;
2R3V
ð3:70Þ
the average of rðtÞ becomes
pffi
hrðtÞi ¼ es2x s ;
ð3:71Þ
where s ¼ t=tD . The quantum yield in the presence of acceptor, WDA , is
1
ð
~
WDA ¼ C
hrðtÞidt;
ð3:72Þ
0
~ is a constant. The quantum yield in the absence of acceptor, WD , can be
where C
calculated from Equations 3.72 and 3.69 for N ¼ 0:
~
WD ¼ C
1
ð
~ D:
et=tD dt ¼ Ct
ð3:73Þ
0
Combining Equations 3.72 and 3.73 yields
WDA
¼
WD
where y ¼
1
ð
pffi
s2x s
e
0
1
ð
ds ¼
ex
2
y2
ð3:74Þ
ds;
0
pffiffi
s þ x, so that s ¼ ðy x Þ2 and ds ¼ 2ðy xÞdðy x Þ. Therefore,
WDA
¼2
WD
1
ð
x 2 y2
e
0
x2
1
ð
ðy xÞdðy x Þ ¼ 2e
y2
e
0
pffiffiffi 2
ydy xe
p pffiffiffi
p
x2
1
ð
ey dy:
2
x
ð3:75Þ
The first integral on the right-hand side equals 1 and the second can be expressed in
terms of the error function, which is defined as
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50
1
ð
0
x
2
2
2
erf ðxÞ ¼ pffiffiffi ey dy ¼ 1 pffiffiffi
p
p
ey dy:
2
ð3:76Þ
Combining Equations 3.75 and 3.76 allows us to express the efficiency in terms of x:
E ¼1
WDA pffiffiffi x2
¼ pxe f1 erf ðxÞg:
WD
ð3:77Þ
Note that if we choose N ¼ N A in Equations 3.60 and 3.70, the concentration
becomes c ¼ 3= 4pR3V . As a result, x in Equation 3.70 is equal to
pffiffiffiffiffi
x ¼ 2=3 p3 N A R30 c;
ð3:78Þ
and because of the definition of c 0 ¼ c 0U in Equation 3.58, we see that x ¼ c=c 0 ,
confirming Equation 3.59.
3.18
Concentration Depolarization
Concentration depolarization is a homotransfer phenomenon. In a system where the
fluorophores belong to a single species, FRET results in a strong depolarization of the
fluorescence. The excitation energy of a molecule that absorbs a photon at a certain
moment may jump from molecule to molecule until emission occurs at a later time.
Thus, a fluorescence photon, which in dilute solution is emitted by the absorbing
molecule, may in concentrated solutions be emitted by another molecule. This process
does not affect the time dependence of the fluorescence intensity, but it broadens the
angular distribution of the emission transition moments and consequently gives rise to
depolarization of the emission. A graph of the fluorescence polarization versus the
logarithm of the concentration shows a constant level of depolarization at low concentrations and a sharp drop at higher concentrations [2]. In his theory of concentration
depolarization, F€orster assumed that only the photons emitted by the primary molecule
are maximally polarized and that the other photons are completely unpolarized [2]. He
derives the polarization as a function of the concentration c for c c0 and for c
c 0,
where c 0 ¼ c0L , that is, the critical concentration for homotransfer:
c0L ¼
3
3
¼
:
4pN 0 R30 4pN A R30
ð3:79Þ
The depolarization depends on p1 , the probability that the fluorescence is emitted
by the initially excited molecule. If depolarization is due to concentration quenching
only and rotational motion can be ignored, p1 is equal to r=r 0 , the ratio of the
anisotropy and the fundamental anisotropy (¼ anisotropy in the absence of motion
or transfer). In the low concentration limit, only the interaction between the primary
molecule and one other is considered, and p1 is given by
1
ð
p1 ¼
0
1 þ t kT j
e dj;
1 þ 2t kT
c c0 ;
ð3:80Þ
j51
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3.18 Concentration Depolarization
ðx
j 3 F€orster Theory
where t is the fluorescence lifetime in the absence of transfer, kT is the rate of
transfer, and j ¼ 0:001 N A cV, where N A ¼ Avogadro’s number, c ¼ concentration
in moles/l, and V ¼ 4pR3 =3– here R denotes the distance between molecules. In the
high concentration limit, the excitation energy is thought to “diffuse” away from the
primary molecule and p1 is given by
p1 ¼ 1 ð1 þ 1:55=cÞe1:55=c ;
c
c0 :
ð3:81Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffi
Here c ¼ ðc=c 0 Þ W=W0 , where W is the quantum yield and W0 is the quantum
yield in the absence of transfer. This theory has been further developed by Knox and
others (see Section 3.19).
3.19
FRET Theory 1965–2012
F€orster’s work inspired an enormous volume of both experimental and theoretical
work, not to mention applications and patents. The concluding section of this
chapter is an overview of the theoretical work inspired by his results. However, this
overview does not include work on kappa-squared. This has been dealt with in
Chapter 4.
The theory of concentration depolarization and quenching has been further
developed by Knox, Craver, and others [36–44] (see Refs [45,46] for reviews). Craver
and Knox compared different theories for concentration quenching in three
dimensions and showed that experimental data were in good agreement with their
extension of F€orster’s theory [39]. Craver [40] has proposed a “universal” curve for
concentration depolarization in three dimensions. This curve, which is shown in
Figure 3.10, fits experimental data quite well [40,47].
The GAF theory deals with the time dependence of transport of electronic
excitation between like molecules that are randomly distributed [44]. The theory
predicts the time dependence of GS ðtÞ, the probability of finding the excitation on
the initial site as a function of the time t after excitation. This function can be
observed in a picosecond transient (holographic) grating experiment. In this experiment, a delayed picosecond probe pulse is Bragg diffracted by a grating that is
optically produced in the sample by the interference of two coherent picosecond
excitation pulses. Absorption by the sample in the overlap region of the two
excitation pulses results in a spatially varying sinusoidal distribution of excited
states resulting in Bragg diffraction of the probe pulse. The intensity of the diffracted
probe pulse is proportional to the square of the difference in the absorption between
the grating peaks and nulls. Time-dependent processes that reduce this peak–null
difference result in the decay of the diffracted signal [44,48]. In the GAF theory, the
Laplace–Fourier transform of GS ðtÞ is expanded as a diagrammatic series. Topological reduction of the series establishes an analogy of diffusion. This diagrammatic
technique also suggests an interesting class of self-consistent approximations. One
of these self-consistent approximations is applied to the specific case of the F€
orster
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52
Figure 3.10 The “universal curve” proposed by
Craver for concentration depolarization. The
ratio r=r 0 , the steady-state anisotropy over that
in the p
absence
ffiffiffiffiffiffiffiffiffiffiffiffi of transfer, is plotted versus
x 0 ¼ 2 FD =pðc=c0 Þ, where FD is the quantum
yield in the absence of transfer, c is the
concentration, and c0 ¼ c0L is the critical
concentration for homotransfer, defined in
Equation 3.79. This curve is in good agreement
with experimental data [40,47].
transfer rate. The solutions obtained are well behaved for all times and all site
densities and indicate that transport is nondiffusive at short times, but diffusive at
long times. The mean-squared displacement of the excitation and its time derivative
are calculated. These calculations illustrate that the time regime in which diffusive
transport occurs is dependent on density. In systems with low density, transport of
electronic excitation becomes diffusive only at times longer than a few minutes;
whereas for high densities, transport becomes diffusive within one lifetime of
the excited state [44]. Baumann and Fayer have discussed excitation transfer in the
disordered two-dimensional and anisotropic three-dimensional systems for the
cases of heterotransfer (direct trapping) in two-component systems and homotransfer (donor–donor transfer) in one-component systems [43]. Using the twoparticle model proposed by Huber et al. [49], Baumann and Fayer calculate the
configurational average of GS ðtÞ. For the isotropic three-dimensional case treated by
Huber et al., excellent correspondence is found with the GAF theory. The anisotropy
of the dipole–dipole interaction is included in the averaging procedure. Two regimes
of orientational mobility are considered: the dynamic and static limit, rotations
being much faster or slower, respectively, than the energy transfer. Several geometrical distributions are investigated. The fluorescence anisotropy decay, which can be
studied in a transient grating experiment or in a florescence depolarization experiment, is a useful observable for GS ðtÞ in homotransfer [43]. Baumann and Fayer
focus on nonradiative transport [43]. A unified treatment of radiative and nonradiative transport was introduced by Berberan-Santos et al. [50] and the role of
radiative transport has been reviewed by the same authors [51]. Huber et al. [49]
report on the time dependence of fluorescence line narrowing. In the system
j53
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3.19 FRET Theory 1965–2012
j 3 F€orster Theory
studied, a background is observed around a narrow band of frequencies. The
appearance of this background in the fluorescence spectra is indicative of the
transfer of excitation from fluorophores inside the band to molecules whose optical
frequencies lie outside the band. The authors treat back-transfer effects in a variety
of approximations and compare their theory with experimental data [49]. Hart et al.
[52] used time-correlated single-photon counting to measure GS ðtÞ by monitoring
the fluorescence concentration depolarization for a dye in glycerol. Hart et al. found
that the three-body GAF theory accurately describes the fluorescence depolarization
at the lower dye concentrations. At higher concentrations, the measured GS ðtÞ was
found to be perceptibly slower than that predicted by GAF theory. The authors
suggest that this deviation may arise from nonrandom dye distributions in solution,
rather than from errors in the three-body GAF theory. They note that the experimental decay can also be described at all concentrations by the Huber–Hamilton–
Barnett model [49]. The review by Knox [37] is primarily concerned with the theory of
excitation migration. However, he also discusses experimental data on the rate of
pairwise excitation transfer between like molecules, with particular attention to
chlorophyll a. In a more recent review [20], Knox notes that the CDA (see
Equation 3.2b) for chlorophyll a is about 68 4 nm6/ps. Kawski’s review [45] on
“excitation energy transfer and its manifestation in isotropic media” is thorough and
lists a large number of relevant references. It discusses essentially all aspects of
energy transfer. However, the paper devotes particular attention to the effect of
excitation energy migration on fluorescence anisotropy [45]. Fluorescence
depolarization due to homo- and hetero-FRET was analyzed by Berberan-Santos
and Valeur [53] and reviewed in Ref. [54], which elegantly describes many other
energy transfer phenomena [54].
The theory of FRET on surfaces and membranes has been an active field [55–64].
Of these references, the work by Wolber and Hudson [56] probably had the most
impact. These authors have found an analytical solution of the FRET problem in two
dimensions for the case where the orientation factor is independent of the donor–
acceptor distance and both donors and acceptors are randomly distributed in a plane
[56]. In Refs [55–64], the emphasis is on heterotransfer. Homotransfer allows
studying the accumulation of proteins in membranes. The theoretical framework
that relates fluorescence anisotropy to cluster size has been provided by Runnels and
Scarlata [65], who employ a theoretical analysis of homotransfer in clusters of like
molecules all containing the same fluorophore. In its simplest form, the Runnels–
Scarlata theory predicts that the anisotropy of a cluster of N molecules equals the
anisotropy of the monomer divided by N [65]. Towles et al. have applied Monte Carlo
simulations to study microheterogeneity and domain size in membranes. They
conclude that Monte Carlo calculations clearly indicate that FRET is indeed sensitive
to domain sizes in the range of 5–50 nm, but that a specific model is required to
obtain a value for the domain size [66]. The idea of tryptophan imaging of membrane
proteins has been proposed and analyzed by Kleinfeld [67]: tryptophans in membrane proteins serve as donors and anthroyloxy fluorophores serve as acceptors with
the anthroyloxy group attached to lipids at various distances from the midplane of
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54
the membrane. Kleinfeld and Lukacovic successfully applied this idea to locate the
tryptophan-109 in cytochrome b5 [68] confirming an earlier conclusion by Fleming
et al. [69]. Other interesting membrane FRET studies are mentioned in Refs [70–75].
Fluorescence studies of membrane heterogeneity has been reviewed by Davenport
[76]. A theory of FRET in micelles has been developed [22].
Photosynthesis motivated substantial theoretical work [77–79,104,105]. Yang et al.
[80] point out that in the theory of energy transfer in photosynthesis, F€
orster’s ideas
can be successfully applied, but that Redfield theory [81] is more appropriate when
the Coulombic coupling is greater than the electron–phonon coupling strength.
Actually, there are three levels of discourse to consider when reviewing the theory: (i)
F€orster process, which is the transfer or delocalization of an initially localized excited
state. (ii) F€orster theory, which is his selection of a definition of rate of transfer and a
method to calculate it. (iii) F€orster’s equation itself, which is a result of his applying
his theory to the dipole–dipole case [20].
Table 3.3, adapted from Scholes [28] with minor changes, presents a history of
coupling models in FRET.
Hauser et al. generalized F€orster’s equation for energy transfer in three dimensions to the case of one, two, or three dimensions [106]. Often it is necessary to
consider excluded-volume effects due to the geometry of the system, which prevents
the acceptor from penetrating a certain volume surrounding the donor. Such
excluded-volume effects have been discussed by Blumen et al. [107], Wolber and
Hudson [56], Duportail et al. [108], and Tcherkasskaya et al. [109]. The authors of Refs
[108,109] made use of the stretched exponential model introduced by Drake et al.
[110]. Dewey [111] has reviewed the relations between FRET and fractals.
If the donor–acceptor distance can change because of the lateral diffusion during
the excited-state lifetime of the donor, FRET can be enhanced [112–116]. The
parameter determining the degree of this enhancement is
Z ¼ DtD =s2 ;
ð3:82Þ
where D is the sum of the lateral diffusion coefficients of donor and acceptor, tD is
the donor lifetime in the absence of transfer, and s is the mean donor–acceptor
distance. Three regimes can be distinguished [113]:
1) Z 1, the static limit, where the transfer is low and constant, that is, there is
essentially no variation with diffusion.
2) Z 1, the intermediate regime, where the efficiency is sensitive to diffusion.
3) Z
1, the rapid diffusion limit, where the efficiency approaches a maximum
value and again becomes independent of diffusion.
Since distances of interest are in the 1–10 nm range and the diffusion coefficient
of a typical fluorophore in aqueous solvents is on the order of 106 cm2/s, the donor
lifetime in the case of rapid diffusion should be several orders of magnitude above
the conventional nanosecond range. This technique of rapid diffusion FRET is
reviewed by Stryer et al. [117]. Kouyama et al. [118] and Mersol et al. [119] have
discussed the effects of restricted rotation in diffusion-enhanced FRET.
j55
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3.19 FRET Theory 1965–2012
j 3 F€orster Theory
Table 3.3 A history of coupling models in resonance energy transfer.
Authors
Application
Comments
Craig and Walmsley [82],
Davydov [83], Kasha et al.
[84], McClure [85]
Exciton states
F€
orster [2,5]
Electronic energy
transfer
Buckingham and
Dalgarno [86]
The interaction of
ground-and excitedstate helium atoms
Dexter [25] and
Merrifield [87]
Triplet–triplet
energy transfer
Koutecky and Paldus
[88,89]
Transannular
interactions
Andrews [90], Avery [91],
Craig and
Thirunamachandran
[92], McLone and Power
[93], Scholes and
Andrews [94]
Azumi and McGlynn
[95], Murrell and Tanaka
[96]
Very long-range
coupling
Dipole–dipole coupling is used to define
the electronic states of molecular
aggregates. This dipole–dipole interaction
arises from Coulomb forces. Higher
multipoles are ignored
Development of a theory for the rate of
energy transfer, through the dipole–dipole
coupling
Interaction is between a ground-state
helium atom and a helium atom in the first
triplet or singlet metastable state. Heitler–
London method is used
Orbital overlap effects considered to arise
via an exchange integral obtained from the
Coulombic integral by permutation of two
orbitals
Calculation of the interactions between
close molecules and perturbations of their
absorption spectra
Quantum electrodynamical theories for the
form of dipole–dipole coupling over very
large distances, including the near field, the
intermediate zone, and the far field
Naqvi [97], Naqvi and
Steel [98]
Exchange-induced
resonance energy
transfer
LMO coupling
model
Harcourt et al. [99],
Scholes and Ghiggino
[100], Scholes and
Harcourt [101], Scholes
et al. [102]
Scholes et al. [103]
Excimers
Special cases in
photosynthesis
Calculation of spectra based on the LMO
(localized molecular orbital) prescription
involving locally excited and charge transfer
configurations
Theory based on the exchange interactions
in singlet/triplet–singlet/doublet energy
transfer
Orbital overlap-dependent coupling (LMO
model), revealing that the significant
overlap-dependent coupling is mediated via
charge transfer configurations
A study of couplings involving the
carotenoid S1 state
If the parameter Z in Equation 3.82 is on the order of 1, the rate of translational
motion is of the same order as the rate of transfer, and FRET can be employed to
measure the lateral diffusion of the donor and/or acceptor [112,115,120–123] or
from fluctuations in the FRET efficiency [124].
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56
Tanaka and Mataga [125] studied theoretically the effects of internal rotation on
the decay and the anisotropy of a donor and an acceptor bound to a spherical
macromolecule. The model system they considered is one in which the donor is
internally rotating around an axis fixed at the macromolecule and the acceptor has a
fixed position and orientation [126]. The relevant parameter is kT =DR , the average
rate of transfer over the rotational diffusion constant. If this parameter is small, both
the donor fluorescence and the anisotropy are single exponentials. However, if this
parameter increases, the deviation from single-exponential behavior becomes more
and more pronounced [125]. In general, rotational motion when present in combination with FRET will affect the time dependence of both the fluorescence and the
anisotropy. This does not mean, however, that time dependence in the fluorescence
anisotropy must result from rotational motion. Energy transfer or other excited-state
reactions can give rise to a strong time dependence in the anisotropy in the absence
of rotational motion [126–128]. This relation with time is due to coupling between
two states with different transition moments [126–128]. Van der Meer et al. [129]
proposed a general method to take into account the effects of motion on FRET. This
method is applicable to both rotational and translational motion and is based on the
idea that a system exhibiting both motion and FRET can be modeled by specifying a
number of “states” and the rates of transitions between them. A state in this context
is a set of conditions and specific coordinates that describe the system at a certain
moment in time. There are excited-donor states (in which the donor is excited, but
not the acceptor), excited-acceptor states (in which the acceptor is excited, but not the
donor), and the states without excitation (neither donor nor acceptor is excited). A
transition from an excited-donor state to an excited-acceptor state represents energy
transfer, whereas a transition from an excited-donor state to another excited-donor
state with a different position or orientation portrays translational or rotational
motion. Fluorescence corresponds to a transition from an excited state to a state
without excitation. Photoselection determines the initial occupation values of the
states. This method results in matrix equations that are linear differential equations
in time. The time dependence of the intensities and anisotropies of donor and
acceptor can be expressed in terms of eigenvectors and eigenvalues of matrices
[129]. The simplest example of this approach is to have a donor–acceptor distance
that can only be equal to R1 (short) or R2 (long) with the distance changing between
these two values at a rate J, and both donor and acceptor having isotropically
degenerate transition dipoles (or undergoing very fast rotations). For this model, the
donor fluorescence at time t after excitation with a short pulse is
I ¼ I 0 exp ððJtD þ 1Þt=tD Þ a exp ðt=tD ÞðR0 =R2 Þ6 Jt=p þ ð1 aÞ
exp ðt=tD ÞðR0 =R1 Þ6 þ Jt=p ;
h
i
2JtD = ðR0 =R1 Þ6 ðR0 =R1 Þ6
ðp 1Þ2
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
with p ¼
h
i 2ffi and a ¼ 2ðp2 þ 1Þ ;
1 þ 1 þ 2JtD = ðR0 =R1 Þ6 ðR0 =R1 Þ6
ð3:83Þ
j57
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3.19 FRET Theory 1965–2012
j 3 F€orster Theory
where I 0 is the initial intensity, tD is the donor lifetime in the absence of acceptor,
and R0 is the F€orster distance. If 2JtD ðR0 =R1 Þ6 ðR0 =R2 Þ6 , the fluorescence
intensity becomes
h
i
1
I ¼ I 0 exp ððJtD þ 1Þt=tD Þ exp ðt=tD ÞðR0 =R2 Þ6 þ exp ðt=tD ÞðR0 =R1 Þ6 ;
2
ð3:84Þ
but for 2JtD
ðR0 =R1 Þ6 ðR0 =R2 Þ6, one finds
I ¼ I 0 exp JtD þ 1 þ ðR0 =R1 Þ6 t=tD ;
ð3:85Þ
which depends only on the distance of closest approach, as expected, and contains
the FRET enhancement factor JtD.
Canley et al. discussed FRET efficiency at high excitation intensity. They derived
the following equation for the FRET efficiency:
E¼
1
L þ ðR=R0 Þ6
;
ð3:86Þ
where L ¼ 1 represents the well-known weak field case. They showed that L can be
significantly larger than 1. The case L > 1 reflects the inability of doubly excited dye
pairs to undergo energy transfer [130].
Raicu has developed a theoretical model for FRET from a single donor to multiple
acceptors and from multiple donors to a single acceptor [131]. Bojarski et al. studied
the possibility of FRET from a single donor to multiple acceptors using Monte Carlo
techniques [132].
Rolinski and Birch have introduced new ideas about donor–acceptor distributions
[133] and lifetime distributions [134]. Swathi and Sebastian pointed out that for
energy transfer from a dye to a nanotube, one can use the dipole approximation for
the dye, but not for the nanotube [135]. Consistent with this finding is the conclusion
by Wong et al. that the point dipole approximation is inappropriate for use with
elongated systems such as carbon nanotubes and that methods that can account for
the shape of the particle are more suitable [136].
In the metal-enhanced fluorescence, a new field with a vast potential for
applications [137], resonance energy transfer plays a significant role [138]. Lakowicz
introduced the radiative plasmon model and showed that this model is consistent
with a wide range of experimental results, including FRET from fluorophores to
nearby metal surfaces [138].
Acknowledgments
I wish to thank Dr. Bob Knox for stimulating discussions, useful advice, and making
me aware of papers I had overlooked. I am grateful to Dr. Joggi Wirz, who discovered
that the 9000-form of the F€orster equation is incorrect while working on his book
[139]. We had highly interesting correspondence about this topic. Thanks to
Dr. David Andrews who shared with me his insights into QED&FRET and the
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58
relevance of the spectral overlap. I am indebted to Dr. Manuel Prieto for sending me
relevant papers and giving me useful suggestions. I am also grateful to Dr. Herbert
Dreeskamp for helpful suggestions and for giving me insights into the brilliance and
work ethics of Dr. Theodor F€orster.
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j59
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WileyTitle/productCd-1405161736.html
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62
4
Optimizing the Orientation Factor Kappa-Squared for More
Accurate FRET Measurements
B. Wieb van der Meer, Daniel M. van der Meer, and Steven S. Vogel
4.1
Two-Thirds or Not Two-Thirds?
Two-thirds or not two-thirds? This is the question. Kappa-squared can vary between
0 and 4, but when the orientations of donor and acceptor dipoles randomize within
the lifetime of the excited state, its value is 2/3. Many authors of FRET papers adopt
this assumption. However, there is strong evidence that kappa-squared is definitely
not equal to 2/3 in many cases. For example, in Ref. [1], a series of DNA conjugates
in which a donor (stilbene dicarboxamide) and an acceptor (perylene dicarboxamide)
are covalently attached to opposite sites of an A:T base pair duplex domain consisting
of 4–12 base pairs yield a FRET efficiency that is strongly nonlinear with varying
distance. For 7–9 base pairs the efficiency drops to almost zero consistent with a
near-zero value of kappa-squared; whereas for 5 and 10 base pairs the efficiency
reaches a maximum consistent with a kappa-squared value of 1 [1]. In another
example [2], a Cy3 donor and a Cy5 acceptor are attached to the 50 -termini of duplex
DNA via a 3-carbon linker to the 50 -phosphate so that they are predominantly stacked
onto the ends of the helix in the manner of an additional base pair [2]. A cartoon
illustrating the first two examples is shown in Figure 4.1a; the third example is
shown in Figure 4.1b. The transition dipoles are essentially perpendicular to the
helical axis, and the periodicity is on the order of 5 base pairs. As a result, kappasquared changes dramatically with the donor–acceptor distance, approaching zero at
13 and 18 base pairs. The graph of FRET efficiency versus donor–acceptor distance
looks like the graph of the height of a bouncing ball versus time (dashed curve in
Figure 4.18). In reality, there is some motional averaging so that for none of the base
pair choices does the efficiency dip to zero, but there are clear maxima and minima
in the efficiency versus distance curve at predictable donor–acceptor distances (we
will come back to this trend with Figure 4.18 in Section 4.9). The error in the
distance by assuming kappa-squared ¼ 2/3 is about 25% at 13 base pairs [2]. In a
third example [3], a Cy3 donor and a Cy5 acceptor are rigidly attached to DNA in such
a way that the dipoles are essentially parallel to the axis of the DNA molecule. In two
cases, a configuration of collinear donor and acceptor dipoles was engineered: one
with Cy3 and Cy5 on the same B-DNA strand and separated by three helical turns
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j63
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.1 (a) A cartoon for the FRET situation
in Refs [1,2]. The double-headed arrows
represent transition moments for donor or
acceptor. The angle between them depends on
the donor–acceptor distance relative to the
helical pitch, reaching near-zero (k2 1) when
the distance equals an even integer times a
quarter pitch and 90 when the distance equals
an odd integer times a quarter pitch (k2 0).
(b) A cartoon for the FRET situation in Ref. [3]
(samples 1 and 2) where the transition
moments are essentially aligned with the
donor–acceptor separation vector
corresponding to k2 4.
(sample 1 in Ref. [3]) and the other with Cy3 and Cy5 on opposite strands and
separated by 2.5 turns (sample 2 in Ref. [3]). In both cases, the two oscillating
dipoles are expected to be collinear for which configuration kappa-squared
reaches its maximum value of 4. The experimentally obtained kappa-squared
values (from the known distance, the measured efficiency, and the known F€
orster
distance R0 ¼ 6:34ðk2 Þ1=6 nm) was 3.2 for sample 1 and 3.5 for sample 2,
indicating the near-parallel alignment of the dipoles with the line connecting
donor and acceptor [3]. These three examples of having a kappa-squared different
from 2/3 are for traditional donors and acceptors attached to DNA. Furthermore,
the 2/3 assumption also fails in FRET experiments using fluorescent proteins as
donors and acceptors, which undergo, usually restricted, rotation independent of
each other that is slow relative to the lifetime of the excited state in the presence
of acceptor.
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64
4.2
Relevant Questions
Kappa-squared needs attention, but this orientation factor problem does not need to
be disorienting! A few relevant questions must be asked. Do the orientations of
donor and acceptor change during the time within which transfer may take place,
that is, effectively during the lifetime of the excited state in the presence of the
acceptor(s)? And, if they do, how? Do they change rapidly during this time? Does the
dynamic averaging regime apply or the static averaging regime or neither? Is the
fluorescence polarized? To what extent? Can kappa-squared be measured? Can
depolarization factors be measured? Are simulations available or is structural
information obtainable that may exclude certain orientations? First, we need to
know how to visualize kappa-squared.
4.3
How to Visualize Kappa-Squared?
Kappa-squared for a given donor–acceptor pair depends on the direction of the
emission transition moment of the donor, the absorption transition moment of the
acceptor, and the line connecting the centers of the donor and the acceptor. We can
introduce unit vectors: ^d along the emission transition moment of the donor, ^
a along
the absorption transition moment of the acceptor, and ^r pointing from the center of
the donor to the center of the acceptor. These three unit vectors are shown in
Figure 4.2.
To visualize better the implications for kappa-squared of this three-dimensional
geometry, the following exercise is recommended. Hold your two index fingers in
front of your face and simulate the donor dipole with your left index finger and that
^ a^, and ^r ; d^ is
Figure 4.2 The unit vectors d,
along the emission transition moment of the
donor, ^a is along the absorption transition
moment of the acceptor, and ^r points from the
center of the donor to the center of the
acceptor. The d^ and ^a vectors are displayed at
arbitrary orientations within the spheres
represented at their locations.
j65
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4.3 How to Visualize Kappa-Squared?
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
of the acceptor with the other index finger. You can then rotate one hand in three
dimensions around its wrist and estimate (see below) how kappa-squared changes
for the given orientation of the other finger and for any of the orientations of the
finger of the one hand, and then rotate the other hand while maintaining the
absolute orientations of the fingers constant and evaluate the orientation factor
again. Rotating the hands around each other demonstrates that significant changes
in kappa-squared also result for transfer in different directions, that is, for different
orientations of the separation vector ^r. The angle between ^
d and ^
a is qT , that between
^d and ^r is qD , and that between ^a and ^r is qA . There are three common ways of
expressing kappa-squared (k2 ) in angles:
k2 ¼ ðcos qT 3 cos qD cos qA Þ2 ;
ð4:1Þ
2
k2 ¼ ðsin qD sin qA cos w 2 cos qD cos qA Þ ;
ð4:2Þ
k ¼ ð1 þ cos qD Þcos v;
ð4:3Þ
2
2
2
where w is the angle between the projections of ^
d and ^
a on a plane perpendicular to ^r
and v is the angle between the electric dipole field due to the donor at the location of
d, and the unit vector along
the acceptor and ^a. The electric field is along
3^r cos qD ^
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
this direction is ^eD ¼ ð3^r cos qD ^dÞ= 1 þ 3 cos2 qD . The angles appearing in
Equations 4.1–4.3 are illustrated in Figure 4.3. The dependence of kappa-squared
on cos qD and cos v expressed in Equation 4.3 is illustrated in Figure 4.4.
Figure 4.3 illustrates in particular the different planes formed by the vectors: the
DR plane through ^d and ^r , the AR plane through ^
a and ^r , the DA plane through ^
d and
^a, and the EDA plane through ^eD and ^a. Note that ^eD lies always in the DR plane and
that, whenever ^a is perpendicular to this plane, ^
a is also perpendicular to ^
d, ^r , and ^eD ,
so that kappa-squared is zero. Equation 4.3 gives insight into the distribution of
kappa-squared values. The highest value possible, 4, can only be realized if ^r and ^
d
Figure 4.3 In this illustration of the angles in Equations 4.1–4.3, uT ¼ 97:18 , uD ¼ uA ¼ 60 ,
^ ^r , and ^eD are in the DR
w ¼ 120 , and v ¼ 48:59 , yielding k2 ¼ 0:7625. The unit vectors d,
plane, ^a and ^r in the AR plane, and, ^eD and ^a are in the EDA plane.
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66
Figure 4.4 Kappa-squared versus the absolute values of cos uD and cos v.
are parallel or antiparallel yielding cos2 qD ¼ 1 and if, at the same time, ^
a and ^eD are
parallel or antiparallel, ensuring that cos2 v is also equal to 1. On the other hand,
whenever ^a and ^eD are perpendicular to each other, kappa-squared equals zero.
Therefore, if we consider all possible orientations, there is a very high probability
that kappa-squared is low and a much smaller probability that it is high. Accordingly,
the isotropic average is 2/3: if all orientations are equally probable in three
dimensions, the average of cos2 v is 1/3 and that of cos2 qD is also equal to 1/3,
so Equation 4.3 predicts the isotropically averaged value of kappa-squared as 2/3.
Expressions of kappa-squared in terms of unit vectors and dot products are also
relevant:
k2 ¼ ð^a ^d 3ð^a ^r Þð^r ^dÞÞ2 ¼ ð^a ^eD Þ2 ð1 þ 3ð^r ^
dÞ2 Þ2 :
ð4:4Þ
The right-hand side is the vector form of Equation 4.3 and the expression in the
middle is the vector form of Equation 4.1.
From these forms, it is clear that kappa-squared does not change if we
1)
2)
3)
4)
flip the donor transition moment, ^d ! ^d,
flip the acceptor transition moment, ^a ! ^a,
allow the donor and acceptor to trade places, ^r ! ^r , and
interchange the donor and acceptor transition moments, ^
a$^
d.
The transition moments can be visualized as rod-like molecular antennas or even
index fingers. It is instructive to choose different orientations and evaluate the
corresponding kappa-squared values as in the examples shown in Figure 4.5.
j67
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4.3 How to Visualize Kappa-Squared?
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.5 Examples of donor and acceptor
orientations with corresponding k2 values. The
donor dipole is along the bar in the center of
each circle with various examples of acceptor
dipoles, also depicted as bars, along the
circumference. For the first circle (a), the donor
and acceptor transition moments are parallel to
each other in the same plane and k2 varies
between 4 and 0, depending on the location of
the acceptor on the circle. These values are
labeled next to the acceptor. Note that even
when the donor and acceptor transition
moments are parallel, k2 can still be zero. For
the circle (b), with donor and acceptor dipoles
again lying in the same plane, the acceptor
dipole is oriented along the electric field of the
excited donor at the location of the acceptor
with k2 values between 1 and 4. For the circles
(c) and (d), the orientation factor is 0 for each
example as the acceptor dipole is perpendicular
to the donor electric field. For the circle (c), the
donor and the acceptor are oriented in the
same (DR) plane, but for the circle (d), the
acceptor is perpendicular to the DR plane. In
each circle, the electric field lines of the excited
donor are shown.
4.4
Kappa-Squared Can Be Measured in At Least One Case
Dale has shown that for the special case depicted in Figure 4.6, kappa-squared can be
measured using time-resolved fluorescence depolarization [4].
The donor and acceptor are assumed not to move with respect to the macromolecule, but the whole system can rotate around its axes, exhibiting rotational
diffusion around the symmetry axis at D== and around any axis perpendicular to
that at D? , where D== and D? are rotational diffusion constant. If both donor and
acceptor fluoresce, three different time-resolved anisotropies can be measured:
r D ,r A , and r T . r D is the donor fluorescence anisotropy (donor is excited and donor
fluorescence is measured), r A is the acceptor fluorescence anisotropy (acceptor is
excited and acceptor fluorescence is measured), and r T is the transfer anisotropy
(donor is excited and sensitized acceptor fluorescence is observed). These anisotropies vary with t, the time after an ultrashort flash, and are given by the
following:
r D ¼ r D ðtÞ ¼ b1D eð2D? þ4D== Þt þ b2D eð5D? þD== Þt þ b3D e6D? t :
b1D ¼
3
3
sin4 qD b2D ¼ sin2 2 qD ;
10
10
b3D
4 3 2
1 2
¼
:
cos qD 10 2
2
ð4:5aÞ
ð4:5bÞ
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68
Figure 4.6 A cartoon of a macromolecule with
a donor (D, emission transition dipole along
^ and an acceptor (A,
the unit vector d)
absorption transition dipole along the unit
vector ^a) rigidly attached to the symmetry axis
of the macromolecule, which undergoes
rotational diffusion around the symmetry axis at
D== and around any axis perpendicular to that at
D? . D== and D? are rotational diffusion
constants. The angles appearing in the
anisotropy decays (uD , uA , uT , and w) are as
shown in Figure 4.4 and defined near
Equation 4.1. This cartoon is similar to the one
presented by Dale [4].
r A ¼ r A ðtÞ ¼ b1A eð2D? þ4D== Þt þ b2A eð5D? þD== Þt þ b3A e6D? t :
b1A ¼
3
sin4 qA ;
10
b2A ¼
3
sin2 2qA ;
10
b3A
4 3 2
1 2
¼
:
cos qA 10 2
2
r T ¼ r T ðtÞ ¼ b1T eð2D? þ4D== Þt þ b2T eð5D? þD== Þt þ b3T e6D? t :
3
sin2 qD sin2 qA cos 2w
10 h
i
3
¼
2ðcos qT cos qD cos qA Þ2 sin2 qD sin2 qA :
10
ð4:5cÞ
ð4:5dÞ
ð4:5eÞ
b1T ¼
ð4:5f ðiÞÞ
3
6
sin 2qD sin 2qA cos w ¼ cos qD cos qA ½cos qT cos qD cos qA :
10
5
ð4:5f ðiiÞÞ
4 3 2
1 3 2
1
¼
cos qD cos qA :
ð4:5f ðiiiÞÞ
10 2
2 2
2
b2T ¼
b3D
Global analysis allows one to obtain the rotational diffusion constants and cos qD
(from r D ), cos qA (from r A ), and cos qT (from r T ), so that kappa-squared can be
calculated using Equation 4.1 [4]. The conclusion for now is that kappa-squared can
j69
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4.4 Kappa-Squared Can Be Measured in At Least One Case
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
be measured in this specific case. However, this approach can probably be extended
to more and perhaps all cases. This particular case is unique in that the orientations
of the transition moments are fixed in the frame of the macromolecule. In most
cases, some motion occurs. The range and frequencies of such motions may differ.
The concept of averaging regimes is useful for understanding the implications of
motion for FRET.
4.5
Averaging Regimes
The initial steps of a FRET experiment involve the absorption of a photon by a donor
fluorophore. Absorption of a photon is rapid, typically occurring within a femtosecond (1015 s), and results in the elevation of a ground-state electron into a myriad
of potential electronic and vibrational excited states. Over the next few hundred
femtoseconds, this array of potential excited-state electronic and rotational–vibrational energy sublevels are consolidated into the Boltzmann rotational–vibrational
level manifold of the lowest-energy singlet excited state, as a result of vibrational
energy loss due to subsequent kinetic interactions between the excited fluorophore
and surrounding molecules. Fluorophores, in general, spend from picoseconds to
tens of nanoseconds in this relatively long-lived lowest singlet excited state before
eventually transitioning back to a ground-state sublevel. With their return to a ground
state, excess excited-state energy will be either emitted as a photon (donor fluorescence), transferred to a nearby acceptor (FRET), or it will be utilized by some other
nonradiative mechanisms. To understand the factors that can influence the probability of energy transfer by FRET, one must understand the types of events that can
occur while a fluorophore is in its excited state. In relation to kappa squared, the
main factors that must be considered is to what extent donor and acceptor
fluorophores can move relative to each other while in the excited state – specifically,
how fluorophore motion may influence the position of an acceptor relative to the
orientation of the donor emission dipole, and how it may influence the orientation of
the acceptor absorption dipole relative to the orientation of the donors excited-state
electric field.
When every donor and every acceptor can take up its entire range of orientations
during the lifetime of the excited donor state in the presence of acceptors, the system
is said to be in the dynamic averaging regime, and the dynamic averaging condition
applies. In this regime, kappa-squared can be replaced by an appropriate average
value, and the average FRET efficiency is given by
ð3=2Þhk2 iR
0
;
6
2
ð3=2Þhk iR0 þ r 6
6
hE idynamic ¼
ð4:6Þ
DA
0 is the F€
where the brackets denote an average, R
orster distance when k2 ¼ 2=3, and
r DA is the donor–acceptor distance. The isotropic condition applies when all
orientations are equally probable. The dynamic isotropic average of kappa-squared
equals 2/3 in the one-, two-, and three-dimensional cases [5]. As discussed above, the
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70
isotropic average is not always valid. The dynamic averaging regime is discussed
further in Sections 4.6–4.9.
When the rates of rotation are small compared to the rate of donor decay in the
presence of acceptor, the system is in the static averaging regime, and the static
averaging condition applies. In this regime, kappa-squared cannot be replaced by a
universal average value, and the average FRET efficiency is given by
*
hE istatic ¼
ð3=2Þk2 R
0
6
0 þ r6
ð3=2Þk2 R
+
6
;
ð4:7Þ
DA
where the symbols have the same meaning as in Equation 4.6. Note, however, the
difference between calculating an average static efficiency and obtaining an average
60 Þ, the
dynamic efficiency. Also note that at large distances when r 6DA ð3=2Þðk2 R
differences between Equations 4.7 and 4.6 vanish. Effective values for kappasquared in the static and dynamic averaging regimes have been derived by Dale
for random spatial distributions of separations of free donors and acceptors in
solutions of three, two, and one dimension with, as appropriate, random three- and
two-dimensional orientational distributions or, for the one-dimension spatial, onedimension orientational case, the inline configuration [4,6]:
Orientational
distribution
3D
Spatial
solution
distribution
3D
Dynamic
average of
kappa-squared
2/3
2D
3D
2/3
1D
3D
2/3
2D
2D
5/4
1D
2D
5/4
1D
1D
4
Static average
of kappa-squared
DpffiffiffiffiffiE2
k2 ffi 0:69012 ffi 0:4762
Dpffiffiffiffiffi 3
3
k2 i ffi 0:73973 ffi 0:4048
Dpffiffiffiffiffi 6
6
k2 i ffi 0:83056 ffi 0:3281
Dpffiffiffiffiffi 3
3
k2 i ffi 0:94622 ffi 0:8471
Dpffiffiffiffiffi 6
6
k2 i ffi 0:94566 ffi 0:7151
Dpffiffiffiffiffi 6
6
k2 i ¼ 4
In the inline configuration (1D, 1D), a single value for kappa-squared applies, so that
in this case the dynamic and static values are identical.
The first report on FRET in 2D free donor, free acceptor solutions was published
by Tweet et al. [7]. Loura et al. [8] confirmed 1D solution FRET in an experimental
system, with the theory given in detail in Ref. [9].
It is possible that the average rate of transfer is on the same order of magnitude as
a dominant rate of rotation for the donor or acceptor. In this case, the system is
neither in the dynamic regime nor in the static regime. This case is discussed in
Section 4.12.
j71
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4.5 Averaging Regimes
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
4.6
Dynamic Averaging Regime
Dale et al. [10] and Haas et al. [11] have shown that in the dynamic averaging regime,
fluorescence depolarization data allow one to remove some of the uncertainty in the
FRET distance resulting from kappa-squared. Dale et al. emphasize depolarization
because of rapid restricted rotations [10], whereas Haas et al. [11] mainly consider
excitation into overlapping transitions as the reason for low polarization values.
However, in the dynamic averaging regime, depolarization due to degeneracy or overlap
of transitions is essentially indistinguishable from depolarization resulting from
reorientations. Indeed, it has been shown that the equation for the average kappasquared derived by Dale et al., Equation 4.10, is the same as the one derived by Haas et al.,
if cylindrical symmetry in the transitions is assumed [12]. In the dynamic averaging
regime, the donor emission moment, which is along the unit vector ^
d, fluctuates rapidly
X
around ^d (unit vector, called donor axis) and the acceptor absorption moment, which is
along the unit vector ^a, fluctuates rapidly around ^
aX (unit vector, called acceptor axis).
These fluctuations may represent rapid restricted rotations or coupling between overlapping transitions. As a result, the kappa-squared value fluctuates around an average
value. And, this average value, which may be used instead of the kappa-squared value
appearing in the FRET efficiency, depends on two parameters d and a (defined below)
and on three variables W, HD , and HA (defined below). The parameter d is the axial
depolarization factor for the donor emission moment:
d ¼ dXD ¼
ðp 3 2
1
3 2
1
cos yD ¼
cos yD sin yD F D ðyD ÞdyD ;
2
2
2
2
ð4:8Þ
0
X
where yD is the fluctuating angle between ^
d and ^
d , and F D ðyD Þ is a distribution
function. Similarly, the axial depolarization factor for the acceptor absorption
moment is
ðp X
3 2
1
3 2
1
a ¼ dA ¼
ð4:9Þ
cos yA ¼
cos yA sin yA F A ðyA ÞdyA ;
2
2
2
2
0
where yA is the fluctuating angle between ^
a and ^
ax , and F A ðyA Þ is the distribution
function. Note that it is assumed here that the distributions are cylindrically
symmetrical. The parameters d and a are second rank orientational order parameters
with values between 0.5 and 1 : 1 when the transition moment is completely aligned
with its axis, 0 when the angle between the transition moment and its axis is equal to
the magic angle at all times or when the transition moment is completely random,
and 0.5 when the angle between the transition moment and its axis is 90 , that is,
when the transition moment is degenerate in a plane perpendicular to the axis. HD is
the angle between the donor axis and the line connecting the centers of donor and
acceptor, HA is the angle between this connection line and the acceptor axis, and W is
the angle between the projections of the donor and acceptor axes on a plane
perpendicular to the connection line. The average value of the orientation factor
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72
in the dynamic averaging regime is [10]:
2 2 1
k ¼ ðd þ aÞ þ dð1 aÞcos2 HD þ að1 dÞcos2 HA þ adk21;1 ;
3 3
with
k21;1 ¼ ðsin HD sin HA cos W 2 cos HD cos HA Þ2 :
ð4:10aÞ
ð4:10bÞ
The depolarization factors d and a can be obtained from fluorescence depolarization
measurements [10]. The “time-zero” value of the donor fluorescence anisotropy value
is proportional to d2 and that of the acceptor is proportional to a2 . Here “time-zero”
must be understood in the context of the dynamic averaging regime, and the so-called
B€
urkli–Cherry [13] plot illustrates the concept of “zero-time anisotropy.”
Figure 4.7 may suggest that time-resolved fluorescence anisotropy measurements
are necessary in order to obtain depolarization factors. However, Corry et al. have
shown that steady-state confocal microscopy also enables one to measure such
factors and that kappa-squared can even be obtained if some knowledge of the
relative geometry is assumed [14].
Because of the proportionality between measured fluorescence anisotropy values
and the square of d or a, the experimentally obtained depolarization factors can be
either positive or negative if d2 and a2 are between 0 and 0.25. These sign
ambiguities may be resolved if independent structural or spectroscopic information
is available.
Figure 4.7 A log–log plot of fluorescence
anisotropy versus time after a flash excitation.
This is also called a B€
urkli–Cherry plot [13]. It
shows a stepwise decrease of the anisotropy
with time and nicely illustrates that “zero-time
anisotropy” in the context of FRET refers to the
anisotropy value reached after the completion
of rotations with frequencies higher than the
average transfer rate. Note that the lifetime of
the excited state (of donor or acceptor) seems
not to matter in this graph, but it is relevant in
practice because of noise: after a few lifetimes,
the time-resolved anisotropy becomes very
noisy and is completely unreliable for times
larger than about five lifetimes.
j73
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4.6 Dynamic Averaging Regime
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Dale et al. found the maxima and minima of hk2 i in Equation 4.10 numerically and
presented a contour plot allowing to read the highest and lowest hk2 i value for each
combination of depolarization factors [10]. It is also possible to find these maxima
and minima analytically by setting the derivatives of hk2 i with respect to HD , HA , and
W equal to zero, solving the set of three resulting equations [15]. As shown at http://
www.FRETresearch.org, there are six candidates for maxima and minima:
k2A ¼
2 2
2
þ a þ d þ 2ad:
3 3
3
ð4:11aÞ
k2P ¼
2 1
1
a d:
3 3
3
ð4:11bÞ
k2H ¼
2 1
1
a d þ ad:
3 3
3
ð4:11cÞ
k2M ¼
2 1
1
1
þ a þ d ad þ ja dj:
3 6
6
2
ð4:11dÞ
k2L ¼
2 1
1
1
þ a þ d ad ja dj
3 6
6
2
ð4:11eÞ
1
4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð1 aÞð1 dÞð1 þ 2aÞð1 þ 2dÞ:
k2T ¼ ð1 aÞð1 dÞ þ
9
9
ð4:11f Þ
The distributions of transition moments can be visualized as ellipsoids with the
symmetry axis equal to 1 þ 2d for the donor and 1 þ 2a for the acceptor and with any
axis perpendicular to the symmetry axis equal to 1 d for the donor and 1 a for
the acceptor. As a result, in the extreme situation where the depolarization factor
equals 1, the distribution behaves like a needle-like “molecular antenna,” and in the
other extreme where it is 0.5, the transition dipole distribution resembles a disklike “antenna.” Figure 4.8 illustrates the meanings of the six candidates using such
ellipsoids and verbal descriptions.
Careful comparison (http://www.FRETresearch.org) of the magnitudes of one
candidate relative to those of the others in all points of the plane formed by
parameter values ð1=2Þ d 1 and ð1=2Þ a 1 leads to the conclusion
that there are nine different regions where the maxima and minima can be
calculated using the expressions for the six candidates in Equations 4.11a–4.11f.
These regions have borders expressed as d ¼ 0, a ¼ 0, C ¼ 0, E ¼ 0, F ¼ 0, or
G ¼ 0, where C, E, F, and G are defined as follows:
1
C ¼aþd :
2
ð4:12aÞ
E ¼ 3a þ 3d þ 5ad þ 1:
ð4:12bÞ
F ¼ 2d 3a þ 2ad 1:
ð4:12cÞ
G ¼ 2a 3d þ 2ad þ 1:
ð4:12dÞ
The regions are shown in Figure 4.9.
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74
Figure 4.8 Description of the candidates for maxima and minima of the average kappa-squared
in the dynamic regime, specified by Equation 4.11. They are also candidates for the most probable
kappa-squared in this averaging regime.
The meaning of the symbols and the properties of the different regions are
specified in Table 4.1.
Note that if both depolarization factors, for the donor and the acceptor, are
positive, the minimum hk2 i is k2P and the maximum is k2A , as pointed out by Dale
A
et al. [10]. The reader may wonder why we split up this region in a central
1
P
A
zone and three sections of
2 around it. The reason is that the six candidates are
P
not only possible maxima and minima but are also potential answers to the question:
j75
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4.6 Dynamic Averaging Regime
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.9 Regions in the ða; dÞ plane showing in each a column with the kappa-squared
maximum indicated by the top letter and the minimum by the bottom letter. Table 4.1 gives
details.
What is the most probable kappa-squared value? Figure 4.9 also serves as the starting
point in our approach to this question.
4.7
What Is the Most Probable Value for Kappa-Squared in the Dynamic Regime?
What is the “most probable” kappa-squared value? This is an ambiguous question! If
we are trying to find the most probable value per se of kappa-squared, that is,
independent of and in isolation from any other FRET parameter, we will get one
answer; but if we want the most probable k2 corresponding to the most probable
separation derived for a given efficiency, a completely different answer emerges. It is
well established that the probability density of kappa-squared per se for a pair of
linear donor and acceptor transition moments (a ¼ d ¼ 1 in Equation 4.10a)
exhibits an infinitely high peak at k2 ¼ 0 (see Equation 4.21 and Figure 4.19)
(also refer to Refs [10,12,16]). Nevertheless, if we consider any nonzero efficiency,
however small, whether or not obtained in an actual experimental situation, deriving
either from a transfer efficiency or a transfer rate, the most probable kappa-squared
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76
Table 4.1 Maxima and minima in the dynamic averaging regime.
Name of
region
Maximum
hk2 i in that
region
Minimum
hk2 i in that
region
Definition of region
A
1
P
k2A
k2P
fa > 0; d > 0; F
G
C > 0g
Yes
A
2
P
k2A
k2P
fa
0; d
G
C
All but not k2T
M
3
H
k2M
k2H
fa
d
M
4
T
k2M
k2T
fa
d < 0; E
C < 0; F
M
5
L
k2M
k2L
fa
d < 0; F
G
H
6
A
k2H
k2A
fa
0; d
M
7
A
k2M
k2A
fa
d < 0; E
H
8
L
k2H
k2L
fa
0; d
0; F
G
0g
All but not k2T
H
9
T
k2H
k2T
fa
0; d
0; F
G
E < 0g
Yes
0; F
0; C
Are all
candidates
valid there?
0g
All but not k2T
0g
G < 0g
All but not k2T
0g
0; E
Yes
All but not k2T
0g
All but not k2T
0g
value cannot be equal to zero, because k2 ¼ 0 means that the efficiency also equals
zero. Interestingly, the explanation of this paradox is based on the link between
kappa-squared and the “relative distance,” which is defined by
r
“Relative distance”
Actual FRET distance
¼
Distance assuming k2 ¼ 2=3
1=6
3 2
:
k
2
ð4:13Þ
In formal mathematical terms, we need three probability functions for this explanation: the range probability, PR k2min ! k2 , the probability density for kappasquared, pðk2 Þ, and the probability density for the relative distance, Q ðrÞ:
P R k2min ! k2 ¼ probability that kappa-squared has a value between k2min and k2 :
ð4:14Þ
p k2 dk2 ¼ probability that kappa-squared has a value between k2 and k2 þ dk2 :
ð4:15Þ
Q ðrÞdr ¼ probability that the relative distance has a value between r and r þ dr:
ð4:16Þ
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4.7 What Is the Most Probable Value for Kappa-Squared in the Dynamic Regime?
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Both pðk2 Þ and Q ðrÞ are proportional to the derivative of P R k2min ! k2 . And,
because of the link between the relative distance and kappa-squared as expressed in
Equation 4.13, it follows that
Q ðrÞ ¼ 4r5
p k2 :
ð4:17Þ
Therefore, the mathematical explanation of the above-mentioned apparent paradox
is that the derivative of the pðk2 Þ will in general not be zero when the derivative of
Q ðrÞ equals zero because of the factor 4r5 in Equation 4.17. It is difficult to visualize
this apparent paradox for the general case of any choice for a and d. However, for the
case that both of these depolarization factors are equal to 1, PR k2min ! k2 ¼
PR ð0 ! k2 Þ is the area under the curve that is obtained when cutting the threedimensional plot in Figure 4.3 at a certain kappa-squared level and projecting the cut
in the jcos qD j jcos vj plane, as shown in Figure 4.10.
In this special case, constant-k2 curves can be calculated from Equation 4.3. The area
of the square formed by all possible values of jcos qD j and jcos vj between 0 and 1
represents the total probability of 1 that k2 has any value between 0 and 4, 0 for cos v ¼
0 and 4 for jcos vj ¼ jcos qD j ¼ 1. We can divide up the square in, say, a hundred
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
strips by drawing the 101 curves jcos vj ¼ k2 =ð1 þ cos 2 qD Þ inside the square
choosing k2 equal to 0 4/100, 1 4/100, . . . , 99 4/100, and 100 4/100. This
way the area of each strip represents the probability that kappa-squared has a value
Figure 4.10 Lines of constant kappa-squared in
the jcos uD j jcos vj are shown for the case in
which both depolarization factors are equal to 1.
The area below the curve labeled 1/3 is equal to
the probability that kappa-squared is between 0
and 1/3, the area between this curve and the 2/3
curve represents the probability that kappasquared is between 1/3 and 3/2, and so on.
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78
Figure 4.11 Pair of diagrams illustrating that
the question “What is the most probable kappasquared value?” is ambiguous. This example
refers to the dynamic regime and a ¼ d ¼ 1.
(a) The diagram is for unknown efficiency with
k2 ¼ 0 as the most probable value. (b) The
diagram corresponds to having a known
efficiency and thus a link between the orientation
factor and relative distance resulting in k2 ¼ 1
being the most probable kappa-squared value.
between the k2 for the lower boundary and that for the upper boundary. Such a
division has been initiated in Figure 4.11a. The very first strip between the 0 and
0.04 curves has by far the largest area and successive strips rapidly decrease in
area, indicating that the most probable value for the orientation factor is 0.
However, nothing is said about the distance or the efficiency. Over that very first
strip, the relative distance is 0 at the lower boundary, but 0.626 at the higher
boundary, whereas the maximum relative distance is 1.35. As a result, the very
first strip in k2 represents 46% of all distance choices.
It seems more appropriate, therefore, to translate the combination of a measured
efficiency and an independently obtained F€orster distance to a distance with an
orientational uncertainty specified by Equation 4.10. In terms of the example of
Figure 4.7, this means we should divide up the square by drawing 101 curves jcos vj ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðð2=3Þr6 Þ=ð1 þ cos 2 qD Þ inside the square by choosing r equal to 0 61=6 =100,
1 61=6 =100, . . . , 99 61=6 =100, and 100 61=6 =100. This way the area of each strip
represents the probability that the relative distance has a value between the r for the
lower boundary and that for the upper boundary. This is indicated in Figure 4.11b,
where careful analysis shows that the strip straddling the left upper corner of the
square has the biggest area, corresponding to r ¼ ð3=2Þ1=6 ¼ 1:07 and to k2 ¼ 1. In
general, the location of the maximum of Q will differ dramatically from that of the
maximum of p, as in the example of Figure 4.11. Therefore, the most probable kappasquared per se will differ from the most probable kappa-squared at a given efficiency.
An algorithm to find the most probable kappa-squared in the second case (at a
given efficiency) is briefly as follows (http://www.FRETresearch.org):
1) Choose the a; d pair that best describes the depolarization properties of the actual
system. (See Equations 4.12c and 4.12d, and the explanations near these. Note that
axial symmetry is assumed. If axial symmetry cannot be justified, see Ref. [11].)
j79
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4.7 What Is the Most Probable Value for Kappa-Squared in the Dynamic Regime?
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
2) Because ð1=2Þ a 1 and ð1=2Þ d 1, this pair must lie within one of the
regions shown in Figure 4.6 and Table 4.1. Use this figure or table to decide which
A
A
H
region
1;
2; . . . ; or
9 applies. Choose B, the number of bins,
P
P
T
and vary the bin number i from 1 to B, obtaining bins with relative distance values
between rmin þ ði 1Þðrmax rmin Þ=B and rmin þ iðrmax rmin Þ=B, with
1=6
1=6
and rmax ¼ ð3=2Þk2max
.
rmin ¼ ð3=2Þk2min
3) For n ¼ 1 to B, set QðnÞ to 0. This QðnÞ is the nth component of a B-dimensional
array, which will in the end become a histogram approximating the frequency
distribution of the relative distance, QðrÞ.
4) Choose N, and in so doing pick N 3 points, varying j, ‘, and m from 1 to N,
calculating cos HD ¼ ðj 1Þ=ðN 1Þ, cos HA ¼ ð‘ 1Þ=ðN 1Þ, and W ¼
pðm 1Þ=ðN 1Þ Substitute these into Equation 4.7 to calculate hk2 i values
1=6
and from there relative distance values r ¼ ðð3=2Þhk2 iÞ . Compare each r with
the lower and upper boundary of each bin. Place each r in the appropriate bin by
adding 1 to each QðnÞ whenever r > rmin þ ðn 1Þðrmax rmin Þ=B and r
rmin þ nðrmax rmin Þ=B with 1 n B.
5) Normalize Q by dividing each component by N 3. As a result, the sum of all QðnÞ
values will become 1, signifying that the probability that Q has any value equals 1.
(For n ¼ 1 to B, QðnÞ ¼ QðnÞ=N 3 .)
We have examined graphs of QðrÞ obtained with this algorithm for a large
number of points in the plane formed by the depolarization factors a and d, varying
these between 0.5 and 1. Results for the most probable kappa-squared are shown
in Figure 4.12.
The definition of the most probable kappa-squared in Figure 4.8 is that value
corresponding to the highest peak in QðrÞ:
2
most probable k2 ¼ r6peak :
3
ð4:18Þ
Whenever one or both of the depolarization factors is negative, the most
probable kappa-squared is k2P . In the region where both depolarization factors
are positive, there is a rather large central region where it is k2L , surrounded by
four regions with k2H as the best value and two regions where k2M is the most
probable value. The uncertainty in the distance as a result of variations in the
orientation factor has two aspects: the most probable kappa-squared may deviate
from 2/3, that is, the location of the peak may differ from r ¼ 1, and, the peak
may be fairly broad, that is, the 67% confidence interval (CI) may have considerable width (the 67% confidence interval is the range of r-values near the peak
where the total QðrÞ adds up to 67%). It is appropriate to call the first aspect a
“peak location error” (PLE) and the second a “broad distribution error” (BDE). We
note that r ¼ 1 is the relative distance value that corresponds to k2 ¼ 2=3 and,
thus, define the PLE as
PLE ¼ ð1 rPEAK Þ
100%:
ð4:19Þ
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80
Figure 4.12 Map indicating the most probable
kappa-squared in the dynamic regime, where this
most probable value is defined as the kappasquared for which the relative distance is the most
likely (see text). When one or both of the
depolarization factors for the donor or acceptor
are negative, k2P is the best. The region where both
depolarization factors are positive consists of four
regions labeled H, where k2H is the most probable,
two regions labeled M where k2M is the best, and
one labeled L, where k2L is the most probable
kappa-squared value. The border between the H
and L regions near the top right corner is well
described by a þ d 0:985ad ¼ 1:012. The
curved border between H and M on top and L on
the bottom, starting at d ¼ 0; a ¼ 0:79 and
ending near d ¼ 0:81; a ¼ 1 follows the trend
a ¼ 0:79 þ 0:504d4:28 ; and the one with H and
M on the right and L on the left is described by
d ¼ 0:79 þ 0:504a4:28 .
PLE > 0 means that k2 ¼ 2=3 overestimates the most probable distance, and
PLE < 0 signifies that this assumption underestimates the distance at the peak.
Figure 4.13 shows examples of distributions and PLE values.
Our definition of the “broad distribution error” is
BDE ¼ 1=2ð67%CIÞ ¼ ðrUL rLL Þ
50%;
ð4:20Þ
where rLL is the lower and rUL is the upper limit of the 67% CI for QðrÞ. In some
cases, the peak is near the center of the confidence interval, but relative distance
distributions can also be highly asymmetric with the peak at the upper or lower limit
of this interval. Figure 4.14 shows examples.
Figure 4.15 shows lines of equal “peak location error” in the ða; dÞ plane.
Near a ¼ d ¼ 1 and a ¼ d ¼ 1=2, the PLE is negative, but in the majority of
points, the PLE is positive with the most probable distance smaller than the one at
k2 ¼ 2=3. A very high positive PLE of about 30% occurs near a ¼ d ¼ 0:96, close to
the red line. On the red line, Q has two equally high peaks. The red line is the border
between two regions where rpeak is calculated differently. As a result, PLE changes
discontinuously at this border. The most dramatic change is at a ¼ d ¼ 0:96 where
the PLE is 6%, corresponding to k2H , at the side where the factors are slightly higher
than 0.96, and þ30%, corresponding to k2L , at the side where the depolarization
j81
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4.7 What Is the Most Probable Value for Kappa-Squared in the Dynamic Regime?
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.13 Examples of probability density of
the relative distance illustrating the definition of
the systematic error. The graph on the left is for
a ¼ d ¼ 0:73, where the main peak
corresponds to k2L with a relative distance
smaller than 1 so that PLE is positive (this Q
has a secondary maximum corresponding to
k2H ). The distribution in the center is for a ¼
1; d ¼ 0:5 or d ¼ 1; a ¼ 0:5, showing one peak
matching k2H ¼ k2M ¼ 2=3, yielding r ¼ 1 and
PLE ¼ 0. The graph on the right is for a ¼ d ¼ 1,
with a peak at r ¼ 1:07 corresponding to k2H ¼
1 and a negative PLE.
factors are slightly smaller than 0.96. The green lines are also borders between
regions where the peak is calculated differently, but with a continuous change in
PLE. A large discontinuous change in PLE also implies a fairly broad distance
distribution and, therefore, a relatively large BDE. Results for BDE are shown in
Figure 4.16.
This diagram shows data for the 67% CI, obtained with our program for finding Q
(available on the Web site) at any choice for the depolarization factors a and d. To run
this program, one must choose an a and a d, a value for B (the number of bins, that
is, the number of bars in the histogram approximation for the Q-function), and a
value for N (a measure for how many times the relative distance is evaluated; the
number of points is N3). After locating the peak (allowing one to confirm the results
of Figure 4.12), the CI is obtained by moving away from the peak in both directions
while adding the Q-values of the bars in the histogram until 0.67 has been reached.
Near the axes, a ¼ 0 or d ¼ 0, the peak is extremely asymmetric with the relative
distance at the peak, rPEAK , coinciding with the lower limit of the CI, rLL , at positive a
or d, and matching the upper limit rUL at negative a or d, as shown in Figure 4.13.
Away from these axes, say for a > 0:1; d > 0:1 or a > 0:1; d < 0:1, or
a < 0:1; d > 0:1, or a < 0:1; d < 0:1, the peak is more symmetric and rPEAK
is close to the center of the CI. A completely different problem arises near the red
borders shown in Figure 4.15. At the red borders, the Q-function has two peaks that
are exactly of equal height. For example, at a ¼ d ¼ 0:96, the Q-function has a peak
corresponding to hk2 i ¼ k2H ¼ 0:948ðrPEAK ¼ 1:06Þ and an equally high peak for
hk2 i ¼ k2L ¼ 0:065ðrPEAK ¼ 0:68Þ. In such cases, the center of the CI should be
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82
Figure 4.14 Examples of probability density for
the relative distance illustrating the definition of
the random error. In each, the 67% confidence
interval (CI) is shaded dark gray and runs from
rLL , the lower limit of the CI, to rUL , the upper
limit of the CI. The three graphs have the same
scale in r and Q. The one in the center is
relatively broad and low. The other two are
narrow and high, actually extremely high, as
both go to infinity at one point on the interval.
The graph on the left is for a ¼ 0:5; d ¼ 0 or
d ¼ 0:5; a ¼ 0 with its peak at rUL and a BDE
of about 1%. The distribution in the center is for
a ¼ d ¼ 1 with its peak near the average of rLL
and rUL and a BDE of about 24%. The graph on
the right is for a ¼ 1; d ¼ 0 or d ¼ 1; a ¼ 0 with
a peak at rLL , and a BDE of about 7%.
chosen at the average of the two rPEAK values, and the CI should be built up from
there. Examples of graphs for the frequency distributions Q versus the relative
distance r are shown in Figure 4.17.
4.8
Optimistic, Conservative, and Practical Approaches
For assessing the kappa-squared-induced error in the FRET distance, there is an
“optimistic” approach that assuming kappa-squared equals 0.67 introduces little or
no error, and there is a “conservative” method based on depolarization factors
resulting in a minimum and maximum kappa-squared (with corresponding minimum and maximum distances) without the ability to pinpoint the most probable
kappa-squared in this range. The optimistic method is that of Haas et al. [11] and
Steinberg et al. [17], and the conservative approach is that of Dale et al. [10]. This
classification is an oversimplification, of course, as both the first group and the
second group of authors have provided a detailed and versatile discussion of errors
j83
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4.8 Optimistic, Conservative, and Practical Approaches
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.15 Lines of constant “peak location
error” are shown with the value of PLE given
next to the lines in percent. At the red curves,
the relative distance frequency distribution has
two equally high peaks. These curves are
borders between regions where the most
probable kappa-squared is calculated differently,
as indicated in Figure 4.12. At one side of a red
curve, one of the peaks is highest and on the
other side, the other peak is highest. As a result,
the PLE changes discontinuously when a red
line is crossed. The blue lines are also borders
between regions where the most probable
kappa-squared is calculated differently, but with
a continuous change in the value of the peak
and of PLE.
resulting from the orientation factor. Nevertheless, neither group has pointed out
that there are at least two different aspects associated with the kappa-squaredinduced error: the PLE, introduced in Equation 4.19, and the BDE, introduced in
Equation 4.20. For lack of a better name, we would like to call the procedure
introduced in the previous section the “practical” approach. Table 4.3 compares the
“optimistic,” “conservative,” and “practical” approaches for a range of cases.
Note that the PLE in itself is not a problem because when the depolarization
factors are known, this error can be accurately predicted using Figure 4.12 and its
definition (Equation 4.19). However, the discontinuous jump in the systematic error
near ða; dÞ ¼ ð0:96; 0:96Þ may cause serious problems, as a value of 0.96 is
experimentally almost undistinguishable from 1 and thus a slight uncertainty in
the depolarization factors near this value may cause the PLE to shift from 6
to þ30%. For such high values of a and d, the BDE is also high (see Figure 4.15).
Comparing the confidence interval for ða; dÞ ¼ ð1; 1Þ with that for (0.81,0.95) in
Figure 4.15 illustrates a problem related to the discontinuity in the PLE: a relatively
minor variation in the depolarization factors may cause this interval to shift from
one that is centered around r ¼ 1 to one that is centered around 0.85. In Ref. [12], it
was assumed that the case a ¼ d ¼ 1 was the worst-case scenario. This is a logical
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84
Figure 4.16 Regions with lower and higher
“broad distribution errors” (BDE), defined in
Equation 4.13. A high BDE corresponds to a
broad QðrÞ, and low BDE values indicate
graphs for QðrÞ with a narrow peak. On the
green lines, BDE equals 5%. The long green line
connects the points (0.5, 0.31), (0.4, 0.45),
(0.3, 0.6), (0.2, 0.66), (0.1, 0.71), (0, 0.78),
(0.1, 0.72), (0.2, 0.66), (0.3, 0.58), (0.4, 0.58),
(0.54, 0.54), (0.58, 0.4), (0.58, 0.3), (0.66, 0.2),
(0.72, 0.1), (0.78, 0), (0.71, 0.1), (0.66, 0.2),
(0.6, 0.3), (0.45, 0.4), and (0.31, 0.5). The
short green line passes through (0.5, 0.25),
(0.33, 0.33), and (0.25, 0.5). In the
region between the green lines, BDE is smaller
than 5% reaching 0% at a ¼ d ¼ 0. At (0.5,
0.5), BDE ¼ 8%. In between the long green
line and the red lines, BDE varies between 5%
(on green) and 10% (on red). At (1, 0.5) and
(0.5, 1), BDE is about 12% and on the short
red curves near these points, RE equals 10%. At
(1, 1), BDE ¼ 24%, and BDE decreases with
decreasing a and/or d reaching BDE ¼ 10% on
the red line connecting (0.45, 1), (0.52, 0.94),
(0.66, 0.9), (0.65, 0.83), (0.7, 0.77), (0.74, 0.74),
(0.77, 0.7), (0.83, 0.65), (0.9, 0.66), (0.94, 0.52),
and (1, 0.45).
assumption as a ¼ d ¼ 0 is the best-case scenario and the kappa-squared-induced
error gets worse and worse when one moves away from a ¼ d ¼ 0. After Ref. [6] was
published, it became possible to generate plots of the frequency distribution of
distances and kappa-squared with a few keystrokes on a computer. So, now we must
set the record straight: a ¼ d ¼ 1 is not the worst-case scenario as far as the
orientation-induced error is concerned in the dynamic regime; it appears that
a þ d 0:985ad ¼ 1:012, the red line in Figure 4.15 where the PLE jumps from
30 to 6%, is the worst-case scenario in this regime.
4.9
Comparison with Experimental Results
It is imperative to be keenly aware of the assumptions underlying any method one
wants to apply. For example, in Refs [1,2], the depolarization factors are not given,
j85
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4.9 Comparison with Experimental Results
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.17 Examples of frequency
distributions for the relative distance with the
67% confidence interval (CI) indicated in each
as an area between red lines. All graphs have
the same vertical scale and the same
horizontal scale. The width of each box refers
to a relative distance of 1.4, and the height of
each box is 9.5 in Q-units. For most choices
of a and d, a distribution with one dominant
peak is found; but for parameter choices near
the red lines in Figure 4.15, more than one
equally pronounced peaks may occur, as is
shown in the right bottom corner for ða; dÞ ¼
ð0:81; 0:95Þ or (0.95, 0.81). Data for these
plots are shown in Table 4.2. The readers will
be able to generate their own graphs for any
choice of a and d by visiting the Web site
http://www.FRETresearch.org.
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86
Table 4.2 Data for Figure 4.17.
a or d
1
2
1
2
1
2
1
2
d or a
rmaximum
rLL
rPEAK
rUL
QðrPEAK Þa)
1
0.953
1.070
0.953
0.953
1.013
1
0.894
1.110
0.958
1.066
1.108
5.613
0.891
1.038
0.986
1.038
1.038
1
0.794
1.134
0.930
0.994
1.056
6.602
0
1.201
0.829
0.949
1.069
1b)
0.891
1.122
0.891
0.891
1.026
1
0.794
1.260
0.887
0.994
1.101
4.295
0.891
1.184
0.929
0.976
1.020
10.077
0
2
1
2
1
2
1
1
3
1
6
1
3
0
4
3
8
3
11
6
4
0.95
0.08
3.379
0
1
0
0.81
rminimum
5
4
5
6
17
12
1
2
1
1
2
1
k2maximum
1
2
1
4
1
3
1
6
0
1
2
1
2
1
k2minimum
0
1.348
0.809
1.051
1.294
2.091
0.702
1.311
0.702
0.848
1.006
2.691
N ¼ 300 and B ¼ 100, but when a or d ¼ 0, data have been calculated analytically (see http://www.
FRETresearch.org).
a) The frequency distribution of kappa-squared is proportional to that for the relative distance [12]
1=6
according to the relation pðk2 Þ ¼ ð1=4ÞQðrÞ=r5 , with r ¼ ð3k2 =2Þ .
b) Mathematically, one can show that the Q-value at the peak is 1, but numerical values depend on B
and N.
but they should be positive. Therefore, the “practical approach” would suggest that
the best kappa-squared value should be k2H , k2L , or k2M. However, in the practical
approach, it is assumed that nothing is known about cos HD , cos HA , or W, the
variables appearing in Equation 4.10. In the spirit of information theory, it is
assumed in this approach that all values of these “hidden variables” are equally
probable when no information about them is available. Nevertheless, for the systems
in Refs [1,2], information about the relative orientation of donor and acceptor is
available: the transition dipoles are essentially perpendicular to the axis of a helix and
the angle between the dipoles should depend on the pitch of the helix. This is
actually an example of the case where the transfer depolarization is known, within
limits, as introduced and analyzed by Dale et al. [10], and in which case equations for
kappa-squared have been derived [13]. The geometry of the donor–acceptor pair in
Ref. [2] suggests that the best kappa-squared value should be a hybrid between k2H
and k2P , k2 ¼ k2HP ¼ ð2=3Þ ð1=3Þa ð1=3Þd þ adcos 2 HT (Equation 38 in Ref.
[15]), and that the angle HT between the preferred directions of their transition
moments should be equal to 180 r DA =pitch. Substituting this value for HT, and
k2 ¼ k2HP , into the expression for the FRET efficiency allows us to model the
efficiency versus distance trend. Such an attempt to model the efficiency expected
for the system in Ref. [2] is shown in Figure 4.18.
j87
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4.9 Comparison with Experimental Results
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Figure 4.18 The FRET efficiency versus
distance expected for the system of Ref. [2].
Assuming k2 ¼ k2HP ¼ ð2=3Þ ð1=3Þa ð1=3Þd þ adcos 2 QT and QT ¼ 180 r DA =pitch,
0 =pitch (R
0 ¼
with g ¼ r DA =pitch and h ¼ R
F€
orster distance when k2 ¼ 2=3) yields a FRET
efficiency of the form: E ¼ ½1 ð1= 2Þa ð1=2Þd þ ð3=2Þadcos 2 180 gh6 =
g 6 þ ½1 ð1=2Þa ð1=2Þd þ ð3=2Þadcos 2
180 gh6 g. For this graph we chose h ¼ 2, and
a ¼ d ¼ 0:8 (solid line) and a ¼ d ¼ 1 (dashed
line). The trend described by the solid line is
similar to that of the experimental data in
Ref. [2].
The kappa-squared in samples 1 and 2 of Ref. [3] is also an example of the
case where the transfer depolarization is known. This kappa-squared should be
essentially equal to k2A (Equation 4.11a) with values for the depolarization factors
close to unity.
The history of the kappa-squared fluorescence depolarization relationship is
interesting and relevant here. In the late 1970s, when time-resolved fluorescence
depolarization was virtually nonexistent, both Dale et al. [10] and Haas et al. [11]
realized that information from fluorescence depolarization can be useful for
unraveling distance effects from orientation effects in FRET. At that time, both
groups had steady-state fluorescence depolarization data in mind. Fairly recently,
Dale revisited the kappa-squared fluorescence depolarization relationship [4] and
came to the conclusion that this unraveling can be much more effective than
previously thought when the full time dependence of fluorescence anisotropy is
taken into account. In terms of Figure 4.7, it is fair to say that a glimpse at a short
interval on one of the plateaus of anisotropy versus time allows one to put limits on
kappa-squared, but a full view of the this curve has the potential to pin down the
orientation factor completely.
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4.9 Comparison with Experimental Results
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
4.10
Smart Simulations Are Superior
Any available information that allows one to exclude certain donor–acceptor orientations will help to narrow down the range of possible kappa-squared values. Simulations can be a powerful tool in this exclusion process. A case in point is the molecular
dynamics simulations performed by Lillo et al. [21]. Following the “conservative
approach,” these authors found for donors and acceptors at specific sites in a PGK
(phosphoglycerate kinase) a fairly large range of possible kappa-squared values and the
corresponding donor–acceptor distances, but they noticed that some of the values for
HD , HA , and W appearing in Equation 4.10 were inconsistent with the crystal structure
of PGK and the excluded volume of the probes at the known sites in PGK. They
performed molecular dynamic simulations of kappa-squared utilizing Equation 4.10,
measured depolarization factors, the crystal structure of PGK, and the known locations
of the donors and acceptors, and found the most probable values of HD , HA , and W,
resulting in an improved kappa-squared value and more precise donor–acceptor
distances [21]. In the same spirit, Borst et al. built structural models of the FRET-based
calcium sensor YC3.60 and noticed that minor structural changes induced by slightly
rotating the fluorescent protein around a flexible linker while keeping the same
average distance between the donor and the acceptor gave rise to any value of kappasquared between 0 and 3, but a fivefold change in orientation factor (from 0.5 to 2.5)
brings only about a 1.3-fold increase in critical distance indicating that the FRET
process in YC3.60 is mainly distance dependent [22]. Gustiananda et al. [23] presented
FRETresults from an intrinsic tryptophan donor to a dansyl acceptor attached to the Nterminus in model peptides containing the second deca-repeat of the prion protein
repeat system from marsupal possum. They used simulations for finding the best
kappa-squared in this system and extended their molecular dynamics simulations out
to 22 ns to help ensure adequate sampling of the dansyl and tryptophan ring rotations.
They found good agreement of the simulated kappa-squared value with 2/3, except
at the lowest temperatures [23]. Deplazes et al. performed molecular dynamics
simulations of FRET from AlexaFluor 488 donors to AlexaFluor 568 acceptors [24].
In their system, the isotropic dynamic condition was met, meaning that all possible
orientations of the transition moments of donor and acceptor and of the line
connecting their centers are equally probable and sampled within a time short
compared to the inverse transfer rate. The frequency distribution (Figure 4.19) of
kappa-squared from the simulation data showed excellent agreement with the
theoretical distribution [12]:
8
pffiffiffi
1
>
>
0 k2 1;
< pffiffiffiffiffiffiffi2 ln ð2 þ 3Þ;
2 3k
pffiffiffi
pðk2 Þ ¼
ð4:21Þ
1
2þ 3
>
>
: pffiffiffiffiffiffiffi ln pffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi ; 1 k2 4:
2 3k2
k2 þ k2 1
Their results show that even in their simple situation, simulations lasting longer than
200 ns would be required to accurately sample the fluorophore separations and
kappa-squared if only a single donor–acceptor pair had been included. Many aspects
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90
Figure 4.19 The probability density pðk2 Þ versus k2 , as described by Equation 4.21, in the
dynamic regime for the case a ¼ d ¼ 1.
of FRET were simulated in this study, including frequency distributions of relevant
angles, donor–acceptor distance, and FRET efficiency. As expected, very low correlation was found between donor–acceptor distance and orientation factor [24]. VanBeek
et al. did find such a correlation in a molecular dynamics simulation of a coumarin
donor and an eosin acceptor, both attached to HEWL (hen egg-white lysozyme) [25].
In the dynamic regime, it is implicitly assumed that kappa-squared is independent of
the donor–acceptor distance. (In the static regime, an indirect correlation between
distance and kappa-squared is expected, as discussed near Equation 4.31). The
correlation between orientation and distance in the molecular dynamics study of
Vanbeek et al. is quite strong and involves both the sign and the magnitude of kappa
(k ¼ cos qT 3cos qA cos qD , the square of which is given in Equation 4.1, where the
angles are also defined). This correlation is illustrated in Figure 4.20, which is a
modification of Figure 6 of Ref. [25], graciously made available for this chapter by Dr.
Krueger. An additional advantage of molecular dynamics simulations is that no
assumptions about timescales need to be made, whereas in the interpretations of
FRETexperiments, the results do depend on whether the system in is the dynamic or
static regime.
Note that the FRET efficiency also shows a relationship with kappa and the donor–
acceptor distance in this illustration. The kappa-squared concept is based on the
ideal dipole approximation that is known to fail when molecules get “too close” to
each other. Mu~
noz-Losa et al. performed molecular dynamics simulations to find out
how “too close” should be defined [26]. They showed that the ideal dipole approximation performs well down to about a 2 nm separation between donor and acceptor
for the most common fluorescent probes, provided the molecules sample an
isotropic set of relative orientations. If the probe motions are restricted, however,
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4.10 Smart Simulations Are Superior
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.20 Modification of Figure 6 of Ref. [25]: a scatter plot of the donor–acceptor distance
against kappa showing the correlation between this distance, kappa, and the FRET efficiency. The
color code on the right is for the efficiency. This graph has been prepared by Dr. Brent Krueger.
this approximation performs poorly even beyond 5 nm. In the case of such restricted
motion, FRET practitioners should worry not only about kappa-squared but also
about the failure of the ideal dipole approximation [26]. In a more recent paper from
the same laboratory, an improved construction of experimental observables from
molecular dynamics sampling has been proposed [27]. Hoefling et al. have introduced a similar analysis [28].
4.11
Static Kappa-Squared
We begin our consideration of the impact of molecular motion during the excited state
on FRET by considering how the rate of FRET is influenced by the separation between
donor and acceptor (rDA) as well as by the orientation of donor and acceptor dipoles
relative to each other (k2). The rate of energy transfer by FRET, kT, is dependent on the
inverse sixth power of the separation between donor and acceptor [29,30]:
1 R0 6
kT ¼
;
ð4:22Þ
t0D r DA
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92
where t0D is the fluorescence lifetime of the donor molecule and R0 is the F€orster
distance, the separation at which 50% of the donor excitation events result in energy
transfer to the acceptor. Furthermore, the R0 value used for any specific donor–
acceptor FRETpair always assumes that the dipole–dipole coupling orientation factor
(k2) will have a value of 2/3, but in reality it can have any value from 0 to 4 in biological
experiments, and can be expressed as [12,17]
k2 ¼ 1 þ 3x 2 z2 :
ð4:23Þ
This is Equation 4.3 with the abbreviations z ¼ jcos vj and z ¼ jcos qD j, where qD is
the angle between the donor emission dipole orientation and the donor–acceptor
separation vector and v is the angle between the donor electric field vector at the
acceptor location and the acceptor absorption dipole orientation. For a typical donor
fluorophore with a fluorescence lifetime of 3 ns, more than 99% of excited fluorophores have returned to their ground state within approximately 15 ns, that is,
within about five lifetimes. It is therefore reasonable to consider (i) if the separation
rDA can change during this period, (ii) if the position of the acceptor relative to the
donor emission dipole orientation can change during the excited state and therefore
(except for change only along the separation vector) the value of qD , and, pari passu,
that of the field vector at the acceptor location, (iii) if the orientation of the donor
emission dipole changes, and thus again the value of qD changes, and finally (iv) if the
angle between the donor electric field vector at the acceptor location and the acceptor
absorption dipole orientation (v) changes within this 15 ns period. Changes in rDA
and/or in qD can be caused by significant lateral motion of the acceptor fluorophore
relative to the position of the donor fluorophore. Thus, our first consideration should
be how far a fluorophore can move by diffusion in 15 ns? Diffusion is a function of the
mass of the molecule, its hydrodynamic shape, and the temperature, as well as the
viscosity of the milieu. Assuming a temperature of 20 C and an essentially aqueous
local environment, a small fluorophore may have a diffusion coefficient between
100–1000 mm2/s, while a larger fluorophore like GFP will have a diffusion coefficient
of 70 mm2/s. Under these conditions, one might expect that a free fluorophore could
diffuse a distance between 1.4–5.5 nm during a 15 ns excited state. Clearly, such
motion could influence the effective value of both rDA and qD in a FRET experiment.
In practice, however, most donor fluorophores will return to the ground state in a
much shorter time span, with a median value (50% of excited states lost) of
ðln 2Þ t0D , in this instance 2 ns, effectively limiting the distance that most
molecules (about 80%) can diffuse by up to 0.5–2.0 nm away from their original
location. Furthermore, when one considers that fluorophores used in biological
FRET experiments are typically coupled to much larger molecules such as protein
complexes or nucleic acids with much smaller diffusion coefficients in aqueous
solution, and even smaller in cell cytoplasm in which the local viscosity for these large
molecules is much higher than that of water, it is typically assumed that lateral motion
during the excited state will be so limited that it will not be responsible for any
alterations in the rDA or qD values for a specific pair of molecules tagged with donor
and acceptor fluorophores.
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4.11 Static Kappa-Squared
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
In addition to lateral diffusion, another type that must be considered is that due to
molecular rotation. Specifically, we will consider if donor and acceptor fluorophores
can rotate during the excited state, and if so, the impact of this rotational motion on
the values of qD and v, and thus on FRET. Molecular rotation is typically parameterized by a rotational correlation time ðtrot Þ, the average time that it takes a molecule
to rotate 1 rad around a specific axis. For spherical molecules, the rotational
correlation time will be the same around all three axes. Nonspherical molecules
can have different diffusion coefficients for each principal axis of rotation. These are
identical for spherical molecules, leading to a monoexponential decay of the
emission anisotropy of a fluorescent probe rigidly associated with this structure,
with a rotational correlation time proportional to the inverse of the diffusion
coefficient. For ellipsoids of revolution, there are two different ones, one for the
axis of symmetry and another for the two principal axes perpendicular to this,
leading, in general, to a triple exponential decay of the anisotropy with three
different correlation times: one associated with rotation of the unique axis being
proportional to the inverse of the diffusion coefficient of the axis of symmetry, and
two associated with both this rotation and that of the equivalent perpendicular
principal axes and differing in the contributing weights of their summed diffusion
coefficients defining the inverse of the correlation times. Rotational correlation
times of fluorescent molecules can be measured experimentally by monitoring the
decay of fluorescence anisotropy as a function of time after a transient excitation
pulse [31]. In the absence of homo-FRET, this decay is primarily caused by molecular
rotation. By fitting the anisotropy decay to a triexponential model, the rotational
correlation time or times can be estimated. In the case of ellipsoids of revolution, the
general form of the time-dependent decay of the fluorescence anisotropy, r(t), is
given by (compare Equation 4.5)
r ð tÞ ¼ r 0 i¼3
X
ai et=troti ;
ð4:24Þ
i¼1
where r0 is the limiting anisotropy, the initial anisotropy at the instant of photoexcitation prior to any rotational depolarization, ai is the amplitude of the ith decay
component, and troti is the rotational correlation time of the ith decay component.
The contribution of all three components to the decay depends on the orientations of
the absorption and emission transition dipoles in the molecular frame: each one
alone or any combination of pairs may appear and, in addition, the anisotropy may
decay monotonically from either positive or negative values or start at zero or a
positive or negative value, then increase or decrease before changing direction
toward zero at long enough times, or even cross zero before turning over and
moving toward zero [32]. In practice, differences in rotational correlation times for
the three axes for most fluorophores are hard to experimentally distinguish, and,
more typically, the monoexponential anisotropy decay will statistically adequately fit
the anisotropy decay data, that is, when rotational diffusion coefficients are similar
enough, the extent of similarity required depending on the level down to which the
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94
anisotropy is accurately recovered [33]:
r ðtÞ ¼ r 0 et=trot :
ð4:25Þ
Here the value of trot is a function of the solution viscosity (g), temperature (T), and
the molar volume of the rotating molecule (V) [33]:
trot ¼
gV
;
RT
ð4:26Þ
where R is the gas constant. For example, small fluorophores, such as fluorescein
(332.31 g/mol), will have a rotational correlation time of 140 ps in water at room
temperature, while a large 28 000 Da fluorophore such as Venus (a yellow GFP
derivative) has a rotational correlation time of 15 ns under the same conditions
[31], presumably because the volume of Venus is approximately 100 times greater
than the fluorescein. When a population or randomly oriented fluorophores
(isotropic) are photoselected using a linearly polarized light source, the highest
anisotropy value theoretically possible (fundamental anisotropy) is 0.4 with onephoton excitation and 0.57 with two-photon excitation [31]. In practice, other factors
can reduce the value of the initial anisotropy value at time ¼ 0. Thus, the limiting
anisotropy measured in a time-resolved anisotropy measurement is usually smaller
than the fundamental anisotropy expected from theory. With time, measured
anisotropy values for fluorophores in solution that are free to rotate in any direction
will decrease as a single exponential with an asymptote at 0. This value indicates the
point where all remaining molecules in the excited state are randomly oriented. The
speed of this orientational randomization is parameterized by the rotational correlation time. For a system decaying as a single exponential, this occurs at 5X, the
rotational correlation time. Thus, for a small molecule like fluorescein, nearcomplete orientational randomization can occur within 700 ps, well within the
excited-state lifetime of fluorescein (4.1 ns). In contrast, for Venus under the same
conditions, this would require 75 ns, much longer than its lifetime of 3 ns. As
mentioned above, most of the excited donor fluorophores in a FRET experiment will
return to the ground state in a much shorter time span, with a median value of
ðln 2Þ t0D , (for Venus, 2 ns). With a rotational correlation time of 15 ns, free Venus
is only expected to rotate 11 in 2 ns. Furthermore, Venus will rotate even slower
when attached to another protein, or if situated in the more viscous cytoplasm found
in cells. Thus, Venus is not expected to rotate much during its excited state. In
contrast, a small fluorophore like fluorescein may be able to rotate during its excited
state. Thus, when considering the value of k2 to use in interpreting a FRET
experiment, it is important to note that the values qD and v may be average values
over many possible angles when small fluorophores are used as FRET donors and
acceptors, while the values for qD and v may be static for any particular donor–
acceptor pair composed of fluorescent protein donors and acceptors. At this point, it
is worth noting and yet again emphasizing that the 2/3 value for k2, so ubiquitously
used in FRET experiments, is based on two assumptions: (i) That, bar a fortuitously
occurring set of static relative orientations leading to this value, qD and v have
random values (i.e., they come from isotropic distributions). (ii) That the values of
j95
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4.11 Static Kappa-Squared
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
qD and v are changing rapidly relative to the fluorescence lifetime (dynamic). From
the above calculations, it should be clear that these assumptions (isotropic dynamic)
might be valid for some FRETexperiments using small fluorophores like fluorescein
that can rotate rapidly, provided that they are attached via flexible-enough chains
linking them to the protein backbone and/or donor and acceptor to different smallenough segmentally flexible units in the protein, but are not generally expected to be
valid for FRET experiments using fluorescent proteins as donors and acceptors
because being bound into the alpha-helical backbone of the protein, they hardly
rotate at all during their fluorescent lifetimes (static, with the possible exception that
they may be bound to separate subunits of the protein, one or both of which may
exhibit rapid segmental flexibility).
What k2 value should be used in a FRET experiment if one assumes that the values
of qD and v are randomly selected from isotropic populations, but the donor and
acceptors are in the static regime, that is, they are hardly rotating during the excitedstate lifetime of the donor? Steinberg et al. [17] have shown that in the static regime,
hk2 i for an isotropic population varies with separation in a sigmoid fashion, starting
essentially at zero at very low distance, eventually leveling off at a value of 2/3 at very
large distances [12]. Dale has derived an approximation for an effective-kappasquared value for use in the static regime: hk2 ief f 2/3ð1 hE iÞ [34]. Recently, Monte
Carlo simulations were used to address this same issue [35]. This study confirmed
Steinberg’s finding that no single value of hk2 i can be used to predict the energy
transfer behavior of a static population (and is in good agreement with the Dale
effective kappa-squared approximation [34]), rather it was found that a hk2 i value
must be calculated from the random values of qD and v on a FRET pair by FRET pair
basis for each pair in the population. What emerged from this study is that even for a
population that has a homogeneous separation that strongly favors energy transfer
by FRET (rDA < R0), because the most probable value of hk2 i for an isotropic
population is zero [12], a large fraction of FRET pairs in a population will only transfer
a negligible fraction of their excitation energy by FRET, and the population behavior will
be heterogeneous with some FRET pairs having very efficient transfer and some
having none (k2 ¼ 0) or essentially none (k2 near 0). With respect to FLIM
measurements of donor lifetimes from an isotropic static population of donors
and acceptors, a simple single-exponential decay is expected only if the rDA value is
much larger than the R0 value (approximately no FRET). In this case, the simple
lifetime decay would be the same as the decay of donor alone. If the rDA value is short
enough to support a significant amount of FRET, a multiexponential decay is expected
even when only a single fixed rDA value is present in the population. In this instance,
the average FRET efficiency calculated from the multiexponential decay may be
smaller than that obtained through steady-state intensity measurements for two
reasons. First, low kappa-squared values are more common than high values, and
second, because a fraction of donor–acceptor pairs with relatively large kappasquared values will exhibit such efficient transfer (approaching unity) that the donor
lifetimes will be beyond the resolution of the measurement and so not appear in the
decay curve.
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96
Is there experimental evidence for static FRET behavior in experiments with
fluorescent protein donors and acceptors? Specifically, for FRET in the static
isotropic regime, we expect to observe (i) a complex multiexponential donor lifetime,
even for a homogeneous population of FRET pairs and (ii) a large fraction of FRET
pairs in the population should fail to transfer energy by FRET because of the
prevalence of low k2 values expected in an isotropic population and the absence of
appreciable rotational motion during the excited state, even when separation
between donors and acceptors are short. In Figure 4.21a, a three different constructs
are depicted, each engineered to express in cells a Cerulean [36] FRET donor (a blue
GFP derivative) covalently attached to a Venus [37] acceptor (a yellow GFP derivative)
via a 5-, 17-, or 32-amino acid linker. These constructs are called C5V, C17V, and
C32V, respectively [38,39]. As a negative FRET control, a single point mutation was
introduced into Venus at Y67 (from Y to C) to form “Amber,” a protein that is
thought to have the same structure as Venus, but cannot form the Venus fluorophore and does not act as a dark absorber in the region of Cerulean fluorescence
[40]. This Amber mutation was then used to create three more constructs; C5A,
C17A, and C32A. While the Cerulean decays of C5A, C17A, and C32A are
indistinguishable (Figure 4.21b), the decays of C5V, C17V, and C32V were all
faster than the Cerulean–Amber constructs, with C5V having the fastest decay,
and C32V having the slowest. Using these Cerulean decays in the presence and
absence of acceptor (Venus), C5V with its short 5-amino acid linker had the
highest average FRET efficiency [(43 2)%], the FRET efficiency of C17V was
intermediate [(38 3)%], and C32V, with the longest linker separating the donor
from the acceptor, had the lowest FRET efficiency [(31 2)%] [38]. Note that C5V,
C17V, and C32V all have complex decays that are clearly not single exponential,
even though every expressed molecule in the population should have one Cerulean donor covalently attached to one Venus acceptor. These complex multiexponential fluorescence lifetime decays for donor covalently attached to acceptors
suggest that the underlying distribution of FRET efficiencies in these populations
is heterogeneous. While this complex decay behavior is consistent with the first
prediction of FRET in the static isotropic regime, somewhat awkward is the
observation that the lifetimes of the three corresponding Cerulean–Amber constructs did not decay as a purely single exponential as the F€
orster theory predicts
for donor-only constructs. This might arise from more complicated photophysics
for fluorescent protein fluorophores, perhaps indicating multiple excited states for
these fluorophores. While such complicated donor-alone decay behavior is problematic, it is quite typical for decays of isolated fluorescent proteins, not to say
ubiquitous, and has been observed in experiments measuring FRET between
spectral variants of many different fluorescent proteins [41]. Regardless, to test the
second prediction of FRET in the static isotropic regime, an analysis method is
needed that can account for the complex decay behavior of the donor-alone. To
look for a fraction of molecules in a population that does not undergo energy
transfer, the data plotted in Figure 4.21b were transformed and replotted as the
time-resolved FRET efficiency (TRE) (Figure 4.21c) This transformation involves
j97
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4.11 Static Kappa-Squared
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
Figure 4.21 (a) Cartoons depicting the FRETpositive protein constructs C5V, C17V, and
C32V and their FRET-negative analogues C5A,
C17A, and C32A, where C stands for Cerulean
(donor), V for Venus (acceptor), and A for
Amber (VenusY67C), a nonabsorbing Venus
with a single-point mutation that prevents
chromophore formation. The number between
C and V and C and A denotes the number of
amino acids in the linker connecting them. (b)
Donor fluorescence intensity, IDA, versus time
after donor excitation in the presence of energy
transfer to Venus for C5V, C17V, and C32V, and
intensity, ID, versus time in the absence of
energy transfer for C5A, C17A, and C32A.
(c) Experimental TRE versus time for C5V, C17V,
and C32V compared to C5A, C17A, and C32A.
(d) Theoretical TRE versus time based on
Equation 4.28 in which IDA(t) is calculated
assuming that the excited donor is
characterized by a monoexponential decay with
time constant equal to the appropriate average
of the measured lifetimes for a population of
donor–acceptor pairs over which kappasquared is randomly distributed in the static
limit, with choices for the relative distance (R0/
rDA with R0 defined for kappa-squared ¼ 2/3)
that yield a strong resemblance to the
experimental curves in panel (c).
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98
calculating the time-dependent change in FRET efficiency normalized to the
fluorescence lifetime decay of the donor:
TREðtÞ ¼
I D ðtÞ I DA ðtÞ
;
ID ðtÞ
ð4:27Þ
where ID(t) is the fluorescence decay of the donor-alone and IDA(t) is the fluorescence
decay of the donor in the presence of acceptor. Note that ID(t) does not have to be
monoexponential, it could just as well have a more complex decay resulting from the
sum of multiple excited states. Similarly, IDA(t) can also be a complex decay resulting
from multiple decay components, but including a component, or components, representing energy transfer by FRET from the donor (or multiple donor excited states) to an
acceptor (or multiple acceptor ground states). If every donor or donor excited state that
registers in the IDA(t) determination undergoes FRET, the TRE curves will start at a value
of 0 at time 0 and eventually asymptote at a TRE value of 1. In contrast, if some donors or
donor excited states never transfer energy by FRET, as predicted for energy transfer in
the static isotropic regime, the TRE curve will still start at a value of 0 at time 0, but appear
to asymptote to a TRE value that is less than 1. This difference represents the fraction of
molecules in the population that do not transfer energy by FRET and/or that transfers
with very high efficiency and is not detected. In Figure 4.21c, we can see that the TRE
curves for the decay data presented in panel (b) for C5V (and C5A), C17V (and C17A),
and C32V (also C32A) all seem to asymptote to a value that is between 0.71 and 0.73,
indicating that for these constructs approximately 27–29% of the donors either do not
transfer energy and/or very efficiently transfer it by FRET (or any other additional
mechanism). This type of behavior is consistent with the predictions of FRET in the
static isotropic regime, but other sources of population heterogeneity [35] may also
participate in producing a TRE curve asymptote of less than 1.
The main advantage of TRE analysis over directly examining fluorescence lifetime
decay curves is that TRE analysis facilitates discriminating between population
FRET behavior in the dynamic and static regimes. If all donor–acceptor pairs in the
sample behave similarly and are expected to have the same overall efficiency, the
TRE curve will be 1 minus a single exponential. In contrast, if a distribution of
efficiency values is present in the system, a sharp deviation of this trend will be seen.
It is expected that a single-exponential TRE curve could be a signature for the
dynamic regime, whereas the static regime may be characterized by a more complex
TRE curve appearing to asymptote to a value less than 1. In the static isotropic
regime, theory predicts that the TRE curve should follow the following trend:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffi ð1
ð1 ð1
erf
ð1 þ 3x 2 Þy
p
2
2
ð4:28Þ
TRE ¼ 1 dx dzez ð1þ3x Þy ¼ 1 dx pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ;
2
ð1 þ 3x 2 Þy
0
0
0
where x and z are introduced in Equation 4.16, erf denotes the error function, and y
is given by
3 R0 6 t
y¼
;
ð4:29Þ
2 r DA t0D
j99
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4.11 Static Kappa-Squared
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
where t is the time, t0D is the average donor lifetime in the absence of transfer, R0 is the
F€orster distance when k2 ¼ 2=3. The rDA values estimated by TRE analysis assuming a
static isotropic regime for C5V, C17V, and C32V (5.0, 5.3, and 5.5 nm, respectively) are
lower than the rDA values estimated from the average efficiency and fluorescence
lifetime decay analysis assuming a dynamic isotropic regime (5.7, 5.9, and 6.2 nm,
respectively). This is expected because a large fraction of the FRETpairs in an isotropic
static regime population will have k2 values close to zero. It is clear that the
experimental TRE data (Figure 4.21c) are not in perfect agreement with the theoretical
TRE results based on Equation 4.28 (compare Figure 4.21c and d). While the basis of
these small discrepancies is not known, we speculate that fluctuations in the separation between donors and acceptors, or deviations from a purely isotropic distribution
of qD and v angles, which are not taken into account in Equation 4.28, may explain this
discrepancy. Regardless, it is quite remarkable that with only one adjustable parameter, 3R60 = 2t0D r 6DA , the agreement between theory and experiment is as good as it is,
clearly indicating, we believe, that the static regime character of kappa-squared is the
major reason for why the time-resolved efficiency for C5V, C17V, and C32V deviates so
dramatically from a single exponential rising from 0 to 1.
If it is known that a population of FRET pairs are in the static isotropic regime,
with a few assumptions it is also possible to estimate the donor–acceptor
separation from experimentally measured hk2 i values using as our starting point
an estimate of the average kappa-squared in the static regime introduced by
Steinberg et al. [17]:
0
ð3=2Þhk2 iR
;
6
2
ð3=2Þhk iR þ r 6
6
hE i ¼
0
ð4:30Þ
DA
0 ¼ R0 is the F€
The angle brackets in this equation denote an average, R
orster
distance when k2 ¼ 2=3, and r DA is the donor-acceptor distance. Steinberg et al.
have shown, in a graph, that hk2 i varies with distance in a sigmoid fashion in the
static regime, starting essentially at zero at very low distance, then rising slowly until
about r DA ¼ 2=5R0 , where hk2 i starts to increase more strongly with increasing
distance until about r DA ¼ 7=5R0 , where hk2 i begins to level off reaching 2/3 at very
large distances [12]. Between r DA ¼ 2=5R0 and r DA ¼ 7=5R0 , hk2 i varies linearly
with distance and is approximately equal to 2=3ðr DA =R0 ð2=5ÞÞ [12]. For example,
the distances between the Cerulean and Venus fluorophores in C5V, C17V, and
C32V most likely fall in this range between 0:4R0 and 1.4R0 (2.2–7.7 nm). Substituting hk2 i ¼ 2=3ðu 2=3Þ (with u r DA =R0 ) into (4.23) yields Equation 4.31 for u:
1 hE i
2
u :
u6 ¼
ð4:31Þ
5
hE i
Solving this equation numerically using the measured average efficiencies and
R0 ¼ 5:4 nm, the estimated rDA values are found to be 5.1, 5.4, and 5.8 nm for C5V,
C17V, and C32V, respectively, in excellent agreement with distance estimates
derived from TRE analysis (5.0, 5.3, and 5.5 nm respectively), and with r DA values
obtained after substituting Dale’s approximation, hk2 i ð2=3Þð1 hE iÞ [34], into
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100
equation 4.30 (5.2, 5.4, and 5.8 nm respectively). Interestingly, this substitution
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0 6 ð1 hE iÞ2 =hE i.
leads to r DA R
With regard to FRET in the static regime, it is important to realize that it is
possible to be in the static regime even when the FRET donor and acceptor used in
an experiment are small fluorophores like fluorescein. Clearly, experimental factors
such as high viscosity or short rigid linkers can restrain the motion of a small
fluorophore. Similarly, if fluorescent protein donors and acceptors are attached to
interacting proteins via a short rigid linker, the values of qD and v, and thus k2, may
be fixed and identical for every FRET pair in the population. If this is the case, FLIM–
FRET analysis will reveal a simple exponential decay that is faster than the decay of
the donor alone, and TRE curves will asymptote from 0 to a value of 1. In this case,
we are still in the static regime, but since the kappa-squared value is unique, the
isotropic assumption is obviously no longer valid.
4.12
Beyond Regimes
It is possible that the average rate of transfer is on the same order of magnitude as a
dominant rate of rotation for the donor or acceptor. In this case, the system is neither
in the dynamic regime nor in the static regime. Molecular dynamics simulations are
extremely useful in this intermediate regime [19–23]. Analysis is still possible by
building mathematical models based on the idea that a system of donors and
acceptors undergoing translational and/or rotational motion during the transfer
time (inverse of the average transfer rate) can be described as a collection of states
with transitions between them [42]. These states can be visualized as snapshots: at a
certain moment, a donor is excited and has a particular orientation, while the
acceptor has another orientation. This donor–acceptor pair is then in a D A state. A
little later the donor or acceptor changes its orientation, that is, a rotational transition
to another D A state has occurred. FRET corresponds to a transition to a DA state. A
systematic description of such time developments implies selecting a representative
set of orientation states, evaluating kappa-squared values, and identifying transfer
rates and rates of rotation. This approach leads to a matrix equation for which the
eigenvectors and eigenvalues must be found, so that intensities and anisotropies can
be calculated [42]. The following example illustrates this method. A donor and
acceptor are at a fixed distance r DA from each other. The acceptor’s absorption
moment has an isotropic degeneracy. The donor’s emission moment is linear and
can only have two orientation states: parallel to the “connection” line (line connecting the centers of donor and acceptor) or perpendicular to it. The rate of rotation of
6
this moment is 1=tR . The FRET rate is ð3=2Þk2 t1
0D r , where t0D is the fluorescence
lifetime of the donor in the absence of FRET and r is the relative distance (r DA
divided by the F€orster distance if kappa-squared would be equal to 2/3). In this
example, k2 equals either 4=3 or 1=3: 4=3 when the donor is in the “parallel” state
with its moment parallel to the connection line and 1=3 when the donor is in the
j101
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4.12 Beyond Regimes
j 4 Optimizing the Orientation Factor Kappa-Squared for More Accurate FRET Measurements
“perpendicular” state with its moment perpendicular to this line. I DA , the fluorescence intensity of the donor in the presence of acceptor after excitation with a very
short pulse of light, is proportional to y== þ y? . Here, y== is the fraction of the donors
with its moment parallel to the connection line and y? is the fraction with this
moment perpendicular to the connection line. For ID, the fluorescence intensity of
the donor in the absence of FRET, y== ¼ y? ¼ 1=2 at all times, but for IDA, y== ¼
y? ¼ 1=2 only at time zero when the system is excited by the flash, whereas at later
times y== > y? until they both decay to zero at times much larger than t0D . The rate
equation for this example is
d
dt
y==
y?
¼
1
t1
t1
0D þ tR ½1 þ ð8=3Þx
R
1
1
t1
t
þ
t
R
0D
R ½1 þ ð2=3Þx
y==
;
y?
ð4:32Þ
where the differentiation is with respect to the time t and x ¼ ð3=4Þr6 t1
0D tR . The
time-resolved efficiency TRE (defined in Equation 4.27) can be calculated from the
solution of (4.32) in terms of the two eigenvectors with the initial condition y== ¼
y? ¼ 1=2 and for this example reads (see FRETresearch.org for details)
!
pffiffiffiffiffiffiffi2ffi
1
1
TRE ¼ 1 1 pffiffiffiffiffiffiffiffiffiffiffiffiffi eðt=tR Þ 1þð5=3Þxþ 1þx
2
1 þ x2
!
pffiffiffiffiffiffiffi2ffi
1
1
1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffi eðt=tR Þ 1þð5=3Þx 1þx :
2
1 þ x2
ð4:33Þ
The special cases for this example are as follows:
No FRET with x ¼ 0 and TRE ¼ 0.
The static regime with x ! 1, tR ! 1, while x=tR remains at ð3=4Þr6 t1
0D ,
2r6 t1
ð1=2Þr6 t1
0D t
0D t
yielding TRE ¼ TRESTATIC ¼ 1 ð1=2Þe
ð1=2Þe
.
The dynamic regime with x ! 0, tR ! 0, while x=tR remains at ð3=4Þr6 t1
0D ,
ð5=4Þr6 t1
0D t
yielding TRE ¼ TREDYNAMIC ¼ 1 e
.
4.13
Conclusions
In FRET situations where the transition moments of donor and acceptor are
isotropically degenerate or reorient rapidly and completely within a time comparable
to the lifetime of the excited donor state in the presence of acceptor, one can be
certain that kappa-squared equals 2/3. Often this simplification is not warranted.
However, we have indicated which methods can be utilized to diagnose the potential
problems caused by the orientation factor, which alternative value can be used if the
experimental conditions allow one to find an average or actual kappa-squared value,
and what can be done in cases where an average value is poorly defined. The concept
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102
of time-resolved FRET efficiency (Equation 4.27) can be useful, especially when
combined with the idea of relaxation of the probability density pðk2 Þ: In the dynamic
regime, pðk2 Þ relaxes from a relatively broad distribution to a narrow peak within a
time much shorter than the lifetime of the excited state of the donor, whereas in the
static regime this relaxation takes much longer than this lifetime.
Acknowledgments
We wish to thank Dr. Bob Dale for many helpful suggestions and stimulating
discussions. Bob also made us aware of important papers we had overlooked. Drs.
Manual Prieto and David Lilley mentioned relevant papers as well. We thank them
for that. Dr. Klaus Suhling gave us useful ideas to improve the explanation of
relevant issues. Dr. David Piston suggested to add electric field lines to Figure 4.5.
We wish to acknowledge Dr. Paul Blank for stimulating discussions on strategies
for fitting TRE decays to characterize separation distance in the static isotropic
regime and Dr. Brent Krueger for designing Figure 4.20 especially for us,
allowing us to use it in this chapter, and for stimulating discussions about
kappa-squared and molecular dynamics simulations. We are indebted to
Dr. Phil Womble for writing a program, allowing us, with help from Sandeep
Kothapalli, to obtain some preliminary data for the preparation of Figure 4.12. We
thank Sarah Witten Rogers for valuable help in calculating frequency distributions for the relative distance. S.S.V. was supported by the intramural program of
the National Institute of Health, National Institute on Alcohol Abuse and
Alcoholism, Bethesda, MD.
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104
5
How to Apply FRET: From Experimental Design to Data Analysis
Niko Hildebrandt
5.1
Introduction: FRET – More Than a Four-Letter Word!
F€orster resonance energy transfer (FRET) is a very special scientific topic because it
inspires and challenges many theoretical and experimental scientists from different
research disciplines ranging from the fundamental life sciences over theoretical
physics and chemistry up to applied technology in physics, electronics, chemistry,
medicine, and biology. Almost as versatile as the topic itself is the discussion about
the acronym FRET or rather about the first letter “F.” Should it be “F” like
fluorescence, which is most often involved in FRET experiments (although FRET
is a nonradiative energy transfer)? Or “F” like F€
orster, who was the first person to
develop a theory relating spectroscopic data such as absorption and emission spectra
to the energy transfer efficiency, donor–acceptor molecule distances and orientations (although many other scientists were involved in the discovery of FRET)? Or
should the “F” be completely erased in order to circumvent the discussion (or to
avoid four-letter words)? Personally, I prefer to use “F€
orster” in acknowledgment of
his achievements and in order to avoid the term fluorescence, but probably the most
important aspect of this discussion is the fact that it is not an important discussion.
FRET is a very useful and interesting technology and its experimental application
and theoretical treatment for the many possible FRET systems should be investigated, discussed, and developed. Although the main theory was contributed by
F€orster in the 1940s, FRET is a very modern technology because the r6 distance
dependence over approximately 1–20 nm fits extremely well into the recent discoveries and investigations in nanoscience and nanobiotechnology [1]. The everincreasing number of donor–acceptor pairs (cf. Chapter 14) is another evidence
for the contemporary relevance of FRET.
This chapter will cover the main aspects of what FRET is, what FRET can be used
for (and for what it should better not be used), how a FRET experiment should be
designed and performed, what mathematics is absolutely necessary, and how the
experimental results can be processed and interpreted. It must also be mentioned
that there is no one recipe for all FRET experiments. The main part of this chapter
should rather be understood as a guide to FRET, providing useful information that
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j105
j 5 How to Apply FRET: From Experimental Design to Data Analysis
must be considered for every FRET experiment in order to receive the correct
answers from the investigated systems. Combination with the theory described in
Chapters 3 and 4 and the specific tools and applications presented at the end of this
chapter as well as the following application chapters will further enlarge the scope of
possibilities of the powerful FRET technology. Moreover, there are several excellent
monographs and review articles available [2–20] that are related to FRET application
for more specific problems that are not covered within this chapter and/or book.
5.2
FRET: Let’s get started!
Before treating the concept, some inevitable mathematics, and the experimental work
related to FRET, I would like to introduce some first ideas about what FRET can be
useful for and what kind of prethoughts should be taken into consideration. If these
first questions are clarified, one can continue with understanding FRET in order to
perform and interpret a successful experiment. Most of the aspects mentioned in the
following paragraph might seem evident and even more than obvious for the FRET
expert. However, often such first simple thoughts can avoid later trouble, when the
project and/or experiment have already been planned or maybe even carried out.
FRET is a strongly distance-dependent transfer of energy between two molecules.
This energy transfer will take place only at a distance range of approximately
1–20 nm, and if the system to be studied (the object of interest) does not provide
such distances, FRET is not a good solution for its investigation. If the distance range
is possibly met by the system, two molecules are required between which FRET can
take place – the so-called FRET pair. The energy donor (D) must be a luminophore
[luminescent molecule or particle – it should be noted that fluorescence (singlet–
singlet optical transition) is a subterm of luminescence, which is the general term
for the emission of light originating from the electronic transition between two
different energy states [15,17,18]]. The energy acceptor (A) must be able to absorb
light in the same spectral range as the emission of D. The absorption and emission
spectra of the FRET pair should be chosen (e.g., from Chapter 14) in a suitable
wavelength range, which fits to the available instrumentation (excitation source and
detection setup) and does not interfere with the object of interest (e.g., excitation or
emission of some components within the investigated system). Moreover, it should
be taken care that the optical properties of the FRET pair are preserved within the
environment of the object of interest (e.g., for experiments that need to be
performed in aqueous solution, D and A should be avoided that are only soluble
in organic solvents). Once a good FRETpair has been identified, it should be ensured
that D and A can be attached to the object of interest (e.g., bioconjugation to a
protein) and that the properties of the object as well as of D and A are only minimally
influenced by this conjugation. Another aspect to be taken into consideration is if
the object of interest will be studied on the single-molecule level or in an ensemble
of many objects. A single FRET pair gives only yes or no answers (FRET was
successful or not) and many of these FRET pairs (or many excitations of the same
FRET pair) need to be analyzed in order to calculate FRET efficiencies. The ensemble
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106
measurement results in averaged luminescence intensities or lifetimes, which must
be analyzed to reveal FRET efficiencies. One should also keep in mind that (due to
the additional FRET energy path) the overall luminescence quantum yield of a FRET
pair (no matter if the luminescence of D or A is measured) is in the most cases lower
than the luminescence quantum yields of D or A alone. Therefore, the use of FRET
only makes sense in cases where it can provide specific information on two sites
within the object of interest due to D–A proximity (ligand–receptor or antibody–
antigen binding, distances of two specific positions within a biological molecule,
colocalization of two molecules, ratiometric D–A sensor, reduced photobleaching of
A by excitation via D, etc.). If only one event needs to be monitored (e.g., the binding
of a specific antibody to the cell membrane), pure luminescence measurements
(using excitation and emission without FRET) are usually the preferred method of
choice and the additional step of FRET can be avoided. Scheme 5.1 illustrates the
main aspects that should be taken into consideration before thinking about an
application of FRET.
Scheme 5.1 Flowchart for prethoughts concerning the application of FRET.
5.3
FRET: The Basic Concept
FRET is an energy transfer process between a luminescent donor molecule or particle
(the donor D) and a light-absorbing acceptor molecule or particle (the acceptor A). The
luminescence energy (in spectroscopy and imaging usually expressed in wavelength,
but wavenumber can also be found) of D must be equal to the absorption energy
(wavelength) of A, which is referred to as resonance condition (FRET ¼ F€
orster Resonance
EnergyTransfer).TheenergyistransferrednonradiativelyfromDtoAwithanefficiency
that is dependent on the distance r between D and A (gFRET r6). The origins of this r6
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5.3 FRET: The Basic Concept
j 5 How to Apply FRET: From Experimental Design to Data Analysis
distance dependence were discovered long before F€
orster’s contributions to FRET
and a very nice historic overview by Robert Clegg describes the early findings of
energy transfer between two molecules separated by distances beyond orbital
overlap [21]. FRET is based on the approximation that dipole–dipole coupling can
be represented by Coulombic coupling (coupling of two charges) VCoul. In fact,
VCoul should be dominant at the usually considered FRET distance range of
approximately 1–20 nm, where orbital overlap-related mechanisms (for very short
distances) and radiative mechanisms (for long distances) play minor roles. The
FRET rate can be represented by Fermi’s golden rule:
kFRET ¼
2p 2
jVj r;
h
ð5:1Þ
where h is the reduced Planck constant, V is the electronic coupling between D and
A, and r is the density of the interacting initial and final energetic states, which is
related to the spectral overlap integral J, describing the overlap of D emission and A
absorption (see below). In Equation 5.1, V can be replaced by the r3 distance
dependent VCoul:
V Coul ¼
kj~
mD k ~
mAj
;
4pe0 n2 r 3
ð5:2Þ
where ~
mD and ~
mA are the transition dipole moments of D and A, k is the orientation
factor between them (cf. Equation 5.9), e0 is the vacuum permittivity, n is the
refractive index, and r is the distance between D and A.
By substituting Equation 5.2 into Equation 5.1, one arrives at the r6 distance
dependence of the FRET rate:
kFRET ¼
9ðln 10Þk2 WD
J;
128p5 N A n4 tD r 6
ð5:3Þ
where WD is the luminescence quantum yield of D, NA is Avogadro’s number, and
tD is the luminescence lifetime of D (in the absence of FRET).
Figure 5.1 shows the basic principle of FRET, including the Coulombic mechanism, where an electronic transition from a higher to a lower energy level in D leads
to an electronic transition from a lower to a higher energy level in A (without
electron exchange!) if these transitions are in energetic resonance.
At a distance r, where the FRET rate and all other decay rates are in equilibrium
1
ðkFRET ¼ kRD þ kNR
D ¼ tD Þ, the FRET efficiency gFRET is 50%. This distance is the socalled F€orster distance (or F€orster radius) R0, which can be calculated by replacing
kFRET with t1
D and r with R0 in Equation 5.3:
1=6
9ðln 10Þk2 WD
R0 ¼
J
:
128p5 N A n4
ð5:4Þ
J is the spectral overlap integral [defined in the wavelength (l) or wavenumber (~
n) scale]:
ð
ð
~
n
J ¼ I D ðlÞeA ðlÞl4 dl ¼ I D ð~nÞeA ð~
nÞd 4 ;
ð5:5Þ
~
n
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108
Figure 5.1 Basic FRET principle. (a) Simplified
energy level scheme (Jablonski diagram)
representing the excitation of the donor (hn)
from an electronic ground state (D) to an
excited state (D ), followed by inner relaxation
(vibrational and rotational – dotted arrow) to an
excited electronic ground state, followed by
radiative decay (kR), nonradiative decay (kNR),
or FRET (kFRET). In order to realize the FRET
process from D to A , the difference between
the respective energy levels need to be equal
(resonance condition: E(D ) E(D) ¼ E(A ) E
(A)), as emphasized by the coupled transitions
(horizontal lines with dots on each end). After
FRET, the acceptor is in an excited state (A ),
followed by radiative or nonradiative decay to its
ground state (A). (b) Different energy pathways
after donor excitation (hnex) possibly leading to
luminescence emission of D (hnD) or A (hnA)
for FRET analysis.
which is dependent on the acceptor molar absorptivity (or extinction coefficient)
spectrum eA and the donor emission spectrum ID normalized to unity (cf. Figure 5.2):
ð
ð
I D ðlÞdl ¼ I D ð~nÞd~n ¼ 1:
ð5:6Þ
Combination of Equations 5.3 and 5.4 leads to the relation between the FRET
rate, the luminescence decay time of the donor, and the distances (r6 distance
Figure 5.2 The overlap (gray area) of the areanormalized emission spectrum of D (cf.
Equation 5.6) and the extinction coefficient (or
molar absorptivity) spectrum of A (eA) defines
the overlap integral J (cf. Equation 5.5), which is
directly proportional to the FRET rate (cf.
Equation 5.3). In this graph, a wavelength scale
was chosen (wavenumber is also possible – cf.
Equations 5.5 and 5.6).
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5.3 FRET: The Basic Concept
j 5 How to Apply FRET: From Experimental Design to Data Analysis
1.0
ηFRET
0.8
0.6
0.4
0.2
0.0
0.5R0
R0
1.5R0
2R0
2.5R0
r
Figure 5.3 FRET efficiency (gFRET) as a function of D–A distance (r). The r6 distance
dependence (cf. Equation 5.8a) leads to a strong sensitivity of gFRET to r in the distance region of
about 0.5R0–2.0R0 (gray background area).
dependence of the FRET rate):
6
1 R0
kFRET ¼ tD
:
r
ð5:7Þ
The FRET efficiency is then
gFRET ¼
kFRET
1
¼
:
kFRET þ t1
1 þ ðr=R0 Þ6
D
ð5:8aÞ
As shown in Figure 5.3, the sensitivity of the FRET efficiency to the D–A distance
is most prominent in a region between about 0.5R0 and 2.0R0, with the efficiency
curve being very steep around R0 (high dynamic range).
The last important variable for the basic FRET concept is the so-called
orientation factor kappa-squared (k2 in Equations 5.3 and 5.4 or k in Equation 5.2), which is often forgotten to be taken into account seriously and is also
often considered too much in detail even though a relatively easy averaging
might be applicable. In this regard, it is very important if the FRET experiment is
performed on a single-molecule level (where only averaging over time will make
sense) or the ensemble (where averaging over time and/or over the molecular
ensemble might be reasonable). In any case, one should seriously think about
kappa-squared for any FRET application and then choose the most appropriate
option of treating the dipole–dipole orientation. Figure 5.4 describes the orientation of the donor and acceptor dipoles within the basic concept of FRET. Taking
the different angles between the transition dipole moments of D and A (~
mD and
~
mA ) and the connection vector between D and A (~
r ) allows the calculation of the
orientation factor:
^D m
^A 3ð^
k¼m
mD ^r Þð^
mA ^r Þ ¼ cos qDA 3cos qD cos qA ;
ð5:9Þ
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110
Figure 5.4 Orientation of the donor emission transition dipole moment ~
mD , the acceptor
r for the calculation of
absorption transition dipole moment ~
mA , and the D–A connection vector~
the FRET dipole orientation factor k (Equation 5.9).
^D , m
^A , and ^r represent the unit vectors of ~
where m
mD , ~
mA , and~
r , respectively, and the
angles qDA, qD, and qA are shown in Figure 5.4.
There are some reasonable averaging conditions, which can provide a good
approximation for k2 to be used for many practical FRET applications. When all
D’s and A’s can take any possible orientation during the FRET time (1/kFRET),
which means that the average rotation rate is much larger than the average FRET
rate ðkrot kFRET Þ, the system is in a dynamic averaging regime and k2 becomes
2/3. This fast isotropic rotation of D and A is often fulfilled if they are bound to
polypeptides or proteins [20]. If D and A are both luminescent, fast isotropic
rotation can be verified by checking if their emissions are unpolarized. If one of
the FRET partners shows average orientation (isotropically degenerate: “sphere”)
and the other has a fixed orientation (well-defined linear dipole: “line”), then k2
(from “sphere” to “line” or from “line” to “sphere”) can take values between 1/3
and 4/3 (for which 2/3 is still not such a bad approximation). In case of FRET
from “line” to “line” (two well-defined linear dipoles), it becomes much more
complicated because the full orientation factor range (0 < k2 <4) needs to be
considered (and 2/3 might be a very bad approximation). In the case where all
donors and acceptors are fixed (no rotational motion), each FRET pair is assumed
to be isolated from all other pairs, and the electronic transitions of D and A are
single dipoles, one can use a static regime approximation [11] for which k2 is
dependent on the D–A distance r and the D–A distance r0, for which k2 would be
2/3. In this case, k2 can take values between 0 (for r 0.4r0) and 2/3 (for
r 1.4r0).
As already mentioned, it is important to take into account the orientation of the D
and A transition dipole moments for every FRET experiment in order to justify an
approximation or the assumption of a special orientation. If the experiments allow a
modification of the D–A distance (so that FRET can be measured at multiple
different distances), one can try to evaluate the FRET efficiency results using F€
orster
distances (R0) calculated with different k2 values in order to get a better idea about
which orientational approximation or assumption might lead to reasonable results.
In any case, an estimated or exact k2 can be calculated and a detailed treatment of the
orientation factor, including the presentation of how to access k2 values, can be
found in Chapter 4.
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5.3 FRET: The Basic Concept
j 5 How to Apply FRET: From Experimental Design to Data Analysis
5.4
FRET: Inevitable Mathematics
Understanding the basic concept of FRET and the r6 distance dependence requires
the equations from Section 5.3. For a profound knowledge of FRET theory and an
exact theoretical calculation of different FRET parameters, Chapters 3 and 4 as well
as the available literature should be consulted [3,4,10,11,15,17–20,22–27]. As already
mentioned in Section 5.1, many different research disciplines make use of FRET
and especially in applied research, it is sometimes tried to avoid mathematics if
possible. However, even the FRET experimentalist will need some mathematics for
the choice of the adequate D–A pair and for the interpretation of the results. In most
cases, only very few (and relatively) uncomplicated equations are necessary in order
to achieve very satisfactory experimental results. The most important FRET parameters are the F€orster distance R0 and the FRET efficiency gFRET because they
combine spectroscopic data (e.g., luminescence quantum yields, intensities, and
lifetimes or emission and absorption spectra) with distances and orientations.
5.4.1
F€
orster Distance (or F€orster Radius)
Equation 5.4 is a general equation that needs a careful choice of units for achieving
the correct value and unit for the resulting distances and/or FRET rates. For the
experimental case, one can predefine commonly used units within the overlap
integral J and merge all constants found in Equations 5.4 into one value:
9ðln 10Þ
¼ 8:79
128p5 N A
1028 mol;
ð5:10Þ
where Avogadro’s constant NA ¼ 6.02 214 1023 mol1. Different examples of
facilitating Equation 5.4 with preassuming different units can be found in Chapter 3.
Probably the most common length unit used at the small distance scale of FRET is
nanometer and, therefore, it makes sense to express r and R0 in nanometers. Quite
often the unit Angstr€om is also used for FRET (1 A ¼ 0.1 nm). Moreover, simplification of Equation 5.4 can be achieved by using commonly used units for optical
spectroscopy in the overlap integral (Equation 5.5): the wavelength l in nanometer
units and the molar absorptivity (or extinction coefficient) eA in M1 cm1 (liter per
mol per centimeter). These predefinitions lead to the following F€
orster distance (for
which k2, WD, n4, and J are dimensionless):
R0 ¼ ð8:79
1028
Taking into account that M
k2 WD n4 J mol M1 cm1 nm4 Þ1=6 :
1
1
cm
ð5:11Þ
1
nm ¼ 10 nm mol , this leads to
R0 ¼ 0:02108ðk2 WD n4 JÞ1=6 nm;
4
17
6
ð5:12Þ
which is the F€orster distance in nanometers. It is very important that Equations 5.11
and 5.12 are valid only if the value for J is calculated in M1 cm1 nm4. Using different
units will lead to a different prefactor on the right-hand side of Equation 5.12.
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112
5.4.2
FRET Efficiency
The FRET efficiency relates the F€orster distance (R0, which can be calculated by
absorption and emission spectroscopy of D and A as demonstrated above) and the
D–A distance (r, which might be known from the system to be measured or which
might be the unknown variable of interest) with spectroscopic data of D and A as
single entities and as a D–A FRET pair. The FRET efficiency gFRET can be determined
by several different methods, which are explained in the following.
5.4.2.1 Determination by Donor Quenching
One possibility of calculating the FRET efficiency is to use spectroscopic data
(luminescence quantum yield W, lifetime t, and intensity I) of D in the absence
(subscript D) or presence of A (subscript DA). Using Equation 5.8b,
kFRET
kFRET
¼
¼ kFRET tDA
kFRET þ t1
kFRET þ kRD þ kNR
D
D
gFRET ¼
ð5:8bÞ
R
and taking into account that WD ¼ tD kRD ¼ kRD =ðkRD þ kNR
D Þ and WDA ¼ tDA kD ¼
kRD =ðkFRET þ kRD þ kNR
D Þ, this leads to the following equation:
1
gFRET ¼
1 þ ðr=R0 Þ
6
¼
R60
R60
WDA
tDA
I DA
¼1
¼1
¼1
:
WD
tD
ID
þ r6
ð5:13Þ
The last part of Equation 5.13 (using emission intensities) is valid only if the
excitation light intensity absorbed by D and all the measurement parameters are
identical for both measurements (D in the absence and in the presence of A). If the
experimental conditions for “D” and “DA” FRET measurements are similar, this is
usually a good approximation leading to adequate results. FRET causes quenching of
the donor luminescence quantum yield, lifetime, and intensity and thus WDA, tDA,
and IDA are smaller than WD, tD, and ID, leading to efficiency values between 1 and 0.
This technique requires the determination of WD, tD, or ID before the FRET
measurement and gFRET is then calculated from data generated by the two different
experiments. Once R0 has been calculated (Equation 5.12), the spectroscopic data
can be used for calculating the D–A distance r by converting Equation 5.13 to
r ¼ R0
WDA
WD WDA
1=6
¼ R0
tDA
tD tDA
1=6
¼ R0
I DA
ID I DA
1=6
:
ð5:14Þ
5.4.2.2 Determination by Acceptor Sensitization
Donor quenching is not an evidence of FRET, as this donor deactivation can also be
caused by other quenching mechanisms. The only sure evidence of energy transfer
from D to A is to measure the luminescence of A after excitation of D. Obviously, a
luminescent acceptor is necessary for this, so this technique cannot be performed
with dark quenchers as FRET acceptors. The FRET efficiency can then be calculated
by the ratio of acceptor luminescence intensity in the presence (IAD) and in the
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5.4 FRET: Inevitable Mathematics
j 5 How to Apply FRET: From Experimental Design to Data Analysis
absence (IA) of D. For the calculation of gFRET by sensitized acceptor luminescence,
one needs to take into account that there is (in almost all cases) direct excitation of A
at the excitation wavelength used for exciting D. Although this direct excitation
might be weak, it needs to be corrected for in order to achieve appropriate results for
gFRET. This correction can be done by subtracting the direct luminescence IA from
IAD and multiplying the corrected luminescence ratio by the ratio of the absorptivities (or extinction coefficients) of A and D (eA and eD) at the excitation wavelength
used for the FRET experiment. The FRET efficiency is then
1
R60
I AD I A
eA
IAD
eA
gFRET ¼
¼
¼
1
¼
:
IA
eD
IA
eD
1 þ ðr=R0 Þ6 R60 þ r 6
ð5:15Þ
This technique requires the knowledge of eA and eD and the measurement of IA
before the FRET experiment. gFRET is then calculated from data generated by the
two different measurements. Once R0 has been calculated (Equation 5.12), the
spectroscopic data can be used for calculating the D–A distance r by converting
Equation 5.15 to
1=6
I A eD
r ¼ R0
1
:
ð5:16Þ
ðI AD I A ÞeA
Cases of incomplete D–A labeling (free A inside the FRET sample) and the use
of two different excitation wavelengths (for cases of weak FRET where the ratio
IAD/IA is close to unity, which can cause significant errors in calculating gFRET)
using this technique with further necessary corrections have been applied by
Clegg et al. [28–30].
5.4.2.3 Determination by Donor Quenching and Acceptor Sensitization
In order to calculate gFRET from a single measurement, the quenched donor
luminescence intensity (D in the presence of A) and the sensitized acceptor
luminescence intensity (A in the presence of D) can be analyzed. This technique
can offer the advantage of high precision in calculating the FRET efficiency because
data from simultaneously measured luminescence spectra are used. However, the
acceptor luminescence caused by direct excitation of A still needs to be corrected for
and thus it needs to be measured by a preexperiment. Moreover, the luminescence
quantum yields of D and A need to be known. For the calculation of gFRET, the
excitations (intensity divided by quantum yield: I/W) of D and A are taken into
account. In this case, the FRET efficiency can be defined as the number of donor
excitations leading to acceptor excitations (FRET) divided by all donor excitations
(leading to FRET and all other radiative and nonradiative deactivation pathways):
R60
ðI AD I A Þ=WA
¼
6
6
6
ðI
IA Þ=WA þ I DA =WD
R
þ
r
1 þ ðr=R0 Þ
AD
0
1
ðI AD IA Þ
WA I DA
¼
¼ 1þ
:
WD I AD IA
ðI AD IA Þ þ ðWA =WD ÞI DA
gFRET ¼
1
¼
ð5:17aÞ
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114
In this equation, IAD is the luminescence intensity of A during FRET (in the
presence of D), which needs to be corrected for acceptor luminescence due to direct
excitation (IA). IDA is the luminescence intensity of D during FRET (in the presence
of A) and WA and WD are the luminescence quantum yields of A and D, respectively.
Once R0 has been calculated (Equation 5.12), the spectroscopic data can be used for
calculating the D–A distance r by converting Equation 5.17a to
1=6
WA IDA
r ¼ R0
:
ð5:18Þ
WD ðI AD I A Þ
5.4.2.4 Determination by Donor Photobleaching
Apart from measuring the luminescence quenching of donor and/or acceptor,
another possibility to determine the FRET efficiency is photobleaching, which is
especially useful in imaging setups, where the necessary light sources, providing
enough power for photobleaching, are often readily available. Using the photobleaching time constant tbl of D in the absence (subscript D) or in the presence of A
(subscript DA), gFRET can be calculated [16,31]:
1
gFRET ¼
1 þ ðr=R0 Þ6
¼
R60
tbl
D
¼
1
:
R60 þ r 6
tbl
DA
ð5:19Þ
In contrast to the luminescence properties W, t and I in Equation 5.13, the
photobleaching time constant of D in the absence of A (tbl
D , no FRET) is found
in the numerator, whereas the photobleaching time constant of D in the presence of
A (tbl
DA , FRET) is found in the denominator on the right-hand side of Equation 5.19.
bl
In this case, tbl
D is smaller than tDA because FRET opens a new energy pathway for
the excited donor to return to the ground state and, therefore, the photobleaching
time constant of the donor is increased in the presence of the acceptor [16]. Similar
to the D or A quenching approaches, this technique requires the determination of tbl
D
before the FRET measurement and gFRET is then calculated from data generated by
the two different experiments (no FRET and FRET). Once R0 has been calculated
(Equation 5.12), the D–A distance r can be calculated by converting Equation 5.19 to
r ¼ R0
tbl
D
bl
tDA tbl
D
1=6
:
ð5:20Þ
5.4.2.5 Determination by Acceptor Photobleaching
In order to be able to determine gFRET from a single sample, one can use acceptor
photobleaching. In this approach, the initially FRET-quenched donor luminescence (D in
the presence of A) is recovered by photobleaching the acceptor (destroying the FRETpath
to A). The FRETefficiency can then be calculated using the luminescence intensities of D
before (superscript pre) and after (superscript post) the photobleaching of A:
gFRET ¼
1
1 þ ðr=R0 Þ6
pre
¼
R60
I DA
¼ 1 post
:
6
6
R0 þ r
I DA
ð5:21Þ
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5.4 FRET: Inevitable Mathematics
j 5 How to Apply FRET: From Experimental Design to Data Analysis
Note that donor and acceptor are still physically connected after photobleaching,
but the acceptor (and the FRET path) is irreversibly “switched off.” The main
advantage of this technique is the avoidance of measuring two different samples
(such as pure D and photobleached D in the previous paragraph). This can be
especially problematic for cellular imaging, for example, due to different protein
expression levels from cell to cell, which will cause variable donor concentrations in
the different cells. Once R0 has been calculated (Equation 5.12), the photobleaching
data can be used for calculating the D–A distance r by converting Equation 5.21 to
pre
r ¼ R0
I DA
post
pre
I DA IDA
!1=6
:
ð5:22Þ
5.4.3
FRET with Multiple Donors and/or Acceptors
In many FRETexperiments, the interaction between multiple donors and acceptors is
possible. For example, this can be the case for random labeling of proteins, cell
surfaces, or nanoparticles, where the amount of D and A that can possibly interact is
mainly defined by the density of D and A within the labeled systems. There can be
different or equal distances between the D’s and A’s, there can be very few D’s
interacting with A’s and vice versa, there can be D’s and A’s that do not interact at all,
and there can be one-, two-, and three-dimensional distributions that can be random or
contain excluded spaces (so that random distribution cannot be assumed anymore).
Raicu has proposed a theoretical model for multiple donor–acceptor interactions,
which becomes more complicated if more possibilities are included in the model [32].
Using an approximation of equal distances between all D’s and A’s and assuming that
all FRETrates are equal for any D–A FRETpair, Raicu derived an equation for the FRET
efficiency (gmulti
FRET ), which is purely dependent on the number of acceptors nA (and not
on the number of donors) and the efficiency of a single D–A pair (gFRET):
gmulti
FRET ¼
nA gFRET
:
1 þ ðnA 1ÞgFRET
ð5:23Þ
The same result was found by Clapp et al. in an experimental study for single D to
multiple A FRET, where several organic dye acceptors were placed around one quasispherical semiconductor quantum dot donor in order to achieve approximately
equal distances [33]. The authors derived (and confirmed experimentally) the
following equation:
gmulti
FRET ¼
nA kFRET
nA R60
¼
;
1
nA kFRET þ tD
nA R60 þ r 6
ð5:24Þ
which is equal to Equation 5.23. An increasing FRET efficiency with an increasing
number of A’s per D can be explained by the fact that there are simply more (nA
instead of 1 for a single pair) possible de-excitation pathways available for the excited
donor and, therefore, the probability of de-exciting D via FRET becomes higher.
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116
The independence of the FRET efficiency from the number of donors is not so
obvious, as in the case of multiple donors with one acceptor, the multiple D’s need to
compete for FRET to the single A (unless there is always only one D or A excited during
the time of excitation, energy transfer, and de-excitation). This problem has been taken
into account by Berney and Danuser (with further developments by Corry et al. for
different geometrical distributions) [34,35]. As the integration of the many possible
parameters for multiple D–A systems inside an analytical model can become very
complicated, numerical approaches are an excellent alternative. The authors developed
a Monte Carlo simulation (MCS) for an experimental setup in which they could control
donor and acceptor concentrations (and thereby the D to A ratio RDA) as well as the
average distance between D and A using a PLL-g-PEG-biotin-coated microscope
coverslip surface and controlled amounts of streptavidin labeled with D or A. The
MCS results were used as a reference to compare different methods from the literature
to use the experimental data for FRET efficiency determination. The beauty of the
numerical approach is the stepwise calculation of the FRETefficiency photon by photon
(or exciton by exciton). In the following, the MCS scheme is briefly outlined [34,35]:
Step 1: The coordinates and types of D’s and A’s are assigned, accounting for a
regular arrangement and for excluded volume effects.
Step 2: The transfer probability from each donor Di to every acceptor Aj is calculated by
P ij ¼ R60 =r 6ij ;
ð5:25Þ
where R0 is the F€orster distance and rij is the distance between the Di–Aj FRET
pairs.
Step 3: The exciton flux (dependent on the photon flux and the extinction coefficient
and concentration of the donors) is calculated by
2
ð5:26Þ
f e ¼ pa2 Ilh1 c1 1 10½ðeD nD Þ=ð1000N A pa Þ ;
where a is the radius of the simulated system, I is the irradiance of the excitation
light source with wavelength l, h is the Planck’s constant (6.626 1034 Js), c is
the speed of light (3 108 ms1), eD is the molar extinction coefficient of the
donor at wavelength l, nD is the number of donor molecules, and NA is the
Avogadro’s constant (6.022 1023 mol1).
Step 4: A time sequence giving the play time of each exciton within the time interval
of excitons being incident on the fluorophores is defined; for each exciton, a target
donor is randomly assigned and the experimental clock is set to zero.
Step 5: The excitons are played (sequentially) to see if they are absorbed by the donor
and, if yes, whether it is de-excited by FRET or fluorescence. First it is checked if
the donor is already “busy” (already excited) and if yes the exciton is lost and the
next one will be played. If the donor is not “busy”, it gets excited, is then set to
“busy” and a list of free acceptors (which are not already excited) around the donor
is generated. The overall rate of energy release is calculated by
!
afree
X
1
1
ð5:27Þ
tT ¼ tD 1 þ
Pij ;
j¼1
j117
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5.4 FRET: Inevitable Mathematics
j 5 How to Apply FRET: From Experimental Design to Data Analysis
where tD is the luminescence lifetime of D in the absence of A (unquenched). The
time for the donor to release its energy in the simulation is calculated by
T D ¼ tT ln ðcD Þ;
ð5:28Þ
where cD is a uniformly distributed random generator delivering a value between
0 and 1. TD defines the time point of energy release of the excited D (the time point
at which the donor is set from “busy” back to “free”).
Next it needs to be decided (using probabilities) whether Di will release its
energy as FRET or fluorescence. This is determined by creating a cumulative
histogram with the classes of all possible pathways, where the probability of the
classes FRET to Aj is (tT/tD)Pij and the probability of the class fluorescence is
tT/tD. Another uniform random number between 0 and 1 is picked to decide for
the de-excitation class. If the selection falls in the class of fluorescence, the
variable Fluo is incremented by 1 and the next exciton is played. If Di was selected
for FRET to Aj, this acceptor is set to “busy” and the variable FRET is incremented
by 1. The time interval of a “busy” Aj (TA) is determined by a MCS step similar to
Equation 5.28, where TA ¼ tA ln (cA) with tA denoting the luminescence
lifetime of A and cA is another random number between 0 and 1. The complete
step 5 is repeated for all excitons.
Step 6: Finally, the simulated FRET efficiency can be calculated by comparing the
number of donors undergoing FRET and fluorescence, respectively:
gFRET ¼
FRET
:
FRET þ Fluo
ð5:29Þ
5.5
FRET: The Experiment
This section will cover the most important aspects of how to design, perform, and
analyze a general FRET experiment using steady-state and time-resolved optical
spectroscopy and microscopy and applying the equations from the previous section.
5.5.1
The Donor–Acceptor FRET Pair
A well-designed FRET experiment can provide a lot of useful qualitative and
quantitative information. As already mentioned in Section 5.2, every FRET experiment starts with considering how the system of interest can be most efficiently
analyzed by FRET, which is closely related to the choice of a suitable donor–acceptor
FRET pair. One of the first considerations should concern the physical parameter to
be determined, which could be the following:
1) Quantitative distance: FRET as a spectroscopic (or molecular) ruler to determine
the distance between two molecules in a range of about 1–20 nm.
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118
2) Qualitative distance: FRET to prove a proximity (colocalization) between two
molecules or FRET as an optical switch between two molecules in about 1–20 nm
distance.
3) Quantitative concentration: FRET to determine the amount of two (or more)
bound molecules in about 1–20 nm distance.
4) Qualitative (or semiquantitative) concentration: FRET to prove the existence of two
(or more) bound molecules in about 1–20 nm distance.
In all cases, a convenient FRET pair should be chosen, which combines bright
luminescence of D and/or A for an efficient detection or signal generation with a
sufficiently large R0 for the distance between the two molecules. It is not always
advisable to choose the highest possible F€orster distance. For example, if R0 ¼ 6 nm
and the D–A distance is r ¼ 2 nm, the FRET efficiency will be very close to 100%
(WDA ¼ IDA ¼ tDA ¼ 0) leading to a pure on–off luminescence signal, which could
cause problems in evaluating and/or quantifying the physical phenomenon behind
(disruption of D–A binding and disappearance of D, photobleaching of D, FRET due
to very close proximity, and other quenching mechanisms independent of FRET). In
most cases, the FRET pair should be chosen such that the distance (or distances) of
interest is in the 0.5R0–2.0R0 distance range (cf. Figure 5.3) because this is the most
sensitive distance range for FRET.
Another important aspect is the technique with which FRETwill be analyzed (donor
quenching and/or acceptor sensitization, donor or acceptor photobleaching) (cf.
Section 5.4) as well as the available equipment because this defines the photophysical
properties (absorption and emission wavelength range, quantum yield, lifetime, etc.)
of D and A. Many fluorophores are available for FRET, such as organic dyes (and dark
quenchers), polymeric and dendrimeric dyes, naturally occurring fluorophores,
lanthanide, and metal-based complexes, as well as nano- and microparticles. For a
detailed overview of the different fluorophores, the reader is referred to Chapter 6 and
to Ref. [1], in which the important topic of bioconjugation (how to attach D and A to
the system of interest) is also outlined. The most comprehensive Chapter 14
concerning FRET data contains much information about F€
orster distances, photophysical properties, availability, and applications of many D–A FRETpairs. It is always
recommended to choose at least three fluorophores, that is, one preferred D–A FRET
pair with at least one alternative D and/or A for control experiments or backup
solution in case the original FRET pair does not perform sufficiently well.
5.5.2
F€
orster Distance Determination
After having made the initial choice of a D–A FRET pair, the F€
orster distance should
be determined (or verified in case an R0 value could already be found in the
literature). Assuming that sufficient donor and acceptor material is available
(especially absorption measurements require higher concentrations than fluorescence detection) and that the orientation factor can be sufficiently well estimated or
calculated, the determination of R0 is usually not a very challenging task, which
j119
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
requires standard steady-state spectroscopy equipment such as absorption and
fluorescence spectrometers. Both spectra (donor emission and acceptor absorption)
should be measured as precisely as possible, but in a reasonable manner. Some
suggestions of acquiring such spectra are outlined below. More details can be found,
for example, in Refs [15,18].
a) Molar absorptivity (or extinction coefficient) spectrum of the acceptor: As many
absorption spectrometers (especially plate readers) provide lower spectral resolution (often limited to minimum 1 nm) than fluorescence spectrometers
(usually well below 1 nm), it is recommended to start with measuring the
absorption spectrum of A (usually the absorbance A or optical density OD is
measured for a light path length of 1 cm). For the calculation of R0 in a
spreadsheet program, it is quite convenient to use the same wavelength steps
for emission and absorption spectra. One can save time erasing out data points
on the computer by already recording the spectra with matching wavelengths. It
does not make much sense to measure the emission spectrum of D (ID(l)) with a
10-fold higher spectral resolution than the absorption spectrum of A because
both spectra are multiplied in the overlap integral (Equation 5.5). However, care
must be taken when spectra with very narrow peaks (e.g., lanthanide emission
spectra) are used, for which the spectral resolution should be high enough not to
omit emission (or absorption) peaks by not measuring them because of too large
wavelength steps or by erasing them in a spreadsheet when calculating the
overlap integral. Apart from the acceptor sample, the pure solvent (or buffer)
should be measured and subtracted from the sample spectrum (background
correction). The OD (for 1 cm light path) of the sample should not be too low
because this can cause large errors after background correction. On the other
hand, too high ODs can cause saturation. In most cases, a maximum absorption
intensity between 0.1 and 3 OD should provide satisfactory results. Measuring an
emission excitation spectrum (variation of the excitation wavelength while
recording a fixed emission wavelength) of the same but highly diluted acceptor
sample on a fluorescence spectrometer is a good option to qualitatively (shape of
the spectrum) verify the absorbance spectrum. Once the background-corrected
absorbance spectrum A(l) has been determined, it can be calculated into the
molar extinction coefficient spectrum e(l) using Lambert–Beer’s law:
AðlÞ ¼ eðlÞ c l ) eðlÞ ¼
AðlÞ
;
cl
ð5:30Þ
where c is the concentration of the sample and l is the light path length (e.g., 1 cm
for a standard cuvette).
b) Emission spectrum of the donor: Most emission spectra (unless they have very
narrow emission bands) can be measured quite precisely by recording an
emission intensity every 0.5 or 1.0 nm (wavelength step). As already mentioned,
it is recommended to use the same wavelength steps as for the absorption spectra
if possible. Important aspects for recording emission spectra are to avoid high
sample concentrations (which can cause inner filter effects), solvent and/or
cuvette contaminations (which might contain other luminescent materials) and
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120
0.008
ID(λ)
ε A(λ)
1.50x105
1.25x105
1.00x105
0.006
7.50x104
0.004
5.00x104
0.002
0.000
400
2.50x104
450
500
550
wavelength (nm)
extinction coefficient (M–1 cm–1)
normalized emission intensity
M–1cm–1
0.00
600
Figure 5.5 Area-normalized (cf. Equation 5.6) donor emission spectrum (left – cf. column 3 in
Table 5.1), acceptor molar extinction coefficient spectrum (right – cf. column 4 in Table 5.1), and
resulting overlap function (shaded spectrum in the center – cf. column 5 in Table 5.1).
light scattering (Raman peaks inside the emission spectrum), and to use an
adequate quantum correction (detector sensitivity changes as a function of
wavelength) in order to obtain a correctly shaped emission spectrum. As the
spectrum is area-normalized for the calculation of R0, total intensities are not
important. However, the relative intensities must be correct.
As an example of calculating R0, I chose two imaginary D and A molecules with
emission and absorption spectra showing the typical shape of organic dye spectra
with a pronounced maximum and a blueshifted (for absorption) or redshifted (for
emission) “shoulder.” The spectra cover a wavelength range of about 400–600 nm
and overlap in the 450–550 nm region (Figure 5.5).
Once the spectra are recorded, the overlap integral and F€
orster distance can be
easily calculated using a spreadsheet program (e.g., Excel or Origin), as shown in
Table 5.1. The first column contains the wavelengths from 400–600 nm (in the
presented case, 0.5 nm steps are used) and the second one contains the determined
emission spectrum ID(l) (in arbitrary units – e.g., photon counts). The sum of all
ID(l) values is calculated (last cell of the second column) and used to calculate the
third column by dividing each ID(l) value with this sum in order to get the areanormalized emission spectrum I D ðlÞ (as a control, the sum of column 3 should be
unity). The fourth column contains the extinction coefficient spectrum of A (eA(l) in
M1 cm1 units) and the fifth column is the product of l4 I D ðlÞ eA ðlÞ. The sum of
this column 5 is the overlap integral J, which can be used (together with the
predetermined values for k2, WD, and n) to calculate R0 (in nm) using Equation 5.12
(as shown in the lower part of Table 5.1 with some arbitrarily chosen values for k2,
WD, and n).
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
Table 5.1 Extract from a spreadsheet to calculate R0 from donor emission and acceptor
absorption spectra (cf. Figure 5.5) and predetermined values of k2, WD, and n.
l (nm)
ID(l) (arb. units)
ID(l)
eA(l) (M – 1 cm – 1)
l4ID(l) eA(l)
(nm4 M – 1 cm – 1)
400
400.5
401
401.5
402
402.5
403
..
.
478.5
479
479.5
480
480.5
481
481.5
..
.
513.5
514
514.5
515
515.5
516
516.5
..
.
597.0
597.5
598.0
598.5
599.0
599.5
600.0
Sum
0
0
0
0
0
0
0
..
.
3.10E þ 05
3.12E þ 05
3.13E þ 05
3.14E þ 05
3.14E þ 05
3.14E þ 05
3.14E þ 05
..
.
1.20E þ 05
1.19E þ 05
1.18E þ 05
1.17E þ 05
1.16E þ 05
1.15E þ 05
1.14E þ 05
..
.
0
0
0
0
0
0
0
3.3E þ 07
0
0
0
0
0
0
0
..
.
9.52E 03
9.56E 03
9.60E 03
9.62E 03
9.64E 03
9.64E 03
9.64E 03
..
.
3.67E 03
3.64E 03
3.61E 03
3.58E 03
3.55E 03
3.52E 03
3.50E 03
..
.
0
0
0
0
0
0
0
1.0
109.4
119.3
130.1
141.8
154.4
168.1
182.8
..
.
5.35E þ 04
5.36E þ 04
5.38E þ 04
5.40E þ 04
5.42E þ 04
5.45E þ 04
5.48E þ 04
..
.
1.54E þ 05
1.54E þ 05
1.54E þ 05
1.54E þ 05
1.54E þ 05
1.53E þ 05
1.53E þ 05
..
.
0
0
0
0
0
0
0
1.6E þ 07
0
0
0
0
0
0
0
..
.
2.67E þ 13
2.70E þ 13
2.73E þ 13
2.76E þ 13
2.79E þ 13
2.81E þ 13
2.84E þ 13
..
.
3.93E þ 13
3.91E þ 13
3.90E þ 13
3.88E þ 13
3.85E þ 13
3.83E þ 13
3.80E þ 13
..
.
0
0
0
0
0
0
0
4.6E þ 15
J (nm4 M – 1 cm – 1)
k2
WD
n
R0 (nm)
4.6E þ 15
0.67
0.55
1.40
5.8
5.5.3
The Main FRET Experiment
With the photophysical properties and the F€
orster distance of the D–A FRET pair in the
pocket, the real FRET experiment can begin. This section will focus on luminescence
spectroscopy. FRET microscopy techniques have been recently treated in two
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122
comprehensive books [4,16]. Photobleaching FRET is mainly used for imaging and has
been covered in Ref. [36], so it will not be treated again in this section.
The main FRET experiment will always include luminescence, because the
emission changes of D or A or both must be measured in order to determine
FRET efficiencies and/or distances. Luminescence quenching can occur due to
many different reasons and therefore it is always recommended to measure acceptor
sensitization in combination with donor quenching. As the sensitization of A must
occur from energy transfer (assuming that direct excitation of A has been taken into
account and properly subtracted), the acceptor detection channel can be coined as
the “FRET-proof channel.” The best solution is to compare D-quenching and Asensitization and if the FRET efficiencies can be calculated as equal for both
partners, the involved mechanism is most probably FRET (or another energy or
charge transfer process – cf. Section 5.6). Luminescence can be measured using
steady-state and/or time-resolved techniques. The latter can be divided into timedomain and frequency-domain techniques. Details about the different experimental
approaches (steady-state and time-resolved) can be found in Refs [15,18], and only a
short technical overview will be presented here. In order to draw the correct
conclusions from the experimental data, it is important to combine as many
experiments as possible (D-quenching, A-sensitization, steady-state and timeresolved measurements, and all the necessary control experiments). The aim should
be the same as it used to be for Theodor F€orster: to search for the most appropriate
solution of a scientific problem, or in his favorite term “The correct interpretation of
an observation” (Die richtige Deutung einer Beobachtung) (cf. Chapter 1).
5.5.3.1 Steady-State FRET Measurements
Steady-state luminescence spectroscopy measures emission spectra, that is, the
emission intensity of the luminophores as a function of wavelength (or wavenumber)
over their complete time period of emission (no temporal resolution). This is usually
achieved by exciting the luminophores at a fixed wavelength, while scanning (e.g., with
a monochromator) over the wavelength of their emission, which is then detected [e.g.,
by using a photomultiplier tube (PMT)] in selected wavelength intervals. Measuring
the full emission spectra offers the advantage that both D and A can be measured
simultaneously within the same sample. The values of ID, IDA, IA, and IAD can then be
extracted from the measured overall spectrum of the sample (containing both D and A
emissions) and used with Equations 5.13–5.18 for the calculation of FRETparameters
and distances. A correct treatment of the overall spectrum requires a deconvolution of
the two spectra followed by integration over each single spectrum in order to obtain
correct values for ID, IDA, IA, and IAD (cf. Figure 5.6). Depending on how spectrally
close the two emission spectra are, the spectral cross talk between them will be weaker
(for well-separated spectra) or stronger (for close spectra). In case of well-separated
emission spectra, it might be sufficient to simply take the peak intensity values of D
and A to obtain ID, IDA, IA, or IAD.
Due to the almost endless choice of possible FRET pairs (which strongly depend
on the application), a generic example of steady-state FRETresults with an imaginary
FRET pair (the same as already chosen in Figure 5.5 for the calculation of the F€
orster
j123
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
(a)
(c)
Figure 5.6 Absorption and emission spectra
resulting from a representative steady-state
FRET experiment with luminescent D and A (cf.
Figure 5.5 for calculation of R0). (a) Peaknormalized absorption (dotted) and emission
spectra of D in the absence of A (black) and A in
the absence of D (gray). (b) Emission spectra of
different mixtures of D and A excited at 420 nm.
FRET causes quenching of donor luminescence
and sensitization of acceptor luminescence.
Therefore, the spectra are composed of
different ratios of the emission spectra of D and
A [from part (a)]. (c and d) Deconvolution of the
D–A spectra leads to the emission spectra of D
(b)
(d)
in the presence of A [part (c)] and of A in the
presence of D [part (d)]. The black curves in
both graphs represent the emission spectra of
D and A in the absence of A and D, respectively
(donor emission without FRET quenching and
acceptor emission due to direct excitation at
420 nm without FRET sensitization). Integrating
over these emission spectra results in the
intensity values ID and IA. The gray curves
represent the quenched donor and sensitized
acceptor emission, respectively. Integrating
over these emission spectra results in the
intensity values IDA and (IAD þ IA) (cf.
Equations 5.13–5.18).
distance R0) is presented in Figure 5.6. The principle of this theoretical example can
be transferred to any practical experiment using real FRET pairs. Many practical
examples using different FRET pairs can be found in Chapters 6–14 and in the FRET
literature.
Figure 5.6 presents the spectroscopic data obtained from the main FRET experiment. Part (a) shows the emission (and absorption) spectra of pure D and pure A,
which need to be measured before the FRET experiment, but under the same
experimental conditions (i.e., concentration, solvent, excitation and emission conditions, etc.). Part (b) presents the luminescence spectra obtained from 11 different
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124
j125
FRET measurements (11 different samples or 1 sample with changing spectra over
time), for which donor quenching and concomitant acceptor sensitization become
quite obvious. In the case where no third luminescent components (e.g., sample
autofluorescence) are present within these spectra, they are composed of different
ratios of the single emission spectra from part (a). Thus, they can be deconvoluted to
single FRET spectra of D and A, as shown in parts (c) and (d). Integration over these
spectra results in the intensities ID, IDA, IA, and IAD, which are necessary to perform
the FRET calculations using Equations 5.13–5.18.
With the obtained intensity values, different interpretations concerning FRET
are possible. We will begin with the analysis of the donor spectra and evaluate
afterward, which advantages the acceptor spectra provide for the interpretation of
the FRET system.
1) One can analyze the results in Figure 5.6c using donor quenching (Section 5.4.2.1).
As summarized in Table 5.2, the normalized donor emission intensity IDA/ID
decreases from 1 to 0 (in steps of 0.1), which can be caused by several reasons:
a) Distance: Assuming that each D is connected with one A (complete labeling),
the FRET efficiencies gFRET of each spectrum can be calculated by Equation 5.13 (Table 5.2, column 4). Using the precalculated R0 of 5.8 nm
(Figure 5.5 and Table 5.1), the D–A distances r can be calculated by Equation 5.14 (Table 5.2, column 5). This leads to the conclusion that all different
Table 5.2 Data resulting from different interpretations of D-quenching (Figure 5.6c) and A-sensitization
(Figure 5.6d) using steady-state FRET measurements.
0
1
2
Experimental data
Measurement
1
2
3
4
5
6
7
8
9
10
11
3
4a)
5b)
Distance
6c)
7d)
Concentration quenching
IDA/ID
IAD/IA
(IAD – IA)/ID
gFRET
r (nm)
KSV [Q]
[DA]/[D]0 or [DA]/[DA]max
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.00
2.43
3.86
5.29
6.71
8.14
9.57
11.00
12.43
13.86
15.29
0.000
0.054
0.108
0.162
0.216
0.270
0.324
0.378
0.432
0.486
0.540
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
>13.0
8.4
7.3
6.7
6.2
5.8
5.4
5.0
4.6
4.0
0.0
0.00
0.11
0.25
0.43
0.67
1.00
1.50
2.33
4.00
9.00
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
8e)
Multiple A’s
nA with r ¼ 6.7 nm
0
Not measured
Not measured
1.0
1.6
2.3
3.5
5.4
9.3
21.0
Not measured
The different results are visualized in Figure 5.7.
a) gFRET calculated with Equation 5.13 for donor quenching, Equation 5.15 for acceptor sensitization using eA/
eD ¼ 0.07, and Equation 5.17a for combined donor quenching and acceptor sensitization using WA/WD ¼ 0.54.
b) r calculated with Equation 5.14 for donor quenching, Equation 5.16 for acceptor sensitization using eD/eA ¼ 1/
0.07, and Equation 5.18 for combined donor quenching and acceptor sensitization using WA/WD ¼ 0.54.
c) Cannot be analyzed by acceptor sensitization.
d) [DA]/[D]0 ¼ 1 (IDA/ID) for D-quenching and [DA]/[DA]max ¼ (IAD/IA) 1)/(IAD/IA)max 1) for A-sensitization analysis.
e) nA calculated with Equation 5.24.
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
(b)
(c)
(d)
SV
(a)
r = 6.7 nm = constant
Figure 5.7 Different interpretations of one and
the same experiment resulting from the analysis
of the donor-quenching emission spectra in
Figure 5.6c taken from the calculated data from
Table 5.2. (a) Different FRET efficiencies due to
different D–A distances. (b) Static or dynamic
quenching with increasing quencher
concentration. (c) Increasing amount of D–A
FRET pairs at fixed D–A distance. (d) Increasing
amount of A’s per D at fixed D–A distance.
samples contain the same concentration of completely labeled single D–A
pairs with different D–A distances (e.g., change of structural confirmation
over time or due to changes in the environment, such as temperature or pH),
which decrease from measurement 1 to 11, as depicted in Figure 5.7a.
b) Concentration quenching: The D-quenching could be caused by any
deactivation process (including FRET), which can be described by the
Stern–Volmer equation:
ID
¼ 1 þ K SV ½Q ;
I DA
ð5:31Þ
where KSV is the Stern–Volmer constant, which is
K SV ¼ K S ¼
½DQ
½D ½Q
ð5:32Þ
in the case of static quenching and
K SV ¼ K D ¼ kq tD
ð5:33Þ
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126
in the case of dynamic quenching. In these equations, [Q], [D], and [DQ] are
the respective concentrations of the quencher, the donor, and the donor–
quencher complex, kq is the dynamic (or bimolecular) quenching constant,
and tD is the luminescence lifetime of D (in the absence of Q). Static or
dynamic quenching will lead to a linear quenching behavior (which is not the
case for combined static and dynamic quenching) as found for the experiment from Figure 5.6 (and shown in Figure 5.7b and Table 5.2, column 6). In
the case of FRET quenching, a possible scenario for which the Stern–Volmer
equation can be applied would be a FRET assay, for which increasing amounts
of an analyte (e.g., a biomarker) are titrated to a constant concentration of Dand A-labeled specific binding molecules (e.g., antibodies against the biomarker). This case will cause static quenching (because the D–A distance r is
fixed) due to addition of the analyte with concentration [Q]. As D and A are in
excess, each addition of an analyte will lead to the formation of a D–A pair
with the concentration [DA] ¼ [DQ] ¼ [Q] (assuming 100% binding efficiency). With [D] ¼ [D]0 [DA], where [D]0 is the initial concentration of
D, Equation 5.32 will become KSV ¼ KS ¼ ([D]0 [DA])1 and Equation 5.31
will become [DA]/[D]0 ¼ 1 (IDA/ID), which is presented in Figure 5.7c and
Table 5.2, column 7.
c) Multiple acceptors: In the case of experimental results without the spectra from
measurements 2, 3, and 11, another possible interpretation from Figure 5.6c
would be an increasing amount of A’s per D (nA from Equation 5.24) with a
fixed distance r (Figure 5.7d and Table 5.2, column 8). In the case for which r is
unknown, Equation 5.24 can be used with r as a free fit parameter (R0 and
gFRET are known from the measurements of Figure 5.5 and 5.6c) in order to
determine the D–A distance.
d) Environmental quenching: Cases (b) and (c) assume stable environmental conditions. If this is not the case and the environment (e.g., temperature, solvent, and
pH) changes during the experiment (over time or from sample to sample),
luminescencequenching[includingFRETduetodistancechangesasmentioned
in case (a)] might also be caused by these factors. Often such changes also lead to
deviations in the luminescence and/or absorption spectra (bathochromic or
redshift, hypsochromic or blueshift, or intensity changes of different luminescence bands from the same luminescent species). Thus, it is wise to also have a
careful look at the spectral features of the different measurements.
2) In addition to donor quenching, one can analyze the results in Figure 5.6d using
acceptor sensitization (Section 5.4.2.2). Analyzing the acceptor spectra has the
advantage that they can provide compelling evidence for FRET (or at least energy
transfer) because they show that A was excited via D, whereas donor quenching
could have other reasons than deactivation via the acceptor. As summarized in
Table 5.2, IAD/IA increases from 1 to 15.29, which can be explained by the same
reasons as for donor quenching and leads to the same results using different
equations for their calculation (cf. footnotes in Table 5.2). However, one should
keep in mind that the present example is an idealized theoretical FRET experiment and for most “real-world” experiments, a verification of the donor
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
IDA
(IAD-IA)
wavelength (nm)
Figure 5.8 (a) FRET quenching of D
(decreasing IDA) and FRET sensitization of A
(increasing IAD–IA, spectra without emission
from direct acceptor excitation) deconvoluted
from the spectra of Figure 5.6b (D in the
absence of A: black curve). (b) The negative
(b)
-slope = ΦA/ΦD
(IAD-IA) / ID
emission intensity (counts)
(a)
normalized emission intensity
quenching results by acceptor sensitization is necessary to draw reliable conclusions about FRET. In the case where D-quenching and A-sensitization provide
similar results using the FRET equations, other quenching effects can be
excluded. This is highly important for justifying results that are based on
FRET, for example, if distances are reported or analyte concentrations are
calculated by assuming that all donor quenching is caused by FRET. In our
example, the distances calculated for donor quenching can be confirmed by
finding similar results from acceptor sensitization analysis (Table 5.2, column 5).
Also, concentration quenching (Table 5.2, column 7) can be confirmed by finding
similar results from A-sensitization analysis using the D–A concentration
([DA]max) found for the maximum acceptor-sensitized emission intensity instead
of the initial donor concentration [D]0. Assuming a fixed distance r, the multiple
acceptors can also be confirmed by acceptor sensitization.
3) Instead of analyzing donor quenching and acceptor sensitization separately, they
can also be combined within Equations 5.17a and 5.18 for calculating FRET
parameters and distances (donor quenching and acceptor sensitization – Section
5.4.2.3). In this case, it is not necessary to know the emission intensity of the pure
donor (ID), but the intensity arising from direct excitation of A (IA) must be
subtracted from IAD and the luminescence quantum yields of D and A need to
be known (cf. Equation 5.17a). As summarized in Table 5.2, IDA decreases, while
(IAD IA) increases (columns 1 and 3, both normalized to ID), as already
discussed above for donor quenching and acceptor sensitization analysis.
Figure 5.8a shows the deconvoluted (from Figure 5.6b) emission intensity
spectra of simultaneous donor quenching and acceptor sensitization. Again,
the same results are found using different equations for their calculation
(cf. footnotes in Table 5.2). Changing Equation 5.17a can be used to calculate
luminescence quantum yields of D and A.
IDA/ID = 1-ηFRET
slope of FRET-sensitized acceptor emission
intensity as a function of FRET-quenched donor
emission intensity (both intensities normalized
to ID) gives the luminescence quantum yield
ratio of A and D.
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128
gFRET ¼
I AD I A
WA
) gFRET
I DA ¼ ðI AD I A Þð1 gFRET Þ
ðI AD IA Þ þ ðWA =WD ÞI DA
WD
) gFRET
WA
I DA
WA I AD I A WA WA IDA IAD I A
I DA ¼ ðI AD I A Þ
) gFRET
¼
)
¼
:
WD
ID
WD
ID
WD WD ID
ID
ð5:17bÞ
The negative slope or the intersection with the ordinate of (IAD IA)/ID
as a function of IDA/ID (Figure 5.8b) is the luminescence quantum yield
ratio of acceptor and donor (WA/WD), and therefore the calculation of
unknown D or A quantum yields becomes possible, in case one of them is
known.
Although all these different possibilities of FRET data analysis exist, many
studies use only donor intensity quenching in order to relate the experimental
data to FRET. This is often not correct, as many other processes (cf. Section 5.6)
can be the cause of donor quenching. The choice of donor quenching, acceptor
sensitization, or the combination of both strongly depends on the experimental
conditions and the required experimental accuracy. In general, it is more
precise to use all the different possibilities and to carefully deconvolve the
different emission spectra in order to avoid spectral overlap problems. However, for well-separated spectra, high emission intensities, and many data
points supporting the experimental interpretation, it can be sufficient to use
only donor quenching. Moreover, highly sensitive luminescence detection
applications make use of optical bandpass filters for spectral separation, which
means that the full spectral information is not available. In such cases, one
should ensure that D and A bandpass filters with minimal spectral overlap to A
and D are used or that the emission spectra are measured before the filterbased FRET measurement, such that this information can be combined with
the filter transmission spectra to achieve an adequate spectral correction.
Measuring emission spectra without an adequate quantum correction (correcting the wavelength-dependent detection efficiency of photodetectors such
as PMTs), autofluorescence from the sample medium, sample scattering and
reabsorption (inner filter effects), and low signal-to-noise ratios are common
sources of error that should be taken into account for FRET measurements.
Please keep in mind that the theoretical generic example presented here was
chosen to demonstrate the different possibilities of interpreting a FRET
experiment. Therefore, donor quenching, acceptor sensitization, and their
combination deliver exactly the same results for FRET calculations. As reality is
usually not so kind to adapt all energy transfer or luminescence quenching
systems to FRET theory, the different approaches leading to different results
will usually be quite helpful to find reasonable explanations for the experimental
data. As the large variety of different energetic excitation and relaxation processes
involved in FRETexperiments can lead to many paths of energy flow and therefore
many paths of interpretation, one should always consider a reasonable amount
of control experiments adapted to each individual FRET system of interest.
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
5.5.3.2 Time-Resolved FRET Measurements
Time-resolved luminescence spectroscopy can be divided into two technologies for
measuring luminescence decay times, namely, time-domain and frequency-domain
measurements [15,18]. Time-domain methods measure the time-dependent luminescence intensity of a sample following a short excitation pulse of light (usually in the
nanosecond range for lasers and up to some microseconds for flash lamps – preferably,
the excitation pulse is much shorter than the decay time of the sample). Frequencydomain methods use intensity-modulated (usually sinusoidal modulation) excitation
light (e.g., I ¼ Iav(ex) þ Ip(ex) cos vt). The modulation frequency ( f ¼ v/2p) is typically
in the same range as the reciprocal of the luminescence decay time of the sample (e.g.,
100 MHz ¼ 1/(10 ns)). The emitted light will follow this modulation frequency, but with
a time delay (e.g., I ¼ Iav(em) þ Ip(em) cos (vt w)), which is usually called phase shift
or phase angle (w). Moreover, the peak intensity (Ip(ex) and Ip(em) for excitation and
emission, respectively) will be lower and the average intensity (Iav(ex) and Iav(em)) can be
different. This is usually expressed in the modulation ratio M ¼ [Ip(em)/Iav(em)]/[Ip(ex)/
Iav(ex)]. Both methods (time-domain and frequency-domain) (cf. Figure 5.9) can be used
to determine single or multiple luminescence decay times (ti).
The mathematical description of a time-dependent luminescence decay (with i
decay times) is the luminescence intensity (I) as a function of time:
X
X
t
t
¼A
:
ð5:34Þ
I¼
Ai exp ai exp ti
ti
i
i
For the frequency domain, the phase shift (w) or the modulation ratio (M) can be
used for the determination of single or multiple decay times. The mathematical
relation between phase shift and decay times is
P
ðai vt2i Þ=ð1 þ v2 t2i Þ
w ¼ arctan Pi
:
ð5:35Þ
2 2
i ðai ti Þ=ð1 þ v ti Þ
(b) 1.0
0.8
0.75
intensity
intensity
(a) 1.00
0.50
0.25
Ip(em)
Ip(ex)
0.6
0.4
Iav(em)
Iav(ex)
0.2
φ
0.00
0
2
4
6
time t (ns)
8
10
Figure 5.9 Examples of time-domain (a) and
frequency-domain (b) measurements for the
determination of luminescence decay times.
Excitation is displayed in black [(a): usually
many pulses, for example, with 80 MHz
repetition rate or one pulse every 12.5 ns, are
12
0.0
0
10
20
30
time t (ns)
40
50
necessary to record a full decay curve; (b):
modulated intensity with 80 MHz modulation
frequency). Emission with a decay time of 2 ns
is displayed in gray [(a): intensity decay; (b):
modulated intensity with 80 MHz).
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130
(b)
1
phase shift φ (º)
or modulation ratio M (%)
luminescence intensity I
(a)
0.1
0
5
10
15
time t (ns)
20
Figure 5.10 (a) Luminescence intensity decay
curve resulting from a time-domain
measurement. (b) Phase shift (gray) and
modulation ratio (black) curves resulting from
frequency-domain measurement. For both
100
80
60
40
20
0
0.1
25
1
10
100
1000 10 000
frequency f (MHz)
results, the decay times are t1 ¼ 2 ns (with
a1 ¼ 0.7) and t2 ¼ 14 ns (with a2 ¼ 0.3). The
single lifetime components are shown in the
dash-dotted (2 ns) and dotted (14 ns) curves.
The mathematical relation between modulation ratio and decay times is
"P
M¼
2
i ðai vti Þ=ð1
#1=2
P
2
2 2 2
þ v2 t2i Þ þ
i ðai ti Þ=ð1 þ v ti Þ
:
P
2
i ai ti
ð5:36Þ
Equations 5.34–5.36 can be used within a least-square analysis, for which the
parameters ai and ti are varied until a best fit between the experimental data and the
mathematical fit values is achieved. Figure 5.10 shows typical curves for timedomain and frequency-domain data, which were generated for a double-exponential
luminescence decay using Equations 5.34–5.36.
No matter how the luminescence decay times for a FRET system are measured,
they can be used to determine FRET efficiencies and distances (in case R0 was
determined before). In most cases, donor quenching (Equations 5.13 and 5.14) is
used for decay time FRET analysis (for decay time analysis using photobleaching,
refer to Ref. [36]). FRET analysis of sensitized acceptor luminescence decays is
usually complicated because both the donor and the acceptor excited states are
involved in FRET. Therefore, the acceptor decay will be a combination of the FRETquenched donor excited-state lifetime (tDA) and the acceptor excited-state lifetime
(tA) [37]. The concentration of an excited acceptor ([A ]) after excitation of the donor
can be expressed as a differential equation:
d½A
¼ kFRET D ðkRA þ kNR
A Þ A ;
dt
j131
ð5:37Þ
where [D ] is the excited donor concentration and kRA and kNR
A are the radiative and
nonradiative decay rates of the acceptor. In this equation, kFRET ½D describes
the increase in the A excited-state population due to FRET from excited D and
ðkRA þ kNR
represents radiative and nonradiative deactivation of excited A.
A Þ½A
Solving Equation 5.37 and assuming the donor decay as single-exponential lead
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
to an excited-state acceptor concentration as a function of time (luminescence decay
function of excited-state acceptors) [18]:
½D kFRET
t
½D kFRET
t
1 0 1 exp A ¼ 1 0 1 þ ½A 0 exp tA
tDA
tDA tA
tDA tA
ð5:38aÞ
or
A
¼
½D 0 gFRET
þ ½A
1 ðtDA =tA Þ
0
½D 0 gFRET
t
t
exp ;
exp 1 ðtDA =tA Þ
tA
tDA
ð5:38bÞ
where [D ]0 and [A ]0 are the initial (at t ¼ 0) concentrations of excited D and A,
respectively, and tA is the luminescence decay time of A in the absence of D. As already
mentioned, these acceptor excited-state decay functions (representing the decay of A in
the presence of D with decay time tAD) are composed of the “pure” acceptor decay (first
term in Equation 5.38a or 5.38b) and the FRET-quenched donor decay (increase of the
acceptor luminescence with the time-component tDA represented by the negative
term in Equation 5.38a or 5.38b). Figure 5.11 shows the excited-state decay curves
(with decay time tAD) of FRET-sensitized A (in the presence of D) for different tA
values in comparison to decay curves of FRET-quenched D (in the presence of A with
decay time tDA) and pure D (in the absence of A with decay time tD). These curves were
calculated from Equation 5.38b for gFRET values of 50 and 95%, respectively, and
assuming no direct acceptor excitation ([A ]0 ¼ 0).
Figure 5.11 shows that the decay times tAD (or the slopes of the black curves) and
tDA (or the slope of the gray curves) are equal for tA tD (gray dotted curves for tD).
The higher the FRET efficiency, the larger the required difference between tA and tD
(for the case of 95% efficiency, Figure 5.11b, a value of tA ¼ 0.1tD already shows
(a)
Figure 5.11 Excited-state decay curves of A
with tA values of 0.001, 0.01, 0.1, 0.5, 1, 2, and 5
times tD, respectively – black curves from
bottom to top calculated with Equation 5.38b
for FRET efficiencies of gFRET ¼ 50% (a) and
(b)
gFRET ¼ 95% (b). Pure donor decays with decay
time tD (dotted gray curves) and FRETquenched donor decays with decay times tDA
(gray curves) are shown for comparison.
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132
clear differences in tAD and tDA). Figure 5.11 also visualizes that the FRET decay
curves for similar tA and tD values can become complicated as they show a rise time
at the beginning of the acceptor decay curves and significantly longer decays than for
tDA. The use of donors with long decay times (e.g., lanthanide complexes as treated
in Section 5.6) and acceptors with short decay times (e.g., organic dyes) allows the
replacement of tDA by tAD in Equations 5.13 and 5.14 and, therefore, a time-resolved
FRET analysis of quenched donor emission and sensitized acceptor emission. One
big advantage of the analysis within the “FRET-proof” acceptor channel is the
absence of pure donor emission (D in the absence of A) and therefore a lower
background signal (non-FRET signal).
5.5.3.3 Interpretation of Time-Resolved FRET Data
In this section, we will only treat donor quenching (acceptor-sensitized timeresolved analysis will be treated in the next section) and only decay time results
from time-domain measurements will be shown (frequency-domain measurements
will result in the same luminescence decay times and therefore lead to the same
FRET results). In the example of Figure 5.6, the luminescence intensity of the donor
is quenched from 100 to 0% of the initial (D in the absence of A) donor intensity (in
steps of 10%). Assuming a monoexponential luminescence decay function (I ¼ A
exp(t/t) with an arbitrary chosen luminescence decay time of t ¼ 5 ns) of the
unquenched donor (D in the absence of A), there are several possible scenarios of
time-dependant donor (D in the presence of A) luminescence intensity decays,
which can lead to the steady-state spectra presented in Figure 5.6. The amplitudes
(AD and ADA) and decay times (tD and tDA) of the luminescence decays can
provide useful information about the investigated FRET system concerning static
(concentration-dependent) and dynamic (distance-dependent) quenching or a mixture of both. This information cannot be found by analyzing only the steady-state
spectra. A comparison of steady-state and time-resolved quenching in the so-called
Stern–Volmer plots (Figure 5.12) can give good evidence of the quenching situation.
In the case where the ratio of initial to quenched steady-state intensity (I0/I) and the
ratio of initial to quenched decay time (t0/t) increase equally over quencher
(a)
(b)
(c)
I0 /I
higher
temperature
1
[Q]
τ0 /τ
τ0 /τ
τ0 /τ = I0/I
1
τ0 /τ or I0/I
I0 /I
τ0 /τ or I0/I
τ0 /τ or I0/I
higher
temperature
1
[Q]
[Q]
Figure 5.12 Stern–Vomler plots of dynamic (a), static (b), and combined dynamic and static (c)
quenching. The influence of temperature on dynamic and static quenching is also indicated within
the graphs.
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
(b)
normalized luminescence intensity
(a)
(c)
(d)
measurement
Figure 5.13 (a and b) [part (b) intensity
normalized with logarithmic intensity scale]
Dynamic luminescence quenching represented
by decay curves (D in the presence of A – gray)
with constant amplitudes and decreasing decay
times compared to the unquenched D curve
(black). (c) Unchanged amplitudes (circles) and
decreasing decay times (squares) as a function
of intensity quenching. (d) The purely dynamic
quenching behavior is confirmed by a Stern–
Volmer plot, for which both the intensity ratio
(triangles) and the decay time ratio (squares)
increase equally from measurement to
measurement.
concentration [Q], the quenching is purely dynamic. If the intensity ratio increases
over quencher concentration and the decay time ratio is unaffected, the quenching is
purely static. If both the intensity ratio and the decay time ratio increase over
quencher concentration but the intensity ratio increases stronger, the quenching is a
mixture of dynamic and static deactivation.
Different from the steady-state results, where one set of spectra (experimental data
in Table 5.2) was used to provide different possible interpretations, we will discuss
here different sets of possible decay curves, which can confirm or disprove the
different possible interpretations from the steady-state measurements. Thus, the
different time-resolved scenarios (Figures 5.13–5.16 and Tables 5.3–5.5) will be
discussed in relation to the steady-state experimental data (spectra from Figure 5.6).
1) Distance (dynamic quenching)
As already mentioned in Section 5.5.3.1, increased quenching of D can be
explained by decreased D–A distances. If the measured samples lead to the spectra
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134
(b)
(c)
(d)
normalized luminescence intensity
(a)
measurement
Figure 5.14 (a and b) [part (b) intensity
normalized with logarithmic intensity scale]
Static luminescence quenching represented by
decay curves (D in the presence of A – gray)
with constant decay times and decreasing
amplitudes compared to the unquenched D
curve (black). (c) Decreasing amplitudes
(circles) and unchanged decay times (squares)
as a function of intensity quenching. (d) The
purely static quenching behavior is confirmed
by a Stern–Volmer plot, for which the intensity
ratio (triangles) increases, whereas the decay
time ratio (squares) is unchanged.
in Figure 5.6c (steady-state measurements) in combination with the decay curves
from Figure 5.13, the FRET quenching was most probably caused by decreasing
D–A distances (e.g., change of structural confirmation over time or due to changes
in the environment, such as temperature or pH), as depicted in Figure 5.7a. Within
the decay time functions (Equation 5.34), the amplitudes ADA (amplitudes for D in
the presence of A) stay at a constant value (ADA/AD ¼ 1), whereas the decay times
tDA decrease (tDA/tD decreases from 1 to 0 in steps of 0.1), which is well illustrated
by the decreasing slopes in the logarithmic plot. The Stern–Volmer plot (for which
the quencher concentration was replaced by the measurement number – in case
concentrations are known, they can be used instead) shows an equal increase of
intensity and decay time ratio, which confirms the purely dynamic quenching
behavior. The FRET efficiencies gFRET (Equation 5.13) and D–A distances (Equation 5.14) calculated by using luminescence intensities (Table 5.2, columns 4 and 5)
are confirmed by the values calculated by using luminescence decay times
(Table 5.3, columns 4 and 5).
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
(b)
normalized luminescence intensity
(a)
(c)
(d)
measurement
Figure 5.15 (a and b) [part (b) intensity
normalized with logarithmic intensity scale]
Combined dynamic and static luminescence
quenching represented by decay curves (D in the
presence of A – gray) with changing decay times
and amplitudes compared to the unquenched D
curve (black). (c) Changing (overall decreasing
tendency) amplitudes (circles) and changing
(overall decreasing tendency) decay times
(squares) as a function of intensity quenching.
(d) The combined dynamic and static quenching
behavior is confirmed by a Stern–Volmer plot,
for which the intensity ratio (triangles) increases
stronger than the decay time ratio (squares).
2) Concentration or environmental conditions (static quenching)
If the steady-state spectra from Figure 5.6c are accompanied by the decay
curves from Figure 5.14, the FRET quenching was most probably caused by
increasing concentrations of D–A pairs described by Equation 5.32 (with A being
the quencher Q) or a change in environmental conditions (e.g., temperature,
solvent, and pH). Within the decay curves, the amplitudes ADA decrease (ADA/AD
decreases from 1 to 0 in steps of 0.1), whereas the decay times tDA stay at a
constant value (tDA/tD ¼ 1), which becomes quite obvious in the logarithmic plot
with all decay curves showing the same slope. The Stern–Volmer plot shows an
increase of intensity ratio in combination with a constant decay time ratio, which
confirms the purely static quenching behavior. In the case of FRET quenching, a
possible scenario would be a FRET assay, for which increasing amounts of an
analyte (e.g., a biomarker) are titrated to a constant concentration of D- and Alabeled specific binding molecules (e.g., antibodies against the biomarker).
Although FRET is a dynamic quenching process, this case will cause static
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136
Table 5.3 Data resulting from purely dynamic or purely static D-quenching (Figures 5.13 and 5.14).
0
1
2
3
4a)
5b)
6
Measurement Overall quenching Distance (dynamic quenching)
IDA/ID
1
2
3
4
5
6
7
8
9
10
11
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
7
8c)
Concentration (static
quenching)
t DA/t D ADA/AD gFRET r (nm) t DA/t D ADA/AD [DA]/[D]0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
>13.0
8.4
7.3
6.7
6.2
5.8
5.4
5.0
4.6
4.0
0.0
a) gFRET calculated with Equation 5.13.
b) r calculated with Equation 5.14.
c) [DA]/[D] 0 ¼ 1 (I DA/I D) ¼ 1 (A DA tDA/A D tD) ¼ 1 (A DA/A D )
measurements.
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
because
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
tDA/tD ¼ 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
for
all
Table 5.4 Data resulting from a combination of dynamic and static D-quenching (Figure 5.15).
0
1
Measurement
1
2
3
4
5
6
7
8
9
10
11
3a)
2
4
5b)
Dynamic and static quenching
t DA/tD
gFRET
r (nm)
ADA/AD
[DA]/[D]0
1.0
0.989
0.952
0.921
0.968
0.685
0.784
0.476
0.357
0.256
0
0.0
0.011
0.048
0.079
0.032
0.315
0.216
0.524
0.643
0.744
1.0
>13.0
12
9.6
8.7
10
6.6
7.2
5.7
5.3
4.9
0
1.0
0.910
0.840
0.760
0.620
0.730
0.510
0.630
0.560
0.390
0
0.000
0.090
0.160
0.240
0.380
0.270
0.490
0.370
0.440
0.610
1.000
a) r calculated with Equation 5.14.
b) [DA]/[D]0 ¼ 1 (ADA/AD).
j137
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5.5 FRET: The Experiment
j 5 How to Apply FRET: From Experimental Design to Data Analysis
quenching (because the D–A distance r is fixed). The D–A pair concentration
([DA]/[D0]) increases in steps of 10% (Table 5.3, column 8).
3) Multiple acceptors (dynamic quenching)
The steady-state spectra from Figure 5.6c and the decay times from Figure 5.13
(in case measurements 2, 3, and 11 are not taken into account) can also be caused
by an increasing amount of A’s per D (nA from Equation 5.24) with a fixed
distance r (Figure 5.7d and Table 5.2, column 8). Although the distance between
D and the multiple A’s is fixed, this configuration leads to dynamic quenching
because the FRET efficiency increases with an increasing number of A’s per D.
This is not the case for static quenching of an increasing number of single D–A
pairs (same FRET efficiency), as discussed in the previous paragraph. In the case
for which r is unknown, Equation 5.24 can be used with r as a free fit parameter
(R0 and gFRET are known from the measurements of Figure 5.5 and 5.6c) in order
to determine the D–A distance. A very nice study of multiple dye acceptors per
semiconductor quantum dots was performed by Clapp et al.. The authors used
steady-state donor quenching, steady-state acceptor sensitization, and timeresolved donor quenching to find the correct interpretation of their FRET
system [33].
4) Distance and concentration (dynamic and static quenching)
If the steady-state and time-resolved measurements lead to the spectra from
Figure 5.6c and the decay curves from Figure 5.15, the luminescence deactivation
was caused by a combination of dynamic (e.g., decreasing D–A distances) and
static quenching (e.g., increasing concentrations of D–A pairs or a change in
environmental conditions). Within the decay curves, the amplitudes ADA as well
as the decay times tDA change. This change usually has a decreasing tendency for
both ADA and tDA (luminescence is quenched), but as amplitude and decay time
can compensate for each other, an interpretation of the different decay curves,
amplitudes, and decay times might not be as facile as for the pure dynamic or
static quenching cases. The Stern–Volmer plot shows a stronger increase of
intensity ratio compared to the decay time ratio, which confirms the combination
of dynamic and static quenching. In the case of FRET quenching, one of the most
important aspects of the time-resolved measurements is the possibility of
calculating distances (using the decay times and Equation 5.14). This would
not be possible for steady-state measurements because the dynamic (decay times)
and the static (amplitudes) quenching parts cannot be distinguished.
5) Multiexponential donor decays and multiple distances
FRET systems can be much more complicated than within the simulated
examples mentioned above. The first complication can already be the pure
donor (D in the absence of A) luminescence decay because it must not
necessarily be monoexponential. In an ensemble measurement, the multiple
donor molecules can take different conformations (e.g., structural or chemical
configurations), which might lead to different decay times for each species and
thus an overall multiexponential luminescence decay function. This means
that each of these multiple decay times (tDi) or an average decay time (ktDi)
must be taken as the pure donor decay time. Averaging is performed using
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138
amplitude-averaged decay times, because FRET is a dynamic quenching
process and a detected signal at a particular time interval is proportional to
the excited-state population (and not to the integrated intensity, for which the
intensity-averaged decay time would be used) [13,38]. Taking the multiexponential luminescence decay function from Equation 5.34 leads to the following
amplitude-averaged decay time:
P
A i ti X
hti ¼ P
¼
ai ti :
ð5:39Þ
Ai
Another aspect making FRET analysis more complicated is the possibility of
having multiple D–A distances within a D–A pair ensemble. This means that
(apart from the multiexponential tD values) the quenched donor decay times
(tDAi) will be multiexponential and depending on the number of different
distances (and thus decay times), the time-resolved analysis can become complicated and high signal-to-noise ratios are necessary to recover the different
amplitudes and decay times.
As if these two difficulties were not enough, complicated FRET systems can
also be composed of dynamic and static quenching processes, which means that
a careful distinction of amplitudes and decay times (which can compensate for
each other within a least-square fit) is necessary for a correct interpretation of the
experimental data. In Section 5.6, we will discuss such a FRET system with
multiexponential donor decay, multiple distances, and mixed dynamic and static
quenching. Moreover, this system uses semiconductor quantum dots as acceptors, which poses another problem, because these nanoparticles are excited at any
wavelength below their emission wavelength. Steady-state measurements with
such acceptors are useless in most cases because the acceptor will be excited very
efficiently (more efficiently than the donor) and the interpretation of quenching
and sensitization becomes very difficult. However, the use of lanthanide-based
donors with very long excited-state lifetimes (up to several milliseconds) allows
the time-resolved analysis of acceptor sensitization due to the large difference in
donor and acceptor excited-state lifetimes (cf. Figure 5.11).
5.6
FRET beyond F€
orster
In more than six decades that have passed since F€
orster’s paper “Energiewanderung
und Fluoreszenz” [22] from 1946, the FRET toolbox has been filled up with many
new possible donor and acceptor fluorophores, including a multiplicity of organic
dyes, metal-based chelates, fluorescent proteins, and nanoparticles (cf. Chapters 6
and 14). Within all the FRET applications that have been developed, one can find
many “nonclassical” approaches, such as FRET from lanthanide donors with
multiplet–multiplet transitions (quintet–septet in the case of Eu and Tb) and
multiple transition dipole moments, FRET with quantum dot nanoparticles (with
diameters of up to 10 nm), which do not present an ideal point-dipole system, and
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5.6 FRET beyond F€orster
j 5 How to Apply FRET: From Experimental Design to Data Analysis
FRET without the use of donor excitation by light [bioluminescence resonance
energy transfer (BRET) and chemiluminescence resonance energy transfer (CRET)]
or energy transfer to metal nanoparticles, which has been related to FRET, nanosurface energy transfer (NSET), dipole to metal particle energy transfer (DMPET), or
nanoparticle-induced lifetime modification (NPILM). Moreover, there are other
energy transfer mechanisms, such as plasmonic coupling, charge transfer, or singlet
oxygen transfer, which can enlarge the distance range of two interacting species
from about 1 to 200 nm. In this section we will discuss such systems, which go
beyond the classical treatment of Theodor F€
orster.
5.6.1
Time-Resolved FRET with Lanthanide-Based Donors
The many advantages of lanthanide-based donors have been known for more than
two decades, and especially Paul Selvin should be mentioned here for a lot of
pioneering work in this area [9,39–45]. Probably the most important property of
lanthanide-based donors for FRET is their long luminescence decay time reaching
up to several milliseconds for some supramolecular lanthanide complexes (e.g.,
chelates or cryptates) [46–52]. This means that the excited-state lifetimes of most
lanthanide-based donors are several orders of magnitude larger than those of any
other acceptor. Thus, the same decay time analysis can be applied for D-quenching
and A-sensitization (cf. Figure 5.11). Moreover, the sensitized acceptor emission can
be measured against a very low background. This can be achieved by using an
acceptor that emits at a wavelength region void of lanthanide emission (cf.
Figure 5.16 for Tb as donor) for minimizing the background of the donor. Many
different acceptors (e.g., fluorescent proteins, organic dyes, and quantum dots) are
available for the best choice of emission wavelength [1,53,54]. In order to suppress
the acceptor background (directly excited acceptor emission), which is usually in the
nanosecond time range, one can use pulsed excitation and gate the detector off for a
Figure 5.16 Typical emission spectrum of a Tb chelate. The arrows indicate wavelength areas in
which an acceptor can be measured without Tb background emission.
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140
short period of time (i.e., several microseconds). This will lead to a pure FRET signal
after the detector has been gated on again because almost any photon that will be
detected then must arise from an excitation via the donor – the acceptor detection
channel becomes a “FRET-proof” channel. This also means that the sensitized
acceptor signal is insensitive to concentration effects and incomplete labeling and
binding because only those species containing both D and A can contribute to the
FRET signal (pure D and pure A signals are completely suppressed).
Another advantage is the possibility of large overlap integrals with different
acceptors due to the multiple emission bands of lanthanides over a wide spectral
range. F€orster distances of 9 nm for an Eu chelate donor and an APC acceptor [55]
and up to 11 nm for a Tb chelate donor and quantum dot acceptors [53] have been
demonstrated. Such large R0 values can significantly increase the FRET distance
range up to about 20 nm (or larger in case of very sensitive detection).
One very comfortable aspect of Eu- and Tb-based (most often used lanthanides for
FRET applications) donors is their unpolarized emission. Due to their multiple
transition dipole moments, they act as randomized donors (even in the absence of
fast isotropic rotation) and the orientation factor k2 is limited to values between 1/3
and 4/3 even if the acceptor has a fixed orientation (cf. averaging conditions for k2 in
Section 5.3). The following example (lanthanide to quantum dot FRET) will illustrate
all the different aspects (including donor quenching, acceptor sensitization, and
dynamic and static quenching) of a sophisticated time-resolved FRET analysis using
lanthanide-based donors.
5.6.1.1 Terbium to Quantum Dot FRET Using Time-Resolved Donor Quenching and
Acceptor Sensitization Analysis
In a recent example, we performed a time-resolved analysis of one Tb chelate donor
and different quantum dot acceptors in a FRET system, for which Tb and QD are
brought in proximity via biotin–streptavidin binding [56]. In this configuration,
several Tb donors can attach to the surface of QDs (consisting of the central
semiconductor QD and a polymer-based coating for biocompatibility). The luminescence decay of the Tb donor is double-exponential with an amplitude-averaged
decay time of ktDi ¼ 2.3 ms and a luminescence quantum yield of 67%. The QD (we
will only discuss one QD here) has an emission wavelength maximum of 655 nm, a
multiexponential decay in the nanosecond time range (about 30 ns average decay
time), and a luminescence quantum yield of 7%. Due to the random labeling of the
Tb donor to the streptavidin protein and the ellipsoidal shape of the QD, the FRET
system consists of a D–A distance distribution. The different samples contain a
constant concentration of Tb donors (0.2 nM) and increasing concentrations of QD
acceptors (0 0.6 nM). Due to the varying ratios of Tb/QD in the different samples,
different concentrations of pure Tb donors and QD acceptors are present in the
FRET systems. The pure Tb donors (at different concentrations) result in varying
intensities (amplitudes) of Tb background emission at a fixed decay time (ktDi),
which leads to different static contributions with significant intensities in the donor
detection channel (optical bandpass filter: 494 20 nm) and minor intensities in the
acceptor detection channel (optical bandpass filter: 660 13 nm). In summary, we
have investigated a FRET system with a multiexponentially decaying donor, multiple
j141
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5.6 FRET beyond F€orster
j 5 How to Apply FRET: From Experimental Design to Data Analysis
(a)
(c)
(b)
(d)
0.1–0.9 ms
Figure 5.17 Time-resolved Tb donor
quenching (a and b) and QD acceptor
sensitization (c and d). (a) Luminescence decay
curves detected within the Tb donor channel for
increasing QD acceptor concentrations: 0 nM
(gray), 0.06, 0.1, and 0.15 nM (black from top to
bottom). The white lines within the curves are
the fitted curves. (b) Time-gated (0.1–0.9 ms)
luminescence intensities detected within
the Tb donor channel for increasing QD
concentrations. (c) Luminescence decay
0.1–0.9 ms
curves detected within the QD acceptor
channel for increasing QD acceptor
concentrations: 0 nM (gray), 0.06, 0.1, and
0.15 nM (black from bottom to top). The
white lines within the curves are the fitted
curves. (d) Time-gated (0.1–0.9 ms)
luminescence intensities detected within the
QD acceptor channel for increasing QD
concentrations. (Adapted with permission
from Ref. [56]. Copyright 2013, American
Chemical Society.)
D–A distances, and dynamic (distances) as well as static (free Tb concentration)
quenching contributions using time-resolved detection of donor quenching and
acceptor sensitization.
The increasing QD acceptor concentration leads to Tb D-quenching and QD Asensitization, as shown in Figure 5.17 in the intensity decay curves as well as in the
time-gated intensities. No background correction was performed for these graphs.
The Tb emission cross talk to the QD acceptor detection channel can be seen in the
lowest decay curve in Figure 5.17c and the time-gated intensity offset in
Figure 5.17d. Due to the relatively low luminescence quantum yield of the QDs,
the sensitized QD emission is relatively weak, but distinguishes significantly from
the Tb background signal. The appearance of new short decay times due to FRET
becomes clearly visible within both the Tb donor and the QD acceptor decay curves.
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142
The FRET-quenched donor curves can be conveniently fitted with triple-exponential decay functions (pure D was fitted with a double-exponential), whereas the
FRET-sensitized acceptor curves require a quadruple-exponential fit function. Due
to strong background fluorescence in the very short time range (strong saturated
signals in the first 10–50 ms mainly due to sample autofluorescence and direct QD
excitation) and the very low signal intensities for the acceptor channel in the very
long time range (weak signal due to the Tb cross talk within the QD acceptor
channel), the time ranges for the fits were chosen differently for D (0.02–8 ms) and A
(0.05–4 ms). In most software tools for least-square fitting of exponential luminescence decays, such fits are called “tail fits,” which means that the fit starts at a
different time t0 for D (t0 ¼ 0.02 ms) and A (t0 ¼ 0.05 ms). However, the complete
luminescence decays of A and D start immediately after the excitation at 0 ms (the t0
values for the fits were chosen differently to improve the fit quality). Although such
tail fits do not change the different single decay times, the single amplitudes (Ai-FIT)
must be corrected (from the t0 fit values to the correct start of the luminescence
decay at 0 ms) to yield the correct amplitudes (Ai) of the complete decay function:
tt t t
0
0
¼ Ai exp ) Ai ¼ AiFIT exp
:
I ¼ AiFIT exp t
t
t
ð5:40Þ
This is especially important when the amplitudes are necessary for the interpretation of the results (e.g., calculation of amplitude-averaged decay times or molecular fractions). For all fits of FRET-quenched and FRET-sensitized decay curves, the
Tb donor decay time was a fixed value. The fitted curves are presented in Figure 5.17
and all fit results are presented in Table 5.5 for the Tb donor detection channel and in
Table 5.6 for the QD acceptor detection channel.
The triple-exponential FRET-quenched Tb donor decay curves were fitted for the
amplitude fractions aDA 1, aDA 2, and aDA 0 and the decay times tDA1, tDA2, and
tDA0, for which the third decay time component was fixed to tDA0 ¼ tD2 [the pure Tb
donor has two decay times of tD1 ¼ (0.56 0.06) ms and tD2 ¼ (2.56 0.5) ms
leading to an amplitude-averaged decay time of ktDi ¼ (2.27 0.5) ms] (cf. Tables 5.5
and 5.6) in order to take into account the emission of unquenched donors. For the
calculation of the average donor decay time in the presence of the acceptor htDA i,
only the first two amplitudes and decay times were used (as the third component
represents unquenched donors). Therefore, the amplitude fractions must be
redefined for these two decay times tDA1 and tDA2:
aDA1 ¼
aDA 1
aDA 1 þ aDA 2
and aDA2 ¼
aDA 2
:
aDA 1 þ aDA 2
ð5:41Þ
As the unquenched donor possesses two decay time components (tD1 and tD2),
htDA i must be corrected for the shorter time component (tD1). As the value of tD1
falls within the time range of the FRET-quenched decay times, the use of an
additional exponential (with fixed tD1) for the fit procedure leads to inconsistent fit
results. Therefore, a correction factor zD (the fraction of unquenched donors in the
short time components) can be applied. zD is determined by comparing the
j143
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5.6 FRET beyond F€orster
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j 5 How to Apply FRET: From Experimental Design to Data Analysis
amplitude fractions of tD2 and tDA0 (tDA0 ¼ tD2) multiplied by the amplitude
fraction aD1:
zD ¼ aD1 ðaDA 0 =aD2 Þ:
ð5:42Þ
The average FRET-quenched decay time is then (with aDA1 þ aDA2 ¼ 1)
htDA i ¼
aDA1 tDA1 þ aDA2 tDA2 zD ðaDA1 þ aDA2 ÞtD1 aDA1 tDA1 þ aDA2 tDA2 zD tD1
¼
aDA1 þ aDA2 zD ðaDA1 þ aDA2 Þ
1 zD
ð5:43Þ
and the average FRET efficiency hgFRET i is calculated by Equation 5.13 using the
average decay times htDA i and htD i.
The quadruple-exponential FRET-sensitized QD acceptor decay curves were
fitted for the amplitude fractions aAD 1, aAD 2, aAD 3, and aAD 0 and the decay
times tAD1, tAD2, tAD3, and tAD0, for which the fourth decay time component was
fixed to tAD0 ¼ tD2 in order to take into account the emission of unquenched
donors, which is much less intense compared to the donor channel, but still
present due to spectral cross talk of the Tb emission in the QD acceptor detection
channel. The correction factor zA (the fraction of unquenched donors in the short
time components) is almost negligible, but is still taken into account for a correct
treatment:
zA ¼ aD1 ðaAD 0 =aD2 Þ:
ð5:44Þ
In order to calculate the average FRET decay time htAD i, only the amplitudes and
lifetimes with i ¼ 1–3 are taken into account (i ¼ 0 represents the unquenched donor
emission). Moreover, the amplitudes aAD i must be corrected by the FRET rates
1
(combination of Equations 5.8b and 5.13) to take into account
kFRETi ¼ t1
ADi htD i
the FRET efficiency-dependent excitation of the acceptors. The corrected amplitude
fractions are (for i ¼ 1–3)
aADi ¼
ðaAD
ðaAD i =kFRETi Þ
:
1 =kFRET1 Þ þ ðaAD 2 =kFRET2 Þ þ ðaAD 3 =kFRET3 Þ
ð5:45Þ
The average FRET decay time is then calculated by
htAD i ¼
aAD1 tAD1 þ aAD2 tAD2 þ aAD3 tAD3 zA tD1
1 zA
ð5:46Þ
and the average FRET efficiency hgFRET i is calculated by Equation 5.13 using the
average decay times htAD i (instead of tDA) and htD i.
For each FRET decay time (from the donor and the acceptor fits), a specific D–A
distance r can be calculated using Equation 5.14. The fractions of FRET pairs found
at the different distances corresponding to tDAi and tADi are given by the amplitude
fractions of these decay times.
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146
5.6.2
BRET and CRET
The discovery of bioluminescence (of bacteria) [57–59] and chemiluminescence (of
organic compounds) [60,61] dates back to the nineteenth century. For both phenomena, luminescence is created by a chemical reaction (as excitation source) inside
(bioluminescence) or outside (chemiluminescence) a living organism. If the chemically excited molecules are used as energy donors in combination with a suitable
acceptor inside a FRET system, the energy transfer is called bioluminescence resonance energy transfer and chemiluminescence resonance energy transfer, respectively. As only the donor excitation is different from FRET and the energy transfer
mechanism is the same, the FRET theory (r6 distance dependence, etc.) can be
applied for BRET and CRET. The first investigations of BRET and CRET date back to
approximately half a century ago [62–64], but BRET and CRET applications have
experienced a recent renaissance, especially due to novel FRET acceptors such as
fluorescent proteins and nanoparticles [65–67]. Most BRET applications use luciferases (e.g., Renilla luciferase “Rluc” or Firefly luciferase “Fluc”), which catalyze the
oxidation of their substrates (e.g., coelenterazine for Rluc or luciferin for Fluc), to
produce emission in the blue to green spectral range (emission peaks of about 480 nm
for coelenterazine and 570 nm for luciferin) for acting as BRET donors. In CRET,
mainly luminol derivatives are used as donors. Luminol oxidation is a nonenzymatic
reaction with much lower efficiency than the bioluminescence reactions [68]. Both
BRETand CRETcan be used with different acceptors such as organic dyes, fluorescent
proteins, or quantum dots. Figure 5.18 shows two recent examples of BRETand CRET.
The BRETsystem presents hybrid molecules consisting of a firefly luciferin donor and
different organic dye acceptors [69]. This approach allowed the development of
luciferins emitting in the near-infrared, which is an important wavelength range
because of deeper tissue penetration compared to UV or visible light. Moreover, these
novel NIR luciferins did not require any ex vivo luciferase manipulation. Although the
brightness of the BRET luminescence was very low, the authors could show NIR
luminescence in live cells and living mice using luciferase-expressing cells. The CRET
system is embedded in a DNA machine [70], for which a nucleic acid scaffold (1) is
hybridized with three DNA footholds. The first foothold is labeled with a FAM dye (2)
or a semiconductor quantum dot (3). The second foothold (4) is initially free and the
third foothold (5) is hybridized to a nucleic acid strand (6) that acts as DNA walker and
contains a hemin/G-quadruplex DNAzyme sequence (caged in the duplex structure
with the third foothold). Addition of a fuel strand (7) leads to strand displacement of the
walker (6) by the formation of a more stable 7/5 duplex and the hybridization of 6
overhang to the second foothold (4). In this configuration, 6 can form a hemin/Gquadruplex DNAzyme, which catalyzes the generation of chemiluminescence in the
presence of luminol and H2O2. The activated luminol is acting as a CRETdonor for the
FAM dye (2) or quantum dot (3), which then produces its own luminescence. Notably,
this process is completely reversible by the addition of an antifuel strand (8), leading to
a strand replacement of 7 to form a stable 7/8 duplex and the reverse walking step of 6
to 5, which switches the chemiluminescence (and the CRET) back to “off.”
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5.6 FRET beyond F€orster
j 5 How to Apply FRET: From Experimental Design to Data Analysis
Figure 5.18 Recent examples of BRET (top)
and CRET (bottom) systems. (a) Emission
spectra of the pure donor aminoluciferin (AL)
and the acceptor–donor complexes Cy5-AL,
SiR700-AL, and Cy7-AL, which give access to the
NIR wavelength range. (b) Detection of BRET
from AL to Cy7 in luciferase-expressing cells
injected to mice. In contrast to the BRET
emission of Cy7-AL (bottom), the pure AL
sample (top) does not show any Cy7
luminescence. (c) Creation of CRET from
activated luminol to a FAM dye or a quantum
dot (on 2 and 3, respectively) by switchable
hemin/G-quadruplex formation. The DNA
machine is switched “ON” by 7, which leads to
a walkover of 6 to 4 and the generation of CRET
followed by light emission of FAM or QD.
Addition of 8 switches the machine back to
“OFF” because of a stable formation of a 7/8
duplex and the reverse walk of 6 to 5, causing
the extinction of CRET. (d) Luminol
chemiluminescence (large peak around
420 nm) and CRET-sensitized FAM
luminescence (small peak around 518 nm). The
inset shows the switchable CRET signals of the
DNA walker system. (e) Luminol
chemiluminescence (peak around 420 nm) and
CRET-sensitized QD luminescence (peak
around 615 nm). The inset shows the
switchable CRET signals of the DNA walker
system. (Parts (a) and (b) reprinted with
permission from Ref. [69]. Copyright 2013,
Wiley-VCH Verlag GmbH. Parts (c–e) reprinted
with permission from Ref. [70]. Copyright 2012,
American Chemical Society.)
5.6.3
Energy Transfer to Metal Nanoparticles (FRET, NSET, DMPET, NPILM, etc.)
The good news about distance-dependent energy transfer to metal (mainly Au and in
some cases Ag is used) nanoparticles or nanoclusters is that it works very efficiently.
However, different mechanisms have been proposed to be responsible for the
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148
distance dependence, which has been investigated in theory [71–76] and in practice
for different energy donors such as organic dyes [77–84], semiconductor quantum
dots [85–90], or fluorescent proteins [91]. Among all these different systems,
different mechanisms have been proposed to be responsible for the energy transfer
and a general model for energy transfer to metal nanoparticles does not exist. The
two most important aspects for influencing the distance dependence are the donor–
acceptor distance and the nanoparticle size. At small distances (separation between
donor and acceptor is smaller than the size of the donor and/or the acceptor),
nonradiative energy transfer is proposed to be the main cause of quenching;
whereas at larger distances, radiative energy transfer will play a major role. One
of the main ideas for short distances is that the point dipole approximation is not
valid anymore leading to a deviation in the FRET distance dependence by overestimating the FRET rate. One can start from a generalization of Equation 5.7 for
resonance energy transfer (RET):
n
D0
kRET ¼ t1
;
ð5:47Þ
D
d
where D0 is the donor–acceptor distance for 50% energy transfer efficiency (R0 in
FRET) and d is the donor–acceptor separation distance (r in FRET). The main
difference between the RET theories can be found in the exponent n, which is n ¼ 6
for FRET. Agreement of the FRET theory with experimental data was shown for Au
nanoparticles with diameters of 1.4 nm [85], 5 nm [89], and 15 and 80 nm [87], all
using quantum dots as donors.
The DMPET model of Carminati et al. [72] takes into account the distance
dependence of radiative (mainly n ¼ 3 with a n ¼ 6 contribution at plasmon resonance) and nonradiative (n ¼ 6) decay rates, which leads to some additional
correction terms compared to FRET [88]. Moreover, nonradiative decay is strongly
enhanced, when the donor radiates at the plasmon resonance wavelength of the
nanoparticle [72]. Moroz reanalyzed Carminati’s DMPET model of a 10 nm diameter
Ag nanoparticle and pointed out that there is a significant contribution (between 50
and 101% of the total value) of higher order multipoles to nonradiative rates even at
5 nm donor–acceptor distance [75]. This theoretical model provided very good
agreement with luminescence decay time quenching of quantum dots by Au
nanoparticles of 10, 15, and 20 nm diameter positioned at distances of about 17,
15, and 13 nm from the quantum dots using DNA origami [86].
The NSET model proposed by Strouse and coworkers [79,80,82–84] uses a d4
distance dependence (n ¼ 4), which significantly increases (about twofold) the
distance range of FRET. They proposed the following NSET transfer rate:
kNSET ¼ 0:225
c3
v2D vF kF d4
WD
;
tD
ð5:48Þ
where c is the speed of light, WD is the donor quantum yield, vD is the angular
frequency (v ¼ 2pcl1) for the donor, vF is the angular frequency for bulk gold, and kF
is the Fermi vector for bulk gold. NSET has mainly been found to be in good agreement
with experimental data (using organic dyes and quantum dots as donors) if the
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5.6 FRET beyond F€orster
j 5 How to Apply FRET: From Experimental Design to Data Analysis
Figure 5.19 (a) Distance dependence of the
quenching efficiency for different sizes of Au
nanoparticles. The 8 nm Au nanoparticle was in
good agreement with NSET theory, whereas the
other two were attributed to radiative energy
transfer and could not be fitted with FRET,
NSET, or DMPET. (b) Increase of the 50%
energy transfer efficiency value (R0) with the
size of gold nanoparticle. (Reprinted with
permission from Ref. [78]. Copyright 2009,
Wiley-VCH Verlag GmbH.)
nanoparticles are of small size (below about 3 nm diameter) and thus do not have any
plasmon bands [79,80,82,84,87,88]. Nevertheless, also larger Au nanoparticles of up to
18 nm diameters showed experimental NSET behavior [77,78,90,91].
Bhowmick et al. proposed a theoretical model with a n ¼ 6 distance dependence of
energy transfer to surface plasmonic modes at large separation between a dye and a
nanoparticle and a 3 < n < 4 distance dependence of energy transfer for short
separation (similar to the nanoparticle size) between dye and nanoparticle [71].
As already mentioned, for large distances the energy transfer is mainly governed
by the radiative rate with a d3 distance dependence (n ¼ 3), leading to a large energy
transfer distance range compared to FRET. Indeed, such energy transfer between
dyes and Au nanoparticles over distances of more than 40 nm was found by steadystate experiments [78] and decay time measurements [81]. In the latter publication,
the acronym NPILM was introduced. Figure 5.19 shows experimental data of energy
transfer over distances of up to 50 nm for different nanoparticle sizes.
5.6.4
Other Transfer Mechanisms
Apart from the FRET-like energy transfer mechanisms mentioned so far, there
are several other energy or charge transfer mechanisms that can enlarge the
distance range of FRET in both the short and the long directions. On the short
end, there are electron exchange (Dexter) or electron transfer (Marcus) mechanisms related to orbital overlap, with exponentially decaying distance dependence. On the long end, there are mechanisms such as plasmon coupling (up to
about 80 nm donor–acceptor distance) or singlet oxygen diffusion (up to about
200 nm). Although all of these mechanisms are not based on nonradiative
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150
Table 5.7 Overview of different distance-dependent energy/charge transfer mechanisms.
Transfer
mechanism
Dexter transfer
Charge transfer
FRET/BRET/
CRET/DMPET
NSET
Plasmon
coupling
Singlet oxygen
transfer
Distance rangea)
Below about 1 nm
Distance dependence
Comments
exp(-r)
(Equation 5.49)
exp(-r)
(Equation 5.50)
1/r6 (Equation 5.7)
Energy transfer by electron
exchange
Below about 2 nm
Electron or hole transfer
(Marcus theory)
Energy transfer without
About 1–20 nm
electron exchange
About 1–40 nm
1/r4 (Equation 5.48) FRET from a donor to a
metal surface
About 5–80 nm (up to
exp(-r)
Size, shape, material, and
300 nm in theory)
(Equation 5.52)
medium-dependent
wavelength shift
About 10–100 nm (up to exp(-r)
Not used for distance
250 nm in theory)
(Equation 5.53)
measurements
a) All values refer to single-step transfer (one donor–acceptor pair). Energy migration or electron/hole
hopping can lead to larger overall transfer distances.
energy transfer due to dipole–dipole interactions and are thus not directly
related to FRET, they will be briefly described here (the interested reader is
referred to further literature within the following sections) in order to give a
broader picture of distance-dependent energy/charge transfer mechanisms. The
different mechanisms, their distance dependence, and their approximate distance range are shown in Table 5.7.
5.6.4.1 Electron Exchange Energy Transfer (Dexter Transfer)
In the case of overlapping orbitals of donor and acceptor molecules, which require
short D–A distances, electron exchange between D and A can occur. This mechanism is different from the Coulombic interaction in FRET or the electron tunneling
in charge transfer (Figure 5.20). The electron exchange rate is related to the orbital
overlap, which is expected to fall off exponentially with increasing D–A distance.
Electron exchange requires energetic resonance of D and A and therefore the
exchange rate will also be dependent on the spectral overlap of D and A. A theory for
electron exchange-mediated energy transfer was developed by Dexter in 1953 [92].
The rate constant of electron exchange energy transfer [or Dexter transfer (DT)] is
given by
2r
kDT ¼ KJ DT exp
;
ð5:49Þ
L
where K is a constant related to specific orbital interactions and JDT is the spectral
overlap integral. This spectral overlap is similar to the J in FRET (cf. Equation 5.9)
with the important difference that both the fluorescence and the absorption
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5.6 FRET beyond F€orster
j 5 How to Apply FRET: From Experimental Design to Data Analysis
Figure 5.20 Different mechanisms for
generating a ground-state donor and an excited
acceptor (D þ A as shown in the center) by
FRET (top left: Coulombic coupling of D and
A), Dexter transfer (DT, bottom left: electron
exchange between D and A and A and D) or
charge transfer (top right, CT: D as electron
donor; bottom right, CTþ: D as hole donor).
spectrum are normalized. This means that (in contrast to FRET) the spectral overlap
integral is not dependent on the molar absorptivity (extinction coefficient). r is the
edge-to-edge separation between D and A and L is the sum of their van der Waals
radii. As the transfer rate of Dexter transfer decreases exponentially with r, kDT
becomes negligibly small for D–A distances of more than one or two molecular
diameters (about 0.5–1 nm). In contrast to charge transfer (next section), the solvent
plays a minor role (apart from establishing the collision of D and A via diffusion) for
the transfer. As the constant K cannot be easily related to experimentally determinable quantities, it is difficult to perform a quantitative experimental characterization
of Dexter transfer. More details about the Dexter theory can be found in photochemistry and spectroscopy textbooks [17,18].
5.6.4.2 Charge Transfer (Marcus Theory)
Similar to Dexter transfer, charge transfer requires orbital overlap and has therefore
exponential distance dependence. The main difference from the Dexter electron
exchange lies in the transfer mechanism, as illustrated in Figure 5.20. Electron
exchange is a concerted two-electron transfer, whereas electron transfer (or charge
separation) requires an electron (or hole) donor and acceptor. Although charge
transfer can occur between molecules in the energetic ground state, an excited
molecule is both a better reducing agent (or reductant) and a better oxidizing agent
(or oxidant) due to a lower ionization potential and a larger electron affinity,
respectively [17]. The tunneling of electrons is dependent on the reactants and
the solvent requiring a reorganization of both, which can be divided into inner
sphere and outer sphere reorganization. The theory of this distance-dependent
charge transfer was developed by Marcus in 1956 [93–95]. The rate of charge transfer
(CT) can be written as
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152
kCT ¼
2p 2 exp ½bðr r 0 Þ
ðDGðrÞ þ lðrÞÞ2
;
J 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp
4lðrÞkB T
h
4plðrÞkB T
ð5:50Þ
where r is the center-to-center distance between D and A, r0 is the distance for which
D and A are in contact, b characterizes the distance dependence of the coupling, J0 is
the contact value of the donor–acceptor electronic coupling matrix element, l(r) is
the distance-dependent reorganization energy, DG(r) is the distance-dependent free
energy change, and h and kB are the reduced Planck’s constant and the Boltzmann
constant, respectively [96]. Equation 5.50 contains many distance-dependent parameters, which shows that a correct treatment of distance dependence can be
complicated and simple exponential models have been applied to fit experimental
data (e.g., for the distance dependence of electron transfer in DNA):
kCT ¼ AET exp ðbET ðr r 0 ÞÞ;
ð5:51Þ
where AET is a preexponential factor and bET characterizes the distance dependence
of the transfer. This short section can only give a first glance into the charge transfer
mechanism. The most important aspects in relation to FRET (the main topic of this
book) are the short distance range (which can take higher values than Dexter transfer
due to the different mechanism of charge transfer) of up to about 2 nm or even
higher values (in the case of electron hopping, over several redox centers) [97,98] and
the exponential distance dependence. Electron (or charge) transfer has been
intensively studied for chemical and biological systems and details can be found
in textbooks and review articles [17,99–115]. Although the D–A distance is limited,
charge transfer has the advantage that it does not require any spectral overlap (in
contrary to FRET or Dexter transfer) and therefore one suitable electron donor (or
acceptor) can be used to quench several different luminescent molecules for
multiplexing purposes. Different biological and chemical sensing concepts using
luminescence quenching of quantum dots by different charge transfer agents have
been recently developed [116–123]. Such charge transfer sensors allowed the
analysis of simultaneous quenching of eight different semiconductor quantum
dots [124].
5.6.4.3 Plasmon Coupling
Upon interaction with light, noble metal nanoparticles (most often Au and Ag are
used) can display localized surface plasmon resonance (LSPR) leading to broad and
strong absorption or scattering bands in the UV-Vis wavelength region. These
unique optical properties can be used for many different biosensing applications
[125,126]. The resonant frequency (or wavelength) of metal nanoparticles depends
on their material, size, shape, and surrounding medium. When two such LSPR
nanoparticles are brought into proximity, their plasmon resonances can couple,
which results in redshifted absorption or scattering bands of the two coupled
particles. This wavelength shift is dependent on the particle separation and can
therefore be used as spectroscopic or plasmonic ruler [127–133]. The distancedependent wavelength shift decays approximately exponentially and covers a large
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5.6 FRET beyond F€orster
j 5 How to Apply FRET: From Experimental Design to Data Analysis
distance range. Interparticle distances of up to about 75 nm have been measured
[130] and theoretical calculations predicted wavelength shifts for separations of up
to about 300 nm [132]. Jain et al. derived an empirical plasmon ruler equation for
the distance dependence of the wavelength shift, which is applicable for different
particle sizes [128]:
Dl
A exp
l0
d=D
;
t
ð5:52Þ
where Dl/l0 is the fractional wavelength shift, A is the magnitude of the fractional
shift, d is the interparticle edge-to-edge separation, D is the particle diameter, and
t is the decay constant of the exponential decay. The authors found that t is similar
for different particle materials, sizes, shapes, and medium electric constant (these
parameters change the amplitude A) and takes a value close to t ¼ 0.23.
Although the distance range of plasmon rulers is significantly larger than for
FRET and there is no dependence on the relative orientation of D and A, there are
several limitations of this technique for absolute distance measurements mainly due
to size and shape inheterogeneity of the nanoparticles, the relatively large size of the
nanoparticles in order to achieve a strong and sensitive scattering signal, and the
dependence of plasmon resonance on the refractive index of the medium [130,131].
This means (although an empirical plasmon ruler equation exists) that each
plasmon ruler must be carefully calibrated before its application for the determination of distances in unknown systems. Moreover, plasmon rulers cannot provide the
inherent ratiometric behavior of FRET (D-quenching and A-sensitization) and are
limited in multiplexed detection.
5.6.4.4 Singlet Oxygen Diffusion
Another possibility to transfer energy over larger distances is to use singlet oxygen
diffusion. This technique was developed by Ullman et al. and commercialized under
the brand name LOCI1 (Luminescent Oxygen Channeling Immunoassay, Behring
Diagnostics Inc.) [134,135]. The energy transfer is based on the following principle: A
nanoparticle charged with a photosensitizer (phthalocyanine) produces singlet oxygen
upon light excitation around 680 nm. The singlet oxygen can diffuse to a nearby
second nanoparticle that is charged with dioxene (or thioxene) that produces chemiluminescence upon reaction with singlet oxygen. As the quantum yield of this
chemiluminescence is very low, an additional fluorophore [9,10-bisphenylethynylanthracene (BPEA) or Eu(TTA)3Phen] is added, which results in a much higher overall
quantum yield. A homogeneous assay format, for example, two LOCI-nanoparticlelabeled antibodies binding to a specific biomarker, can fix both nanoparticles at a
distance, for which singlet oxygen can diffuse from particle one to particle two. The
produced chemiluminescence intensity is then proportional to the biomarker concentration. The same principle is used today in the commercial biosensing platform
AlphaLISA1 by Perkin Elmer [136] and the detection of different biomarkers using
this technology can be found in the literature [137–141]. As the concentration of singlet
oxygen, which can generate chemiluminescence within the second nanoparticle, is
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154
dependent on diffusion, the distance dependence of the energy transfer (or the single
oxygen concentration) can be calculated by Fick’s first law and is given by [134]
cSO
#
ra
pffiffiffiffiffiffiffiffiffiffiffi exp pffiffiffiffiffiffiffiffiffiffiffi ;
¼
4prDð1 þ a= D=kD Þ
D=kD
s
"
ð5:53Þ
where cSO is the concentration of singlet oxygen at a distance r from the center of the
first nanoparticle, S is the rate of singlet oxygen formation by the particle, a is the
particle radius, kD is the singlet oxygen decay constant in water, and D is the diffusion
coefficient in water.
Due to the relatively large nanoparticles (150 nm diameter), which need to
contain high amounts of sensitizers and chemiluminescence compounds for the
generation of intense luminescence signals, this technology is not suited for
distance measurements (or at least – to my knowledge – it has not yet been tried
out). Similar to plasmon coupling, LOCI is not inherently ratiometric and needs to
be carefully calibrated.
5.7
Summary and Outlook
In summary, FRET is a very powerful technique for the measurement of distances
and concentrations with very high precision and sensitivity on a length scale of
about 1–20 nm. F€orster’s theory for the relation between spectroscopic data and
the FRET distance dependence dates back to 1946 and therefore FRET is probably
one of the first optical superresolution techniques. Thanks to the development of
many types of fuorophores over the last decades, there are numerous possibilities
of choosing an adequate donor–acceptor pair (cf. Chapters 6 and 14) for the
nanometric system of interest (cf. Chapters 6–13). Before planning a FRET
experiment, one should also carefully think about the expected distances and
the (biological) recognition mechanism in which donor and acceptor will be
involved. FRET can be characterized by different technologies using luminescence
quantum yields, intensities, and lifetimes and both the donor (quenching or
photobleaching) and the acceptor (sensitization or photobleaching) can be analyzed in order to achieve accurate results. When planning the experiments as well
as when analyzing the results, one should always have in mind that there are other
energy or charge transfer mechanisms that can be responsible for the quenching
of a donor and/or the sensitization of an acceptor, and that there are complementary techniques to enlarge the distance range of FRET. The design of novel energy
transfer concepts and probes by efficient combination using the large variety of
fluorophores and technologies will make FRET (and the other energy/charge
transfer technologies) an equally or even more important and powerful technology
in the future. FRET on, FRET jocks!
j155
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5.7 Summary and Outlook
j 5 How to Apply FRET: From Experimental Design to Data Analysis
Acknowledgment
I would like to thank Dr. Daniel Geißler for his comments on and review of this
chapter.
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References
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6
Materials for FRET Analysis: Beyond Traditional Dye–Dye
Combinations
Kim E. Sapsford, Bridget Wildt, Angela Mariani, Andrew B. Yeatts, and Igor Medintz
6.1
Introduction
The intrinsic sensitivity (r6 dependence) of F€orster (or fluorescence) resonance
energy transfer (FRET) to nanoscale changes in the donor/acceptor separation
distance has made FRET an invaluable biophysical tool in a variety of applications,
ranging from studying the structure and conformation of proteins and nucleic acids
to examining biomolecular interactions, including its use in in vitro and in vivo
bioassays [1–7]. While the myriad of FRET configurations and techniques currently
in use are covered throughout this book, here we focus primarily on the materials
utilized as donor or acceptor probes in FRET rather than the process itself [3,5,8,9].
Our 2006 review paper on this topic serves as the foundation for this updated
chapter [3]. The materials were divided into three main categories: organic materials
that include “traditional” dye fluorophores, dark quenchers, polymers, and carbon
nanomaterials (NMs); inorganic materials such as metal chelates, metal, and
semiconductor nanocrystals; and fluorophores of biological origin such as fluorescent proteins (FPs), amino acids, and fluorescence generated from enzymatic
bioluminescence (BL) and chemiluminescence (CL). These materials may function
as FRET donors and/or acceptors, depending upon experimental design. Many of
the new materials developed and/or new donor–acceptor probe combinations used
address some of the inherent complications of more traditional FRET materials,
including photobleaching, spectral cross talk, and direct excitation of the acceptor
species, and examples of these will be highlighted and discussed throughout the
chapter. Since the vast majority of FRET applications are biological in nature, they
routinely involve some type of biomolecule labeling strategy, which ultimately plays
a significant and fundamental role in the success and interpretation of the resulting
FRET. Therefore, we begin the chapter with a brief discussion of the bioconjugation
techniques commonly utilized for FRET and points to consider, followed by sections
highlighting the current and emerging materials that are used, or have the potential
to be used, in FRET applications.
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
6.2
Bioconjugation
A large number of FRET-based applications involve the use and labeling of some
type of biomolecule (e.g., cell membrane, antibodies, nucleic acids, protein, and
peptides). Given the sensitivity of FRET to a number of parameters, the ability to
control the donor/acceptor labeling in the system under investigation is paramount
to obtaining well-controlled and reproducible results that will aid in subsequent
interpretation of experimental data. The extent of such control is initially dictated by
a combination of factors, including (i) the nature of the system under study (i.e., are
inter- or intramolecular studies desired?), (ii) the availability/number (and reactivity,
where applicable) of attachment/incorporation sites on the biomolecule(s) for the
donor/acceptor probes, (iii) the nature of the donor/acceptor probes (e.g., organic
molecule, fluorescent protein, and NM), (iv) the size of the donor/acceptor probes
(especially protein-based and NMs) relative to the biomolecule(s), which can
influence the system under study, and (v) the availability of the donor/acceptor
probes with the desired reactivity for bioconjugation and the nature of the linker
(e.g., length and flexibility), connecting the donor/acceptor probes to the biomolecule. For quantitative FRET the microenvironment dependency of the fluorophore’s photophysical properties and the uncertainty in probe position and
orientation relative to the biomolecule should be considered when choosing
donor/acceptor probes and bioconjugation strategies [6]. Donor/acceptor probe
attachment to a biomolecule can be achieved via a number of labeling techniques
that can be chemically or biologically inspired in nature (Figure 6.1); for recent
reviews see Refs [10–12].
Bioconjugation based on forming interactions, typically covalent bonds between
the biomolecule and the probes, represents the most popular and traditional group
of chemistries used to date, and will likely remain the workhorse in the near future
due to the commercial availability of a wide variety of donor/acceptor probes
modified with a number of reactive functionalities that facilitate bioconjugation.
In the case of protein labeling, for example, the predominant chemically based
bioconjugation strategies target the naturally occurring amino acids lysine (Lys –
primary amine) and cysteine (Cys – thiol) with succinimidyl ester (NHS) or
maleimide reactive groups, respectively. Control of the donor/acceptor probe
locations and stoichiometry is one of the many important considerations when
designing FRET studies [5]. In the case of deoxyribonucleic acid (DNA)/ribonucleic
acid (RNA) and short synthetic peptides, control of location and stoichiometry can be
programmed into their structure via inclusion of the donor/acceptor molecules
themselves or site-specific incorporation of thiol/amine groups for subsequent
labeling during synthesis [13,14]. However, proteins are generally more complex
because they contain a number of primary amines that can cause difficulty in
controlling the location of labeling and usually results in variable dye-to-protein
(D/P) ratios. Targeting thiols on Cys residues with maleimide chemistry is more
specific and can reduce the labeling variation, as these residues are far rarer.
However, Cys residues are often critical to protein structural conformations as
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166
Figure 6.1 Bioconjugation methods separated into chemistry- and biology-inspired techniques.
part of disulfide bonds and are typically buried below the protein surface, which can
limit access depending on the size of the chosen donor/acceptor probe. Thiols can
be chemically (typically via Lys interconversion) or recombinantly introduced into
the protein surface [15–17]. However, this too can be problematic as additional Cys
residues can “thiol-scramble” the protein structure during folding, and surfaceexposed thiols can result in the formation of protein dimers, trimers, and so on,
which, when purified, necessitate further reduction prior to labeling. There are a
couple of excellent resources available for researchers interested in bioconjugation
protocols in general [18] and fluorescent labeling in particular [19].
Bioorthogonal reactions (reactions that do not interfere with other biogroups
besides the target), which were born out of the desire to study biomolecules in their
native environment, have the ability to address many of the controlled labeling
concerns outlined earlier [12,20]. Many of these reactions are based on organic
chemistry-inspired covalent modifications and include the Staudinger ligation
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6.2 Bioconjugation
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
reaction, ketone/aldehyde condensation reactions (bioorthogonal, depending on the
system under study), and a variety of cycloaddition reactions, including the
quintessential “click chemistry” azide/alkyne cycloaddition.
There are a number of biologically inspired bioconjugation strategies that are
gaining popularity, which, although perhaps not bioorthogonal in the strictest sense,
possess many of the stipulations and benefits required to be considered as
bioorthogonal reactions [12,21]. Fluorescent proteins (FP) such as green fluorescent
protein (GFP) can be appended to existing proteins using recombinant techniques
generating protein chimeras, and although not considered a bioorthogonal chemistry, this does allow the site-specific incorporation of the FP to the protein of interest
(see Section 6.4.3) [22]. Likewise, nonnatural amino acid residues (Section 6.4.2),
short peptide tags, and full proteins (such as enzymes), that are either fluorescent or
allow specific labeling with fluorophores, can also be incorporated genetically into
protein structures [10,12,23]. For example, the tetracysteine/biarsenical system,
originally developed by Tsien and coworkers, demonstrated that proteins expressing
an optimized Cys-Cys-X-X-Cys-Cys sequence [where X ¼ could be any amino acid,
but is traditionally proline-glycine (Pro-Gly)] would react with biarsenical-functionalized fluorophores (e.g., FlAsH and ReAsH) (Figure 6.2) [21,24,25]. Oligohistidine
(His) peptides (e.g., His6) are peptide tags that have been used for conjugation. They
are known to bind nickel-nitrilotriacetic acid (Ni2þ-NTA)-functionalized molecules,
while the oligoaspartate (Asp) sequence (D4-tag, Asp4) has a strong binding affinity
to multinuclear zinc(II) complexes [10,12,26,27].
There are an expanding number of biologically inspired techniques that
harness genetically encoded peptide handles combined with enzymes to catalyze
small-molecule (e.g., biotin and fluorescent dye) conjugation [10–12,16,23,28,29].
Figure 6.2 Bioconjugation using peptide
recognition. (a) Schematic showing the labeling
of an engineered protein displaying a linear
tetracysteine motif with bisarsenical containing
fluorophores. (b) Chemical structures of FlAsH
and ReAsH. (Reprinted with permission from
Ref. [25]. Copyright 2011, American Chemical
Society.)
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168
Jager et al., for example, modified a model protein, chymotrypsin inhibitor 2 (CI2),
with a transglutaminase (TGase)-tag (Pro-Lys-Pro-Gln-Gln-Phe, where Gln is glutamine and Phe is phenylalanine) at its N-terminus [16]. TGase facilitated the coupling
of the TGase-tag-modified CI2 with AlexaFluor 647 (Alexa647, A647) cadaverine
(A647-(CH2)6-NH2), forming an isopeptide bond between the TGase-tag Gln residue
and the primary amine on the A647 fluorophore. In another example, the Escherichia
coli enzyme biotin ligase has been shown to ligate biotin to proteins tagged with an
acceptor peptide sequence Lys-Lys-Lys-Gly-Pro-Gly-Gly-Leu-Asn-Asp-Ile-Phe-GluAla-Gln-Lys-Ile-Glu-Trp-His (where Leu is leucine, Asn is asparagine, Asp is aspartic
acid, Ile is isoleucine, Ala is alanine, and Trp is tryptophan) [28]. The biotin ligase
also accepted a ketone isostere of biotin as a cofactor resulting in ketone-functionalized proteins that could be subsequently modified with hydrazide- or hydroxylamine-functionalized molecules. The HaloTagTM [haloalkane dehalogenase (DhaA)]
and SNAPTM-tag [O6-alkylguanine-DNA alkyltransferase (hAGT)] are labeling techniques that actually involve fusing the full enzymes (which self-label themselves) to
the protein of interest. The HaloTag utilizes fluorescently labeled haloalkane
substrates, while the SNAP-tag uses fluorescent benzylguanine derivatives to
generate fluorescently labeled targets [10–12].
Nanomaterials are increasingly being used as donor/acceptor probes in FRET
studies due to their many unique properties, and as such many of the bioconjugation techniques described earlier are applicable here as well [8,9]. However, taking
into account their nanoscaffold nature, additional concerns should be considered
during bioconjugation [5,30–32]. NM surfaces can be quite complex, comprising not
only the NM itself but also oftentimes additional stabilizing ligands that help
maintain its aqueous solubility (e.g., colloidal stability) and prevent undesirable
interactions such as aggregation–agglomeration. In addition NMs are generally
much larger than your typical fluorescent/quencher organic molecules and are often
on a similar size and scale or larger than most biomolecules, therefore the potential
influence of this size on the system under study should be carefully considered.
Other factors to consider regarding bioconjugation include how the NM is stabilized
in solution and whether the reaction conditions might affect the stability or physical
properties of the NM. A prime example that highlights this issue is the use of
carbodiimide coupling chemistry to link carboxylic acid (COOH)-modified NMs
with the primary amines on a protein, as discussed in a recent review by Algar et al.
[30]. COOH-terminated ligands are commonly used to impart charge-based solubility and stability to inorganic NMs at basic pH. However, carbodiimide activation
(often added in huge excess due to rapid hydrolysis of the reaction intermediate)
converts the COOH to a less soluble o-acylisourea intermediate and hence can cause
reduced solubility and NM aggregation, severely impacting product quality and
reproducibility. Another concern is whether the stabilizing surface ligands influence
subsequent interactions involving either the biomolecule attachment reaction or the
subsequent biorecognition event. Dennis et al. used FRET to investigate eight
distinct quantum dot (QD) coatings and their influence on the self-assembly of a
His-tag-labeled mCherry FP that interacts directly with the QD surface via metal
affinity coordination [33]. This coordination relies substantially on access of the
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6.2 Bioconjugation
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
His-tag to the QD surface, and the researchers found that even subtle changes in the
organic coating could significantly alter the accessibility and hence His-tag–
mCherry coordination.
In another example of reaction conditions that can impact the NM, the copper
(Cu) in the widely used Cu-catalyzed click chemistry has been found to be extremely
detrimental to the luminescent properties of QD materials [34]. As an alternative
Bernardin et al. used a Cu-free strained click chemistry technique, coupling strained
cyclooctyne-functionalized QDs with azido biomolecules, and the QDs in this case
retained their strong luminescent properties [34].
Surface ligands and the attachment chemistry used in bioconjugation can also
affect the performance of the NM bioconjugate in the desired application. For
example, while developing a FRET-based QD–peptide sensor for monitoring botulinum neurotoxin A (BoNT A) activity, Sapsford et al. found that the stabilizing
ligand sterically hindered the BoNT A from interacting with the peptide substrate
assembled on the QD surface via metal affinity coordination, resulting in a nonresponsive sensor [35]. The situation was mitigated by conjugating the peptide to the
terminal groups of the QD-stabilizing ligand, improving access for the BoNT A. As
with any type of bioconjugation involving a surface, the conformation/orientation of
the biomolecule upon immobilization is an essential component of its subsequent
functionality and should be considered during study design. Loss of biomolecular
activity is to be expected if the recognition site of the biomolecule is positioned in
close proximity to the surface [30]. In a study of QD–DNA bioconjugates, Boeneman
et al. found that the attachment chemistry strongly influenced the orientation of
DNA on a QD-poly(ethylene glycol) (PEG) surface [36]. His-tag-modified DNA
attached directly to the QD surface resulted in a structure that, as predicted,
extended out from the surface. Biotin-labeled DNA bound to streptavidin (SA)modified QDs, however, did not follow predicted models, and the DNA was found to
take a number of random orientations on the QD surface, which was attributed to
the random attachment of SA to the QD. Random orientations are likely to result in a
distribution of biomolecular activities, which can affect reproducibility of experimental results [30].
Clearly, there is a wide range of bioconjugation techniques available to researchers, and choosing the most suitable method depends on the nature of the system
under study. Some of these labeling techniques can be complex, requiring for
example genetic engineering expertise; however, the increase in commercial
reagents and kits (from companies such as Life TechnologiesTM, Sigma-Aldrich,
and Promega) for these types of bioconjugation reactions, especially with the
introduction of newer bioorthogonal chemistries, is encouraging more widespread
adoption. Regardless of the method chosen, having both the donor/acceptor probes
at known and distinct locations on biomolecule(s) is most desirable in terms of
postexperimental analysis. Care should be taken to ensure that donor/acceptor
probe modification does not influence the biomolecule functionality, especially
when trying to determine the functional characteristics of a biomolecule (where
labeling may interfere with/alter structure, biomolecule conformational changes, or
biomolecule interactions).
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170
6.3
Organic Materials
As highlighted in this section, organic materials that possess the necessary photophysical properties to be utilized as FRET donors or acceptors are a widely diverse
group and include molecules, macromolecules, polymers, and NMs.
6.3.1
Ultraviolet, Visible, and Near-Infrared Emitting Dyes
The majority of donor/acceptor materials currently used in FRET applications are
ultraviolet (UV), visible (Vis), and near-infrared (IR) emitting organic dyes. These
“traditional” dyes are usually the first type of FRET material tested with other new or
non-“traditional” fluorescent materials in potential FRET systems. The most common organic dye classes, shown in Figure 6.3, have several advantages, such as
commercial availability, cost-effectiveness, extensive characterization of FRET properties, easy bioconjugation through NHS-ester, maleimide, hydrazide, or amine
chemistries, availability in reactive form, and high quantum yields (QYs) and
solubilities [37,38]. Recent advances in click chemistry now allow companies
such as Lumiprobe to provide organic dyes conjugated to azide and alkyne chemical
moieties for further bioconjugation as well.
Despite all the advantages of these traditional dyes, there are disadvantages too.
For instance, some have a high rate of photobleaching, may be sensitive to pH, and
have a propensity to self-quench when highly substituted on biomolecules. Some of
the redder dyes have low solubility in aqueous solvents and for FRET in particular,
the broad absorption/emission profiles and small Stokes shifts often lead to direct
excitation of the acceptor, complicating subsequent analysis. The quest for new
organic dyes with the potential to overcome these limitations continues, most
recently with materials such as the Chromeo [39] (currently sold by Active Motif),
CS1-6 near-IR (NIR) [40], and alkyne carbocation “cyanine-like” dye families [41–43].
Researchers have recently demonstrated a series of organic molecules that undergo
excited-state intramolecular protein transfer (ESIPT) for use in the development of
fluorescent chromophores with a large Stokes shift (LSS) [44–46].
Many resources are available to aid in choosing suitable donor–acceptor pairs,
including a number of FRET reviews [15,47–49], as well as the Molecular Probes
Handbook [19] and a review by Wu and Brand [50] that offers an extensive list of
donor–acceptor dye pairs and their respective R0 values. Life Technologies’ Fluorescence SpectraViewer (http://www.invitrogen.com/site/us/en/home/support/
ResearchTools/Fluorescence-SpectraViewer.html) and Zeiss’ Fluorescence Dye
and Filter Database (https://www.micro-shop.zeiss.com/us/us_en/spektral.php)
are Web-based programs that allow researchers to plot multiple dye absorption/
emission profiles to optimize spectral overlap and choose appropriate filters. An
excellent comparison of the physical and spectroscopic properties of a number of
red-absorbing dyes is provided by Buschmann [51]. See also the extended and
updated tables collated by van der Meer and provided later in this book.
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6.3 Organic Materials
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j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
172
Many current applications still rely on traditional dye–dye FRETcombinations due
to the many advantages of organic dyes as described earlier [3,47,52]. For instance,
FRET-based biosensors have led to a deeper understanding of a number of biological
phenomena such as integrin adhesiveness and signaling dynamics [53], plasma
membrane biophysical interactions [54], host–pathogen interactions [55], and
protein folding geometries and conformational states [56]. Similar dye combinations
are also useful for FRET-based biosensing, including glucose sensors [57] and
biological agent detection [58].
Dye–dye FRET combinations have had tremendous impact on biomedical
research, specifically in the areas of nucleic acid analysis, DNA sequencing, and
genotyping [13,59–62]. In addition, molecular beacon probes used in nucleic acid
analysis and Scorpion real-time PCR assays are often FRET based [13,63]. Interestingly, use of DNA scaffolds incorporating donor/acceptor dyes has led to a more
fundamental understanding of the orientational dependence of the dyes on FRET
efficiency [64–66]. DNA microarrays, in which FRET-based DNA probes are immobilized on solid surfaces, are quickly becoming an exciting application with the
potential to increase sensitivity, specificity, and throughput of gene expression as
well as large-scale single-nucleotide polymorphism (SNP) discovery, detection, and
genotyping [67]. There is no doubt that new applications will continue to drive the
development of novel donor–acceptor dye combinations that overcome current
deficiencies in existing organic dyes.
6.3.2
Quencher Molecules
The use of quenching molecules in FRET-based applications continues to be
popular. The primary advantage of using these molecular acceptors over their
fluorescent counterparts is the elimination of background fluorescence due to
direct acceptor excitation or reemission. Typically, quenchers take the form of
organic molecules or metallic materials such as gold (Au) (Section 6.5.3). Figure 6.4
offers a visual representation of a variety of organic quencher families that are
commercially available. Two of the most common quenching acceptor molecules,
Dabcyl (4,-(40 -dimethylaminophenylazo)benzoic acid) and Dabsyl (4-dimethylaminoazobenzene-40 -sulfonyl), have absorption maxima centered at 485 and 466 nm,
respectively. Another recent addition to nonfluorescent quencher dyes is IRDye
QC-1, which is characterized by a broad absorption peak between 550 and 950 nm,
3
Figure 6.3 Organic UV and visible fluorescent
dyes. (a) Structures of the common organic UV
and visible fluorescent dyes. Typical
substituents at the R position include CO2,
SO3, OH, OCH3, CH3, and NO2; Rx marks
typical location of the bioconjugation linker.
(Reprinted with permission from Ref. [3].) (b)
Plot of fluorophore brightness versus the
wavelength of maximum absorption (max) for
the major classes of fluorophores. The color
of the structure indicates its wavelength of
maximum emission (em). For clarity, only
the fluorophoric moiety of some molecules
is shown. (Reprinted with permission from
Ref. [37]. Copyright 2008, American
Chemical Society.)
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6.3 Organic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.4 Organic quencher molecules. (a)
Example of structures of the common quencher
molecules. Substituents R are listed. Rx marks
typical location of the bioconjugation linker.
(Reprinted with permission from Ref. [3].)
(b) Some common, commercially available,
quencher families along with absorbance
maxima and spectral regions covered by a
particular quencher family. (Adapted with
permission from Ref. [3].)
effectively allowing the quenching of both near-infrared and the more commonly
used visible donor dyes [68]. Other quencher families that tend to have wide-range
absorption spectra include the trademarked QSY, QXL, ATTO, BlackBerry, and Black
Hole Quenchers. These broad absorption spectra decrease design constraints and
allow quencher molecules to function as acceptors for many dyes. One application
where quenchers are often applied is DNA analysis, specifically molecular beacons
coupled with organic dye donors [13,48,49]. The primary advantage of this donor–
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174
quencher configuration is that singular or individual donor channels can be
monitored and, if sufficient spectral separation is achieved, utilized for “multiplexing” with a variety of other donor–quencher pairs. Typical applications of these
methods have measured DNA permeability of polyelectrolyte thin films [69] and
utilized catalytic DNA biosensors to detect lead (Pb) ions [70]. Another technique
employs quencher-labeled substrate analogues used in conjunction with dye-labeled
proteins for FRET-based biosensing of nutrients through displacement [71].
Reduced size of donor/quencher pairs can also improve the accuracy in determining
protein dynamics. For example, the use of thioamide as a quencher fabricated from
the protein’s own backbone, through a single-atom substitution, minimized perturbation of the system [72]. Current techniques also look into increasing the
efficiency of quencher molecules through the use of binding molecules with
advantageous three-dimensional conformations and charge density allowing
increased local dye concentrations [73]. One of the few examples of FRET, where
organic quencher molecules are coupled to nonorganic fluorophores, involves QD
donors (see Section 6.5.5).
6.3.3
Environmentally Sensitive Fluorophores
While the vast majority of fluorophores will respond to a certain extent to a
perturbation in their microenvironment, some exhibit much higher sensitivity
than others and as such are classified as environmentally sensitive. These fluorophores exhibit some change in their spectral characteristics (absorption/emission
profiles) in response to a change in their microenvironment, such as pH, ion
interactions, or another moiety such as oxygen (O2), solvation, polarity (solvatochromic fluorophores), or rigidity, and these dyes are usually defined by the analyte
or condition that they respond to most favorably [19,47]. A large number of
environmentally sensitive fluorophores are found in the small organic molecules
class of fluorescent probes, however, other classes of fluorophores such as FPs have
also been found to be sensitive to specific changes in their environment [37,74–79].
Life Technologies offers a wide range of environmentally sensitive fluorophores,
including dyes sensitive to reactive oxygen species (ROS), pH, calcium (Ca2þ),
magnesium (Mg2þ), Zn2þ, sodium (Naþ), chloride (Cl), potassium (Kþ), and
membrane potential [19]. The dyes are offered in a variety of forms depending on the
application, including cell-permeant and cell-impermeant, or can be modified with
functional groups that aid in subsequent conjugation if desired. Many of the target
ions are important signaling molecules in molecular cell biology, and intracellular
measurements are essential to understanding the processes that govern cellular
function [76,77]. In the case of intracellular pH, for example, two functional
microenvironments should be considered, the cytosol (pH 6.8–7.4) and the acidic
organelles (pH 4.5–6.0), with the exact choice of fluorescent probe dependent on its
pKa [19,76]. Oregon Green and LysoSensors are appropriate for the more acidic
organelle environment, while fluorescein derivatives, the polar 20 ,70 -bis-(2-carboxyethyl)-5-(and-6)-carboxy-fluorescein (BCECF) derivative (developed by Tsien) and
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6.3 Organic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
the proprietary seminaphthorhodafluors (SNARF) dyes, function optimally in the
pH 6.0–8.0 range and are popular choices for cytosol pH measurements [19,80].
Nakata et al. recently developed two new SNARF derivatives, SNARF-F and SNARFCl, which, while maintaining the characteristic spectral changes of the original
SNARF dye, have improved cell permeability and in the case of SNARF-F an
improved pKa (7.38) for cytosol measurements (Figure 6.5) [81]. Tweaking of
the fluorophore chemical structure can improve the fluorescent properties, and
the target interactions of many of these fluorescent probes and combinatorial
approaches offer an interesting alternative to more traditional and rational design
methods for identifying new improved fluorescent candidates, recently reviewed in
Ref. [82].
While environmentally sensitive fluorophores function alone adequately as
qualitative intensity-based fluorescent probes, the combination of FRET using
environmentally sensitive dyes has been demonstrated for detection of pH, ammonia (NH3), and carbon dioxide (CO2) [83,84]. When target quantification is desired,
especially in studies involving complex cellular environments, FRET represents one
mechanism in which to achieve ratiometric measurements that are independent of
fluorescent signal fluctuations [77,85]. Signal fluctuations can result from variations
in local probe concentration, sample thickness, pH, or temperature, which make
Figure 6.5 Environmentally pH-sensitive
SNARF dyes. (a–c) Absorbance (solid line)
and fluorescence (dashed line) spectra of
10 mM of (a) SNARF, (b) SNARF-F, and (c)
SNARF-Cl at pH 5.0 (red) and pH 10.0
(blue), excited at the isosbestic point,
respectively. (d and e) Photos of (d) color
and (e) fluorescence of SNARF (10 mM),
SNARF-F (10 mM), and SNARF-Cl (10 mM) at
pH 5.0 and pH 10.0. (Reprinted with
permission from Ref. [81]. Copyright 2011,
Elsevier.)
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176
subsequent interpretation of single-intensity data complicated. Ratiometric FRETbased sensors for the analysis of nucleoside polyphosphates, pH, temperature,
hydrogen peroxide (H2O2), mercury (Hg), and chromium (Cr) ions have all been
demonstrated [79,86–90].
Environmentally sensitive fluorophores are commonly incorporated into nanoparticles (NPs) for sensing applications. For example, Childress et al. developed dyedoped polymer NPs for ratiometric fluorescence detection of Hg(II) ions in aqueous
solution [89]. NPs of the conjugated polymer (CP) poly[(9,9-dioctylfluorenyl-2,7diyl)-co-(1,4-benzo-{2,10 -3}-thiadiazole)] (PFBT), which fluoresced green-yellow,
were doped with a nonfluorescent Hg(II)-responsive rhodamine dye. The rhodamine dye, upon interacting with Hg(II) ions, converts to an orange-red fluorescent form, resulting in FRET between the donor PFBT NPs and the activated
acceptor rhodamine dye. The sensing NPs could measure low levels of Hg(II) ions in
the 0.7–10 ppb range, and the ratiometric nature of the FRET sensor eliminated any
issues related to environmental or instrumental fluctuations. Using a more conventional platform, Kurishita et al. developed FRET-based ratiometric chemosensors
for detection of nucleoside polyphosphates such as adenosine-50 -triphosphate (ATP)
[87]. The sensor was based upon a large off–on fluorescence enhancement that
occurred when a xanthene-based Zn(II) complex bound ATP (Figure 6.6a). The
chemosensor combined a coumarin (blue fluorescence) donor with the xanthenebased Zn(II) complex acceptor, which developed green fluorescence upon ATP
binding. Ultimately the chemosensor was tested in live Henrietta Lacks (HeLa) cells,
where initial staining resulted in green fluorescence due to the presence of ATP in
the cells (Figure 6.6c). Introduction of 2-deoxyglucose (2-DG) and/or potassium
cyanide (KCN), which inhibited ATP synthesis, resulted in a significant decrease in
FRET, causing an increase in the blue donor emission compared to untreated cells
(Figure 6.6d and e).
Nucleic acid binding dyes represent a specific class of environmentally
sensitive organic dyes that warrant special mention [91,92]. These dyes form
complexes with nucleic acids, resulting in significant off–on fluorescence
enhancements, which also incorporate intermolecular homo-FRET to a large
extent. Dyes include 40 ,6-diamidino-2-phenylindole (DAPI), the bisbenzimidebased dyes (collectively called the Hoechst dyes), OliGreen, ethidium bromide
(EtBr), propidium iodide, and the cyanine dyes (PicoGreen, YOYO, and TOTO
families of dyes; SYBR Green I and SYBR Gold) [91,92]. Cosa et al. performed a
comprehensive study comparing the photophysical properties of a number of
these dyes alone and upon binding single-stranded DNA (ssDNA) or doublestranded DNA (dsDNA) [91]. All these dyes interact with dsDNA, with some
such as DAPI and the Hoechst dyes, binding specifically with the minor groove
of adenine (A)–thymine (T)-rich sequences [91,92]. Most of the dyes also seem
to interact with ssDNA and some, such as EtBr, have also been found to interact
with RNA [91,92]. The combination of nucleic acid sensitive dyes and FRET has
been used in a number of studies dealing with understanding how the dyes
interact with DNA [92–94] and in the detection of single-nucleotide polymorphisms (SNPs) and short tandem repeats (STRs) [95–97].
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6.3 Organic Materials
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6.3.4
Dye-Modified Microspheres/Nanomaterials
There are a wide range of materials that can and have been modified with organic
dyes to generate fluorescent microspheres or NMs, although the most common
platforms are either polymer or silica based. Modification typically involves either
encapsulation of the fluorophores within the material core or interaction with the
particle surface. Recent advances in NM synthesis and improved surface functionalization techniques have allowed the increased use of dye-labeled NMs in particular,
which, from a size perspective, is a benefit in FRET-based applications. Dye-labeled
nano- and micro-sized particles have been prepared through ionic interaction [98],
miniemulsion [99,100], covalent conjugation [101], or encapsulation of fluorophore
molecules during synthesis [102–105], and the benefits of these formats result in
increased signal, decreased photobleaching, increased surface functionalizability,
and lower limits of detection than small-molecule fluorophores [106]. Due to the
popularity of diagnostic and research techniques utilizing fluorescence detection
systems, commercial fluorescent particles are available from a wide variety of
sources such as Molecular Probes, Phosphorex, Spherotech, Bangs Laboratories,
Sigma-Aldrich, and Polysciences. Besides standard fluorophores, fluorescent microspheres loaded with europium (Eu) chelates are available, extending the utility of
such labels to time-resolved energy transfer configurations (Section 6.5.1) [107].
A current trend in microspheres and NM synthesis involves using FRET to tune
the spectral properties of the resulting fluorescent microspheres/NMs, generating
fluorescent FRET-based tags that have improved Stokes shifts and unique fluorescent signatures that can be excited by a single wavelength (Figure 6.7)
[99,100,102,108–111]. These FRET systems can also be designed to contain
Figure 6.7 Polymeric FRET-based NPs for in
vivo imaging. The particles were assembled
from diblock copolymers of poly(D,L-lactic-coglycolic acid) and maleimide-activated PEG,
which were also encapsulated in both the
donor (1,10 -dioctadecyl-3,3,30 ,30 tetramethylindodicarbocyanine) and acceptor
(1,10 - dioctadecyl-3,3,30 ,30 tetramethylindotricarbocyanine) fluorophores.
FRET resulted in a large Stokes shift (>100 nm)
of the emission maxima, and the transfer
efficiency could be fine-tuned by further
adjusting the doping ratio of the donor and
acceptor fluorophores. The optimized
formulation was less than 100 nm in size,
brighter than quantum dots, stable in
biological media, and demonstrated similar
biodistribution to most NMs. (Reprinted with
permission from Ref. [102]. Copyright 2012,
American Chemical Society.)
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6.3 Organic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
photochromic dyes (discussed further in Section 6.3.6) that increase signal detection
by decreasing background emission [99].
A variety of hybrid fluorescent core–shell silica NPs with interesting optical
properties have been developed, such as, dye-labeled silica-coated silver (Ag) NPs
with enhanced FRET properties [112,113] and Cornell dots (CU dots) [114,115]
developed by Wiesner at Cornell University. CU dots are synthesized by covalently
conjugating dye molecules to a silica precursor before being condensed to form a
dye-rich core. Silica sol–gel monomers are then added to form a denser outer
silica network.
The use of dye-labeled microparticles and NPs in FRET-based analytical and
research assays continues to grow as these materials are exploited in nanoscopic
ruler measurements [116], biosensing of infectious agents [105,111], in vivo biolabeling [102], flow cytometry [117,118], SNP genotyping [119,120], and disease
diagnosis using protein nanoarrays [121].
6.3.5
Dendrimers and Polymer Macromolecules
Dendritic and polymer macromolecules are increasingly being used in fluorescence-based applications. Dendritic architectures represent a class of repeatedly
branched or tree-like polymeric structures of which the subclasses of dendrimers
and dendrons have found particular application in molecular imaging, sensing,
photovoltaics, and energy harvesting [122–124]. Dendrimers, in particular, are
highly ordered macrostructures comprised of a distinct core, branched mid, and
branched surface/periphery regions. The ability to tailor dendrimer structures
with inclusion of multiple functional groups during synthesis allows precise
control over the position and orientation of fluorophores and attachment of
biomolecules leading to well-defined macromolecules [122–124]. This precise
structural control has made dendrimers interesting synthetic platforms in which
to mimic Nature’s light-harvesting structures, reviewed in Ref. [124], and in the
development of new photovoltaic materials [125]. Of the many types of dendrimers reported, the poly(amidoamine) (PAMAM)-based materials are the most
utilized because the many primary amines enable facile functionalization
[122,123]. The ability to label these dendritic structures with multiple fluorophores results in increased absorption cross sections and higher fluorescence
intensities, which is ideal for bioassay and imaging applications [122,123]. This
strategy is employed in a class of dendron-based fluorogenic dyes known as
dyedrons, which comprise multiple donor Cy3 dyes coupled to a single malachite
green (MG) acceptor [126]. Free in solution, the MG acceptor acts as a quencher
due to unconstrained internal structural rotations, however, upon binding to
fluorogen-activating proteins (FAPs) such as single-chain variable fragment antibodies, the MG acceptor becomes activated, making it highly fluorescent when
excited via FRET from the Cy3 donors. Such dyes have potential application as
targeted probes in sensitive homogeneous (no wash) imaging. Inherently fluorescent cationic dendritic structures comprising primarily phenylene-ethynylene
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180
have been used as donors for the detection of peptide nucleic acid (PNA)/DNA
hybridization, where the neutral PNA probe was labeled with a fluorescein
acceptor [127]. Davis et al. used inherently fluorescent cationic and anionic
diphenylacetylene dendrimers doped into cellulose acetate to generate solid-state
electrospun nanofiber sensor arrays for protein detection [128]. These nanofiber
films selectively interacted with proteins (including metal- and nonmetal-containing proteins), which resulted in fluorescent quenching in distinct patterns, due to
varying interactions with the different protein structures; this allows specific
protein identification even in complex mixtures. Dendrimers have also been used
as carriers for multiple materials such as combinations of drugs, nucleic acids,
antibodies, fluorescent tags, and/or contrasting agents that can be used for
imaging, drug delivery, or bioassay applications [123]. For example, Myc et al.
used folic acid modified dendrimers to target delivery of a FRET-based apoptotic
sensor to cancer cells that could be used to determine the efficacy of a chemotherapeutic or other targeted treatment by monitoring cell death in real time [129].
Although synthetic procedures for dendrimer synthesis are available in the
literature, dendrimers are also commercially sold with functionalities that can
be further modified by the end user, which may aid in more widespread use
(Dendritech, Polymer Factory Sweden AB, and Dendritic Nanotechnologies Inc.).
Qiagen offers dendrimers specifically functionalized to bind both DNA and cells
for cellular transfection.
Fluorescent polymers are a related class of fluorophores that can be either
intrinsically fluorescent such as CPs or functionalized with multiple fluorophores
[3,130]. Similar to dendrimers, fluorescent polymers are characterized by large
molar absorption coefficients and therefore high fluorescence. However, due to their
inherent polydispersity the emission from fluorescent polymers is typically not
localized, resulting from energy transfer processes along the whole chain, with a net
result of diffuse emission [131]. Thus fluorescent polymers cannot be considered
point donors for FRET. Nonetheless, fluorescent polymers, especially CPs, have
found application in a number of fluorescence-based studies, including FRET [130].
Fluorescent CPs, cationic conjugated polymers (CCPs), and conjugated polyelectrolytes (CPEs) are particularly popular for developing FRET-based DNA biosensors
[132], with applications ranging from detection of DNA [133,134], DNA hybridization [135], DNA methylation [136], and SNPs [137]. They have also been incorporated
into sensing schemes for proteins [138] and Hg ions [89,139]. The group of McNeill
and coworkers recently developed a series of multicolor conjugated polymer dots
(CPdots) (Figure 6.8) [140–142]. These polymer dots, referred to as CPdots and later
Pdots, are made from semiconducting polymer materials such as PPE, PFPV, or
PFBT (see Figure 6.8 for full chemical name), are 4 nm in diameter with high
fluorescent intensities, and could be readily functionalized [140–142]. Others have
studied these Pdot materials, including Chan et al. who developed FRET-based Pdots
with photoswitching capabilities [143,144]. These were created through the incorporation of photochromic spiropyran molecules into a PFBT polymer and were
intended for use in bioimaging applications. In another example, a pH-sensing Pdot
was created by functionalizing PPE Pdots with pH-sensitive fluorescein [145].
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6.3 Organic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.8 Conjugated polymer dots (CPdots).
(a) Chemical structures of fluorescent CPdot:
the polyfluorene derivative poly(9,9dioctylfluorenyl-2,7-diyl) (PFO), the copolymer
poly[{9,9-dioctyl-2,7-divinylene-fluorenylene}alt-co-{2-methoxy-5-(2-ethylhexyloxy)-1,4phenylene}] (PFPV), the poly[(9,9dioctylfluorenyl-2,7-diyl)-co-(1,4-benzo-{2,10 ,3}thiadiazole)] (PFBT), and the poly(phenylene
vinylene) derivative poly[2-methoxy-5-(2ethylhexyloxy)-1,4-phenylenevinylene] (MEHPPV). (b) Photographs of aqueous CPdot
suspensions under room light (left) and UV
light (right) illumination. (c) Absorption spectra
and (d) fluorescence spectra of the conjugated
polymer dots. (Reprinted with permission from
Ref. [140]. Copyright 2008, American Chemical
Society.)
6.3.6
Photochromic Dyes
Materials that can reversibly switch between two forms/states upon exposure to
electromagnetic radiation, in which each form/state has different photophysical
properties, are known as photochromic dyes [146,147]. While there are both
inorganic and organic photochromic materials, organic photochromic dyes are
the most popular, having a wide range of uses from decoration and eyeglass lens
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182
coatings to optical switches and data storage. There are a number of photochromic
dyes and various mechanisms that cause their photochromic transformations,
and these have been extensively reviewed [146–150]. Of these, spiro-based (e.g.,
spiropyran) and increasingly diarylethene-based photoswitchable compounds
have found particular application in FRET, so-called photochromic FRET
(pcFRET) [147,149,151–153]. The pcFRET technique is particularly useful in
FRET imaging applications, especially on a single-protein level, where pcFRET
can be used to turn the FRET process “off” or “on” thereby creating an internal
control and eliminating false-positive or false-negative signals due to high
intrinsic autofluorescence, interactions with other endogenous proteins, and/
or low FRET efficiencies [152,154–157]. FRET imaging sensitivity can be further
enhanced when pcFRET is used in conjunction with techniques such as optical
lock-in detection (OLID) [156,158].
Spiro-based materials represent one of the more prominent types of photochromic dyes, and exist in a closed spiro (colorless) form featuring an absorbance at
<400 nm, which undergoes a ring-opening rearrangement upon UV exposure to an
open merocyanine (colored) form with an absorbance from 500 to 700 nm
(Figure 6.9a) [151]. Photoswitchable spironaphthoxazine (NISO) has been conjugated to tetramethylrhodamine (TMR) in a FRET-based strategy to enhance intracellular imaging [159]. When NISO is present in its merocyanine (colored) form, it
acts as a FRET acceptor for TMR diminishing its emission. However, when it is
switched to its spiro (colorless) state, TMR donor emission increases due to
diminished FRET. Spiropyran-based photochromic materials have been incorporated into a number of FRET formulations, including hyperbranched polymer
micelles containing a hydrophobic fluorescent dye nitrobenzoxadiazolyl derivative
[160], gadolinium-complexed materials for use in magnetic resonance imaging
(MRI)-based deep tissue gene expression mapping [161], and QDs [162]. Using a
spiropyran-based nitrospirobenzopyran (Nitro-BIPS)-conjugated fluorescent protein acceptor, FRET could be modulated with cycles of 365 and 546 nm light.
This technique has been used to measure FRET efficiencies below 1% within a
cell [157]. Also utilizing photochromic BIPS, a photoswitchable QD (psQD) has been
developed for pcFRET [162]. By exposing the QD to white or UV light, the BIPS is
transferred from colored merocyanine that acts as a FRET acceptor to colorless
spiropyran that will not act as a FRET acceptor to the QD donor. In this way the
emission of the QD can be modulated. Spiropyran-based dyes have also been
incorporated into a number of luminescent NM-based probes for bioimaging
[99,154,163,164]. Chen et al., for example, prepared FRET-based multicolor fluorescent and photoswitchable polymer NPs by incorporating two fluorescent dyes (EANI
and NBDAA) (Figure 6.9b) and photoswitchable spiropyran into methyl methacrylate-based NPs via copolymerization (Figure 6.9b) [99]. By varying the ratios of
the dyes, the emission signatures could be tuned such that the NPs exhibit multiple
colors under a single excitation.
Another increasingly common class of organic photochromic dyes includes the
diarylethene-based photoswitchable compounds, which, like the spiro-based materials, undergo a structural open–closed photochromic transition [152,153,165–167].
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6.3 Organic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.9 Spiro-based photochromic dyes. (a)
The closed spiro form (SP – colorless)
undergoes a ring-opening rearrangement upon
UV exposure to the open merocyanine (MC –
colored) form. (b) Generation of FRET-based
multicolor photoswitchable fluorescent NPs by
covalently incorporating two (EANI and SPMA)
or three fluorescent dyes (EANI, NBDAA, and
SPMA) under excitation at 385 nm [4-ethoxy-9allyl-1,8-naphthalimide (EANI) and allyl-(7-nitrobenzo[1,2,5]oxadiazol-4-yl)-amine (NBDAA)].
(c) Fluorescence emission spectra of three NP
samples with different NBDAA feed (for
samples NP-N1, NP-N3, and NP-N5, the
NBDAA feed increased at a certain value) after
visible light irradiation and UV irradiation. (d)
Photograph of three NP dispersions (NP-N1,
NP-N3, and NP-N5) after visible light
irradiation and UV irradiation in the dark
environment. (Reprinted with permission from
Ref. [99]. Copyright 2012, American Chemical
Society.)
Diarylethene materials have been used to create photoswitchable dendrimers, where
the diarylethene acts as a FRET acceptor that quenches the attached Cy3 donor
emission via FRET, when switched off in the closed form [167]. Photochromic FRET
imaging using this dendrimer was demonstrated within both HeLa cells and zebra
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184
fish, with the potential for use in detailed imaging of cellular processes within cells
or organisms. Photoswitchable QDs were developed by Diaz et al. by coating QD
donors with an amphiphilic polymer containing diheteroarylethene acceptors and a
spectrally separate Alexa647 dye to act as an internal standard by facilitating
ratiometric measurements (Figure 6.10) [165,166]. The properties of this NP could
make it potentially useful for intracellular imaging applications.
Figure 6.10 Diarylethene-based photochromic
dyes, and generation of photoswitchable QDs
(psQDs). (a) The open diarylethene form
(oPC – colorless) undergoes a ring-closing
rearrangement upon UV exposure to the closed
diarylethene form (cPC – colored). (b) Spectral
signatures of the dual-color psQD components.
Superposition of absorbance (solid lines) and
emission (filled areas) spectra of PC, QD, and
Alexa647, demonstrating the PC spectral
overlap with the QD but not with the Alexa647.
The spectra are normalized by their peak values.
(c) Schematic of the dual-color psQD. The
fluorescence of the QD is modulated by the
photoconversion of the PC, while the Alexa647
fluorescence is constant. The PC in the open
form (oPC) is photoconverted with UV
irradiation to the closed form (cPC), which
can then be photoreversed by direct excitation
with visible light, or via FRET from the QD
acting as a donor. (Reprinted with
permission from Ref. [165]. Copyright 2012,
American Chemical Society.)
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6.3 Organic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
In addition to organic dyes for pcFRET, photoswitchable FPs that can be encoded
in the genome have also been demonstrated, and are discussed in more detail in
Section 6.4.3 [155,168,169]. The use of pcFRET shows great promise for sensitive,
high-resolution (diffraction unlimited) imaging of cellular processes, including rare
protein interactions and individual protein movement within a cell. As a greater
toolbox of photoswitchable materials for pcFRET continues to develop and researchers work on improving their inherent properties, pcFRET applications are sure to
continue to grow.
6.3.7
Carbon Nanomaterials
Carbon NMs represent a diverse class of materials with a variety of differing physical
and chemical properties. This diversity is a direct result of a range of allotropic
carbon material forms, including diamond, fullerene spheres and nanotubes,
graphite and graphene, along with amorphous carbon. Of these many types,
graphene-based sheets, nanodiamonds (NDs), luminescent carbon nanodots (Cdots), carbon NPs (CNPs), and carbon nanotubes (CNTs) possess relevant optical
properties of interest for FRET applications.
Of the graphene family of materials, graphene oxide (GO) sheets are reportedly
fluorescence “superquenchers” that possess long-range energy transfer properties
that make them ideal in FRET studies [170]. Most of the GO-based FRET sensors to
date use DNA-based molecular recognition, in the form of molecular beacons,
aptamers, or DNAzymes, for the specific detection of a range of target analytes from
small molecules, such as heavy metals and mycotoxins, to proteins including
thrombin, DNA, and even whole cancer cells [170–175]. Donor species range
from traditional organic fluorophores to QDs and upconverting NPs (UCNPs);
the diversity reflects the superquenching abilities of the GO materials. Wu et al., for
example, demonstrated the simultaneous detection of the mycotoxins ochratoxin A
(OTA) and fumonisin B (FB1) using two types of UCNPs modified with specific
aptamers [173]. GO was used as the universal acceptor in the sensing scheme
(Figure 6.11). In the absence of the target mycotoxins, the aptamer-modifed UCNPs
interacted with the GO surface resulting in FRET and effective quenching of the
UCNP luminescence. Addition of the mycotoxins, which bind to the aptamermodifed UCNP, altered the GO–aptamer-modifed UCNP interaction, resulting in
an off–on sensor whose resulting luminescence spectra was mycotoxin specific.
Dependent on the synthetic approach, GO sheets, especially the reduced form, in
suspension or solid thin films can exhibit luminescent properties and have been
used as donors in combination with Au NP acceptors for FRET detection of DNA
hybridization and microcystins [176–178]. Graphene sheets smaller than 10 nm
have also been found to possess photoluminescent (PL) properties [including
upconversion (UC) and downconversion PL], and are referred to as graphene
quantum dots (GQDs) [179,180]. Fan et al. found that 2,4,6-trinitrotoluene (TNT)
effectively quenched GQDs luminescence via FRET upon the p–p stacking interaction that occurs between the two species [181].
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186
Figure 6.11 GO sheets as universal
quenchers in FRET-based assays. (a)
Preparation of aptamers–UCNPs for
mycotoxin detection. (b) Schematic
illustration of the multiplexed upconversion
FRET bioassay using aptamers–UCNPs
(donors) and GO (universal acceptor) for
FB1 and OTA detection. (Reprinted with
permission from Ref. [173]. Copyright 2012,
American Chemical Society.)
CNTs comprise graphene tubes and, like the sheets, can either possess luminescent or superquenching properties depending upon morphology, synthesis, and
purity. In general single-walled CNTs (SWCNTs) and sometimes double-walled
CNTs (DWCNTs) are found to have luminescent properties [182], while multiwalled
CNTs (MWCNTs) are considered superquenchers [183]. CNTs have successfully
been used as donors and acceptors in FRET applications where they have been
coupled with traditional organic dyes, QDs, and even lanthanide ions [184–187]. For
example, QD-labeled ssDNA is found to undergo a strong interaction with CNTs,
resulting in significant quenching of the QD luminescence [187]. Binding of the
target influenza A virus DNA resulted in a significant decrease in the DNA–CNT
interaction and an increase in QD emission, with a limit of detection (LOD) of
9.4 nM and excellent single-base mismatch discrimination. Synthesis and purity of
the CNTs appear to be a key requirement for their successful application in FRET.
While studying the fluorescence quenching of the dyes dansyl hydrazine and
panacyl bromide covalently attached to SWCNTs, Chiu et al. found that the panacyl
bromide quenching, unlike dansyl hydrazine, was very sensitive to the CNT
purification method, specifically the metal impurities left over from CNT manufacture, suggesting care should be taken when interpreting data [185].
As an alternative to CNTs and GO sheets, which can be quite large as discrete
labels, CNPs, NDs, and C-dots are relatively small and compact labels that are
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6.3 Organic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
starting to find application in FRET [188–191]. CNP acceptors (quenchers) coupled
with UCNPs have been applied to the detection of thrombin, using aptamers, and
matrix metalloproteinase-2 (MMP-2), using a polypeptide substrate [192,193]. NDs,
whose intense fluorescence properties arising from nitrogen-vacancy (NV) point
defects in their nanocrystalline structure, have been investigated as donors in FRET
studies with a number of near-IR dyes [194–196]. C-dots that are sub-10 nm particles
that become fluorescent upon surface passivation have yet to be applied to FRET
applications, but like NDs have great potential as donors.
Many of these carbon NMs are still relatively new and studying their inherent
physical properties and understanding the mechanisms that govern them is still very
much a work in progress. This is hampered somewhat by the fairly complex and
normally poorly controlled methods typically used to generate carbon NMs, such as
chemical vapor deposition, electric arc discharge, or laser ablation. These methods
typically produce a range of products containing a variety of impurities that have to
undergo some type of purification in order to obtain the desired end product. That
said, there are an increasing number of manufacturers who offer various carbon
NMs (e.g., Sigma-Aldrich, Carbon Solutions Inc., Nano-C1, Microdiamant, and
NanoAmor: Nanostructured and Amorphous Materials Inc.), oftentimes premodified with functional groups that aid in solubility and bioconjugation, which may
encourage more widespread application.
6.4
Biological Materials
Biological materials and biologically inspired materials (i.e., nonnatural amino
acids), similar to the organic materials, are a diverse group including, molecules,
proteins, and protein complexes. In addition, biological reactions creating bio- or
chemiluminescence are an interesting alternative to the requirement for an external
excitation source.
6.4.1
Natural Fluorophores
Of the various naturally occurring fluorophores, including certain amino acid
residues, reduced nicotinamide cofactors (NADH and NADPH), flavins (FAD
and FMN), porphyrins, and pyridoxal derivatives, it is the aromatic amino acids,
Trp, tyrosine (Tyr), and Phe shown in Figure 6.12 that dominate FRET applications
[47]. The primary advantage to using these naturally occurring amino acids is that
they have an endogenous presence in proteins, and when combined with FRET
analysis can be used to study protein structure and dynamics [197]. Imaging studies
of proteins can thus be completed with limited to no modification and even if these
residues are not present in a protein, they generally can be incorporated into the
peptide sequence with a minimal effect on its size, structure, and subsequent
interactions. The strong UV absorbance of proteins at 280 nm (commonly used for
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188
Figure 6.12 Naturally fluorescent amino acid residues. Structures of the aromatic amino acids,
tryptophan (Trp), tyrosine (Tyr), and phenylalanine (Phe).
quantitation) as well as an emission at 340–360 nm, originate mostly from the
indole ring of Trp; Tyr and Phe contribute to a much lesser extent [47]. The negligible
QY (0.02) of Phe makes it less amenable to FRET, except perhaps in intraprotein
configurations. Tyr is prone to quenching and energy transfer to Trp, leaving Trp as
the most reliable residue for FRET (detailed in Refs [47,50,198]). A potential liability
in the use of Trp for FRET is that the excitation lines and any donor/acceptor dyes
will be confined to the UV region. The fluorescence from these residues is also
environmentally sensitive and so their placement deep within a protein structure
will produce results that differ from those at the terminus of a small peptide.
The primary application of endogenous fluorophores, in particular Trp, is to study
the structure and function of proteins and peptides. FRET exchanges often occur
between Trp and other fluorophores [such as nonnatural amino acids (see Section
6.4.2), or organic dyes], but FRET can also occur between two Trp residues, termed
homo-FRET. Because of the low QY of Trp and its random distribution in molecules
of interest, this homo-FRET rarely occurs. However, Kayser et al. found it to be a
particularly useful tool for studying structure–function relationships in monoclonal
antibodies, which were found to have an unusually high Trp content [199]. Another
use of Trp as a natural fluorophore for FRET is to probe protein folding/unfolding,
an important yet poorly understood biological process [200–202]. For example, Jha
et al. used FRET to study the unfolding of a small protein, monellin [202]. The
transition of this small protein, from an unfolded to a folded state, is not completely
understood but by using a naturally occurring Trp and additionally labeling the
protein with the FRET acceptor thionitrobenzoate, researchers were able to determine that monellin unfolds gradually rather than all in one motion [202]. Visser et al.
utilized Trp homo-FRET to characterize protein folding of apoflavodoxin, demonstrating the potential of this method as a powerful means to understand some of the
still unknown mechanisms of protein folding [201]. Another salient example
leveraging Trp’s fluorescent properties to determine protein structure and function
is its use in understanding the membrane transport protein LacY [203]. LacY is a
sugar/Hþ symporter of E. coli bacteria and is widely studied. Trp fluorescence or
quenching was used to determine the conformation of LacY and the function of the
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
symporter. Understanding protein structural variations could also aid in determining the pathogenic process of certain diseases. Lee et al., studying the human
a-synuclein protein associated with Parkinson’s disease, used FRET between a fixed
Trp donor and a modified 3-nitrotyrosine acceptor to demonstrate an elongated
structure for the mutant protein associated with the disease [204].
While amino acids tend to dominate endogenous fluorophore FRET research,
porphyrins, which physiologically form transition metal complexes [e.g., iron (see
Section 6.5.2)], are found to have strong luminescent properties and have been
demonstrated as FRET acceptors and donors in various formats. Lovell et al., for
example, employed a caspase-3-specific peptide sequence modified with a rhodamine donor and porphyrin acceptor to monitor caspase activation in single cells
following induction of cell death [205]. In the pursuit of artificial light-harvesting
systems, porphyrin donors immobilized onto a clay surface (acceptor) were found to
reach energy transfer efficiencies approaching the ideal 100% [206].
6.4.2
Nonnatural Amino Acids
Intrinsic natural probes such as Trp, Tyr, and Phe are highly useful for visualization
of protein structure, movements, and interactions, and as mentioned are either
naturally occurring or can be introduced without significantly impacting the protein
structure. However, due to low QYs of both Phe and Tyr, Trp is the only widely used
natural fluorescent probe. To overcome this limitation nonnatural (also called
unnatural or noncanonical) amino acids have been fabricated [207–213]. These
nonnatural amino acids can provide larger QYs and new FRET pairs for protein
structure function analysis. One recently developed fluorescent nonnatural amino
acid p-cyanophenylalanine (PheCN) can be incorporated into a protein, minimally
disturbing the native protein structure [214], and can act as a FRET donor to Trp
(Figure 6.13) [207]. The photophysics of this useful nonnatural amino acid has
recently been characterized [211,215]. The Trp–PheCN FRET pair has been used to
determine detailed protein folding and unfolding in two small proteins, the villin
headpiece subdomain (HP35) and the lysin motif (LysM) domain [200]. Two other
nonnatural amino acids, 7-azatryptophan (7AW) and 5-hydroxytryptophan (5HW)
(Figure 6.13), were recently found to be FRET acceptors to PheCN [210]. The
7AW–PheCN FRET pair had a greater separation of fluorescent spectrums than
PheCN–Trp. Moreover PheCN, Trp, and 7AW can be used in a multistep FRET
system to investigate interactions of three points on a protein (see Section 6.6) [210].
Even newer nonnatural FRET pairs are continuously being developed. Recently,
L-4-cyanophenylalanine (pCNPhe) and 4-ethynylphenylalanine (pENPhe) were used
as FRET donors to Trp in order to probe the hydrophobic core of the protein
T4 lysozyme [216]. Another nonnatural amino acid was created by combining
p-aminophenylalanine derivatives with BODIPY fluorophores, generating a material
with an emission wavelength greater than 500 nm [208]. These amino acids were
incorporated into a calmodulin-binding peptide and FRET used to probe protein
binding and resulting conformational changes.
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190
Figure 6.13 Nonnatural amino acids. (a)
Structures of some selected nonnatural amino
acids, p-cyanophenylalanine (PheCN), 7azatryptophan (7AW), and 5-hydroxytryptophan
(5HW), derived from the naturally fluorescent
amino acids with the chemical modifications
shown in red. (b) Improving Stokes shift in
eCFP using FRET with a nonnatural amino acid.
Three-dimensional model of eCFP, which
carries the fluorescent amino acid (1) at the
surface-exposed position 39, is based on the
crystal structure of eCFP (PDB entry 2WSN).
Chemical structures of (bottom) the eCFP
fluorophore 4-[(1H-indol-3-yl)methylidene]
imidazolin-5-one (5; lex ¼ 434 nm,
lem ¼ 476 nm) and the fluorescent nonnatural
amino acid L-(7-hydroxycoumarin- 4-yl)
ethylglycine (1; lex ¼ 360 nm, lem ¼ 450 nm)
that together form a FRET pair. Normalized
absorption and fluorescence spectra of 1 [Abs
(1) and Flu(1)] and eCFP [Abs(eCFP) and Flu
(eCFP)]. The major absorption band of eCFP
shows considerable overlap with the
fluorescence spectrum of 1, thus fulfilling a
prerequisite for efficient FRET. (Reprinted with
permission from Ref. [217]. Copyright 2011,
American Chemical Society.)
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Nonnatural amino acids can also be used to modify FPs to enhance their
fluorescent properties via intramolecular FRET [209]. The nonnatural amino acid
L-(7-hydroxycoumarin-4-yl)ethylglycine, for example, was incorporated into recombinant cyan FP (CFP) [217]. The modified FP underwent FRET between the
nonnatural amino acid (donor) and the FP’s natural chromophore (acceptor),
resulting in emission at 476 nm with a 365 nm excitation wavelength (Figure 6.13).
This large apparent Stokes shift of 110 nm is much greater than the natural 40 nm
Stokes shift of CFP alone.
Nonnatural amino acids have also been applied to time-resolved FRET (TR-FRET),
which can be used to evaluate protein folding dynamics. Historically, Trp has been
used as a donor for TR-FRET measurements; however, a significant drawback is that
it exhibits a high degree of variation in its fluorescent lifetime, depending on protein
conformations. In an attempt to overcome this, an analogue of Trp, 5-fluorotryptophan (5F-Trp) has been proposed as a better candidate for TR-FRET [212]. The 5FTrp has more homogenous decay kinetics than Trp and is less environmentally
sensitive, making it an ideal donor for TR-FRET for the determination of molecular
structure in proteins.
As new nonnatural fluorophores are designed, and the study of these and
natural fluorophores progress, these materials could provide an even
greater utility for understanding proteins at a molecular level utilizing FRET
techniques.
6.4.3
Green Fluorescent Protein and Derivatives
FPs represent an increasingly diverse class of fluorophores that have shown great
potential as genetically encoded fluorescent tags for assessing protein location and
function (monitoring protein–protein interactions) in cell studies and the development of in vivo (signaling dynamics such as calcium ions) and in vitro
biosensors [4,22,168,218–221]. While GFP derived from the jellyfish Aequorea
victoria represents the prototypical fluorophore of this protein family, various GFP
mutations and Anthozoa (coral) homologues provide an increasingly diverse
range of photophysical properties (Table 6.1 and Figure 6.14), which stem
from their internal chromophores [155,168,169,218,222–224]. Newman et al.
give an excellent monograph of the FP basics [168]. To briefly summarize, FPs
self-generate their intrinsic chromophore from key internal amino acid residues,
which nestle deep in the core of the characteristic 11-stranded b-barrel FP
structure. The final photophysical properties of the mature FP are governed by
the extent of p-conjugation, subsequent chromophore transitions, and interactions with the surrounding amino acid microenvironment with the chromophore
(Figure 6.14) [155,168,169].
Key to the success of FPs has been the ability to genetically encode them via
commercial plasmids that can be expressed in a variety of cells/organisms
(available from ClonTech Laboratories, Inc., Life Technologies, Evrogen, and
MBL Intl. Corp.). The genetically encoded FPs are commonly attached to
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192
Table 6.1 Properties of some representative FPs summarized from www.microscopyu.com and
Ref. [168].
Protein
Source
In vivo
structure
A. victoria
E. quadricolor
D. striata
A. victoria
A. victoria
E. quadricolor
Monomera)
Monomer
Monomer
Monomera)
Monomera)
Monomer
A. victoria
Copepod sp.
A. victoria
E. quadricolor
Clavularia
coral
Emission
max. nm
Extinction
coefficient
M – 1 cm – 1
Quantum
yield
383
399
402
439
435
458
445
456
467
476
477
480
29 900
52 000
51 000
32 500
35 000
37 000
0.31
0.63
0.48
0.4
0.51
0.57
Monomera)
Dimer
Monomera)
Monomer
Monomer
395/475
482
484
483
493
509
502
507
506
509
21 000
70 000
56 000
56 500
70 000
0.77
0.53
0.6
0.6
0.8
E. quadricolor
A. victoria
A. victoria
A. victoria
Monomer
Monomera)
Monomer
Monomera)
508
514
516
517
524
527
529
530
64 000
83 400
77 000
104 000
0.6
0.61
0.76
0.77
D. striata
D. striata
Cerianthus sp.
E. quadricolor
Monomer
Monomer
Tetramer
Dimer
540
548
548
553
553
562
573
574
6000
71 000
60 000
92 000
0.7
0.69
0.64
0.67
D. striata
E. quadricolor
D. striata
A. sulcata
D. striata
D. striata
Tetramer
Monomer
Monomer
Tetramer
Monomer
Monomer
558
555
568
576
574
587
583
584
585
592
596
610
75 000
100 000
38 000
56 200
90 000
72 000
0.79
0.48
0.3
0.05
0.29
0.22
D. striata
D. striata
E. quadricolor
E. quadricolor
Monomer
Monomer
Monomer
Dimer
598
590
600
605
625
649
650
670
86 000
41 000
67 000
70 000
0.15
0.1
0.2
0.06
Absorbance
max. nm
Blue
EBFP
TagBFP
mBlueberry2
ECFP
CyPet
TagCFP
Green
GFP (wt)
Turbo GFP
EGFP
TagGFP2
mWasabi
Yellow
TagYFP
EYFP
mCritrine
Ypet
Orange
mBanana
mOrange
OFP
TurboRFP
Red
DsRed
TagRFP
mTangerine
AsRed2
mStrawberry
mCherry
Near-IR
mRaspberry
mPlum
mNeptune
eqFP670
a) Weak Dimer formation.
b) E ¼ Entacmaea genus.
c) D ¼ Discosoma genus.
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.14 Fluorescent proteins. (a)
Structure of A. victoria GFP showing the
dimensions of the protein, the intrinsically
derived p-HBI chromophore, and several
key residues surrounding the
chromophore (image generated using
PyMOL open access and PDB ID 1w7s).
(b) Chromophore structures of representative
FP color variants within each spectral class.
The conjugated ring structure of each
chromophore is colored according to its
emission profile. (Reprinted with permission
from Ref. [168]. Copyright 2011, American
Chemical Society.)
proteins of interest through the creation of FP chimeras that can subsequently be
used in cellular studies of protein location, protein–protein interactions, and the
development of biosensors to monitor cell signaling processes [4,168,219,220]. In
addition to the benefit of genetic manipulation, there are a number of advantages
and disadvantages to the use of FPs as fluorescent tags that should be factored
into their use as FRET donors/acceptors. FPs have a wide range of QYs (see
Table 6.1), ranging from 0.04 for AQ143 to 0.91 for ZsGreen, which depend on
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194
the mutations present and final chromophore structure, although the majority
are generally good with QYs > 0.5 [168]. Certain FPs have been found to possess
two-photon absorption properties that can be very advantageous in deep tissue
imaging applications [225,226].
Photophysically, FPs can take several hours to fully mature as the final
chromophore is formed through the protein folding process and any subsequent
chemical transitions [155,169,168,221]. The relative brightness of their fluorescence intensity is found to be intimately linked to the efficiency of the FP folding
process and mutation time [155,168,221]. FPs generally have relatively broad
absorption and emission profiles that may preclude “multiplex” analysis. FPs are
also prone to photobleaching and have known susceptibilities to pH, temperature, O2 concentration, and other environmental conditions. FPs are of a fairly
large size from a fluorescent tag point of view, Mw 25–30 kD and upwards,
which can be problematic in terms of maintaining the desired function of the
labeled target protein. In addition, certain FPs have a tendency toward the
formation of oligomers (dimers and tetramers), which can further confound
the size issue [168]. Also, location of the FP-tag in the target protein must be
carefully chosen so as not to significantly impact FP maturation and therefore
brightness [168]. Researchers continue to develop FP mutations that attempt to
address a number of these issues, including improved photostability [223],
decreased oligomerization [222], emission in the near–far IR region [169,227],
improved Stokes shifts [155], or photoactivatable (including photochromic)
properties [155,168,169,228].
Use of FP pairs in FRET and bioluminescence resonance energy transfer (BRET)
(see Section 6.4.6) applications is ever expanding, with dramatic implications for in
vivo imaging, biosensors, and cellular studies in particular [22,155,168,219,229–235].
FPs have revolutionized the detection and study of cellular events, and the more recent
combination of FPs and FRET imaging has taken this detection to new levels of
precision, allowing the study of protein–protein interactions and tracking biochemical
and protein signaling dynamics, reviewed in a number of excellent publications
[22,155,168,219,220,229,232,236]. There are two main FRET–FP strategies employed
when studying cellular processes, the nature of which is dependent on the process
being investigated. In the first strategy, typically employed for measuring intermolecular protein–protein interactions, it is common to tag each protein with either
the donor or acceptor FP (Figure 6.15a), as FRET emission will only take place when
the two (or more) proteins of interest interact. In the second strategy a protein or
biosensor construct is labeled with both the donor and acceptor FPs, and interaction
with the target species of interest results in some measurable change in the FRET
signal. There are a number of different biological processes that can be monitored
using the second strategy, including protease activity and activation, Ca2þ ion
fluctuations, measuring second messengers such as cyclic adenosine monophosphate
(cAMP) and cyclic guanosine monophosphate (cGMP), studying phosphoinositide
dynamics, and G protein-coupled receptor (GPCR) activation, and hence a wider range
of formats are/can be employed, some of which are highlighted in Figure 6.15b, and
recently reviewed in Refs [22,168,236].
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.15 Representative FRET-based
sensor formats that incorporate FPs. (a)
Monitoring protein–protein interactions. Here,
each protein is labeled with a FP that upon
interaction results in FRET. (b) Biosensors in
which binding of a small molecule induces the
association of two distinct moieties within the
single polypeptide chain. (c) Biosensors for
posttranslational modification. (d) Biosensors
in which a protein undergoes a conformational
change upon binding its small-molecule
ligand. (e) Biosensors for protease activity.
The donor is CFP and the acceptor is YFP in
these representations, however, a variety of
other FP FRET combinations could be
substituted. (Reprinted with permission
from Ref. [22]. Copyright 2009, American
Chemical Society.)
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196
While the use of FP pairs in FRET has been constantly expanding, advances need
to be made continually to enhance its effectiveness. Shortcomings in FP–FRET
include a large range in brightness in FPs, cross talk due to large emission spectra of
FPs, slow development of intramolecular sensors, and limited ability to create stably
transfected cells lines with FRET FPs. Though recent advances have achieved some
success in expressing FP–FRET pairs in a cell line [237,238], difficulty still exists in
achieving this goal [236]. With advances in developing cell lines to express FP–FRET
pairs, more research can be conducted using these systems, as researchers will be
able to more readily conduct experiments without the difficulty of transiently
transfecting cells. Brightness and cross talk issues can be mitigated by further
improving FPs for FRET. Development of additional FPs for FRET has also led to
multiparameter imaging using dual FRETpairs. Development of this technology has
important research implications as entire signaling cascades could potentially be
imaged in the same cell. The most commonly used FRET pair is CFP–yellow FP
(YFP), but even with this pair significant cross talk exists [229]. New, recently
developed FPs include enhanced GFP (EGFP) and mCherry, which have similar
brightness and reduced cross talk compared to CFP–YFP [239]. Lam et al. demonstrated a Clover–mRuby2 FP–FRET pair combination for monitoring kinase acitivity, guanosine triphosphate hydrolase (GTPase) activity, and transmembrane
voltage with significantly improved photostability, FRET dynamic range, and emission ratio changes versus CFP–YFP [224]. An orange fluorescent protein with a large
Stokes shift (LSSmOrange) has been developed, which can be used for intracellular
imaging, potentially allowing two FRET pairs in combination with CFP–YFP [240].
In a salient example of multiparameter imaging, four different cellular events were
recorded simultaneously using FP–FRET imaging [241]. Here, two CFP–YFP FRET
sensors that could be spatially resolved were combined with a spectrally distinct
mCherry–mORange FRET pair and a fourth sensor Fura Red. The development of
new FRET protein pairs for multiple parameter imaging could greatly expand the
use of FP–FRET and will accelerate discovery of cellular processes [242], cancer
research [236], and toxin detection [243].
Photoswitchable FPs, a subset of the larger FP community, for pcFRET have also
been demonstrated and have great potential for high-resolution imaging applications [155,168,169]. Photochromic/photoswitchable FPs are under continuous
development, and the various mechanisms/factors that govern photoswitching
have recently been reviewed [155,168,244]. Switching is thought to occur primarily
through a cis–trans isomerization of the FP chromophore, as demonstrated with
isolated synthetic chromophore analogues [245,246], however the chromophore
environment within the FP structure also plays a key role in determining a FPs
switchability [78]. Recently, it has been discovered that substitution of certain key
amino acids in the chromophore environment within the FP structure can improve
and/or restore the photochromic behavior of the FP chromophore, leading to
improved photoswitchable FP mutations for pcFRET studies [78,244,247]. Grotjohann et al., for example, generated a reversibly switchable EGFP (rsEGFP) mutant
that could be cycled 1200 times before experiencing a 50% reduction in
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
fluorescence, in stark contrast to FP Dronpa that experiences a 50% reduction after
only 10 cycles [247]. The red FP (rsTagRFP) can be photoswitched from “on” and
“off” fluorescent states using 445 and 570 nm lights, respectively [248]. The
rsTagRFP was subsequently used as an acceptor with an enhanced YFP (EYFP)
donor to monitor protein interactions in pcFRET studies of living cells, where the
on–off switching provided confirmation of the FRET signal and the protein
interaction. Other photoswitchable FPs include Dronpa [249] (and variants
bsDronpa and Padron [228]), rsCherry [250], and rsCherryRev [250].
While pairing two FPs for FRET is the most common combination when
utilizing FPs, there are increasing examples of FP donors or acceptors being
paired with other fluorescent materials for FRET applications. There are a number
of BRET examples discussed in Section 6.4.6 and also multi-FRET examples where
the FP is coupled with light-harvesting complexes or proteins (see Section 6.6).
Rice created a kinesin C-terminal GFP fusion and labeled the kinesin with
tetramethylrhodamine, allowing FRET monitoring of protein conformational
changes upon binding nucleotides [251]. Hoffman dual labeled a GPCR system
with CFP and the FlAsH system to monitor receptor activation demonstrating
that, unlike the equivalent CFP–YFP-labeled system, downstream signaling was
not disrupted by the FlAsH acceptor [252]. FP acceptors combined with QD
donors are becoming an increasingly common combination, especially in the
development of biosensors for measuring protease activity [230] and intracellular
pH (Figure 6.16) [79].
Clearly, FP-based FRET has already made a significant impact on our understanding of cellular processes, and as the materials themselves continue to evolve
and improve, more sophisticated applications can be expected.
I
Figure 6.16 QD–FP FRET-based pH sensor.
(a) Schematic demonstration of the pHdependent energy transfer between the QD and
the FP. In an acidic environment, energy
transfer to the FP FRET acceptor is minimal,
yielding a high QD signal; at neutral or basic
pH, energy transfer is more efficient, producing
an enhanced FRET signal. (b) A pH titration of
QD–FP probes containing the FP acceptor
mOrange M163 K showing increased energy
transfer at alkaline pHs with a clear isosbestic
point. Cellular imaging of QD–mOrange pH
sensor. (c) Schematic of probe color changes
during progression through the endocytic
pathway. FRET efficiency is high in the neutral
pH of the extracellular environment and early
endosome. FRET efficiency decreases as the
endosome matures and the endosomal pH
drops, resulting in diminished emission from
mOrange and recovery of some QD signal. Any
probe that escapes the endosome regains its
elevated FRET efficiency in the pH neutral
cytoplasm. (d) Fluorescence microscopy
images immediately after delivery of the probe
and 2 h post delivery. The QD images (left)
demonstrate consolidation of the probe in
the endosomes over time; images of the
direct excitation of mOrange (center) and FRET
emission (right) indicate a clear decrease in
the mOrange emission and the FRET
efficiency of the probe with maturation of the
endosome. (Reprinted with permission
from Ref. [79]. Copyright 2012, American
Chemical Society.)
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
6.4.4
Light-Harvesting Proteins
Phycobiliproteins (PBPs) are the colored component proteins found in naturally
occurring phycobilisome-based light-harvesting complexes (see Section 6.6)
[253,254]. Their intense color originates from the combination of chromophores
they contain, termed phycobilins. Examples of phycobilins include phycocyanobilin (PCB – blue), phycoerythrobilin (PEB – red), phycourobilin (PUB – yellow),
and phycobiliviolin (PXB – purple). In phycobilisome-based systems, there are
four main PBPs: allophycocyanin (APC), phycocyanin (PC), phycoerythrin (PE),
and phycoerythrocyanin (PEC); some spectroscopic details are summarized in
Table 6.2 [254,255]. Peridinin–chlorophyll–protein (PerCP or PCP) is a lightharvesting complex found in dinoflagellates and has a smaller MW (35 kDa) than
most of the 100–240 kDa PBPs mentioned, which can be beneficial when the size
of the fluorescent label is a concern. Since their inception as fluorescent probes,
the purified PBPs themselves (e.g., phycofluor probes), complexes containing
multiple PBPs (e.g., PBXL), or the smaller PerCP materials have become
common fluorescent labels in bioassays, especially in flow cytometry
[254,256–259]. Their use as fluorophores in FRET has been more limited to
date, and may be due in part to their relatively large size – although some of the
smaller materials being developed (e.g., PerCP and CryptoFluorTM) may address
this concern. That said, they have been demonstrated in sandwich-based peptide
and antibody FRET assays for target analyte detection and for demonstrating
FRET in combination with Au and QD NMs [121,257,260–264]. The combination
of APC (acceptor) and Eu-cryptate (donor) has been used for the time-resolved
FRET-based detection of telomerase activity [262], inhibitors of hepatitis C virus
core dimerization [264], and small-molecule inhibitors of HIV-1 fusion [263]. A
number of companies sell PBP- and PerCP-based materials, including Life
Table 6.2 Properties of some representative phycobiliproteins summarized from
www.columbiabiosciences.com and Ref. [254].
Protein
Allophycocyanin
(APC)
R-Phycoerythrin
(RPE)
B-Phycoerythrin
(RPE)
Approx. Types of Approximate
MW
phycobilins number of
kDa
present
phycobilins
100
240
240
PCB
PEB and
PUB
PEB and
PUB
6
34
34
Extinction
coefficient
M – 1 cm – 1
Quantum
yield
657.5
2.4 105
0.68
573
6
1.96 10
0.84
572
2.41 106
0.98
Absorbance Emission
max. nm max. nm
652
625a)
565
498a)
545
563.5a)
Note: Exact properties are dependent on the origin of the protein PCB: phyocyanobilin, PEB:
phycoerythrobilin, and PUB: phycourobilin.
a) Additional absorbance peak.
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200
Technologies, Jackson ImmunoResearch (mainly streptavidin antibody-labeled
and secondary antibody-labeled materials), the SureLight1 series from Columbia
Biosciences, and the CryptoFluor materials from Martek Biosciences Corp. (sold
by Sigma-Aldrich).
6.4.5
DNA-Based Macrostructures/Nanotechnology
DNA is an incredibly complex polymeric material comprising four monomers –
adenine (A), thymine (T), guanine (G), and cytosine (C) – that can be single
stranded (ss) or doubled stranded (ds), which results when two complementary
strands hybridize [265]. Researchers are increasingly interested in using the
polymeric nature of DNA to synthesize unique 2D and 3D DNA-based macromolecular/nano structures [265–268]. The use of functionalized DNA nanostructures for light harvesting and charge separation has recently been
reviewed [269]. Researchers have already demonstrated the potential of these
DNA structures as fluorescent labels using some relatively simple DNA
constructs. Accumulation of perylene- and pyrene-based fluorophores in
DNA duplexes has been shown and produces fluorescent excimer structures
very strongly, which possess large Stokes shifts, making them ideal donors
in FRET applications [270,271]. Kumar and Duff engineered some unique
DNA–protein complexes that demonstrated potential as light-harvesting complexes [272]. The Armitage group developed DNA tetrahedron and duplex
fluorescent nanotags using FRET to shift the emission of the DNA nanotag
further into the red region relative to the donor dye alone (Figure 6.17)
[273–275]. Although the majority of these DNA-based structures are designed
in-house, the DNA sequences themselves are often synthesized and purchased
commercially [ from companies such as Integrated DNA Technologies (IDT)].
Genisphere1 sells a 3DNA-based dendrimer that is marketed for signal
amplification in a number of bioassays. Given the ease with which fluorescent
dyes can be incorporated into these unique structures, through either intercalation or covalent attachment, it seems likely that the utility of these materials
as fluorescent labels and their subsequent use in FRET-based applications will
increase in the future.
6.4.6
Enzyme-Generated Bioluminescence
Enzyme-generated bioluminescence (BL) is used in a particularly advantageous
variant of FRET known as BRET. BL is a naturally occurring phenomenon found
in certain beetles and bacterial or marine species, where various substrates
(luciferins) react with enzymes (luciferases) in the presence of O2 (and sometimes
other cofactors) to produce light emission (Table 6.3) [276–281]. The exact wavelength of the light emission is found to be dependent on a number of factors,
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.17 DNA NMs for FRET. (a) Assembly
of DNA tetrahedron nanotags. Four strands
with partially complementary sequences form
the DNA tetrahedron nanostructure template
for the self-assembly of intercalator dyes. Black
sections represent two-nucleotide long, singlestranded hinges. (b) Schematic description of
ET (energy transfer) in a tetrahedron nanotag
loaded with YOYO-1 intercalated dyes and
covalently attached Cy3 acceptor dyes.
(c) Fluorescence emission of tetrahedron
nanotags with 0–4 covalently attached Cy3
molecules. Spectra acquired by excitation at
440 nm. Samples contained 50 nM DNA
tetrahedron and 1.28 M YOYO-1. ET efficiencies
given in legend were determined by the
percentage of decrease in the YOYO-1 emission
at 509 nm. (Reprinted with permission from
Ref. [274]. Copyright 2009, American Chemical
Society.)
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including the structure of the luciferin, the nature of the luciferase, and the
presence of accessory proteins, physiologically, GFP or its derivatives [277]. BL
itself has found application as a reporter in many bioassays, both in vitro and
in vivo [278–282].
The use of the BL reaction as a donor within energy transfer mechanisms is, in
fact, an intrinsic process observed in many sea creatures such as A. victoria
(jellyfish) and Renilla reniformis (sea pansy), where accessory proteins (e.g., GFP)
modify the color of the emission through BRET [277]. Researchers have used
BRET in a number of applications, most notability for studying protein–protein
interactions, leading to drug discovery, and increasingly for biosensing and in vivo
imaging [283–288]. As with FRET, BRET depends upon spectral overlap between
the donor emission and the acceptor absorption, and it is similarly efficient over
distances up to 10 nm [278,284,287]. The principal advantage of BRET is removal
of the excitation source, negating problems such as light scattering, high background noise, direct acceptor excitation, photodamage to cells, and photobleaching effects [287,289].
The most commonly exploited luciferases for BL are the eukaryotic firefly and
Renilla luciferases (Rluc), with the wild-type enzymes generating blue-green emission. DNA vectors with the desired luciferase gene or plasmids can be purchased
through a variety of sources such as Promega, New England Biolabs, and Targeting
Systems. These vector complexes are then internalized by the cell of choice, where
the luciferase gene can be transcribed by ribosomes to produce the desired enzyme.
Luciferases can also be fused to other proteins or fragmented to monitor protein
interactions of interest [276,290].
Improving the BL properties of these systems is an active field, and research
ranges from generating a wider variety of BL colors, spanning the visible to nearinfrared wavelengths, to improving the emission kinetics of the BL, by increasing
the intensity and/or decay of half-lives (reviewed in Ref. [278]). Research in this
area is two pronged, focusing on the luciferases themselves and the luciferin
substrates, with a wide range of protein mutants and substrate analogues now
produced/utilized (reviewed in Ref. [278]). Sun et al. recently reviewed progress in
D-luciferin amino analogues that produced emissions ranging from 460 to 609 nm
with wild-type luciferase [291]. Other D-luciferin analogues, reviewed by the
Meroni group, give insight into a variety of chemical manipulations that may
result in altered emitted light [292]. Caged luciferin, for example, is an alternative
firefly luciferase substrate designed for intracellular delivery available from
Molecular Probes [293]. Caged luciferin has also recently been synthesized for
the real-time in vivo imaging of H2O2 production in living mice [294]. Coelenterazine substrates have similarly been altered to provide both enhanced brightness and enhanced duration of photon emission, including ViviRenTM and
EnduRenTM from Promega, and several analogues with different emissions
are available from Molecular Probes and Biotium [295,296]. In an effort to
continuously improve BRET, recent studies by Zhang and coworkers have shown
improvements in both sensitivity and limit of detection by 10-fold and 7-fold,
respectively, through the use of an enhanced buffer environment [297].
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
As illustrated in Table 6.3, a variety of luciferase types can be combined with
essentially three different chemical substrates to produce BL for BRET applications. Bacterial luciferases, for example, catalyze the oxidation of reduced flavin
mononucleotide (FMNH2) and a long-chain aliphatic aldehyde in the presence of
O2, yielding blue light [298,299]. Bacterial luciferase, however, is not optimized for
most mammalian cell lines and the substrate, FMNH2, is rapidly oxidized in air,
generating short bursts of light and not a steady BL emission [300]. Firefly
luciferases differ from bacterial luciferases in that they require an additional
cofactor, ATP, in order to catalyze the oxidation of the substrate luciferin, leading
to the emission of green-yellow light. Initial BL in this case is intense and then
decays to a low-sustained luminescence, which can be aided by an additional
cofactor, coenzyme A, to yield more stable, high-intensity luminescence [301].
Rluc is one of the most commonly utilized luciferase systems and uses the
substrate coelenterazine in the presence of O2. It has been widely adapted to
mammalian cell lines, and hRluc is available from a variety of sources, including
Promega and PerkinElmer Life Sciences; cofactors are not needed. Improvements
have been made upon the wild-type enzyme, producing the often used mutants,
namely Rluc2 and Rluc8, which have improved BL properties [287,302,303].
Another coelenterazine-based luciferase that has begun finding wide application
is derived from Gaussia princeps (Gluc or hGluc) and marine copepods (BL
crustacean), and has been optimized for expression in both bacterial and mammalian cells [304,305]. The low molecular mass of Gluc (20 kDa) compared to Rluc
(36 kDa) addresses problems associated with steric constraints in chimeric protein
fusions. Gaussia luciferase expressed in mammalian cells reportedly generates
light up to 1000-fold brighter than that of native Renilla [306,307]. BL photoproteins from jellyfish and hydroid species, namely aequorin (from A. victoria)
and obelin (from Obelia longissima), respectively, are also coelenterazine-based
enzymes that differ from luciferases in that the enzyme is complexed to its
coelenterazine substrate and is Ca2þ sensitive [308]. The principal application of
these photoproteins has been as Ca2þ reporters [309,310]. In BRET applications
aequorin has been employed to monitor the protein–protein interactions between
SA and a biotin carboxyl carrier protein [311].
In terms of BRET these BL enzymes are most commonly coupled with FPs, a
combination that has been fueled by the desire to push the BRET emission further
into the near-IR for optimal in vivo imaging. This has been facilitated by the
increasing number of mutant BL enzymes, substrate analogues, and mutant FPs
that allow good spectral overlap of the generated BL with the FP absorption
[155,218,278]. As a result there are a variety of BL enzyme–FP BRET configurations,
termed BRET x [288,302,312,313]. In BRET1 the BL enzyme variant is Rluc or Rluc8
and the accepting protein is a GFP variant, YFP. Oxidation of the substrate
coelenterazine-h by Rluc results in BL with a 480 nm peak, which, through energy
transfer to YFP, generates a fluorescent emission peak at 530 nm. Typical uses of
BRET1 are ligand screening applied to real-time detection of protein–protein and
protein–ligand interactions, such as agonist-induced interactions of the GPCRs
family of receptors [287,288,314]. BRET has been used to study a number of the
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206
GPCRs, irrespective of their G protein-coupling selectivity [287,288], and is particularly amenable to high-throughput formats [287]. BRET2 utilizes the BL enzyme
variants Rluc, Rluc2, or Rluc8 and acceptor GFP2 (a GFP variant with Ex 400 nm and
Em 511 nm). Reaction of the coelenterazine analogue substrate, DeepBlueC (coelenterazine 400A, sold commercially by Biotium, Inc., PerkinElmer, and NanoLight
Technology), with the Rluc enzyme causes a BL emission at 400 nm, resulting in
excitation of GFP2 and an endpoint emission at 511 nm [287,288,314]. This
configuration works like a standard BRET assay, but has a larger apparent Stokes
shift resulting in more spectral resolution between the donor–acceptor pair. This
technique was successfully applied to visualize protein–protein interactions in mice
[312] and RNA detection and quantification (Figure 6.18a) [315]. BRET3 again uses
Rluc, Rluc2, or Rluc8 and the fluorescent protein mOrange with a coelenterazine
substrate [313]. Advantages of the BRET3 combination include several-fold improvement in light intensity, as well as improved spatial and temporal resolution for
measuring intracellular events in a single cell. This improved BRET strategy allows
the visualization of protein–protein interactions within small living animals
[287,288,313,314]. The Gambhir group has subsequently demonstrated additional
BRET x systems with various combinations of Rluc variants (Rluc8 and Rluc8.6)
combined with two red FPs, TagRFP, and TurboFP635, using the substrates
coelenterazine and its analogue coelenterazine-v to generate a red light-emitting
600–650 nm reporter system for in vivo protein–protein association studies [302].
BRETx systems are initially characterized/optimized by generating a fusion
protein of the BL enzyme and the FP, and these fusion proteins represent
interesting tags in their own right and may be useful labels for a variety of bioassays
[316]. For example, they have been used in sequential BRET–FRET assays, termed
SRET, for detection of heteromerization in plasma membranes and ratiometric
protease assays [286,314,317,318]. Extended BRET (eBRET) typically uses the
enzyme variant Rluc or Rluc8 with YFP (Ex 480 nm and Em 530 nm). A presubstrate,
a protected form of coelenterazine (EnduRen from Promega), is metabolized by
endogenous esterases into coelenterazine-h similar to that used in BRET1. This
provides a steady supply of substrate for luciferase oxidation within cells for
extended periods of time up to 24 h [285,287,314].
Although less common, BL enzymes have also been coupled with traditional
organic dyes and increasingly NMs, especially QDs as acceptors [283,286,319–321].
Currently QD–BRET has been used for sensing protease activity, protein–protein
interactions and in vivo imaging, as reviewed in Ref. [283]. Enhanced BRET between
the firefly Photinus pyralis luciferase variant PpyGRTS quantum rods (QRs) as the
energy acceptor has also been described recently, with BRET ratios dependent upon
enzyme loading, rod aspect ratio, and donor–acceptor distances (Figure 6.18b) [320].
Protease activity sensing in a QD–BRET system relies on a peptide substrate linkage
between the luciferase and the QD that is cleaved in the presence of the protease of
interest, reducing the BRET-based QD emissions [321]. QD–BRET has also been
used to study protein–protein and receptor–ligand interactions. For example, Rao
and coworkers fused luciferase (Luc8) to HaloTag protein and functionalized QDs
with HaloTag ligands to study the resulting BRET that occurred when the HaloTag
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6.4 Biological Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.18 (a) General strategy for BRETbased RNA detection. Probe1 consists of a 20mer oligonucleotide conjugated at the 50 end to
the thermostable bioluminescent protein (RL8).
Probe2 consists of a 20-mer oligonucleotide
conjugated at the 30 end to the fluorescent
protein GFP2. Both the probes are
complementary to different portions of the
same mRNA target gene. Thus, the target
mRNA serves as a scaffold upon which the
probes can bind, bringing the proteins into
proximity to one another. When RL8 oxidizes its
substrate, the energy produced is nonradiatively
transferred to GFP2, which then emits photons
at a characteristic wavelength as its
chromophore returns to the ground state. A
dual probe assay testing sensitivity with mixed
populations of in vitro-transcribed cRNA as
targets. RL8 and GFP2 were combined with
various amounts of Fluc cRNA, while keeping
the level of total cRNA constant by
supplementing with nontarget cRNA.
Statistically significant BRET signal was seen for
as little as 1 mg Fluc cRNA. Inset: raw image
obtained in IVIS-200. Rows from top to bottom
match columns left to right of figure. Left image:
shows GFP2 filter; Right image: shows RL8 filter.
(Reprinted with permission from Ref. [315].
Copyright 2008, American Chemical Society.)
(b) BRET between QRs and firefly luciferase
enzymes. (i) BRET efficiency plots for PpyGRTS
donors and QR acceptors. The summary of the
BR measured with respect to aspect ratio at
L ¼ 5 and 10 for (ii) CdSe/CdS and (iii) CdSe/
CdS/ZnS QRs. (iv) Illustration of the
microstructure of the particular QRs studied,
including dot-in-dot, rod-in-rod, and dot-in-rod
types. (Reprinted with permission from
Ref. [320]. Copyright 2012, American Chemical
Society.)
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208
protein irreversibly bound the HaloTag ligands [286]. Interestingly, in vivo imaging
with a QD–BRET system has the potential to overcome the natural tissue scattering
and autofluorescence, which affects a large number of BRET acceptors with short
wavelength emissions. QDs are available with emission in the red and near-IR
ranges, which coupled with their broad absorption profiles makes them an excellent
acceptor for BRET. This was first shown in a mouse model where superficial and
deep tissues were imaged using QDs with a 655 nm emission, which were coupled
to Luc8 [319]. As highlighted later in the QD section (Section 6.5.5), the relatively
narrow emission profiles open up the possibility of multiplexed sensing of protein–
protein interactions using a number of QD–BRET pairs [286,321].
The BRET platform has been used for sensing a variety of analytes, including
Ca2þ, through the use of the described photoproteins and ATP. BRET is possibly
most often used for monitoring protein–protein interactions such as the earlier
described GPCR activation as well as the QD–BRET system for determining
reaction kinetics of HaloTag protein binding to HaloTag ligands [286]. Similarly,
BRET has been utilized for nucleic acid hybridization assays and immunoassays,
with the latter available for purchase from a variety of companies. As an example
of a nucleic acid hybridization assay, Kumar et al. utilized Rluc bound to an
oligonucleotide probe and a QD on the nucleic acid target [322]. Hybridization of
the probe to target strands increased resonance energy transfer and QD emission.
Cell-based BRET assays as well as in vivo BRET imaging are also becoming more
popular as more BRET pairs become available for the selected applications as
described, although care should be taken if quantitative BRET data is desired
[285,287,314].
6.4.7
Enzyme-Generated Chemiluminescence
Conceptually, there is little difference between the mechanism of BL (Section
6.4.6) and enzyme-generated chemiluminescence (CL), other than in CL the
luminophore is a synthetic substrate [278]. CL substrates include luminol and its
derivatives, 1,2-dioxetanes and acridinium esters, which are brought to an excited
state through an enzymatically catalyzed reaction [282]. In direct CL, enzymatic
activity upon the substrate leads to electromagnetic radiation and an electronically
excited intermediate, which luminesces. Indirect or sensitized CL occurs when
the energy is instead donated to another molecule, which in turn luminesces
[323]. Table 6.4 describes some common CL substrates, processing enzymes, and
chemical reactions. Applications of CL include immunoassays, protein blotting,
DNA probe assays [324], detection systems in separative and flow-assisted
analytical techniques [325], measurement of target analytes with biospecific
probes, measurements of substrates, cofactors, or quenchers, and in vitro and
in vivo imaging [282].
CL resonance energy transfer (CRET) is a concept and laboratory technique that is
widely underutilized in current research; however, enhanced substrates, altered
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6.4 Biological Materials
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enzymes, and NM amplification are slowly widening the range of useful applications
[282,323,326,327]. The most widely used enzymes for CRET systems include
horseradish peroxidase (HRP) and the HRP mimic hemin/G-quadruplex DNAzyme
[327–329]. Although a variety of CL substrates exist for the HRP enzyme, luminol
and its luminogenic derivatives remain the most popular (Table 6.4) [282,330,331].
As illustrated in the table, HRP oxidizes luminol to a luminescent species in the
presence of hydrogen peroxide, yielding blue emission at 425 nm. Luminol is
usually employed in conjunction with an enhancer such as luciferin, fluorescein,
or a phenolic compound (e.g., para-iodophenol) [332–334], which is thought to
increase the sensitivity of the assay through intermolecular energy transfer. HRP
enzymatic conversion of acridan substrates generates higher luminescent intensity
than luminol, when the luminescent acridinium esters intermediates decay, emitting yellow light (530 nm) [335–337]. Alkaline phosphatase is another enzyme that
has shown promise in CRET applications. This enzyme catalyzes the oxidation of
1,2-dioxetane luminogenic substrates as shown in Table 6.4 [338,339].
CRET has shown promise in microchip electrophoresis [340], measurement of
target molecules and proteins such as ATP [341], human immunoglobulin G (IgG)
[342], alpha fetoprotein (a cancer marker) [343], microRNA [344], DNA, metal ions,
and aptamers [328], with biospecific probes that are often single-stranded DNA.
Analogous to BRET, there is no outside excitation, though generally the QY in CL is
lower than BL. Much work has been done using NMs, including QDs [326], Au NPs
[343], and graphene to enhance the QY, overall CRET brightness, and usability. A
great review of many of these techniques can be found in Ref. [327]. In addition to
NPs, magnetic beads have also been used to create a sensing platform that aids in a
separation protocol when working with complex protein samples such as serum
[342]. Recently, work by the Willner group has focused on using CRET to generate
photocurrents. Through the use of a QD acceptor associated with electrical leads,
CRET occurring through the enzymatic action of hemin/G-quadruplex HRP on
luminol with triethanolamine as an electron donor, results in a detectable photocurrent [345].
CL and CRET research continues to evolve at a relatively slow pace compared to
FRET and BRET. Recent advances with the use of QDs and other NMs, coupled with
the large number of recombinant enzymes available, the low-cost commercial
substrates, and control over emission wavelength, will drive further exploration
of CRET for sensors and other applications.
6.5
Inorganic Materials
Inorganic materials typically take the form of chelates, doped nano- or microparticles or NMs. They have a range of unique properties including bright luminescence, strong quenching abilities, large Stokes shifts, and long luminescent
lifetimes that make them highly desirable for energy transfer applications as
discussed in more detail later.
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
6.5.1
Luminescent Lanthanide Complexes and Doped Nano-/Microparticles
Luminescent lanthanides are a prominent class of long-lifetime fluorophores used
by the energy transfer research community for a wide range of bioapplications,
mainly focused on in vitro and in vivo sensing and imaging [9,346–349]. The majority
of the trivalent lanthanide ions are luminescent, with terbium (Tb), Eu, samarium
(Sm), thulium (Tm), and dysprosium (Dy) emitting in the visible spectrum, while
ytterbium (Yb), neodymium (Nd), and erbium (Er) emitting in the near-IR. Their
emission spectra are comprised of several well-separated narrow lines coupled with
long excited-state lifetimes on the order of several milliseconds. Long lifetime dyes
(fluorescent lifetime t > 100 ns–ms) have a number of technical advantages over
conventional fluorescence dyes (t ¼ 1–5 ns). The principal benefit arises from the
ability to gate out (through time-resolved measurements) background fluorescence
from direct excitation of acceptor dyes, scattering, and autofluorescence from cells
and biomolecules, which can dramatically improve sensitivity. Use of time-based
measurements may also necessitate more complex equipment than steady-state
fluorimeters. However, because these are long-lifetime dyes (microsecond–millisecond) many standard microtiter well plate readers are available with measurement
capabilities in this timescale.
For bioapplications, lanthanide ions are either complexed within an organic
chelate/cryptate ligand producing classical coordination metal complexes [luminescent lanthanide complexes (LLCs)] or doped into ceramic-type materials and
formulated as nano-/microparticles. These complexes help to improve the optical
properties of the lanthanides as well as their photostability and chemical stability,
discussed in more detail later [9,347–349].
The LLC chelate ligands vary in form, but include derivatives of polyaminocarboxylates, cyclen, hydroxyquinoline, salicylamide, and phenylporphyrin, which
have been recently reviewed [348]. The chelate ligands fulfill a number of
functional roles in the development of successful LLC bioprobes, with ongoing
research to further improve/match their properties to target applications
[3,347–351]. First, the lanthanide ion must be tightly bound within these chelate
complexes, resulting in higher thermodynamic and photochemical stability,
which shields the lanthanide ion from the quenching effects of the surrounding
solution. Second, compared to common dyes, lanthanide ions have very low
extinction coefficients (1 M1 cm1), making them difficult to excite directly.
Thus, the chelate label contains an organic chromophore, referred to as the lightharvesting antenna molecule or sensitizer, which is placed in close proximity to
the ion. The sensitizing molecule absorbs incident light and due to close
proximity transfers this energy to the lanthanide ion, presumably by a Dexter
mechanism. Finally, the chelate label should possess a reactive group allowing
bioconjugation. Commercial sources of lanthanide probes include CIS-Bio International (cryptate-based probes), PerkinElmer (LANCE1), Life Technologies
(LanthaScreenTM), GE Healthcare (europium–TMT chelates), Lumiphore, and
Sigma-Aldrich.
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212
Other than their long luminescent lifetime, LLCs have a number of other
properties that make them excellent donors in luminescent resonance energy
transfer (LRET) studies. For example, LLCs generally have a large effective Stokes
shift, due to the separation of the absorption (by the organic chelate) and the
emission spectra of the complex (from the lanthanide ion following energy transfer
from the organic chelate), which reduces the potential for direct excitation of the
acceptor. In addition, their emission spectrum manifest in the form of multiple,
distinct, and sharp emission bands, allowing LLCs to be coupled to multiple acceptor
dyes [352,353]. Tb, for example, has good spectral overlap with fluorescein, rhodamine, Cy3, and a number of AlexaFluor dye acceptors (Figure 6.19a)
[346,352,353]. LLCs have also been found to undergo a phenomenon termed
nonoverlapping FRET (nFRET), a mechanism not fully understood, which occurs
between a LLC donor and a spectrally nonoverlapping acceptor [354,355]. Using a
DNA hybridization assay, Vuojola et al. investigated nFRET between Eu(III) chelate
and various AlexaFluor dyes (with varying degrees of spectral overlap with the Eu
donor). They found nFRET to be very efficient over short distances, more efficient
than predicted using conventional FRET theory, and unlike FRET, nFRET was found
to be temperature dependent, leading the authors to conclude that a thermal
excitation process was involved as part of the nFRET mechanism [354].
LRET using LLCs has been applied in a number of applications, including
monitoring protein–protein interactions in cells [356], monitoring orthogonal ligand-dependent protein–peptide binding events [352], high-throughput screening of
potential drug candidates [357], and numerous in vitro bioassays [347,353,358–361].
Kupstat et al., for example, developed a homogeneous time-resolved immunoassay for
prostate-specific antigen (PSA) that was sensitive and quantitative, and could be
incorporated into a point-of-care testing (POCT) device [360]. A sandwich immunoassay format was used in which the two antibody species that recognized and bound to
different epitopes on the PSA were labeled with either the donor (Eu trisbipyridine) or the acceptor (APC protein). The presence of PSA brought the two
antibodies and hence the donor/acceptor species into close proximity, resulting in
LRET, with LODs two orders of magnitude below the clinical PSA cutoff of 4 ng/
ml. A similar format, using a Tb donor and five different acceptor dyes, was
recently used to detect five different lung cancer tumor markers simultaneously in
a 50 ml human serum sample [362]. Li et al. developed an adenosine sensor using
an aptamer-based sensor design, which functioned by inducing a conformational
change that disrupted the LRET (Figure 6.19b) [361]. The sensor was able to detect
selectively 60 mM of adenosine in undiluted serum samples.
The marriage of LLC donors and QD acceptors is a powerful combination in LRET
studies and takes full advantage of the many unique properties each brings to the
table, such as bright fluorescence (QDs), large Stokes shifts (both the QDs and
the LLCs), and time-gated measurements (LLCs) [363]. This donor/acceptor combination has found application in luminescent microscopy, time-resolved immunoassays, measuring protease activity, and detecting nucleic acid hybridization
[364–367]. Algar and coworkers in particular have developed a series of time-gated
FRETrelays, demonstrating the use of QDs as simultaneous acceptors and donors in
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6.5 Inorganic Materials
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j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
214
bioassays for monitoring protease activity and nucleic acid hybridization [365,366].
In the case of the protease activity bioassays, the authors were able to demonstrate
multiplex protease activity detection using a single QD color (Figure 6.20) [368].
Here, the QD (which acts as both a donor and an acceptor) was functionalized with
peptide substrates for trypsin (labeled with a luminescent Tb complex donor) and
chymotrypsin (labeled with an AlexaFluor dye acceptor). Activity of chymotrypsin
resulted in a decrease in prompt FRET (between the QD and the AlexaFluor dye),
while trypsin activity resulted in loss of the time-gated FRET (between the Tb
complex and the QD).
LLCs have also been incorporated into thin-film layers or NPs, either within the
core–shell structure or bound to ligands on the NP surface, for a range of
applications, including LRET-based bioassays, molecular imaging, and multiplex
signal labels [369–373]. Song et al. developed core–shell nanostructures aimed at
improving the LRET efficiency of the NMs, which comprised a rhodaminefunctionalized silicon dioxide (SiO2) core surrounded by a Tb chelate-modified
SiO2 shell [372]. The resulting core–shell nanostructures had an energy transfer
efficiency of 80%, a large F€orster distance range of 5.7–11.3 nm, and an emission
lifetime of 0.25 ms.
Besides LLCs, lanthanide ions are also doped into host ceramic materials, such as
oxides and fluorides, to generate phosphor/luminescent materials with unique
upconverting properties [upconverting phosphors (UCPs)]. Upconversion is a
nonlinear phenomenon where a material sequentially absorbs long-wavelength
photons and subsequently emits shorter wavelength emission, that is, converts
red to visible light, a different mechanism to multiphoton absorption, where the
photons are absorbed simultaneously [348,374]. The UCPs are routinely formulated
as NPs (UCNPs), where they have all the benefits of the LLC materials (i.e., timeresolved measurements, sharp emission profiles, etc.), but in addition UC of the
excitation light makes them excellent biolabels for in vivo imaging and in vitro
bioassays. UCNPs allow the use of cheaper red excitation sources, avoid background
autofluorescence from complex biological samples (improving sensitivity), and use
near-IR excitation (typically 980 nm) allowing greater tissue penetration depths,
while minimizing photodamage to biological samples [375–379].
The most common crystalline host material used for generating UCNPs is the
fluoride NaYF4 that is either doped with one type of lanthanide species or, as is more
common, codoped with two lanthanide species [374,377]. Codoping improves
the UC efficiency with Yb3þ and Er3þ, representing a popular combination.
3
Figure 6.19 LLC materials for FRET. (a)
Excitation (Ex) and emission (Em) spectra of
Tb3þ chelate (black) versus fluorescein (green),
and Alexa633 (red). (Reprinted with permission
from Ref. [352]. Copyright 2007, American
Chemical Society.) (b) Scheme of the adenosine
sensor design based on a Tb complex
conjugated to a DNA aptamer. (c) Steady-state
emission spectra of the aptamer sensor upon
the addition of increased concentrations of
adenosine in the HEPES buffer solution
(lex ¼ 344 nm). (d) Emission intensity of the
sensor at 545 nm as a function of adenosine
concentration. Inset: Shows the selectivity of the
sensor toward adenosine over other
nucleosides at 5 mM concentration. (Reprinted
with permission from Ref. [361]. Copyright
2012, American Chemical Society.)
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.20 LLC–QD combinations. (a)
Principle of the time-gated Tb ! QD ! A647
FRET relay. Optical excitation of the
conjugates yields excited-state Tb and an
excited-state QD ( ), and FRET2 is observed
on a prompt timescale (emission <100 ns
and integration time 20 ms). The extent of
FRET2 is measured via the ratio of prompt
A647 and QD PL, rp. Following a suitable
time delay (60 ms) during which the QD
returns to its ground state, FRET1 and
subsequent FRET2 can be observed. The
extent of FRET1 is measured in a time-gated
observation window via the ratio of gated
QD and Tb PL, rg. (b) Schematic of a time-
gated FRET relay for multiplexed protease
sensing. A central CdSe/ZnS QD is coated
with compact zwitterionic ligands (CL4) and
assembled with polyhistidine (His6)appended peptide substrates. The peptides,
labeled with either Tb or A647, serve as
substrates, SubTRP and SubChT, for TRP
and ChT, respectively. The cleavage sites are
highlighted in the peptide sequences.
Proteolytic activity disengages FRET and
alters the prompt and gated PL ratios, qp
and qg, which are used as analytical
signals. (Reprinted with permission from Ref.
[365]. Copyright 2012, American
Chemical Society.)
Here, the Yb3þ dopant acts as the near-IR absorbing ion (sensitizer), while the Er3þ
acts as the emitter/activator ion [374]. UCNPs can be prepared using a number of
synthetic procedures, including precipitation/coprecipitation, hydrothermal/solvothermal thermolysis-based techniques, and laser annealing; for more detail refer to
recent publications [377–384]. Ultimately, the goal is to prepare highly crystalline
structures (which improves the overall UC efficiency) that have a small particle size
combined with low size distribution, uniform dissemination of the doped lanthanide ions, good aqueous solubility, and the ability to bioconjugate, if required
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216
[374,377,380,385,386]. Common techniques to improve the aqueous solubility of
these inherently hydrophobic materials include polymer surface coatings (such as
silica shells), layer-by-layer techniques, ligand exchange, and surfactant addition
(including phospholipids), reviewed in Refs [376,377,380].
Lanthanide materials doped into oxides and fluorides, which take advantage of
time-resolved measurements (but not the UC potential), have been used in LRET
studies for a range of applications including labels in bioassays, imaging, and NP/
bioconjugation characterization [387–390]. However, fully exploiting the UC properties is more common and UCNPs have a wide range of applications, including
display devices, solar cells, optoelectronics, lasers, catalysis, and biolabeling, such as
bioassays, imaging, and therapy, which have been the topic of recent reviews
[374,377,380,385,386,391,392]. In most cases the UCNPs donors are coupled
with the traditional organic fluorophore acceptors, although there have been reports
of UCNPs coupling with QD [393] or Au NP [394] acceptor NMs. LRET-based in vitro
sensors using UCNPs have been successfully developed for small molecules, such
as ammonia [395] and glucose [394], nucleic acid hybridization [396], and protein
detection, such as caspase-3 [397] and avidin [392]. UCNPs combined with energy
transfer assays have also been used in various imaging studies, for example, to look
at the intracellular fate of small interference RNA (siRNA) upon uptake into cells
[398]. Cheng et al. developed multicolor UCNPs for multiplex in vivo mouse imaging
by tuning their emissions via LRET [399]. NaYF4 NPs doped with Er3þ/Yb3þ (green
emission – donor) were functionalized with an amphiphilic polymer before being
loaded with the fluorophores rhodamine B, rhodamine 6 G, or the quencher Tide
Quencher 1 (acceptor) to produce three different colored UCNPs (Figure 6.21). To
demonstrate the imaging utility of these materials, five UCNP materials – the three
described plus unmodified NaYF4: Yb, Er (green) and NaYF4: Yb, Tm (red) – were
injected subcutaneously into the back of nude mice, excited using a 980 nm laser
and imaged using a MaestroTM imaging system (PerkinElmer), which captured
multispectral fluorescence images (Figure 6.21). Spectral unmixing by the Maestro
imaging system clearly distinguished where each population of the UCNPs was
located in the mouse model, demonstrating the multiplex capability of the LRETcolor tuned UCNPs, when combined with the spectral imaging technology.
6.5.2
Luminescent Transition Metal Complexes
Transition metals integrated into organic complexes, either as classical coordination
metal complexes or as organometallic compounds (metal complexes containing at
least one metal–carbon bond), are found to have unique luminescent properties that
typically arise from a triplet metal–ligand charge transfer process and are reviewed
in Refs [9,400–404]. These complexes possess a number of favorable characteristics
that make them suitable for luminescent applications, including long excited-state
lifetimes (100 ns–ms), high photostability, and often a large Stokes shift. These
complexes have found particular application in cell imaging [9,400–404]. Of the
transition metals, ruthenium (Ru) complexes remain the most popular, however
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.21 Multicolor imaging of UCNPs.
(a) Multicolor UCL images of three UCNP–
dye complexes and a mixture of the three.
The images were obtained by the Maestro in
vivo imaging system after spectral unmixing.
(b) UCL emission spectra of solutions of
UCNP1, UCNP2, UCNP1/RhB, UCNP1/R6 G,
and UCNP1/TQ1 recorded by the Maestro in
vivo imaging system under the 980 nm NIR
laser excitation. Inset: Fluorescence spectra
of RhB and R6 G under green light
excitation. (c) Multicolor in vivo UCL imaging
of LRET-tuned UCNPs in mice. Left image: In
vivo multicolor UCL images of a nude mouse
subcutaneously injected with five colors of
UCNPs solutions after spectral unmixing.
Right image: A white light image of the
imaged mouse. (Reprinted with permission
from Ref. [399]. Copyright 2011, American
Chemical Society.)
increasingly iridium (Ir), rhenium (Re), and occasionally osmium (Os) and platinum (Pt) have been used in cell imaging applications [9,400–405]. The current factor
limiting widespread adoption of these types of materials is probably commercial
availability, as most of the materials are synthesized in-house. Sigma-Aldrich offers a
series of reactive Ru complexes, originally developed by Lakowicz as anisotropy
labels [406,407]. These Ru complexes have lifetimes of t 500 ns, small extinction
coefficients (14 500 M1 cm1), relatively low QYs (0.05), high photostability, fairly
large Stokes shift, and absorption close to the visible spectrum, but, most importantly, they are functionalized with moieties that facilitate bioconjugation.
While cell imaging dominates the biological applications of these luminescent
transition metal complexes, there have been some examples of their use in LRETbased studies. Ru complexes have been used as donors in immunoassays for human
serum albumin (HSA) [407,408] and for CO2 when coupled with the environmentally sensitive Sudan III disazo acceptor dye [409]. There are also examples of Ru
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218
complex acceptors, in metal complex – protein binding studies and thrombin activity
assays [410,411]. More recently, Ru complexes have played the role of both acceptors
and donors in a three-color FRET relay for studying DNA and polypeptide dynamics
and interactions [412,413]. Os(II) complexes have been coupled as acceptors in
FRET studies to QD donors [414,415], and Ir(III) FRET probes have been developed
for cysteine and homocysteine detection [416]. A Zn porphyrin cofactor in Zn(II)substituted horse heart cytochrome c was shown to serve as a donor to a Alex660
acceptor in cytochrome c unfolding studies [417]. CPEs (see Section 6.3.5), modified
with transition metal complexes, have also been developed for protein sensing
applications [138,418]. The CPEs are composed of main donor segments and
transition metal complex-modified acceptor units, which in aqueous solution
undergo polymer aggregation, resulting in efficient FRET. Addition of certain
proteins disrupts the polymer aggregate structure, resulting in a measurable
decrease in FRET efficiency. Demonstrations include HSA detection using Pt(II)modified CPEs [418] and histone detection using Ir(III)-modified CPEs [138].
6.5.3
Noble Metal Nanomaterials (Gold, Silver, and Copper)
Au, Ag, and other noble metal, such as Cu, NMs exhibit unique size- and shapedependent optical properties, due to surface plasmon resonances in the visible range
(see Figure 6.22 for Au example) [419,420]. These particles typically have larger
extinction coefficients (105 cm1 M1), more stable/nonfluctuating signal intensities, and greater resistance to photobleaching when compared to small-molecule
fluorophores [421]. Due to their strong absorbance, they are often used as quenchers
Figure 6.22 Au NPs. (a) Normalized UV–Vis
absorption spectra of Au NPs with different
sizes. (b) Photographs of the colloidal Au NPs
with different diameters (2.4–89 nm).
Concentrations of Au NPs are 670 nM (2.4 nm),
56 nM (5.5 nm), 17 nM (8.2 nm), 2.3 nM
(16 nm), 0.17 nM (38 nm), and 0.013 nM
(89 nm). (c) TEM images of Au NPs. Average
size and standard deviation are reported for
each sample. Scale bars are 20 nm (top) and
40 nm (bottom). (Reprinted with permission
from Ref. [419]. Copyright 2011, American
Chemical Society.)
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
(acceptors) in FRET applications; however, highly luminescent Au and Ag QDs or
nanoclusters have been synthesized, leading to their potential role as fluorescent
FRET donors/acceptors [422–424]. Excellent reviews on the properties of Au
[425,426] and Ag [427–429] NMs commonly used in optical applications can be
found in the literature.
Au NPs can be produced in various sizes using either the citrate reduction (16–
147 nm diameter) or the Brust–Schiffrin method (1.5–5.2 nm diameter) [425,430].
These NPs can also be produced in various shapes such as spheres, rods, shells,
cages, and plates [431–433]. Similarly, Ag NPs are often produced in various sizes
through the reduction of Ag salts, typically a stronger reducing agent leads to smaller
sized particles (<40 nm), which are often less stable over time than the larger NPs
[434]. Biogenically produced nanoAg provides an environmentally friendly synthesis
route [435], and various oligonucleotide sequences have been used to template Ag
nanoclusters [422]. Commercial sources of Au and Ag NMs are available in a wide
variety of geometries such as spheres, rods, and shells from relatively newer
manufacturers such as nanoComposix, NANOCS, and NanoPartz. More specialized
companies such as NanoRod, LLC or Microspheres-Nanospheres offer a wide
variety of Au nanorods or metallic nanospheres, respectively. Commercially available copper NPs are less common but can be purchased in organic solution from
SkySpring Nanomaterials, Inc.
One of the intrinsic benefits of using Au and Ag NPs is that they are readily
functionalized with ligands containing specific terminal chemical moieties (e.g.,
carboxyl or amine) or biomolecules through reactions with exposed thiol groups that
directly attach to the NM surface via formation of an Au–sulfur (S) [436] or AgS
bond [437]. Companies such as Structure Probe Inc., Nanoprobes, EB Sciences, and
Research Diagnostics Inc., offer an extensive array of colloidal Au in many sizes,
which are available functionalized with a variety of bioconjugates. British Biocell
International offers a variety of colloidal Au and Ag also prefunctionalized as
chemical or biological conjugates.
Au is by far the most commonly used material in optical applications, and while
Ag materials are mostly utilized for their antimicrobial properties, the increased use
of Ag NMs in optical applications stems from their high QYs, photostability, and
strong fluorescence intensities [427,438–443]. As a result of their native oxide layer,
copper NMs have been observed to enhance fluorescence signal [444], however,
recent syntheses that decrease the native oxide layer may increase the use of Cu NPs
as fluorescence quenchers in future optical applications [445].
In terms of energy transfer studies, the interaction of noble metal NMs and
fluorophores can be quite complex, resulting in either quenching or plasmonic
enhancement of the proximal fluorophores fluorescent signal [446]. Plasmonic
enhancement, observed in metal NPs coated with fluorescent dyes, is an energy
transfer-type phenomenon between the excited-state fluorophore and the plasmon
resonance of the proximal metal surface/particle [428,429,447–449]. Successful
plasmon enhancement requires careful spacing between the fluorophore and the
metal structure and factors such as metal type, NP size, and fluorophore can all
influence this complex process [450–456]. Plasmon enhancement has been
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220
exploited to increase FRET efficiency between DNA bound fluorophores [453–456],
and more viable configurations are expected in the near future.
Au and Ag (to a lesser extent) NMs are more commonly used for their “superquencher” abilities, that is, the ability to quench fluorescence over a broad range of
wavelengths. The fluorescence quenching ability is dependent on a number of
factors, including the NP size and shape, fluorophore distance from the NP surface,
fluorophore dipole orientation, and the amount of overlap between fluorophore
emission and NP absorption spectra, all of which influence the radiative and
nonradiative decay rates [432,445,457–459]. A number of detailed studies have
characterized the fluorescence quenching, via dipole–metal interactions, of various
fluorophores attached near the surface of Au NPs, and both FRET and nanometal
surface energy transfer (NSET) mechanisms have been proposed for emission
quenching, which have a d6 and d4 distance dependency on efficiency, respectively [445,460–465]. The NSET model extends the efficient nonradiative quenching
distance between the fluorophore and the proximal Au NP, effectively extending the
molecular ruler capabilities, and this has been put to good use in a number of energy
transfer studies [445,460–465].
The quenching abilities of Au NMs in FRET/NSET configurations are commonly exploited in a number of bioassay formats. Molecular beacon-based assays
for DNA sensing measurements, for example, produce 100-fold sensitivity
enhancements using Au NMs compared to previous dye–dye combinations
[466–469]. Au NP–fluorophore complexes show promise for in vitro diagnostic
applications as “noses,” with the ability to discern between various bacteria
species and strains, proteins in complex solutions, and between cancerous and
healthy cell lines [470]. These complexes have also been used for the detection of
malaria antigens [471], DNA analysis [472,473], and for in vivo probes for reactive
oxygen species, hyaluronidase, and protease detection systems [458]. Aptamers
modified with fluorophores and subsequently combined with Au NPs have been
used for the multiplex detection of adenosine, Kþ ions and cocaine [474], and
nanorulers for measuring binding-site distances on live cell surfaces [475]. In
addition, Au NPs have been tested as quenchers for semiconductor QDs (see
Section 6.5.5). QD–Au NP systems have been used as probes to monitor real-time
intracellular gene expression [476], to detect DNA hybridization events [477–480],
and for TNT detection [481]. Polystyrene microspheres surface modified with Au
NPs and QDs have been proposed as suitable FRET-probes for bioassays,
including measuring protease activity [482]. Results from these Au NP–QD
quenching demonstrations suggest that this FRET configuration has tremendous
potential. Besides the lower background and improved sensitivity, the ability
to label both the Au NP and QD with multiple biological moieties may
improve avidity.
While Au and Ag NPs are typically used for their quenching abilities, other
applications utilizing their ability to scatter or fluoresce light are increasing. Highly
fluorescent Au and Ag QDs consisting of only a few clusters of noble metal atoms
have been synthesized [423,424], and they show potential as labels in in vitro and
in vivo imaging [483]. Larger clusters of a few nanometer thicknesses show promise
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
as low photobleaching alternatives in cancer cell imaging [484]. Much like their
semiconductor counterparts, these Au and Ag QDs (or nanodots, NDs) have sizetunable emission maxima, shifting to longer wavelengths with increasing nanocluster size, although emission can also be influenced by other factors such as
surface ligands and crystallinity of the NM [424].
Although not strictly energy transfer based, plasmonic rulers consisting of two
plasmonic particles in close proximity, capable of detecting molecular binding and
folding events, offer several advantages over traditional dye-based FRET applications
in that they prevent photobleaching as well as allow for a 10-fold increase in
measurement range [485,486]. Plasmonic rulers may also be fabricated in three
dimensions allowing a more spatially complete understanding of complex molecular events [487].
The wide variety of materials and applications incorporating the light-altering
properties of noble metal NPs suggests the increasing importance of these particles
in optical applications.
6.5.4
Silicon-Based Materials
A number of Si-based materials, considered metalloid in nature, have been found
to have intrinsic fluorescent properties that are worth mentioning. Silole molecules and polymers, for example, are Si-containing five-membered cyclic dienes
structures that are found to become highly fluorescent upon aggregation [488].
The silole molecule 1,1,2,3,4,5-hexaphenylsilole (HPS) generates a strong aggregation-induced luminescence at 495 nm. Amorphous silica (SiO2) NPs have also
been found to exhibit inherent luminescence due to oxygen-stabilized defects in
the SiO2 lattice [489], although it is more common to dope silica NM structures
(core, core–shell, and shell structures) with organic fluorophores in the pursuit of
fluorescent NMs (see Section 6.3.4). Si NPs are a much more commonly utilized
luminescent form and are increasingly used as bioimaging agents due to their low
toxicity, resistance to photobleaching as well as their bright size-dependent
photoluminescence and broad excitation spectra [490–495]. Si NPs have been
investigated as fluorescent tags for DNA [496], photonic barcode devices [497],
potentially nontoxic materials for in vivo and in vitro imaging [498] including
biodegradable imaging systems [499], theranostic systems in which particles can
image as well as potentially treat cancer cells photodynamically [500,501], and
biomodal imaging systems in which iron-doped Si particles exhibit magnetic as
well as fluorescent properties [502]. The synthesis of Si NPs remains tricky, but
new methods for synthesizing and stabilizing them have been reported [503–505],
including those that provide a variety of particle geometries such as “flowerlike”
polyhedron [506], nanowires, and clusters [507]. An extensive review of Si NP
synthesis and physical properties can be found in Refs [495,508]. Future applications using Si-based NPs as FRET donors can be expected because of the
incredible photostability, tunability, and facile surface modification of these
materials.
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222
6.5.5
Semiconductor Nanocrystals
Colloidal luminescent semiconductor nanocrystals, or QDs, have a range of potential applications, including optoelectronics (lighting and advanced displays), optics
(lasers), solar energy, biotechnology, and medicine [509]. However, since their
inception as biological labels, applications in the biological arena have developed
exponentially [283,510–515]. QDs can function either as a passive fluorescent label
or in a more integrated/active role, where the QD both acts as a scaffold for
biorecognition and is intimately involved in signal transduction, through mechanisms such as FRET, BRET, charge transfer (CT), or CRET [283,512,513,516–518].
QDs possess a number of unique electro-optical properties that make them ideal
energy transfer labels [283,512,513,515,518,519]. Benefits include a size and chemical composition dependent emission that is narrow and symmetric in profile, high
quantum yields and extinction coefficients (enabling single-molecule detection),
broad absorption profile, large Stokes shift, large two-photon absorption properties,
and excellent resistance to photobleaching and chemical degradation
[283,512,513,515,518–521]. QDs have been synthesized from a range of binary
and ternary alloys such as ZnS, CdSe, CdTe, InP, GaN, PbS, ZnO, InGaAs, and
CdZnS, and their exact emission, which can span from UV-Vis to infrared, is found
to be dependent on both the chemical composition and NP size, resulting in a
tunable emission profile (Figure 6.23) [515,522,523]. For FRET, in particular, this
means that QD donors can be size-tuned or “dialed in” to have better spectral overlap
with a particular acceptor dye, improving FRET efficiency. The broad absorption
spectra and large Stokes shift found in QDs is also of benefit for FRET studies, as it
allows excitation of mixed QD donor populations at one wavelength far removed
from their emissions and also facilitates selection of an excitation wavelength that
corresponds to the acceptors absorption minima, thus reducing direct excitation
background signals. The ability to excite multiple QD donors using a single
excitation wavelength, combined with their narrow and symmetric emission (which
makes deconvolution of multiple fluorescent signals simpler), makes them attractive labels for multiplex applications [32,321,513,524–529].
As with any of the potential FRET labels discussed in this chapter, there are issues
to consider before using QDs. QDs have been found to blink under continuous
excitation, which may be problematic for single-molecule studies. QDs have a finite
size that can be both a benefit and a liability for FRET. In addition, the “as
synthesized” semiconducting nanocrystals are inherently hydrophobic, requiring
some type of modification, that is, surface coating, to facilitate water solubility while
maintaining their optical properties. Aqueous solubility can be achieved using three
main approaches: direct aqueous synthesis using hydrophilic stabilizing agents, cap
exchange of hydrophobic surfactants with hydrophilic ligands, and encapsulation/
coating with amphiphilic species, polymers, or silica coatings, reviewed in Refs
[512,513,515,519,530]. Encapsulation, in particular, can significantly influence the
hydrodynamic radius of the final QD and hence impact the distance-dependent
FRET efficiency [512,515,518,519]. A number of researchers have focused on
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.23 Dependence of fluorescence
emission wavelengths of QDs on their
chemical composition. The CdSe group is
expanded to demonstrate the sizedependent absorption and emission
profiles of the CdSe QDs, obtained by Peng
synthesis and different heating times: 3, 5,
7, 10, 14, 20, 25, and 30 min. (Reprinted
with permission from Ref. [515]. Copyright
2013, Elsevier.)
developing ligands that can facilitate both aqueous solubility and subsequent
bioconjugation of CdSe/ZnS QDs, while keeping the overall hydrodynamic radius
compact [512,513,515,519,531]. These ligands have evolved from simple designs
that facilitate aqueous solubility to multifunctional modular designs that comprise
an anchor group that interacts with the QD surface (commonly a monodentate or
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224
bidentate thiol), a hydrophilic segment that imparts solubility (e.g., PEG, zwitterionic nature), and a terminal functional group that can provide solubility and be used
for bioconjugation (e.g., OH, NH2, COOH, Biotin, and azide or
alkyne for click chemistry) [518,531,532]. Susumu et al., for example, designed
compact zwitterionic inspired ligands for preparing QDs and Au NPs [533]. The
zwitterionic nature of the ligands greatly improved the pH stability of the QDs,
compared to dihydrolipoic acid (DHLA) only preparations, without impacting the
hydrodynamic radius of the functionalized QDs (Figure 6.24) [533].
In situations where FRET efficiency is found to be low, the finite QD size can be an
advantage allowing multiple acceptors to be assembled around the central QD
scaffold, improving the FRET efficiency and potentially enhancing subsequent
biomolecular interactions (as recently demonstrated in proteolytic digestion studies
[368]), but this may not be desirable for all applications [3,518]. In addition,
dimensionality of the NM may be a factor influencing the FRET efficiency, as
found in the case of a QD donor (spheres versus rods) coupled to multiple acceptors
[534–536].
The broad absorption profile of QDs serves them well as FRET donors, however it
can be problematic for their application as FRET acceptors, where direct excitation of
the QD by the excitation source is an issue [517]. With careful choice of the donor
species, there are a number of instances where QDs are excellent energy transfer
acceptors, including BRET and CRET assays (Sections 6.4.6 and 6.4.7, respectively),
which do not require an excitation source, or the use of long-lifetime donors,
therefore allowing the performance of time-gated/resolved measurements, which
can factor out any direct QD excitation [517,524].
There are a number of commercial suppliers of QD materials, recently reviewed
in Ref. [515], that are either functionalized with chemical handles that facilitate
bioconjugation (e.g., OH, NH2, COOH, and -biotin) or are bioconjugated
with SA or various secondary antibodies (e.g., goat antihuman, goat antimouse,
or goat antirabbit). While there are increasing varieties of commercially available
QD materials, the most popular ones still remain the CdSe and CdTe core
materials and the CdSe/ZnS core–shell QDs. There are reviews and detailed
monographs describing QDs synthesis using various materials, generally involving
wet chemistry techniques such as high-temperature organometallic synthesis,
microwave or gamma irradiation, and aqueous colloidal and sol–gel methods
[515,523,537,538]. Various biotemplated fabrication approaches have also been
proposed for QD production, ranging from whole organism synthesis (bacteria,
yeast, and viruses) to biomolecule-based ligands that facilitate nucleation and
capping of the QDs during synthesis (nucleic acids and peptide sequences)
[539–543]. While greener in terms of reagents and reaction conditions, these
biofabrication methods tend to produce lower quality QDs, in terms of QY and
size polydispersity, compared to high-temperature chemical synthetic techniques,
but this may improve as our understanding of the underlying mechanisms that
govern these syntheses grows [539–543].
As discussed in Section 6.2, there are a number of diverse strategies that exist for
attaching biomolecules to QDs, including covalent coupling, electrostatic/metal
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.24 Improving aqueous solubility of
QDs through DHLA surface ligands. (a)
Chemical structures of DHLA and the DHLAbased ligands used to stabilize QDs. (b–d)
Physical characterization of a series of compact
ligand (CL)-coated QDs. (b) Gel electrophoretic
separation of 550 nm emitting QDs capexchanged with the indicated ligands. Gels were
run on 1% agarose gel in 1 TBE buffer (pH 8.3)
at 7 V/cm for 10 min. (c) Hydrodynamic size
distribution of 550 nm emitting QDs capexchanged with DHLA: 10.8 (2.7 nm), CL1: 8.6
(1.8 nm), CL2: 9.3 (1.7 nm), CL3: 9.5 (2.1 nm),
CL4: 9.8 (2.2 nm), and DHLA-PEG750-OCH3:
11.5 (2.5 nm) measured by dynamic light
scattering. Data is plotted in arbitrary units of
scattering intensity. (d) PL images (left) for a set
of 0.5 mM QDs capped with the CL1 compact
ligands in different buffers at pH 2–13. The
550 nm emitting CdSe/ZnS QDs were used and
excited with a UV lamp at 365 nm. Images were
taken <20 min and 4 weeks after sample
preparation. PL images (right) for a set of
0.5 mM–550 nm emitting QDs coated with
DHLA or the indicated compact ligands in 3 M
NaCl solution. Images were taken 1 day after
sample preparation for DHLA and after 90 days
for CL1CL4. (Reprinted with permission from
Ref. [533]. Copyright 2011, American Chemical
Society.)
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226
affinity-driven self-assembly, and biotin–avidin chemistry (Figure 6.25) [283]. However, given their NM nature, additional issues (also discussed in Section 6.2), such as
the influence of the surface ligand on bioconjugation reactions and subsequent
biomolecular interactions and how the attachment chemistry influences the NM
stability and biomolecule orientation, should be considered for QDs [30,33–36,515].
QDs as donors in FRET applications have been coupled to a range of
acceptor materials for energy transfer studies, including fluorescent dyes, NMs
(such as Au and carbon), fluorescent proteins, and polymers (Figure 6.26a)
[79,184,283,462,482,513,516,517,520,524,544–548]. As mentioned earlier, they
are also adept FRET acceptors when coupled with the appropriate donors, such
Figure 6.25 QD bioconjugation – an
illustration of some selected surface
chemistries and conjugation strategies that are
applied to QDs. The gray periphery around the
QD represents a general coating. This coating
can be associated with the surface of the QD via
(e) hydrophobic interactions, or ligand
coordination. Examples of the latter include (a)
monodentate or bidentate thiols, (b) imidazole,
polyimidazole (e.g., polyhistidine), or
dithiocarbamate (not shown) groups. The
exterior of the coating mediates aqueous
solubility by the display of (c) amine or carboxyl
groups, or (d) functionalized PEG. Common
strategies for bioconjugation include (a) thiol
modifications or (b) polyhistidine or
metallothionein (not shown) tags that penetrate
the coating and interact with the surface of the
QD, (f) electrostatic association with the
coating, (g) nickel-mediated assembly of
polyhistidine to carboxyl coatings, (h)
maleimide activation and coupling, (i) active
ester formation and coupling, and (j) biotin
labeling and SA–QD conjugates. The figure is
not to scale. (Reprinted with permission from
Ref. [283]. Copyright 2010, Elsevier.)
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6.5 Inorganic Materials
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j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
228
as long-lifetime lanthanide materials (Figure 6.26b) [513,517,549]. QD donors/
acceptors have also been applied in a number of studies looking at multi-FRET
processes, discussed in more detail in Section 6.6. Algar et al., in addition, recently
demonstrated QDs as simultaneous acceptors and donors in time-gated FRET
relays bioassays for monitoring protease activity and nucleic acid hybridization
(Figure 6.20) [366]. QDs have also been shown to be sensitive to CT processes and
coupling with redox active species, such as dopamine, Ru, rhodamine B, and Os,
which often leads to a competition between energy and charge transfer processes
in the resulting complex (Figure 6.26c) [415,513,550–553].
Since our previous review [3], the use of QDs in energy transfer-based applications
has truly blossomed and has been reviewed in a number of excellent monographs
[283,513,515–517,524,554,555]. In vitro applications dominate the QD FRET literature, including assays for detection of specific targets ranging from small molecules
to proteins and whole organisms (e.g., bacteria), enzyme activity monitoring,
tracking intracellular gene delivery, solid-phase assays, and QD-enabled singlemolecule detection. There are hosts of biomolecular interactions/processes that are
studied using QD energy transfer formats and these include nucleic acid interactions, binding protein conformation changes, antibody binding, aptamer interactions, and protease cleavage [283,513,515–518,524,554]. Assay formats found in
conjunction with QD FRET are quite varied and include (i) cleavage-based assays (e.
g., proteases, kinases, and DNAzymes) (Figure 6.27) [321,365,368,526–529,556–
558], (ii) conformational change-based assays (e.g., aptamers, binding proteins, and
DNA molecular beacons) [518,559–561], (iii) displacement assays (e.g., antibodies
and binding proteins) (Figure 6.28) [554,562], (iv) various immunoassays (including
direct, displacement, and sandwich) [367,562–564], (v) nucleic acid hybridization
[518,555], and (vi) assays based on acceptor spectral changes (mainly pH or ion
sensitive dyes) (Figure 6.16) [79,527,556]. Given the unique photophysical properties
of QDs, our increasing fundamental understanding of these unique materials when
used in energy transfer configurations, and the availability of improved synthesis
and bioconjugation methods, we can expect continued utilization in many FRETbased biological assays, with increasing emphasis on multiplexed and in vivo
detection [321,524,526–529,549,565].
3
Figure 6.26 QDs as FRET acceptors and
donors. (a) QDs are good FRET donors for
fluorescent proteins (FPs), dye, and Au NP
acceptors. The dashed circle represents an
arbitrary F€
orster distance (R0) measured from
the QD center. The scale on the right indicates
how R0 proportionally increases as the number
of proximal acceptors (a) increases. Conversely,
QDs can function as acceptors for Tb
complexes and BL luciferase donors. (b)
Qualitative spectral overlap (shaded) for a
625 nm emitting CdSe/ZnS QD as (i) donor to
fluorescent dye acceptor (Alexa647, A647) and
(ii) acceptor to a Tb chelate donor. (c) CT
quenching is an alternative method of
modulating QD PL: (i) an electron acceptor (e.
g., quinone) has an unoccupied energy level
intermediate in energy to the 1Sh and 1Se bandedge states to which the excited QD transfers
an electron, and (ii) an electron donor (e.g., Ru
phenanthroline) has an occupied intermediate
energy level and transfers an electron to the
QD. Charge transfer inhibits radiative
recombination of the exciton. Both the redox
active species are illustrated as peptides
conjugates. (Reprinted with permission from
Ref. [513]. Copyright 2011, American Chemical
Society.)
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6.5 Inorganic Materials
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.27 Cleavage-based FRET assays. (a) A
protease assay where (i) an acceptor dyelabeled peptide is assembled on a QD donor via
a polyhistidine tag. The QD-dye proximity in the
bioconjugate is sufficient for FRET. (ii) Protease
activity (scissors) cleaves the peptide and
disrupts FRET, restoring the QD PL. (Reprinted
with permission from Ref. [283]. Copyright
2010, Elsevier.) (b) Proteolytic assay data from
exposing a constant concentration of 550 nm
emitting QDs conjugated to four Texas Red
substrate peptides to a constant concentration
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230
6.6
Multi-FRET Systems
Multistep FRET is a naturally occurring process exemplified by the light-harvesting
systems found in many biological species, which allows them to harness light not
readily absorbed by chlorophyll for photosynthesis [254,566]. Phycobilisomes are
supramolecular complexes found in blue-green cyanobacteria and various algae
such as glaucophytes, red, and cryptomonad [253,254]. Phycobilisomes have a
variable composition that is organism dependent, but typically consists of multiple
PBP subunits (see Section 6.4.4). As mentioned in Section 6.4.4, within the
phycobilisome system there are four main types of PBP – PC, PE, PEC, and
APC – that bind the phycobilin chromophores (e.g., PUB, PEB, and PCB) that
give these proteins their intense colors [254]. The multi-FRET process and flow of
energy in phycobilisomes is PE–PC–APC–photosynthetic reaction center (chlorophyll) [254]. Energy transfer efficiency in this system approaches nearly 100%, and
researchers have yet to match experimentally the complexity or efficiency of this
naturally selected energy harvesting system.
An increasing number of biologically inspired and artificial synthetic multi-FRET
systems have been developed to precisely space or orient multiple fluorophores with
the goal of characterizing and mimicking the natural light-harvesting process. Such
systems have potential use in solar cells, nanoscale photonic devices, and other
optoelectronic applications [269,567,568]. More commonly, these multi-FRET configurations are developed as a means to extend the optical ruler and are used to
elucidate biological configurations, study protein and DNA interactions, and for
biosensing applications [135,210,365,366,412,413,569].
While artificial synthetic building block structures have been developed, such as
perylene bisimide-calix[4]arene arrays by Hippius et al., to control the position and
orientation of chromophores, biologically inspired platforms are more common
[570]. DNA is perhaps the most attractive biologically inspired platform for multiFRET configurations due to (i) its predictable structure/chemistry, (ii) the inherent
ability to introduce fluorophores at specific sites, (iii) the ability to hybridize multiple
dye-labeled oligos to a complimentary strand, and (iv) the ability to control the
orientation of the attached fluorophores [3]. DNA can be synthesized with multiple
fluorophores at specific terminal or internal sites or with thiol/amine/biotin or other
3
of caspase-3 enzyme. Derived Km and Vmax
values are given. An R2 of 0.98 was obtained for
the fitting of the curve. (Reprinted with
permission from Ref. [556]. Copyright 2010,
American Chemical Society.) (c) Multiplexed
assay of proteases by using QDs with different
colors on a glass slide. SA-QD525, SA-QD605,
and SA-QD655 were used (from left to right).
Biotinylated peptide substrates for MMP-7,
caspase-3, and thrombin were conjugated to
the AuNPs, and then the resulting Pep-AuNPs
were associated with SA-QD525, SA-QD605,
and SA-QD655, respectively: (i) SA-QDs only,
(ii) SA-QDs þ respective Pep-AuNPs, (iii) SAQDs þ Pep-AuNPs þ MMP-7, (iv) SAQDs þ Pep-AuNPs þ caspase-3, (v) SAQDs þ Pep-AuNPs þ thrombin, and (vi)
QDs þ Pep-AuNPs þ mixture of the respective
protease and its inhibitor. (Reprinted with
permission from Ref. [528]. Copyright 2008,
American Chemical Society.)
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6.6 Multi-FRET Systems
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.28 Displacement format using
antibody-functionalized QDs for FRET-based
TNT detection. (a) Schematic of the assay.
When TNB-BHQ-10 is bound to the QDTNB2-45 conjugate, QD fluorescence is
quenched via FRET. As TNT is added to the
assay, it competes for binding to the
antibody fragment and the QD fluorescence
increases following TNB-BHQ-10 release
from the conjugate. (b) Results from titration
of the QD-TNB2-45-TNB-BHQ-10 assembly
with TNT and the indicated TNT analogues.
These assemblies were constructed using
530 nm emitting QDs. Each data point is an
average of three measurements, and error
bars represent the standard deviation.
(Reprinted with permission from Ref. [562].
Copyright 2005, American Chemical Society.)
modifications allowing custom labeling. Altering donor/acceptor spacing is facile in
this configuration and allows fine-tuning of FRET efficiency [569]. Such fine-tuning
and control of multi-FRET using DNA constructs has been used for light harvesting
and charge separation using DNA nanostructures [269,567], development of combinatorial FRET-tags for SNP detection, [571] and DNA-based photonic wires [568].
Proteins have also been used in the development of multi-FRET configurations.
Maltose binding protein (MBP), for example, has been either triple labeled with
FAM, tetramethylrhodamine, and Cy5, [572] or dual labeled with QD and Cy3 before
binding Cy3.5-labeled b-cyclodextrin [71] in the development of maltose biosensors.
Rogers et al. incorporated a multi-FRET PheCN, Trp, and 7AW system into
two model protein systems: HP35 and a designed bba motif (BBA5) to study
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232
urea-induced conformational changes [210]. The nonnatural amino acid fluorophores, PheCN and 7AW (Section 6.4.2), were incorporated by mutation of the Cand N-terminus. Such a three-color FRET system extends the working range of the
molecular ruler and yields information about the relative positions between the
three fluorophores.
In addition to the use of the more traditional organic fluorophores for multi-FRET
applications, substantial development in the areas of NMs, time-resolved fluorescent
reagents, and BRET has led to material combinations, with unique advantages in
multi-FRET applications. QDs NMs can act as donors and acceptors in FRET
configurations as well as provide a scaffold in which to immobilize the multiple
components of a multi-FRET system. Medintz et al. developed a multi-FRET maltose
biosensor using QDs (initial donor) functionalized with Cy3-labeled MBP that
further bound Cy3.5-labeled b-cyclodextrin, a sugar analogue that was displaced
from the QD–MBP complex in the presence of maltose [71]. Boeneman et al.
developed DNA photonic wires using a QD modified with an ssDNA backbone
template that bound four separate short complementary sequences (labeled with
different dyes) (Figure 6.29) [568]. The system was used to study the sequential
FRET from the initial QD donor to Cy3/Cy5/Cy5.5/Cy7, and it was found that while
the initial QD-quenching efficiency was high (80–90%), the amount of energy
subsequently emitted by Cy5 and Cy5.5 was relatively low at 2.2 and 1%,
respectively, with the Cy7 acting as an IR quencher. QDs can also function as
simultaneous donors and acceptors in multi-FRET systems, as demonstrated in
DNA hybridization and protease activity detection assays [135,365,366].
The use of long-lifetime dyes, such as Ru complexes and LLCs, can provide
additional dynamic information about a system or enhance the biosensing capabilities of a platform [365,366,412,413]. The groups of Kumke and Bannwarth, for
example, created a three-color FRET system for protein and DNA analysis using a
carbostyril donor–Ru complex (acceptor/relay)–anthraquinone (quencher) combination [412,413]. In the case of DNA analysis, they found that the short luminescent
lifetimes gave information about the rotation of the dye molecules themselves, while
the long lifetimes yielded information regarding the overall dynamics within the
DNA macromolecule itself [412]. Algar et al. developed and characterized multiFRET systems for monitoring DNA hybridization and protease activity [365,366].
Here, a Tb chelate–QD–Alexa647 combination was used in which the Tb chelate
assumed the role of initial donor and facilitated time-gated measurements, ultimately allowing multiplexed biosensing based on a single-color QD scaffold
(discussed in more detail in Sections 6.5.1 and 6.5.5, and also see Figure 6.20).
SRET, the sequential combination of BRET and FRET, is a fairly recent development in the multiresonance energy transfer arena [317,318,573]. Carriba et al., for
example, labeled three different membrane receptor-interacting proteins with Rluc,
GFP, YFP, or DsRed, using SRET to study the heteromers that formed upon
exposure to agonists [317]. Protease activity has also been monitored via SRET
(Figure 6.30) [318]. Here, the peptide-based probe comprised a peptide sequence
(containing the protease-specific cleavage site) flanked by a thermostable firefly
luciferase that produced yellow-green BL (BRET), and a red FP labeled with a near-
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6.6 Multi-FRET Systems
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
Figure 6.29 Multi-FRET systems using DNA
templates. (a) Schematic of the configuration
consisting of 530 nm QDs self-assembled
with four (His)6-peptide-DNA hybridized with
Cy3 in 1/Cy5 in 2/Cy5.5 in 3/Cy7 in 4. (b)
Composite PL spectra from 530 nm QD
donors self-assembled with unlabeled DNA,
DNA with Cy3 in position-1, Cy3 in 1/Cy5 in
2, Cy3 in 1/Cy5 in 2/Cy5.5 in 3, Cy3 in 1/Cy5
in 2/Cy5.5 in 3/Cy7 in 4. (Reprinted with
permission from Ref. [568]. Copyright 2010,
American Chemical Society.)
infrared fluorescent dye (Alexa680) (FRET). The intact peptide probe undergoes
efficient SRET, resulting in acceptor emission of the near-infrared fluorescent dye (at
705 nm). Addition of the protease results in a decrease in acceptor emission, due to
disruption of the SRET process. Xiong et al. developed SRET-based NPs for near-IR
in vivo imaging of the lymphatic networks and vasculature of xenografted tumors
in mice [573]. The NPs were composed of a fluorescent polymer, poly[2-methoxy-5((2-ethylhexyl)oxy)-p-phenylenevinylene] (MEH-PPV), which was subsequently
doped with the near-IR dye (NIR775) and its surface modified with a COOH-
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234
Figure 6.30 Multi-FRET systems – sequential
BRET then FRET – for protease sensing. (a–c)
Factor Xa detection using a unique sequential
BRET–FRET combination. (a) The peptidebased probe comprised a peptide sequence
(containing the protease-specific cleavage site)
flanked by a thermostable firefly luciferase that
produces yellow-green BL, and a red FP labeled
with a near-infrared fluorescent dye (Alexa680).
(b) When intact the peptide probe undergoes
efficient BRET/FRET resulting in acceptor
emission of the near-infrared fluorescent dye (at
705 nm). (c) Addition of the protease factor Xa
results in a decrease in acceptor emission, due
to disruption of the BRET/FRET process, as
illustrated in the time course spectra.
(Reprinted with permission from Ref. [318].
Copyright 2011, Elsevier.)
terminated PEG polymer that facilitated Luc8 and tumor-targeting ligand (RGD
peptide) bioconjugation. BRET occurred between the Luc8 and MEH-PPV in the
presence of substrate coelenterazine, with sequential FRET occurring between the
MEH-PPV and NIR775. The NPs demonstrated good blood circulation and tumor
targeting in mice models. Although there have been fairly limited SRET demonstrations to date, given the improved sensitivity afforded by the self-illuminating
nature of these SRET-based systems utility is bound to increase.
j235
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6.6 Multi-FRET Systems
j 6 Materials for FRET Analysis: Beyond Traditional Dye–Dye Combinations
6.7
Summary and Outlook
FRET is clearly an invaluable biophysical tool for a variety of applications, ranging
from fundamental studies of the structure and conformation of biological materials
and the in vivo examination of biomolecular interactions, to more applied uses
where FRET signal transduction has been utilized for in vitro and in vivo bioassays,
for healthcare diagnostics/screening, defense, environment, and food safety. The
range of new and improved donor/acceptor probe materials continues to expand to
address some of the inherent complications of more traditional FRET materials,
including photobleaching, spectral cross talk and direct excitation of the acceptor
species. NMs, in particular, are increasingly being used as donor/acceptor probes in
FRET studies due to their many unique photophysical properties and their inherent
nanoscaffolding capabilities that can be used to improve FRET efficiency. Hand in
hand with donor/acceptor materials development that has expanded the use of
FRET has been the evolving bioconjugation techniques, especially bioorthogonal
methods that facilitate greater site-specific control of the donor/acceptor labeling.
With further advances in the areas of NMs and bioconjugation techniques, we
anticipate FRET to become an increasingly appreciated tool in a wide range of
fundamental and applied applications.
Acknowledgments
K.E.S acknowledges Division of Biology, FDA and MCMi, FDA for financial support.
K.E.S would also like to thank Ms. S. Spindel and Dr. K. Butler for their comments
and review of this chapter. The mention of commercial products, their sources, or
their use in connection with material reported herein is not to be construed as actual
and/or implied endorsement of such products by the Department of Health and
Human Services.
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Part Two
Common FRET Techniques/Applications
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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7
In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
Samantha Spindel, Jessica Granek, and Kim E. Sapsford
7.1
Introduction
F€orster (fluorescence) resonance energy transfer (FRET) is of particular interest to
scientists due to its intrinsic sensitivity to small variations in molecular distance and
orientation. When appropriately configured, qualitative and quantitative information about the system under study can be determined using FRET. FRET has
numerous applications in the study of biological phenomena such as structure
elucidation, inter- and intracellular processes, and in vivo diagnostics, which are
covered in other chapters. FRET is increasingly being used in the area of molecular
in vitro diagnostics (IVDs – which can be genomic, epigenetic, or protein-based
assays) for sensing applications in the medical arena, such as clinical diagnostics/
prognostics and personalized medicine. The desire for high-throughput, real-time,
simple, and rapid assays has been one of the driving forces behind the increased
interest in FRET as a signal transduction mechanism. In particular, FRET has shown
great potential in the area of point-of-care (PoC) diagnostics, which is discussed in
more detail later [1]. Some inherent complications of FRET using more traditional
reagents include photobleaching, spectral cross talk, and direct excitation of the
acceptor, which can all increase background and reduce sensitivity. The production
of high-quality reagents that address some of these issues, along with substantial
progress in the field of nanotechnology, have increased the utility of FRET [2].
There are a number of potential in vitro target analytes of interest, including
proteins, metabolites, and other small molecules, such as drugs (both recreational
and doping), toxins, nucleic acids, human cells, microbes, and other pathogens
highlighted throughout this chapter [1]. Target analytes that fall under the label of
“biomarker” are of particular interest from a clinical diagnostic and personalized
medicine perspective [3]. The consensus definition of a biomarker is “a characteristic that is objectively measured and evaluated as an indicator of normal
biologic processes, pathogenic processes or pharmacologic responses to a therapeutic
intervention” [4]. Biomarkers have a range of potential clinical utilities, including
identifying the presence of disease and characterizing disease subtype
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
(diagnosis), determining disease prognosis, aiding in selection of appropriate
therapeutic doses, predicting clinical benefit or adverse response to therapy, and
monitoring treatment outcomes [3]. FRET configurations used for sensing these
target analytes are diverse in nature, relying on a number of potential mechanisms, including cleavage, binding, sensitive absorption/emission profiles, and/
or structural rearrangements (conformational changes), which ultimately alter the
FRET between the donor/acceptor molecule(s), resulting in a measurable change
in the FRET signal. Examples of these various mechanisms will be highlighted
throughout this chapter. We have chosen to discuss FRET applications in terms of
the “sensing/recognition” molecules that interact with the target analyte of
interest, resulting in measurable FRET changes. These sensing/recognition
molecules can take a variety of forms, including small organic molecules,
polymers, carbohydrates, antibodies, proteins and peptides, nucleic acids [including deoxyribonucleic acid (DNA) and ribonucleic acid (RNA)], and aptamers.
7.2
Small Organic Molecules and Synthetic Organic Polymers
There are a number of organic molecules (sometimes referred to as probes) that
have unique absorption or emission profile responses to particular analytes, which
make them useful for FRET configurations [5]. The group of Lakowicz as well as
others, for example, has developed a number of lifetime-based FRET sensors based
upon organic molecules sensitive to changes in pH, NH3, and/or CO2 [6–9].
Although the spectroscopic change (absorbance or fluorescence-based) of the
organic molecule is often measured directly [10], when the organic molecule has
an absorbance-based response to an analyte, incorporating a fluorescence component to the detection mechanism, such as via FRET may improve assay sensitivity
[7,9]. Ruedas-Rama and Hall developed a FRET-based sensor that measures pH
changes in response to the activity of enzymes such as urease and creatinine
deiminase by immobilizing the enzymes and a pH-sensitive calcium red dye (CaR)
to the surface of quantum dots (QDs) [11].
The established interaction between boronic acid moieties and various cis-1,2- or
1,3-diol-containing molecules, such as saccharides and dopamine, has led some
researchers to develop FRET-based glucose or sugar sensors [12,13]. For example,
Freeman and coworkers created fluorescently labeled galactose, glucose, and dopamine as analyte analogues in competitive assays that used phenyl boronic acidfunctionalized QDs as the FRET donor. In the presence of the analyte (galactose,
glucose, or dopamine), the labeled sugar/dopamine (analyte analogue) was displaced from the QD, reducing FRET and increasing QD emission. Wang et al.
designed thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) microgels that
incorporated FRET donor and acceptor dyes along with N-acryloyl-3-aminophenylboronic acid (APBA) for glucose and temperature sensing [13]. Increased temperature caused the microgels to shrink, enhancing the FRET signal, while the addition
of glucose under specific temperature conditions caused the microgels to expand,
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272
weakening the FRET signal. A similar concept for Kþ sensing was achieved by
replacing the boronic acid moieties with crown ethers [14].
The response of various polymeric materials to pH or protein adsorption has
been investigated using FRET transduction [15–18]. Chiu et al. used the pHsensitive conformational change that occurs in N-palmitoyl chitosan (NPCS),
conjugated with a Cy3 [Cyanine 3 (dye)]donor dye and a Cy5 [Cyanine 5 (dye)]
acceptor dye, to measure pH changes in biological environments via FRET
(Figure 7.1) [16].
7.3
Carbohydrate–Lipid
Due to the numerous physiological roles carbohydrates play in human biology, there
has been increasing interest in their use as recognition elements for sensing
applications, especially for protein and bacterial targets, although their combination
with FRET is presently somewhat limited [19,20]. Song et al. designed a multi-FRET
system using labeled GM1 (monosialotetrahexosylgangliosides) (carbohydrate/lipid
components of the cell plasma membrane) to monitor their interaction with cholera
toxin [21]. Ma and Cheng developed a mix-and-detect assay using dye-labeled GM1
and polydiacetylene (PDA) vesicles [22]. Cholera toxin bound the dye-labeled GM1,
preventing GM1 incorporation into the PDA vesicles and its subsequent quenching
via FRET. McGiven et al. developed a competitive assay for detection of anti-Brucella
antibodies in serum using Brucella smooth lipopolysaccharide (LPS –carbohydrate/
lipid structure found in the outer membrane of Gram-negative bacteria) and antiBrucella monoclonal antibody labeled with a long-lifetime donor terbium chelate
fluorophore [23]. The use of time-resolved fluorescence allowed a significant
reduction in the background fluorescence of the serum sample matrix and therefore
increased the sensitivity of anti-Brucella detection.
7.4
The Biotin–Avidin Interaction
The avidin–biotin complex is worth highlighting, as it represents one of the
strongest known noncovalent interactions (Ka 1015 M1) and as such it is often
used as a model system for protein–ligand interactions and for testing new materials
for sensing applications [24–27]. The latter is particularly true in FRET studies,
where researchers have used the avidin–biotin interaction to test new donor–
acceptor combinations, including luminescent lanthanide complexes (LLCs) and
nanoparticles (NPs) (europium and terbium) with QDs [28–30], gold nanoparticles
(Au NPs) with QDs [31], conjugated polyelectrolytes and tetramethylrhodamine
(TMR) [32], dye-labeled silica NPs with various dyes [33], and a two-photon excitable
organic molecule with a dark quencher [34]. While the detection of biotin is the more
clinically relevant of the biotin–avidin pair, since it is an essential component of
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7.4 The Biotin–Avidin Interaction
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
Figure 7.1 FRET-based pH-responsive
polymer sensors. (a) Design and working
principle of the FRET-based pH-responsive
polymer sensor developed by Chiu et al. [16].
N-palmitoyl chitosan (NPCS) was labeled with
either Cy3 (donor) or Cy5 (acceptor) before
being mixed to form the FRET sensor. Changes
in pH caused a conformational change in the
polymer structure that resulted in measurable
changes in the FRET signal. (b) Nonnormalized
FRET spectra showing the increase in FRET
obtained from the nanosensors as the pH
decreases from 8.0 to 4.0. (c) Dual emission
images of Cy3/Cy5/chitosan – 15%
nanoparticle suspensions obtained with an
in vivo imaging system. (Reprinted with
permission from Ref. [16]. Copyright 2010,
American Chemical Society.)
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274
vitamin B, most researchers use this complex for avidin sensing in a competitive
assay format [31,32,34].
7.5
Proteins and Peptides
There is a wide range of protein- and peptide-based recognition events that can be
probed using FRET transduction and hence used for sensing applications. Antibodies are an obvious example and are discussed separately in Section 7.6. The main
examples here include binding proteins, epitope-derived peptide sequences, and
protease-specific peptide sequences.
7.5.1
Binding Proteins
There are a wide variety of binding proteins, in addition to antibodies, with sites that
recognize and bind specific analytes, which make them attractive elements for
FRET-based sensing. A popular example of binding proteins is the protein switch,
which is composed of proteins that undergo conformational changes upon either
covalent modifications or molecular recognition [35].
The conformational changes of protein switches such as periplasmic binding
proteins (PBP) have routinely been studied via FRET [35–37], with glucose
binding protein (GBP) and maltose binding protein (MBP), of particular interest
due to the clinical relevance of their target analytes [38–39]. These hinge-based
proteins typically transition from an open to a closed conformation upon target
binding, somewhat akin to the Venus flytrap. A number of researchers have used
this inherent conformational change for FRET-based glucose and maltose sensing [38,40–46]. Two main issues with GBP sensors are that they possess a narrow
dynamic range and are oftentimes too sensitive for clinical use, detecting glucose
in the micromolar range as opposed to the more desirable millimolar range. Jin
et al. attempted to address this issue by developing a series of GBP mutants, one
of which demonstrated a more physiologically relevant glucose detection range of
0–32 mM [46].
By using the conformation change that occurs in bovine serum albumin (BSA)
when it binds to long chain fatty acids, Dezhurov et al. developed a BSA-based sensor
for oleic acid. Here, BSA labeled with an acceptor dye was self-assembled onto CdSe/
ZnS QDs (donor), resulting in FRET. The binding of oleic acid to BSA caused a
conformational change in BSA, decreasing the distance between the donor and
acceptor, resulting in an increase in FRET efficiency [47]. In an alternative approach
that relies on conformational change, Thurley et al. designed hairpin peptide
beacons, analogous to DNA-based molecular beacons (MBs), comprising a protein-specific peptide sequence (that recognizes the target protein) flanked by two
complementary peptide nucleic acid (PNA) arm segments, labeled with a donor–
acceptor pair [48]. Binding of the target protein, in this case Src kinase, resulted in a
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7.5 Proteins and Peptides
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
conformational change within the hairpin peptide beacon that ultimately separated
the PNA arms and hence changed the FRET signal.
As an alternative approach to using a protein’s inherent conformational change
(which can produce a very tight sensor dynamic range) or for binding proteins that
do not undergo significant structural changes upon target analyte binding, researchers have investigated the competitive displacement format. Medintz et al. demonstrated a number of iterations of this assay format using MBP for maltose detection,
taking advantage of the weaker association of MBP for b-cyclodextrin than its target
analyte maltose (Figure 7.2) [41,49–51]. Labeled b-cyclodextrin was allowed to bind
to labeled MBP, resulting in FRET. Upon addition of maltose, the b-cyclodextrin was
displaced (through competitive displacement) and a change in FRET resulted. Initial
studies investigated the use of standard dye–dye or dye–quencher combinations for
Figure 7.2 Competitive displacement assays
using binding proteins. (a) Schematic
representation of homogeneous FRET-based
competitive displacement assay. Here, the
donor-labeled binding protein interacts with an
acceptor-labeled target analogue resulting in
FRET. Introduction of the target analyte causes
displacement of the target analogue, disrupting
the FRET and causing an increase in the donor
emission. (Adapted with permission from Ref.
[49].) (b) Schematic representation of
heterogeneous FRET-based competitive
displacement assay. Here, the acceptor-labeled
(in this case quencher) binding protein interacts
with a donor-labeled target analogue, resulting
in FRET, with both components immobilized on
a microplate well. Introduction of the target
analyte causes displacement of the target
analogue, disrupting the FRET and causing an
increase in the donor emission. Due to the
immobilization of the sensor components, the
system can be regenerated by simply washing
away the target analyte. (Adapted with
permission from Ref. [51].)
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276
the donor–acceptor FRET pair [49], while later studies focused on the use of QD
donors for the design of single- and multi-FRET systems [50]. A unique system
capable of regeneration, a highly desired biosensor quality, was also designed to
overcome the single-use limitation (Figure 7.2b) [51]. Here, biotin-labeled MBP was
bound to a NeutrAvidin coated surface and b-cyclodextrin was immobilized in close
proximity to the MBP, via a flexible biotinylated DNA oligonucleotide. Varying the
MBP mutant and DNA linker arm attachment allowed the ability to tune the sensor’s
sensitivity and dynamic range, significantly improving the utility of the configuration. Competitive displacement assays have also been adopted for detection of
glucose with glucokinase or concanavalin A (ConA) acting as the binding protein
[52–59]. Cheung et al. developed a glucose sensor based on TMR-ConA and
fluorescein-dextran (Mw 200 kDa) encapsulated within hydrogel pads and subsequently overcoated with polyelectrolyte multilayers, via layer-by-layer self-assembly
[58]. The resulting sensor could measure glucose from 0–10 mM, had selective
permeability – only allowing monosaccarides and disaccarides to reach the sensor
biochemistry – and was reusable. Kim et al. used QD-labeled ConA in combination
with Au NP-labeled dextran to sense protein glycosylation (specifically mannosylated
proteins), which have been implicated in a number of diseases [60,61].
There are also a few instances in the literature where researchers have used the
target binding or environmental spectral sensitivity of a protein to develop FRETbased sensors [62–64]. Stianese et al., for example, used the absorbance spectral
changes that occur in cytochrome c peroxidase (CcP) upon binding nitric oxide (NO)
to develop a FRET-based NO sensor by modifying the CcP with a near-infrared (IR)
fluorescent dye [63]. Dennis et al. used the pH environmentally sensitive fluorescent
protein (both excitation and emission spectra varied with pH), mOrange, coupled
with QDs to develop a ratiometric pH sensor [64].
7.5.2
Antigens and Epitope-Based Peptide Sequences
Detection of antibodies is important from a clinical perspective as they can be used to
diagnose exposure to infectious agents, autoimmune diseases, and allergies [65]. A
couple of interesting FRET sensor designs have been proposed for antibody detection
and involve using either the full antigen (the antibody’s target analyte) or epitopebased peptide sequences derived from the antibody’s target antigen (Figure 7.3).
Sukhanova et al. measured autoantibodies of systemic sclerosis using QD-coded
microbeads functionalized with the antigen topoisomerase I (topoI) in a flow
cytometry-type assay [66]. Once the topoI autoantibodies in the patient sera bound
the microbeads, dye-labeled antibodies then bound to the microbead captured
autoantibodies, resulting in FRET. Rather than using the full antigen, Tian and
Heyduk designed a FRET assay using two epitope-based peptide sequences, derived
from cardiac troponin I, which is used to diagnose acute myocardial infarction (AMI)
(Figure 7.3a) [67]. The two epitope-based peptide sequences were conjugated to
flexible linkers modified with dye-labeled complementary oligonucleotides. Introduction of the antibody to cardiac troponin I caused the peptide sequences to bind to the
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7.5 Proteins and Peptides
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
Figure 7.3 Antibody detection using epitope
peptide FRET-based sensors. (a) Schematic
representation of a FRET-based sensor using
two separate antibody epitopes, each
conjugated with short complementary
oligonucleotides via flexible linkers and labeled
with fluorescent probes. The oligonucleotides
were designed to be short enough to not
hybridize is the absence of the target antibody.
Hybridization occurs in the presence of the
target antibody, resulting in efficient FRET
between the donor/acceptor fluorophores.
(Adapted with permission from Ref. [67].) (b)
Schematic representation of a FRET-based
sensor using two antibody epitopes linked via a
flexible linker and labeled with fluorescent
probes. The fluorescent probes in this case
were cerulean and Citrine fluorescent proteins
designed with hydrophobic surface mutations
that caused the proteins to interact in the
absence of the target antibody, resulting in
efficient FRET. Introduction of the target
antibody resulted in separation of the
fluorescent proteins measured as a decrease
in FRET efficiency. (Adapted with permission
from Ref. [69].)
antibody, bringing the complementary oligonucleotides into close proximity, allowing
them to hybridize and cause an increase in the FRET signal. To improve the multiplexing ability of this assay, the technology has been transitioned to a solid-surfacebased format for the detection of a range of target analytes, including antibodies and
bacteria [68]. Golynskiy et al. developed a FRET based sensor for human immunodeficiency virus (HIV)-1 antibody in serum and saliva [69]. High FRET is observed in
the absence of the antibody, where hydrophobic mutations on the protein surface
caused a closed conformation of the fluorescent domains of the FRET-based sensor. In
the presence of the antibody, bivalent binding between the antibody and two antigen
epitope regions on the FRET-based sensor caused separation of fluorescent domains
and a decrease in FRET (Figure 7.3b).
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278
7.5.3
Peptide Sequences for Enzymatic Sensing
Proteolytic enzymes (proteases) selectively cleave peptide bonds and have important
physiological roles in many biological processes [70,71]. From a clinical perspective,
they are key participants that are up- or downregulated in a number of diseases, and
as such a variety of peptide-based assays have been developed to detect and monitor
protease activity [70–73]. Many of these assays take advantage of FRET for detection;
the basic sensing scheme is shown in Figure 7.4a, with some examples summarized
in Table 7.1 and highlighted later. In general, a peptide sequence containing the
protease-specific substrate is labeled with the donor and acceptor species, flanking
the cleavage site. The close proximity of the donor–acceptor pair on the intact
peptide sequence results in FRET. Protease activity causes peptide cleavage, increasing the distance between the donor/acceptor molecules and hence decreasing FRET,
which is typically measured as increasing donor emission intensity. Proteases have a
range of substrate specificities and many require only limited sequence recognition
prior to cleavage. For example, trypsin recognizes single amino acids, cleaving the
carboxyl side of lysine (K) and arginine (R) residues (except when followed by
proline-P), while caspase-3 is tetrapeptide specific, recognizing the sequence motif
D-X-X-D and cleaving after the aspartic acid residues (D) (X represents any amino
acid). In contrast, botulinum neurotoxin A, which comprises a light chain protease
and a heavy chain receptor binding protein, binds an optimum peptide substrate
sequence of 16 residues, found in its physiological target synaptic protein SNAP25,
prior to cleavage [81,82]. The specificity of the protease and the designed FRET
substrate can be an issue when these types of sensors are applied to complex clinical
samples, such as blood or sera, which may contain a number of physiological
proteases that might increase the risk of false-positive responses. In some instances,
purification, such as immunoextraction, or inclusion of inhibitors, which inhibit
proteases other than the desired target, may be required to improve specificity.
The serine protease trypsin, found in the digestive system, is a common target
enzyme used by researchers when demonstrating initial proof-of-concept FRET
protease assays, in part due to its well-characterized nature, single amino acid
specificity (K and R residues), and commercial availability [83–87]. Trypsin is
particularly popular with researchers when demonstrating new FRET donor–acceptor combinations or materials, such as silica nanobeads or QDs [83–86], or new
detection platform technologies [86]. The group of Medintz and coworkers has
developed a number of QD-peptide-FRET-based sensing platforms for a range of
clinically relevant proteases, including caspase-3 (found to be downregulated in a
number of cancers) [75,76], caspase-1 (a mediator for inflammation), thrombin (an
important blood clotting protein), collagenase (an enzyme involved in cancer
metastasis) [78], and botulinum neurotoxin A [79]. Cathepsin S, a cysteine protease
that has been associated with obesity, atherosclerosis, and Alzheimer’s disease, was
measured using an Abz-LEQ-EDDnp FRET peptide substrate [88]. Once optimized
in buffer, the assay was applied to tissue homogenates, where a cocktail of inhibitors
was required to prevent hydrolysis of the FRET peptide substrate by other
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7.5 Proteins and Peptides
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
Figure 7.4 Protease sensing using peptide
FRET-based sensors. (a) Schematic
representation of a FRET-based sensor
comprising a relatively short peptide sequence
that encompasses the specific protease
cleavage site flanked on either side by
fluorescent probes. When intact, the fluorescent
probes are in close proximity and undergo
efficient FRET. However, introduction of the
protease causes peptide cleavage, resulting in
disruption of FRET and an increase in donor
emission. (b) Factor Xa detection using a
unique sequential BRET–FRET combination,
termed SRET. The peptide-based probe
comprised a peptide sequence (containing the
protease-specific cleavage site) flanked by a
thermostable firefly luciferase that produces
yellow-green bioluminescence, and a red
fluorescent protein labeled with a near-infrared
fluorescent dye (AlexaFluor 680). When intact,
the peptide probe undergoes efficient BRET/
FRET resulting in acceptor emission of the nearinfrared fluorescent dye (at 705 nm). Addition
of the protease factor Xa results in a decrease in
acceptor emission, due to disruption of the
BRET/FRET process, as illustrated in the time
course spectra. (Reprinted with permission
from Ref. [91]. Copyright, Elsevier.)
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j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
physiological proteases such as the serine, metallo, aspartic, calcium-dependent,
and caspase families. A FRETpeptide cleavage mechanism was also proposed for the
potential diagnosis of thrombotic thrombocytopenic purpura (TTP) by measuring
the decrease in ADAMTS13 activity [89,90].
Brancini et al. took the FRET peptide cleavage format a step further, designing a
sequential bioluminescence resonance energy transfer (BRET)–FRET multienergy
transfer assay platform based on firefly luciferase bioluminescence, for the detection
of caspase-3, thrombin, and factor Xa activity [91]. The sensor was composed of
firefly luciferase, which generates yellow-green bioluminescence and a red fluorescent protein (RFP) covalently labeled with a near-infrared fluorescent dye
(Figure 7.4b). The firefly luciferase and RFP are connected via a decapeptide
sequence, containing the protease-specific recognition/binding site; BRET occurs
upon the addition of luciferase substrates. The subsequent FRET occurs between
the RFP and the near-infrared fluorescent label. The advantage of this system is
that BRET is activated via addition of chemical substrates rather than an external
excitation source, making the signal background extremely low. Also, spectral
resolution between the firefly luciferase bioluminescence (560 nm) and the nearinfrared fluorescent label (Em 705 nm) is excellent due to the sequential BRET–
FRET format, improving assay sensitivity. BRET alone has also been demonstrated
for measuring the protease activity of thrombin with improved sensitivity versus
FRET [92]. Using a slightly modified format to that described in Figure 7.4a, Gratz
et al. developed a FRET peptide assay for measuring the activity of the protein
kinase CK2, which has been found to be upregulated in a number of cancers [93].
The assay relies on the ability of CK2 to block proteolytic cleavage of a FRET
peptide substrate by CK2 serine phosphorylation of the elastase substrate S–D
cleavage site. In addition to physiological human proteases, the detection of
specific bacterial or viral enzymes/proteases can be used to indirectly diagnose
infection, such as the bacteria Gram-positive Bacillus anthracis, the causative agent
of anthrax, and the Clostridium species botulinum and tetani, as well as the virus
severe acute respiratory syndrome coronavirus (SARS-CoV) [79,94–99]. Such
rapid assays also provide the ability to screen for potential inhibitors that may
prevent bacterial disease progression [95].
7.6
Antibodies
The ability to generate antibodies to a wide range of target analytes and their
resulting specific nature make them very attractive biorecognition elements for
FRET-based biosensing and diagnostics [100]. The sandwich assay represents the
mainstream immunoassay format; however, it can be less practical from a FRET
perspective due to the relatively large dimensions of the resulting antibody–antigen–
antibody complex [20]. Researchers have overcome this limitation by using newer
FRET materials, such as QDs or lanthanide complexes, unique labeling strategies, or
through the use of antibody fragments, which for various reasons can improve FRET
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282
efficiency, as illustrated in Figures 7.5–7.7 [101–109]. Wei et al., for example, took
advantage of the high quantum yields of QDs to extend the F€
orster distance R0,
measuring estrogen receptor b-antigen using full antibodies in a sandwich format
[101] (Figure 7.5). The group of Hildebrandt and coworkers have developed
homogeneous sandwich immunoassays using QD/lanthanide FRET combinations
for detection of prostate-specific antigen [108] and alpha-fetoprotein (AFP) [109]
(Figure 7.5b). Use of the long-lifetime lanthanide complexes allowed time-resolved
measurements, which decreased background and improved assay sensitivity.
Heyduk and coworkers devised a unique oligonucleotide antibody-labeling system
that has been used by others to detect a range of target analyte types (both protein
and bacterial) via a homogeneous sandwich assay [107,110,111]. The methodology
uses antibodies, specific for distinct epitopes on the target analyte, labeled with short
complementary oligonucleotides, and modified with either a donor or an acceptor
species. Binding to the target analyte brings the complementary single-stranded
deoxyribonucleic acid (ssDNA) into close proximity, resulting in hybridization and
hence FRET (Figure 7.6). They have also modified the technology for use with solidsurface-based assays to facilitate multiplexing [68]. Chemiluminescence resonance
energy transfer (CRET) between luminol and various acceptors (graphene nanosheets and Au NPs), catalyzed by horseradish peroxidase (HRP), has been demonstrated for detection of C-reactive protein, a biomarker of inflammation and
cardiovascular diseases [106] and alpha-fetoprotein, a cancer biomarker [112]. An
alternative approach to improving FRET efficiency for sandwich formats is to
decrease the overall distance between the donor and the acceptor dyes through
the use of antibody fragments (Figure 7.7). Sasajima et al. used fragments from the
antibody variable domain (Fv) to develop an immunoassay for tyrosine phosphorylation [103], while Ohiro et al. used the larger Fab (fragment, antigen binding)
antibody region combined with a leucine zipper motif for human serum albumin
detection [102].
Other suitable antibody formats that have proven successful for target detection
include competitive, competitive displacement, and direct detection, as illustrated in
Figure 7.8 [20]. Competitive and competitive displacement assays are popular,
although they require the design of a labeled target analyte analogue
[20,67,100,113–116]. For example, Tan et al. demonstrated a competitive assay for
D9-tetrahydrocannabinol, a major component of cannabis, in saliva (Figure 7.8a) [114],
while Kattke et al. used a competitive displacement assay to detect the presence of a
mold Aspergillus amstelodami [116]. Here, quencher-labeled Aspergillus fumigatus was
incubated with anti-Aspergillus antibody conjugated with QDs, with the resulting
antibody–antigen complex causing a significant reduction in QD emission due to
FRET. Addition of the target analyte, A. amstelodami (for which the antibody had a
higher affinity), caused displacement of the quencher-labeled A. fumigatus and an
increasing QD emission. An alternative direct detection technique was developed by
the Grant group based on the conformational change an antibody undergoes upon
antigen binding (Figure 7.8b) [117]. This format has been used to detect the pathogens
Listeria [118], Salmonella [118,119], porcine reproductive and respiratory syndrome
virus (PRRSV) [120], and the clinical analytes cardiac troponin Tand I [121]. In the case
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7.6 Antibodies
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
Figure 7.5 FRET-based sandwich
immunoassays. (a) Schematic representation
of a FRET-based sandwich immunoassay.
Two antibodies (blue and purple) specific for
different epitopes on the target analyte are
labeled with either the donor or the acceptor
fluorescent probe. Introduction of the target
analyte brings the antibodies into close
proximity, resulting in FRET. (b) Examples of
some of the unique materials used to
improve the FRET efficiency, when designing
a sandwich immunoassay. Here, antibodies
specific to alpha-fetoprotein (AFP) are
labeled with either QD-doped microparticles
or luminescent terbium chelates
(LTCs). Introduction of AFP brings the
antibodies into close proximity, resulting
in FRET between the LTC donor and QD
acceptor species. The emission (LTC and
QD) along with the absorption (QD)
spectra are illustrated along with the timeresolved luminescent decay measurements
of the QDs alone (red squares), LTC
alone (black triangles), and the QD–
antibody1–AFP–antibody2–LTC complex (blue
circles). (Reprinted with permission from
Ref. [109]. Copyright, Elsevier.)
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284
Figure 7.6 FRET-based sandwich
immunoassays using unique oligonucleotide
FRET-based labels. (a) Schematic
representation of the FRET-based sandwich
immunoassay. Two antibodies (blue and
purple) specific for different epitopes on the
target analyte are labeled with either the donor
or the acceptor fluorescent probe, comprising
short complementary oligonucleotides labeled
with fluorescent probes and connected to the
antibody via flexible linkers. Hybridization
occurs in the presence of the target analyte,
resulting in efficient FRET between the donor/
acceptor fluorophores. (Adapted with
permission from Refs [107,110].) (b) Example
of the above FRET-based sandwich
immunoassay used for the detection of E. coli
O157:H7 cells. Fluorescent images of the 96well microplate wells containing indicated
amounts of target E. coli O157:H7 cells or
control E. coli K12 cells. Upper panel shows
donor emission image (Ex 488 nm and Em
530 nm) and lower panel shows acceptor
emission due to FRET (Ex 488 nm and Em
690 nm). (Reprinted with permission from Ref.
[110]. Copyright, Elsevier.)
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7.6 Antibodies
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
Figure 7.7 FRET-based sandwich
immunoassays using antibody fragments.
(a) Schematic of a full antibody, highlighting the
antibody fragments commonly incorporated
into FRET-based assays. Both the Fv fragments
– VH (variable heavy)/VL (variable light), and the
Fab fragments contain the antigen-binding site
of the antibody (illustrated as the red region on
the antibody illustration). (b) FRET-based
sandwich immunoassays using Fv antibody
fragments. Fv fragments from the same
antibody, comprising the VH and VL regions
are labeled with donor or acceptor species.
Introduction of the target antigen brings
these Fv fragments into close proximity,
resulting in efficient FRET. (c) FRET-based
sandwich immunoassays using Fab
antibody fragments. Fab fragments from two
antibodies (blue and purple) specific for
different epitopes on the target antigen are
labeled with donor or acceptor species.
Introduction of the target antigen brings
these Fab fragments into close proximity,
resulting in efficient FRET.
of PRRSV detection, the carrier protein (Protein A) was conjugated to either an Au NP
or a QD before the fluorescently labeled antibody was introduced, resulting in the
FRET-sensing complex [120]. As illustrated in Figure 7.8b, antigen binding – in this
case PRRSV – resulted in a conformational change in the antibody structure, resulting
in a measurable change in the FRET signal.
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286
Figure 7.8 Alternative FRET-based
immunoassay formats. (a) Competitive
displacement immunoassay format. Donorlabeled antibody is preincubated with acceptorlabeled antigen analogue, resulting in FRET.
Introduction of the target antigen causes
displacement of the antigen analogue, resulting
in a decrease in FRET and an increase in donor
emission. Note that if the antigen analogue and
target antigen are simultaneously incubated
with the antibody, the format is referred to as a
competitive format. (b) Direct immunoassay
format. Here, the acceptor-labeled antibody is
modified with a donor-labeled carrier molecule
(CM), typically protein A or G, resulting in FRET.
Introduction of the target antigen causes a
conformational change in the antibody
structure, altering the distance between the
donor–acceptor pair and therefore changing the
measured FRET signal.
7.7
Nucleic Acid (DNA/RNA)
One of the main areas in which FRET has played a significant role in clinical
applications is in nucleic acid-based genetic testing technologies. Completion of the
Human Genome Project, concomitant whole genome sequencing of model organisms, the advent of next generation sequencing technologies, and genome-wide
association studies have revolutionized our understanding of the role of genetic
variation in human disease [122–125]. There are a number of genetic variations
found in the human genome, including single nucleotide variants [single nucleotide
polymorphisms (SNPs), insertions, or deletions – indels] and structural variants
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7.7 Nucleic Acid (DNA/RNA)
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
[copy number variations (CNVs), insertions, deletions, inversions, repeats, translocations, duplications, etc.] [123,126]. SNPs (substitutions) represent the most
frequently studied genetic variation to date [127]. Through genome-wide association
studies, SNPs have been found to be important markers linking sequence variation
to phenotypic changes for a number of diseases [123,127,128].
While FRET can be applied to DNA sequencing in the form of FRET primers,
FRET terminators, and FRETcassettes [20,122,124,129], FRET has had a much more
significant impact on molecular diagnostic technologies for detecting specific,
relatively short DNA or RNA sequences (typically identified during DNA sequencing) for infectious disease diagnosis, genotyping, and pharmacogenomics [127,130–
136]. These technologies rely on the detection of target DNA hybridization and/or
amplification. Hybridization and FRET have been applied to DNA microarrays for
DNA and RNA detection [130,131,137–141]. However, real-time, homogeneous, and
high-throughput assays are desired and FRET-based technologies, such as molecular
beacons and amplification primers or probes, can uniquely address these requirements [20,130,133,135]. Some of the more common technologies are summarized
later followed by a discussion of their medical application.
7.7.1
Molecular Beacons
Since their inception in 1996, MBs [142] have been employed to detect DNA
hybridization and select DNA sequences, gene mutations (e.g., SNPs), proteins,
viruses, and changes in mRNA [130,139,143,144]. MBs have been used for a variety of
other purposes as well such as to monitor polymerase chain reaction (PCR) amplification in real time. MBs are single-stranded nucleic acid probes that in their native
state adopt a stem–loop or hairpin structure (Figure 7.9a). They are typically 25–35
nucleotides in length, comprising three main parts: (i) a loop portion (15–30 nucleotides) complementary to the known target DNA, (ii) a stem portion (5–8 nucleotides)
consisting of two complementary arm sequences annealed on either side of the target
sequence, and (iii) FRET donor/acceptor molecules labeled at the 50 and 30 ends
[20,139,144,145]. In the presence of a target sequence, the molecular beacon unravels,
separating the donor and acceptor, resulting in a measurable change in the FRET
signal. A major advantage of MBs is that the target DNA does not need to be labeled,
and multiplexing can be accomplished by selecting different donors and/or acceptors
[130,146,147] or applying wavelength-shifting molecular beacons [143,145]. However,
as with any of these assays, optimization is a key step to selective and sensitive
detection of the target, and MB design is a fundamental aspect for the successful
application of these types of probes. The distance between the FRETpair on the MB is
important, and ideally the probe sequence should be more than double the length of
the stem portion to ensure the FRET pair are far enough apart after hybridization to
generate a significant FRET response. The melting temperature of MBs depends on
the control of pH and temperature as well as length of the stem, the GC (guanine/
cytosine) content, and the ionic concentration of the buffer [144]. Although MBs are
somewhat limited in their use because they can only detect relatively short DNA
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288
Figure 7.9 Hybridization probes for nucleic
acid-based assays. (a) Molecular beacons
(MBs) comprise a stem–loop DNA structure
that unravels in the presence of the target
DNA, resulting in a decrease in FRET. (b)
Probe–probe-based FRET hybridization
probes comprise two probes (labeled with
either donor or acceptor species) that upon
hybridization to the target DNA come into
close proximity, resulting in FRET. A
subsequent melting curve analysis can be
used to locate SNPs.
sequences [144,146], once optimized, they can be used as detection probes, following
amplification (typically PCR), for a number of pathogens [148] and viruses [149–151].
MBs have also demonstrated excellent mismatch discrimination and therefore show
application in SNP detection [127,139,144,147,152–154]. In addition, although less
common than homogenous solution-based assays, MBs have been immobilized onto
DNA microarrays for rapid detection [130,139–141].
7.7.2
Polymerase Chain Reaction and FRET
Used to create thousands–millions of copies of a particular DNA sequence, the PCR
has been an indispensable biological tool since its establishment in 1983 [155]. PCR
has evolved into a variety of techniques, all based around the basic PCR principle,
with a range of applications, including DNA sequencing and gene analysis, forensic
studies (such as determining DNA fingerprints), diagnosis of hereditary diseases,
and detection of infectious diseases [155]. Over several heating and cooling cycles,
DNA is melted [to separate double-stranded deoxyribonucleic acid (dsDNA)] and
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7.7 Nucleic Acid (DNA/RNA)
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
replicated using each ssDNA as a template, with the help of a DNA polymerase
(typically isolated from bacterium Thermus aquaticus called Taq polymerase). Short
oligonucleotide sequences known as primers – complementary to the 30 ends of the
target DNA – hybridize to the target and initiate amplification in the presence of the
DNA polymerase and deoxynucleoside triphosphates. Once the target DNA is
replicated, this new strand is used as a template for further replication, allowing
the DNA sequence to be amplified by several orders of magnitude. Traditionally,
detection was performed after amplification and included colorimetric, chemiluminescent, or gel electrophoresis techniques. However, the advent of closed
tube DNA thermal cyclers combined with DNA interchelating dyes (such as
ethidium bromide or SYBR Green) or the subsequent FRET-based detection
methods for real-time monitoring of PCR amplification have revolutionized the
technique by limiting the possibility of contamination, allowing continuous monitoring and accurate quantitation [155]. While the interchelating dyes are simple to
use, they lack specificity, detecting both specific and nonspecific amplification.
Hence, labeled nucleic acid probes were developed to address this issue [156]. There
are now a number of FRET-based probes and primers for quantitative real-time PCR
R
monitoring, including FRET hybridization probes, TaqMan
probes, MB probes,
R
Snake probes, and Scorpion primers, among others [20,130,133,135,145,157]. In
addition, many of these probes–primers, especially the hybridization probes, TaqMan and Scorpion assays, are commercially available, with companies offering a
number of common test kits and custom probe design services [see Life Technologies, Integrated DNA Technologies (IDT), and Sigma-Aldrich].
7.7.2.1 FRET Hybridization Probes
In addition to MBs, discussed above, there are two main FRET-based hybridization
probe schemes: primer–probe and probe–probe (Figure 7.9b) [134,158]. In the typical
case where donor dye–acceptor dye FRET combinations are used, FRET occurs when
the PCR cools and the target/probe annealing process begins, resulting in a measured
increase in fluorescent signal from the acceptor dye [158]. Subsequently, when the
temperature is ramped back up to start the next cycle, the target–probe complex
becomes separated and the acceptor dye fluorescence decreases, thus allowing realtime monitoring of PCR. Studying the melting curve of the target/probe and
determining the probe melting temperature (Tm) is an excellent method for genotyping [134,158,159]. The probe–probe scheme is generally more popular in melting
curve analyses and uses a donor probe, designed to span a specified mutant site on the
target DNA sequence, and an acceptor probe, designed to remain annealed to the
target DNA sequence (the template) while the donor probe melts. When the donor
probe, typically designed for the wild-type target DNA, encounters a mutation in the
sequence, its Tm is generally lower than that of the wild-type Tm (for which it is perfectly
matched). The extent of Tm variation is dependent upon the type and position of the
mismatch, and the neighboring base pairs [134,158]. This assay format forms the basis
R
technology, and these FRET hybridization probes,
of the popular Roche LightCycler
combined with melt curve analysis, have been used in a number of clinical applications, including detection of bacteria [160–162], viruses [163,164], fungal species [165],
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290
and parasites [166], as well as for use in disease diagnostics/prognostics [134,167–170]
and forensic analysis [171]. The use of PNA probes has also been proposed as more
stable and sensitive alternatives to their DNA analogues [172,173].
7.7.2.2 TaqMan
The TaqMan assay (Figure 7.10) has three components: the template, an energy
transfer (ET) probe specific to a certain sequence, and a primer that is needed for
PCR amplification [20]. Originally developed by Cetus Corporation [174], the assay is
Figure 7.10 The TaqMan assay. The ET probe
is complementary to the sequence under
investigation and is labeled with a donor–
acceptor pair that results in FRET. During the
PCR sequence extension stage by Taq
polymerase, the ET probe becomes cleaved,
separating the donor–acceptor pair and
resulting in decreased FRET and increased
emission from the donor. Upon completion of
the extension reaction, the ET probe is
completely dissociated from the target DNA.
The donor emission signal increases with
increasing PCR cycles.
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7.7 Nucleic Acid (DNA/RNA)
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
commercially available from Roche (clinical applications) and Life Technologies
R
(research use), and requires real-time optical instrumentation, such as the COBAS
developed by Roche. The ET probe, complementary to the sequence under investigation, has a donor–acceptor pair (in this assay, the donor is referred to as the
“Reporter” and the acceptor is typically a quencher species). The primer is located in
a region upstream of the probe and is extended by Taq polymerase. As the extension
reaction reaches the probe, the probe is cleaved, releasing the donor that emits light.
The probe and primer anneal to the template, and only in the presence of a fully
complementary sequence will the probe and template completely hybridize. Single
point mutations can be detected and are indicated when no fluorescence is detected
due to the probe “falling off” the template instead of being cleaved. This assay is
favorable because it determines the mutational status in one step during PCR.
Despite some studies that claim that traditional SYBR Green and nest PCR are more
cost-effective, sensitive, and quicker than the TaqMan assay [175,176], it is routinely
used for a number of potential clinical applications such as detection of parasites
[176] and a number of viruses [177–179].
7.7.2.3 Scorpion Assay
The Scorpion primer was originally developed by AstraZeneca scientists [180], and is
now owned by QIAGEN (via DxS Ltd.). The Scorpion combines the PCR probe and
primer into a single molecule, with the probe–primer sections linked by a “blocker”
sequence that prevents copying of the probe portion of the Scorpion, which would
lead to false-positive signals [20,157]. There are two Scorpion formats known as the
stem–loop format and duplex format (also known as, linear format) (Figure 7.11a)
[157,181]. In both formats, a dye–quencher FRET pair combination is common with
the probe containing the donor fluorophore, which is quenched in the presence of
the acceptor quencher attached either on the stem–loop structure (stem–loop
format) or on a short complementary hybridized strand (duplex format) [20].
The primer becomes annealed to the target sequence, and is extended via PCR.
At the end of the heating and cooling cycles, the temperature is increased, causing
the template and extended primer to denature, at which point the probe can
hybridize with its target sequence in the extended primer, located downstream
of the initial primer sequence, resulting in an increase in the donor fluorescence
(Figure 7.11b) for the stem–loop format. There are various advantages and disadvantages to each Scorpion format, although the duplex format is easier to produce
and purify, and has a more pronounced FRET response due to larger separation in
the distance between quencher and fluorophore upon hybridization to the extended
primer [157]. The Scorpion assay is valuable because unimolecular hybridization
(primer–probe combination) is faster than bimolecular hybridization (such as
TaqMan), and the reagents are commercially available from a number of sources,
including QIAGEN, Sigma-Aldrich, and Premier Biosoft International [20,181].
Scorpion primers can distinguish SNPs in a one-step process and are suitable for
use with a LightCycler [181,182]. The Scorpion assay has been applied to bacterial,
parasitic, and viral detection [182–184], and can be used for point mutation analysis
found in many diseases [181,185–187].
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292
Figure 7.11 The Scorpion assay. (a) The
Scorpion combines the PCR probe and primer
into a single molecule, with the probe–primer
sections linked by a “blocker” sequence that
prevents copying of the probe portion of the
Scorpion. There are two Scorpion formats
shown, the stem–loop format and duplex
format (also known as, linear format), both of
which typically use a donor/quencher FRET
combination. (b) Typical PCR amplification
reaction using the stem–loop Scorpion format.
Prior to the PCR, the Scorpion probe–primer
molecule undergoes efficient FRET.
Introduction of the target DNA causes the
primer to become annealed and extension is
initiated via addition of DNA polymerase and
nucleotide bases. At the end of the extension
process, the temperature is increased, causing
the template and extended primer to denature.
This allows the probe portion of the Scorpion
molecule to hybridize with its target sequence
in the extended primer, located downstream of
the initial primer sequence. Subsequently, the
FRET is disrupted, resulting in an increase in
the donor fluorescence.
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7.7 Nucleic Acid (DNA/RNA)
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7.7.2.4 Others
There are a couple of other noteworthy examples in the literature of FRET-based
probes or primers for use with PCR. Ahmad and Ghasemi sought to create novel
FRET primers instead of probes for use in quantitative real-time PCR, taking
advantage of the fact that primers are generally specific and are designed to have
a low possibility of annealing to other sequences besides the target DNA [135]. In
addition, the use of labeled primers avoids the need for additional probes, hence
speeding up the PCR. The FRET primers were shown to be more efficient than
unlabeled primers detected using the DNA interchelating dye SYBR Green I.
PCR has also been monitored in real time using the Snake assay that uses FRETbased probes for detection. The Snake assay combines features of both the TaqMan
and Scorpion assays [156]. The assay uses a PCR primer that carries a unique 50 -flap
sequence that later causes the PCR amplicon to fold into a stem–loop structure, much
like a Scorpion assay. A FRET-based probe then binds the folded PCR amplicon and
forms a cleavage structure optimal for 50 nuclease activity, which, like the TaqMan
assay, cleaves the FRET probe causing a measurable change in the FRET signal [156].
7.7.3
Isothermal Amplification Reactions and FRET
There are a number of amplification techniques that do not require the thermal
cycling necessary for PCR, making them interesting candidates for PoC diagnostics,
discussed later. These approaches are referred to as isothermal techniques and
include nucleic acid sequence-based amplification (NASBA), helicase-dependent
amplification (HDA), recombinase polymerase amplification (RPA), transcriptionmediated amplification (TMA), loop-mediated isothermal amplification (LAMP),
rolling circle amplification (RCA), single primer isothermal amplification (SPIA),
smart amplification process version 2 (SMAP2), strand displacement amplification
(SDA), nicking and extension amplification reaction (NEAR), isothermal chain
amplification (ICA), and isothermal and chimeric primer-initiated amplification
of nucleic acids (ICAN) [188,189]. A number of these techniques use FRET-based
probes for detection. NASBA often combines MB probes with a primer plus a threeenzyme cocktail for RNA detection, and has been demonstrated for SARS-associated
coronavirus, human bocavirus, and Aspergillus species detection [149,190–192]. The
use of TaqMan probes, in combination with HDA, has been investigated for
detection of Vibrio cholerae and B. anthracis [193], while Becton, Dickinson and
Company (BD) developed a dual dye-labeled hairpin probe in combination with SDA
for Chlamydia trachomatis and Neisseria gonorrhoeae detection [194]. These isothermal techniques typically require a number of specialized primers combined with
multiple enzymes, which can increase the assay cost, and some methods suffer from
limited specificity and sensitivity. To address the sensitivity issue, Jung et al.
proposed a combination of ICA with FRET-based cycling probe technology (CPT)
and were able to demonstrate single-copy sensitivity for C. trachomatis [188]. This
method, called isothermal target and signaling probe amplification (iTPA) was also
used by Kim et al. for detection of Salmonella enterica [195]. The iTPA methodology
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294
was shown to detect a specific gene found in Salmonella species and was used to
distinguish 10 infection-causing Salmonella strains from 40 non-Salmonella strains.
R
assay is also an isothermal amplification technique that uses a
The Invader
structure-specific flap endonuclease and two probe oligos, an Invader oligo probe
and a FRET-labeled detector probe [130,196–198]. The assay has been made
commercially available by Third Wave Technologies (subsidiary of Hologic Inc.)
and has been used for SNP genotyping [196,198,199]. The Invader Plus assay [200]
combines the Invader assay with PCR and has been used to distinguish between a
wild type and a vaccine mutant of the varicella-zoster virus [159].
7.7.4
Clinical Applications of Nucleic Acid Detection Using FRET
As our understanding of the molecular basis of disease continues to advance, there
is little doubt that genetic testing technologies will become a fundamental set of tools
in the areas of disease diagnosis, oncology, pharmacogenomics (and therefore
companion diagnostics) and prognostic applications (determining disease susceptibility) [123,201,202]. FRET-based nucleic acid assays have been used for a number
of clinical applications highlighted later.
7.7.4.1 Detection of Pathogens
Nucleic acid-based sensing technologies that incorporate FRET for signal transduction have been used to distinguish pathogens from one another, to identify agents
used as biological weapons, and to measure helpful organisms that are indicative of
good health. The highlighted real-time FRET-based techniques are much quicker
than traditional cell culture and can allow more precise characterization of pathogens. Detection of pathogens such as bacteria and viruses, especially genotyping,
can aid in diagnosis of disease, which in the case of outbreaks can also link the
patient to the source, and help identification of drug-resistant strains, allowing
appropriate therapeutic treatment for the patient [136,203].
Rapid detection of biothreat agents is an area of clinical concern and a number of
researchers are actively involved in studies to address this need. FRET-based sensing
has been employed for genotyping B. anthracis, the bacteria associated with anthrax
[193,204]. Yersinia pestis, associated with the bubonic plague, has also been detected
using the LightCycler [161]. Life Technologies offers commercial TaqMan kits for
measurement of both these bacterial species.
Respiratory infections due to bacteria and viruses, in particular influenza viruses,
are also common clinical targets of interest, and a number of researchers have
used LightCycler (Roche) FRET probes and melting curve analysis to detect types
and subtypes of influenza viruses [205,206]. The TaqMan assay has been demonstrated to quantitatively detect avian influenza A virus with a limit of detection of 100
copies/reaction and no false-positive results [178]. Severe acute respiratory syndrome (SARS) coronavirus was measured using MB assays [149], while multiplex
RT-PCR (reverse transcriptase–polymerase chain reaction) assays that use FRET
probes can be used to detect 13 different respiratory viruses [164]. Mycobacterium
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7.7 Nucleic Acid (DNA/RNA)
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
tuberculosis (MTB), the bacteria that causes tuberculosis (TB) has been measured
with Roche’s commercial diagnostic TaqMan kits as well as via use of the LightCycler
combined with hybridization probes [160].
Gastroenteritis can result from viral, bacterial, and parasitic infections, and occurs
from exposure to contaminated food, water, or infectious individuals. Life Technologies offer a number of commercial TaqMan kits for detection of common foodborne
bacterial pathogens, including the E.coli O157:H7, Campylobacter jejuni, S. enterica,
and Listeria monocytogenes. Isothermal amplification techniques have been demonstrated for detection of S. enterica [195] and V. cholerae [193]. Optimized MBs have been
used as detection probes, following PCR amplification, for E. coli 0157:H7 [148]. FRET
based PCR techniques have been developed for detection of adenoviruses that typically
result in infections of the upper respiratory tract, however, serotypes 40 and 41
manifest as gastroenteritis [179]. TaqMan assays have been used for detection and
genotyping of genogroup I and II noroviruses [203], while Scorpion probes have been
developed for detection of parasites such as Giardia lamblia [184].
Other targets of clinical significance that have been detected using FRET-based
nucleic acid assays include human papillomavirus (HPV) [150,183,170,207], hepatitis
B virus (HBV) [151,208,209], and HIV. Roche have commercial diagnostic TaqMan kits
for detection of HIV, hepatitis C virus (HCV), and HBV, while Hologic offers Invaderbased kits for HPV detection. The Invader and the LightCycler technologies have been
used for detection and differentiation of wild-type and vaccine-mutant varicella-zoster
viruses (etiologic agent of childhood chicken pox and adult shingles) [163,200].
TaqMan assays have been used to diagnose the reactivation process of viruses
such as human cytomegalovirus and human herpesvirus-6, which can occur when
an infected person becomes immunocompromised [177]. LightCycler and TaqMan
assays have also been used to detect the parasite Toxoplasma gondii [166,176], whereas
isothermal amplification techniques have been used for detection of human bocavirus
and Aspergillus species detection [190–192]. BD developed a dual dye-labeled hairpin
probe in combination with isothermal SDA for C. trachomatis and N. gonorrhoeae
detection [194]. Jung et al. proposed a combination of ICA with FRET-based CPT to
demonstrate single-copy sensitivity for C. trachomatis [188].
Another very important application of DNA genotyping, from a therapeutic
perspective, is the detection and identification of drug-resistant pathogen strains
[210]. FRET nucleic acid assays have demonstrated the detection/identification of
rifampin-, isoniazid-, and multidrug-resistant MTB [162], clarithromycin-resistant
Helicobacter pylori (which causes gastritis) [182], ciprofloxacin-resistant Y. pestis [161],
and azole-resistant Candida species (fungal) [165]. Genotyping of HCV has been
useful from a clinical perspective, as genotype can influence the clinical outcome,
when using current anti-HCV therapies [209].
7.7.4.2 Prognostic and Diagnostic Applications
In addition to pathogen detection, genotyping has been employed for a variety of
medical purposes, including prognostic, diagnostic, and therapeutic purposes.
FRET probes have been used to identify many polymorphisms associated with
illnesses (Table 7.2). However, it is important to note that discovering an
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296
Table 7.2 Biomarkers detected by FRET genotyping and analyzed using melting curve analysis.
Biomarker
Disease association
Reference
Chromosomes 9p21.3 and 4q25
Coronary artery disease and
atrial fibrillation
Liver metabolism of drugs
Myocardial infarction
protection
Thromboembolism and
haemochromatosis
Deep vein thrombosis
[123]
Polymorphisms of CYP2C and CYP2C19
Polymorphism FXIII-A Val34Leu
Factor V Leiden
Factor V Leiden (G1691A) and prothrombin
(G20210A)
Varicella-zoster virus vaccine and wild-type
strains
Newborn screening of b-globin
IRGM tetranucleotide promoter oligorepeats
HLA-B27 (human leukocyte antigen)
TNF-a
JAK2
Polymorphisms of endothelin-1, endothelin-2,
and endothelin receptor A
Polymorphisms of the NOS3 Gene R389G,
ADRB1, and CAV1 gene
Polymorphisms of interleukin-6
[211]
[212]
[213–216]
[167]
Shingles
[163]
Hemoglobinopathies
Immunity
Autoimmune diseases
Septic shock risk factor
Thrombophilia
Vascular disease susceptibility
[217]
[218]
[219]
[220]
[221]
[222]
Hypertension susceptibility
[223–225]
Coronary heart disease
[226]
association between a disease and genetic variation is different from causation.
Identifying areas of a genome correlated with a disease simply suggests that this
location could have important variants, which could then lead to defining the
functional significance of variants.
Some cardiac conditions/diseases have strong genetic associations, such as the
correlation between coronary artery disease (CAD) and mutations on chromosome
9p21.3 or the strong association between atrial fibrillation and mutations at chromosome 4q25 [123]. The LightCycler has been employed in a number of studies that are
looking for genetic associations with cardiac conditions. Arjomand-Nahad et al., for
example, looked at polymorphisms of endothelin-1, endothelin-2, and endothelin
receptorA,whichmayinfluencesusceptibilitytovasculardiseasessuchashypertension
(high blood pressure) and cardiac disease [222]. Jia et al. looked at the relationship
between polymorphisms of interleukin-6 (IL-6) and coronary heart disease [226].
Hypertension, a leading cause of cardiac disease, has also been the subject of investigation, with FRET-based assays used to determine if polymorphisms of the NOS3 gene
R389 G, ADRB1, or CAV1 gene influence susceptibility to hypertension [223–225].
Shemirani and Muszbek utilized the LightCycler to detect a polymorphism (FXIII-A
Val34Leu) associated with protection against myocardial infarction [212].
Blood diseases such as thrombophilia, which increase the risk of thrombosis, and
hemoglobinopathies, such as sickle-cell disease, represent another current area of
research. Ameziane et al. reported the use of FRET probes to detect mutations
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7.7 Nucleic Acid (DNA/RNA)
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
(factor V Leiden – G1691A and prothrombin – G20210A) associated with deep vein
thrombosis, with a throughput of 72 samples/90 min, significantly faster than the
6 h needed to perform restriction fragment length polymorphism (RFLP) [167].
Detection of factor V Leiden, which may be associated with hereditary thromboembolism and haemochromatosis, has also been demonstrated [213–216]. Thrombophilic mutations of Janus kinase 2 (JAK2) gene [221] and newborn screening of
hemoglobinopathies [217] have also been studied using FRET-based detection.
Other clinical areas of prognostic interest include genotyping of genes encoding
immunity [218], genotyping of TNF-a (tumor necrosis factor-a) (a risk factor for
septic shock) [220], and identifying mutations associated with hereditary pancreatitis
[227]. FRET-based assays have also been used to investigate human leukocyte
antigen (HLA)-B27, which is associated with autoimmune diseases [219] and a1antitrypsin protein deficiency, linked to inherited mutant alleles designated PI Z
and PI S, which can lead to obstructive lung disease in adults and liver cirrhosis in
children [169].
While the examples above mainly describe the use of genetic biomarkers to
predict susceptibility to disease, there are other genomic markers that can be used
to make a definitive diagnosis of disease. FRET probes have been used to detect a
range of mutations/variations in genomic sequences, which can be used to
diagnose diseases [123,130]. The use of genetic differences among individuals
has increased the understanding of a number of diseases, such as Crohn’s
disease, cancer, asthma, malaria, and heart disease. For example, FRET-based
genotyping has been employed to assist in the diagnosis of chronic myeloproliferative disorders (CMPDs), such as chronic myeloid leukemia (CML)
[168]. Mutations in the KRAS gene, which encodes the KRAS protein – a GTPase
involved in many signal transduction pathways – has been implicated in various
types of cancers, including lung and colon cancer, and has been subject to a
number of studies using FRET-based signal transduction [152,154]. Clayton et al.,
for example, discovered that 44% of adenocarcinomas in lungs had one of 7
known mutations in the KRAS oncogene [152]. The quantitative nature of these
results, obtained by combining RT-quantitative PCR with ARMS allele-specific
amplification, could be used to dictate the analytical sensitivity needed for
diagnosis of KRAS mutations. QIAGEN offers a number of Scorpion kits for
detection of somatic mutations (acquired rather than germline mutations) found
in various oncogenes, including PIK3CA, KRAS, EGFR, and BRAF [185,187].
Somatic point mutations in the GNAS gene have been linked to fibrous dysplasia
(FD) of bone/McCune–Albright syndrome (MAS) [172].
7.7.4.3 Pharmacogenomics and Personalized Medicine
The discovery that genomic variation in a patient population can influence drug
response (pharmacogenomics) has led to the concept of personalized medicine, that
is, tailoring treatment to the individual patient characteristics, which in turn has led
to companion diagnostics [3,228]. The use of diagnostics to discriminate between
allelic variants for therapeutic purposes is becoming increasingly common and
FRET-based detection can be advantageous in this arena.
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298
A prime example of linking genomic analysis to an improved therapeutic
output is the dosing of warfarin to treat venous thrombosis [123]. While warfarin
is a common treatment for thromboembolism, this drug is associated with
adverse effects, has a narrow therapeutic range, and patients demonstrate a wide
variation in response. Variability in the effectiveness of the drug can be due to
patient age, size, drug use, diet, fitness level, and preexisting conditions. Two
gene polymorphisms have been found to be important in the pharmacogenomics
of warfarin, specifically the genes encoding the enzymes cytochrome P459
enzyme CYP2C9 and vitamin K epoxide reductase complex subunit 1 VKORC1.
In 2007, the United States Food and Drug Administration (FDA) approved
updated package labeling for warfarin, which was revised to state that these
genetic variations may influence how a patient may respond to the drug [229].
Since then, FDA has increasingly approved certain drugs with companion
diagnostic tests, where strong evidence of genetic variation and pharmacogenomics has been demonstrated. For example, Zelboraf (vemurafenib) in combination with the Cobas 4800 BRAF V600 mutation test has been approved for latestage skin melanoma [230].
Op den Buijsch et al. used FRET assays for rapid genotyping of the OATP1B1
polymorphisms A388 G and T521C that have been found to alter the pharmacokinetics of the cholesterol-lowering drug pravastatin and the oncology drug
irinotecan, in certain ethnic populations [231,232]. Variability in the CYP2D6
gene, which encodes the cytochrome P450 2D6 enzyme, is found to influence the
pharmacokinetics of an analgesic tramadol used to treat moderately severe pain
[233]. The uses of a LightCycler and melting curve analysis were shown to be
useful in the detection of allelic variants of CYP3A and ABCB1 genes that
influence the pharmacokinetics of Tacrolimus, an immunosuppressant prescribed following renal transplantation [234].
7.8
Aptamers
Aptamers are short-chain nucleic acid (RNA and ssDNA) and peptide molecules
that bind target analytes with high specificity and selectivity, which are finding
application in a number of clinical areas such as recognition of molecules in
diagnostic assays [235–239]. They are considered akin to antibodies in terms of
their molecular recognition abilities, but also offer some unique advantages,
including thermal stability, large-scale production, and low immunogenicity
[236,237,239,240]. Some disadvantages of aptamers include binding of nonspecific proteins in complex matrices (such as serum) and metal ion sensitivity
[241]. Aptamers can be generated against a wide variety of target analytes, from
ions, low molecular weight molecules and proteins through microorganisms and
are typically isolated from a combinatorial library by an in vitro procedure called
SELEX (systematic evolution of ligands by exponential enrichment) that can be
automated [236,242,243]. The potential of aptamers for use in diagnostic and
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7.8 Aptamers
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
biosensing applications, including FRET-based homogeneous assays, has recently
been reviewed [236,237,239].
Due to the large structural rearrangement that often occurs as a result of
aptamer target recognition, FRET has proven a particularly useful signal transduction mechanism in aptamer-based assays. Examples of assay formats include
sandwich and competitive displacement assays (similar to the antibody equivalents) and molecular aptamer beacons (akin to MBs). The sensitivity of FRETbased aptamer assays is influenced by several factors: affinity for the target, the
number of fluorophores incorporated into the aptamer, the proximity of the
fluorophore to the quencher, and the purity of the FRET complex after chromatographic separation [244].
One of the most popular targets for aptamer detection is thrombin, a regulator
of tumor growth, metastasis, and angiogenesis, in blood serum [245], and a
number of FRET-based aptamer assay formats have been demonstrated for this
protein. The thrombin aptamer is an example of a guanine-rich ssDNA sequence
that forms an intramolecular quadraplex structure upon target binding (reviewed
in Ref. [246]). Assay formats for thrombin include the stem–loop aptamer beacon
[241], the random coil [247], and a structure-switching signaling assay [248]
(Figure 7.12). Recently, some unique FRET materials have been incorporated
into FRET-based assays for aptamer-based thrombin detection, including graphene, which acts as a quencher [245,249], quantum dots [249], upconverting
phosphors, and carbon nanoparticles [250]. Heyduk and later Lee and coworkers
developed an aptamer FRET format somewhat akin to a sandwich antibody in
which two aptamers, specific for different epitope regions on the thrombin
protein, are labeled with short complementary oligonucleotides modified with
the FRET pair molecules [251,252]. Upon aptamer binding to thrombin, the short
complementary oligonucleotides become close in proximity, resulting in FRET.
Lee and coworkers used a Cy3–Cy5 FRET pair and measured thrombin via singlemolecule photon-burst detection, which has the interesting potential to be
combined with microfluidic systems for real-time analysis [252].
Besides thrombin, various FRET-based aptamer assays have been developed for a
number of clinically relevant targets, including methylphosphonic acid, a metabolite
of several organophosphonic based nerve agents [253]; foot and mouth disease
biomarkers [244]; drugs such as cocaine [254,255] and theophylline [256]; adenosine
deaminase (ADA, an enzyme needed for purine metabolism) [257]; epithelial
marker mucin 1, a biomarker for diagnosis of epithelial cancers [258]; plateletderived growth factor (PDGF), a protein that promotes angiogenesis and regulates
cell growth [235,259]; and angiogenin, a protein also linked with angiogenesis [260].
Given the specificity offered by aptamers, multiplexed detection is possible and
was recently demonstrated for the detection of cocaine, potassium, and adenosine
[261]. Here, the assay takes advantage of the “superquencher” abilities of gold
nanoparticles to quench fluorescence from three aptamers labeled with different
fluorophores. Binding of the target analyte to the aptamer causes that specific
aptamer to become displaced from the Au NP surface, resulting in an increase in
fluorescence.
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300
Figure 7.12 Thrombin detection using FRETbased aptamer sensors. (a) Random coil
format. DNA-based aptamer undergoes a
conformational change upon thrombin binding
that brings donor and acceptor (quencher)
labels into close proximity, resulting in FRET
and reducing donor emission. (b) Aptamer
beacon. DNA-based aptamer adopts stem–loop
structure that unravels in the presence of
thrombin, changing the FRET efficiency and
increasing the donor emission. (c) Two-stem
duplex assembly. Probe ssDNA sequences,
labeled with either donor or acceptor
(quencher) species bind complementary
portions of the DNA-based aptamer, resulting
in FRET. Thrombin binding to the aptamer
causes a conformational change that displaces
one of the probe sequences, disrupting FRET
and increasing the donor emission. (Adapted
with permission from Ref. [246].)
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7.8 Aptamers
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
7.9
High-Throughput and Point-of-Care Devices
As demonstrated in the previous sections, FRET has been used to monitor a wide
variety of molecular interactions and has been applied to the field of sensing for
clinical diagnostics and personalized medicine. Since the vast majority of the FRETbased assays illustrated in this chapter are homogeneous in nature and are often as
simple as “mix and detect”, there is great potential for incorporation into highthroughput technologies and/or miniaturized platforms for use in clinical laboratories and ultimately as PoC diagnostic devices [1,146,262].
FRET-based nucleic acid tests have impacted the area of high-throughput technologies for clinical laboratories, as evident from the number of commercial
instruments and test kits available that allow real-time detection of target DNA
amplification, either by PCR or by isothermal-based techniques. Here, advances in
the platform technology, rather than the assay probes themselves, have been the
primary driving force behind transitioning to high-throughput methods. Leading
examples include the Roche LightCycler 1536 instrument, where the 1536 highdensity multiwall plate enables real-time PCR monitoring of 0.5–2 m l samples, and
the BD ViperTM System with XTRTM Technology, based on SDA isothermal
amplification, which uses a 96-well plate format and has fully automated sample
processing, delivering 736 results/8.5 h. Both technologies use FRET-based nucleic
acid assays developed for earlier low- and medium-throughput iterations of the
device platforms. Many of the other FRET-based assay formats described in this
chapter could readily be combined with standard fluorescent microplate readers
(e.g., Tecan, Biotek, and PerkinElmer), which, when combined with liquid handling
and robotics platforms, can become high-throughput.
While high-throughput technologies suitable for clinical laboratories are highly
desirable, the ultimate goal of many IVDs researchers and developers is use in a PoC
environment, where real-time results in a clinical setting or at home can reduce the
time, sample, and reagent volumes, and hence overall cost of the test. The current
status and future of PoC diagnostics was recently described in a comprehensive
review by Gubala et al., where the authors highlighted many of the technologies that
are enabling IVDs to transition from a clinical laboratory to a PoC environment [1].
The article identified key trends such as personalized medicine, home testing, and
multiplexing, and revealed unmet needs for these types of technologies.
7.9.1
PoC Technology Advances
FRET-based signal transduction has much to offer, and likewise, has benefited from
many of the technologies developed for PoC diagnostic applications such as
microfluidics, lab-on-a-chip, and improved optical detection (i.e., better excitation
and detection sources) [1,146,262,263]. Microfluidics and lab-on-a-chip technology
are key areas for PoC devices, enabling the miniaturization and integration of
components (sampling, testing, and detection that comprise the complete assay) to
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302
create benchtop and portable/handheld instruments [1,264]. Simple “mix-anddetect” FRET assays have been demonstrated for protease detection using a miniaturized fluorimeter, comprising spatial electroluminescent (EL) or light-emitting
diode (LED) excitation coupled with CCD (charge-coupled device) detection, for
botulinum neurotoxin A or trypsin activity detection [86,98,265]. Results obtained
with the miniaturized fluorimeter were comparable to a standard benchtop fluorescence plate reader. There are some commercial handheld fluorimeters (for
example, AquaFluorTM and Picofluor by Turner Designs and QuantiFluorTM by
Promega) containing UV (ultraviolet), blue, yellow, and/or green LEDs for excitation, but they are typically single sample (cuvette) devices (not high-throughput) and
have not yet been applied to FRET-based assays.
Nucleic acid detection has been an area of interest for PoCtechnology manufacturers,
especially considering potential applications in personalized medicine, where PoC
detection could facilitate appropriate and timely treatment [202]. Detection of DNA
hybridization has been demonstrated via FRET in microfluidic channels (Figure 7.13)
[266–268] and microfluidic droplets, so-called “droplet assays” [269]. In addition,
performing traditional PCR in a microfluidic (microPCR) environment is highly
desirable [270]. Of all the assay formats described in this chapter, PCR is one of the
most complicated to transition to a microfluidic or miniaturized platform, as it involves
repeated and precise heating and cooling cycles that can put strain on the materials used
and the power requirements of the device [270]. MicroPCR techniques can be classified
intotwomaintypes:well-basedandcontinuous-flowchips[270].DigitalPCRrepresents
the state-of-the-art in this field and can be either array- or droplet-(a continuous-flow
Figure 7.13 FRET-based DNA hybridization
detection in microfluidic chips. Schematic
illustration of an alligator teeth-shaped
PDMS microfluidic chip used for FRET
detection of DNA hybridization.
Fluorescence emission spectra were
recorded at different positions along the
microfluidic channel, demonstrating the
increase in FRET as increasing amounts
of DNA targets and probes hybridize.
(Reprinted with permission from Ref. [266].
Copyright, Elsevier.)
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7.9 High-Throughput and Point-of-Care Devices
j 7 In Vitro FRET Sensing, Diagnostics, and Personalized Medicine
technique) based [186,271,272]. There are a number of commercial benchtop digital
PCR instruments available (Fluidigm Corporation, Life Technologies, Bio-Rad Laboratories,andRainDance), whichtypicallyincorporateTaqManand/or Scorpionprobes for
detection [186,272,273]. Digital PCR technology has been used to quantify lung cancer
EGFR alterations [186] and KRAS mutations [273].
Girkin et al. recently described a miniaturized, fully integrated genotyping system
that performed PCR and used FRET-based hybridization probes to carry out melting
curve analyses to detect SNPs [274]. This instrument performed an assay in 18 min
using both purified DNA and saliva samples contained in capillary tubes with a
sample size of 4 ml. Isothermal amplification techniques that do not require the
repeated thermal cycles needed for PCR are also emerging for use in combination
with microfluidic technologies for PoC applications [189,275].
7.9.2
PoC Material Advances
In addition to advances in technology that incorporate FRET and PoC, substantial
progress has been made in the area of new and improved materials for FRET. In
particular, nanomaterials can address some of the inherent complications of FRET,
that is, photobleaching, spectral cross talk, and direct excitation of the acceptor to
propel the wider application of FRET for signal transduction [2]. Of the many types of
materials that have the potential for use in FRETapplications (discussed in chapter 6),
QDs, lanthanide-based materials, and superquenchers (such as gold and graphene)
seem the most common to date for clinical diagnostic applications [276–278].
QDs in particular have found utility in FRET-based assays, primarily as donors, but
are increasingly used as acceptors in a number of studies [276,279–283]. QDs possess
photophysical properties that make them ideal for FRET applications, particularly
those destined for PoC technologies. QDs have narrow photoluminescent (PL)
emission profiles that are continuously tunable through control of the QD size
and material, and across a broad spectral range, allowing relatively straightforward
multiplexing of assays in various formats [147,284]. Broad absorption profiles result in
the ability to excite QDs at wavelengths from the UV to the blue side of their emission,
resulting in the potential for a large Stokes shift, thus reducing background signals
that result from ambient excitation light and direct excitation of the acceptor. The
broad absorption profiles suggest that PoC technologies may only require one
excitation source for different colored QDs, which is ideal for multiplexing while
simplifying PoC instrumentation. QDs typically have high quantum yields and due to
their particle nature (i.e., nanoscaffold properties), multiple acceptors can be linked to
the QD surface to enhance energy transfer efficiency [279,281]. Such properties can be
important for sensor performance, especially when designing PoC devices where
there may be trade-offs in terms of excitation power/intensity and device size/weight.
Other materials, including lanthanide-based materials and superquenchers, such
as Au NPs, carbon nanotubes (CNTs), and graphene sheets, have unique properties
that make them useful for energy transfer-based assays. Lanthanide-based materials,
which include LLC and lanthanide-doped upconverting phosphors (UCPs), are
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304
typically used as donors and possess a number of narrow donor emission peaks
(Figure 7.5b), with a large Stokes shift [276,277]. They also have long-lived fluorescent lifetimes, making time-resolved, as opposed to steady-state (or frequency),
measurements possible. This property of lanthanide-based materials allows timegated measurements that eliminate background fluorescence, thereby improving
the signal-to-noise ratio of the sensor [285]. Lanthanide donors have been coupled to
a range of acceptor materials, including organic dyes [108,286], carbon nanoparticles
R
[250], and QDs [29,109,287,288]. TRACE
technology, a LLCs-based fluorescent
R
immunoassay, forms the basis of the detection scheme used by the KRYPTOR
series of commercial plate reader systems and was demonstrated for the detection of
prostate-specific antigen [108]. So-called “superquenchers” are materials capable of
quenching luminescence from a wide range of donor materials, which makes them
useful for multiplexing, and they have been demonstrated in a number of FRETbased sensing measurements [245,249,261,289].
7.10
Conclusions
This chapter has demonstrated the huge potential of FRET-based signal transduction for clinical IVD applications and personalized medicine. The intrinsic
distance dependence of FRET makes it ideal for monitoring a wide range of
molecular recognition events, and detecting many types of target analytes. The
diverse array of sensing molecules, ranging from small organic molecules to
relatively large polymers, which can be used for FRET, makes this technique very
versatile. Nucleic acid, followed by protein-based (e.g., binding proteins, peptide,
and antibody) FRET assays, are the main types of FRET-based sensors currently
being used, with aptamers being increasingly utilized. Advances in microfluidics,
nanotechnology, and materials have the potential to revolutionize FRET-based
assay formats by simplifying platform designs. Mainstream use of PoC devices for
diagnostic, prognostic, and therapeutic clinical applications, as well as for environmental, defense, and other needs may become a reality in the not too distant
future. With further advances in technology, we anticipate FRET to become a more
greatly appreciated analytical tool.
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322
8
Single-Molecule Applications
Thomas Pons
8.1
Introduction
Recent years have witnessed major progress in fluorescence microscopy instrumentation, raising its detection sensitivity to the single-molecule level. Observation
of single molecules has since brought a wealth of information and allowed a better
understanding of many physical, chemical, and biological processes [1–6]. Singlemolecule fluorescence has become in particular a powerful tool to study biomolecular functions [7–12]. Indeed, these functions most often involve conformational changes and/or multimolecular association/dissociation. This implies that, in
the absence of an external synchronization, biomolecules in solution fluctuate
between different states independently of each other. Whereas ensemble experiments provide only average measurements over all these different states, singlemolecule measurements can reveal both heterogeneity in the population (in the
equilibrium distribution of states) and dynamics (i.e., sequence of transitions,
frequencies, rates, etc.).
Single-molecule F€orster (or Fluorescence) resonance energy transfer is certainly
one of the most fertile single-molecule fluorescence techniques [13–19]. The vast
majority of smFRET studies involve labeling of the target biomolecules with a donor
and an acceptor fluorophore at specific sites. The FRET distance dependence
translates changes in donor–acceptor separation distance into measurable photophysical parameters, such as donor/acceptor emission ratios, lifetimes, and anisotropy. This in turn provides a tool to follow conformational changes in a single
biomolecule or association/dissociation dynamics in a single complex of interacting
partners.
Observation of single-molecule fluorescence signals raises several difficulties,
including weak fluorescence signals and the need to isolate the signal from one
molecule from the large background of other molecules, without perturbing the
functional integrity of the biomolecule. These challenges can be overcome using
mainly two categories of microscopy modalities. The first modality relies on
immobilization of molecules on a substrate. A time trace of fluorescence signals
FRET – Förster Resonance Energy Transfer: From Theory to Applications, First Edition.
Edited by Igor Medintz and Niko Hildebrandt.
Ó 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.
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j 8 Single-Molecule Applications
can then be recorded, giving access to the full dynamics of molecular conformational
changes. The second modality uses molecules dissolved in solution and freely
diffusing in and out of a confocal detection volume, resulting in the rapid acquisition
of series of short fluorescence bursts from many individual molecules. Analysis of
these bursts reveals sample heterogeneity and allows identification of subpopulations and their repartition under equilibrium conditions. For each modality, we will
briefly present the corresponding experimental techniques and analysis methods,
discuss their capabilities, and present a few examples to illustrate their potential
applications, with a strong focus on biophysical studies. Finally, we will present
other single-molecule FRET schemes that involve multiple interacting FRET
partners.
8.2
Single-Molecule FRET of Immobilized Molecules
This section presents an overview of experimental techniques used to immobilize
biomolecules on substrates, with the standard data analysis methods and some
illustrative examples of applications. An advanced trace analysis technique is finally
presented.
8.2.1
Experimental Setup
8.2.1.1 Molecule Immobilization
Protocols used for molecule immobilization must be carefully designed to attach the
biomolecule without interfering with its functionality and to avoid its nonspecific
interactions with the substrate. One of the most common methods used for
biomolecule immobilization is the biotinylation of the biomolecule and its subsequent attachment to surface-bound streptavidin [16]. This provides a highly specific
interaction with a high affinity and allows subsequent washing of the surrounding
solution without risking the detachment of the biomolecule of interest. However,
extreme care must be taken to minimize potential interactions between the
biomolecule and the rest of the substrate surface. Single DNA and RNA studies
are usually performed using substrates coated with biotinylated BSA and then
streptavidin [20,21]. Several studies have indeed verified that the conformation of
oligonucleotides is not perturbed when immobilized on these surfaces [20,22,23],
probably thanks to the electrostatic repulsion between the negatively charged
oligonucleotides and the negatively charged glass, BSA, and streptavidin at neutral
pH.
In contrast, single proteins tend to present much more pronounced nonspecific
adsorption on these surfaces and require better passivated substrates. Several
methods have been proposed to reduce these undesired interactions. Most of
them require the glass slide to be activated with aminosilanes first, followed by
the covalent coupling of molecules to form a “furtive” coating, with a few biotin
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324
groups for further specific biomolecule attachment. Covalently surface-linked and
cross-linked BSA layers present a more uniform and robust surface coverage
compared to their adsorbed counterparts, which result in a lower level of nonspecific
protein adsorption [24]. Dense layers of polyethylene glycol are another popular
coating and can indeed strongly reduce nonspecific adsorption when sufficiently
long PEG chains are used [25]. These flexible PEG brushes have, however, been
shown to intermingle with attached proteins and modify their conformation after a
cycle of denaturation and refolding [26]. In comparison, cross-linked star-shaped
PEG coatings seem to reduce these interactions since individual immobilized
proteins refolded in their initial conformation after successive exposition to denaturation and refolding buffers [26,27].
Finally, an interesting alternative to direct attachment of biomolecules to the
substrate is their confinement in lipidic nanovesicles [28]. The biomolecules are
encapsulated within large (typically 100 nm) unilamellar vesicles containing a few
biotinylated lipids, which allow subsequent immobilization of the vesicles on avidinfunctionalized supported lipid bilayers [28–31]. This method is attractive since the
biomolecule remains in solution but is confined in a volume smaller than the
diffraction limit of the microscope, and is therefore available for prolonged
observation. The lipid vesicle is impermeable to the biomolecule of interest but
may be made permeable to other smaller molecules by incorporating small pores in
its membrane. This allows the controlled modification of the chemical environment
of the biomolecule (ions, nucleotides, etc.) from the outside of the nanovesicle
container [32–34]. Detailed sample preparation protocols are available in Ref. [33]
and references therein. Irrespective of the immobilization technique used, appropriate control experiments must be performed to ensure that the biomolecules are
indeed not perturbed. These may include testing different immobilization techniques, measuring their enzymatic activity, checking for dye anisotropy, and so on
(see Section 8.2.3).
8.2.1.2 Fluorophore Photostability
The choice of fluorescent labels must be optimized to provide strong and stable
signals. The fluorophores should possess high extinction coefficients, fluorescence
quantum yields, and photostability to allow long observation times and high signalto-noise ratios, and present limited photophysical effects (e.g., transient blinking).
The most common single-molecule fluorophore pairs include Cy3–Cy5 and their
Atto and AlexaFluor equivalents. The excitation rate of dyes in single-molecule
experiments is much higher compared to ensemble measurements, leading to
much faster photobleaching. Several reactants should therefore be added to the
buffer solution to enhance the dye photostability. Molecular oxygen should be
removed since it accelerates photobleaching through the formation of radical
species. This is usually obtained using an enzymatic oxygen scavenger system
composed of glucose oxidase, catalase, and b-D-glucose [35]. Other antioxidants may
also be used, such as propyl gallate, ascorbic acid (vitamin C) [36], and cysteamine
[37]. Oxygen is, however, also an efficient quencher of the triplet state, and removing
it increases the lifetime of this dark state. Other triplet state quenchers thus need to
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8.2 Single-Molecule FRET of Immobilized Molecules
j 8 Single-Molecule Applications
be added in the buffer solution, such as Trolox [37], an analogue of vitamin E, or
mercaptoethylamine [36]. The nature and optimal concentration of oxygen and
radical scavengers and triplet state quenchers may depend on the type of dye used
[36]. Alternatively, oxygen removal may be coupled with the addition of an appropriate combination of reducing and oxidizing agents, such as ascorbic acid and
methylviologen [38].
8.2.1.3 Optical Setup
The solution above the surface is easily washed from residual fluorophore-labeled
molecules; however, fluorescence from the immobilized smFRET molecules must
still be isolated from out-of-focus background to improve the signal-to-noise ratio.
This can be achieved by confocal microscopy or most frequently by total internal
reflection fluorescence (TIRF) microscopy [9,39,40]. Confocal detection consists in
focalizing a laser beam through an objective using a pair of excitation and detection
pinholes to eliminate fluorescence photons from outside a three-dimensional,
diffraction-limited (<1 mm3) confocal volume. The fluorescence signals from
molecules inside this volume are detected using photomultipliers or avalanche
photodiodes, allowing high acquisition speed. However, these detectors only acquire
data from one molecule at a time, and measuring a statistically significant number of
single molecules becomes very time consuming. In contrast, TIRF microscopy uses
wide-field illumination with an excitation beam that hits the substrate with an angle
larger than the total internal reflection angle [40]. No light thus propagates into the
medium above but the excitation light is confined to a thin (<200 nm) evanescent
layer above the surface, and the intensity decays exponentially from the surface.
Under these conditions, excitation is confined to fluorophores on or immediately
above the substrate, and eliminates background from the solution above. In practice,
this may be realized by focusing a laser beam on the edge of a high-NA objective
back pupil to create a parallel beam tilted with respect to the objective optical axis. In
this case, fluorescence photons are collected through the same objective. Alternatively, the laser may be focused on a prism placed on top of a thick quartz slide to
create the evanescent wave (see Figure 8.1), and a high NA objective is placed below
the sample to collect fluorescence photons. Fluorescence light is then split into
donor and acceptor channels using dichroic and bandpass filters to form two
separate images on a high-sensitivity, low-noise cooled EM-CCD camera. This
allows parallel imaging of typically up to a few tens of single FRET pairs.
8.2.2
Data Analysis
The first step in the analysis of single-molecule FRET data obtained by wide-field
TIRF microscopy is the isolation of pixels and group of pixels containing single
donor–acceptor pair signals. This is usually performed by selecting pixels above a
predefined threshold, averaging a small area (e.g., 5 5 or 7 7 pixels) around the
center pixel to integrate the point spread function of the microscope, and removing
an average background value corresponding to neighboring “empty” pixels.
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326
Figure 8.1 (a) SmFRET setup for the
observation of molecules immobilized on a
substrate, using prism-based (i) or objectivebased (ii) TIRF microscopy. The donor and
acceptor fluorescence images are separated
into two halves. (b) Example of smFRET donor
and acceptor and FRET time traces showing
acceptor blinking and photobleaching events
and three distinct FRET states. (Reproduced
with permission from Ref. [16]. Copyright 2008,
Macmillan Publishers Ltd.)
Molecules with only one active fluorophore present donor-only or acceptor-only
fluorescence signals and may then be discarded. The time traces obtained from
signal intensities in the donor and acceptor channels, SD and SA, and their ratio,
Eapp ¼ SA/(SA þ SD), qualitatively reflect the evolution of the separation distance
between the two fluorophores with time. Low Eapp values correspond to long
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8.2 Single-Molecule FRET of Immobilized Molecules
j 8 Single-Molecule Applications
separation distances, while high Eapp values correspond to shorter distances. There
are, however, several factors that should be taken into account for a more quantitative analysis and calculation of true FRET efficiencies E, including direct acceptor
excitation, spectral cross-talks of the donor emission into the acceptor channel and
vice versa, and differences in fluorescence quantum yields and collection efficiencies between the two fluorophores. The signals in the donor and acceptor channels
are related to the real molecular fluorescence intensities IA and ID and to the
collection efficiencies through
SD ¼ RDD I D þ RAD I A þ BA ;
ð8:1Þ
SA ¼ RAA IA þ RDA I D þ BD ;
ð8:2Þ
where Rij describes the instrument response and collection efficiency of signal i into
channel j (i, j ¼ D, A) and BA,D represents the background signal from the detector
(dark signal) and from spurious photons. The Rij elements may be determined by
careful calibration using samples composed of donor-only and acceptor-only single
fluorophores or fluorescent beads to correctly evaluate the corresponding ID and IA
intensities. Due to the spectral shape of organic fluorophores, usually only the donor
signal leaks into the acceptor channel, and the signals may be corrected by
ID ¼ aD SD BD ;
ð8:3Þ
IA ¼ aA SA BA bSD ;
ð8:4Þ
where a and b constants take into account effects of channel cross-talks and
detection efficiencies. Fluorescence intensities of the donor and acceptor molecules
depend on their respective absorption cross sections, fluorescence quantum yield,
and FRET efficiency as follows:
ID ¼ sD I exc ð1 EÞWD ;
ð8:5Þ
IA ¼ ðsD E þ sA ÞI exc WA ;
ð8:6Þ
where s D(A) and WD(A) are the donor (acceptor) excitation cross section at the laser
excitation wavelength and fluorescence quantum yield, respectively, Iexc is the laser
excitation intensity, and E is the FRET efficiency. Assuming that the acceptor direct
excitation is negligible (s D E s A ) or correctly accounted for, the FRET efficiency
can then be evaluated as
E ¼ I A =ðI A þ cI D Þ;
c¼
WA
:
WD
ð8:7Þ
ð8:8Þ
However, this assumes that c is identical for all individual FRET pairs. This is not
necessarily true because of inhomogeneity in the fluorophore environment due to
the substrate or the macromolecule conformation. However, the values of the
c correction factor and the FRET efficiency may often be determined for each
individual FRET pair. Indeed, the limited donor and acceptor photostability finally
leads to permanent photobleaching of both emitters. In the case of the common
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328
Cy3–Cy5 pair, the Cy5 acceptor often photobleaches before the Cy3 donor does. This
leads to an instantaneous suppression of FRET processes and a corresponding
recovery of donor emission. The amplitude of the donor recovery is directly related
to the FRET efficiency before photobleaching since E ¼ (ID0 ID)/ID0, where ID0 is
the final donor intensity after photobleaching, in the absence of any acceptor. In
addition, the c factor corresponds to the ratio of the intensity changes before and
after photobleaching DID and DIA: c ¼ DIA/DID. It can therefore be useful to
compare the c values obtained for each individual molecule to the value obtained
by average measurements.
Single dyes often display complex photophysics that need to be taken into account
for a correct single-molecule FRET interpretation. For example, organic dyes tend
to “blink” and present short dark periods attributed to a triplet state (Figure 8.1b)
[41–43]. Moreover, additional donor dye–acceptor dye interactions may take place at
short separation distances [44]. These effects should not be confused with abrupt
changes of FRET efficiencies. A good safeguard against incorrect interpretation of
smFRET data is to look at the weighted sum of the fluorescence signals c ID þ IA,
which should remain constant when FRET is the sole source of fluorescence
fluctuations.
Analysis of single-molecule FRET trajectories usually starts with identifying the
different FRET states presented by the observed biomolecules. This is most often
performed using simple thresholding, that is, defining a specific FRET efficiency
range for each state (e.g., 0 < E < 0.2 for state s1, 0.35 < E < 0. 5 for state s2, and so
on; see Figure 8.1). The first available information is the average distribution of
FRET values (often presented as a histogram) or of states (e.g., at any given time
molecules have a P1 ¼ 50% probability of being in state s1, P2 ¼ 20% probability of
being in state s2, and so on). The free energy Gi of each conformation may then be
simply evaluated using Gi ¼ kT ln(Pi) [45]. The second important information
available is the sequence of conformational changes, for example, determining
whether transitions always occur from s1 to s2, and then to s3, or directly from s1 to
s3, and the frequency of the different transitions. Finally, another important
parameter is the distribution of dwell time of each state, as this can be directly
related to the corresponding transition rates. In particular, for states involved in
single-rate kinetics, the distribution of dwell times t may be fitted with a monoexponential decay, exp(kt), where k is the transition rate out of the state. In the
following section, we will present a few typical examples to illustrate the potential
and limitations of smFRET on immobilized molecules.
8.2.3
Applications
Since its demonstration using near-field scanning microscopy [46] in 1996, soon
followed by its application to confocal microscopy [41,47], single-pair FRET measurements have been applied to a wide range of immobilized molecules, including
oligonucleotides and proteins, to study various problems such as folding kinetics
and bimolecular interactions.
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8.2 Single-Molecule FRET of Immobilized Molecules
j 8 Single-Molecule Applications
The hairpin ribozyme has been extensively studied by smFRET and provides a
good illustration of what can be achieved using smFRET on immobilized molecules:
identifying subpopulations, measuring transition rates between these subpopulations, and the sequence of events occurring during a particular reaction. This
ribozyme is an RNA enzyme capable of cleaving a specific RNA substrate into two
products. The proposed reaction pathway starts with binding of the substrate RNA to
the ribozyme. The hairpin ribozyme then consists in a four-arm DNA junction
containing two internal loops. The ribozyme fluctuates between an extended
unfolded conformation, in which the loops are far apart, and an active folded
conformation, in which the two internal loops are interacting and close to each other.
In the folded state, the cleavage reaction occurs and the resulting products finally
dissociate from the ribozyme [48]. These conformational fluctuations may thus be
observed by labeling one loop with a donor fluorophore and the other loop with an
acceptor, and measuring changes in the FRET interactions on single molecules. In
2002, smFRET experiments were performed on a minimal form of the hairpin.
Several FRETstates were identified with high FRET values corresponding to “folded”
conformations and lower FRET values to “unfolded” conformations [49]. The
cleavage reaction of the substrate finally occurs leading to a third distinct “cleaved”
state. It was shown in particular that 90–95% of the single ribozyme molecules
jumped to the cleaved state from the folded state, not from the unfolded state. The
remaining 5–10% of FRET trajectories were attributed to contributions of short-lived
folded state that were not observable with the limited (2 s) time resolution. SmFRET
measurements thus allowed verification of the proposed reaction pathway, with
cleavage occurring only in the folded state. In addition, measuring the dwell times in
both folded and unfolded states revealed simple rate kinetics for the folding
transition, but more complex multiexponential dynamics for unfolding transitions.
This suggested the existence of different folded states. Moreover, a large heterogeneity in the unfolding kinetics was observed, with some time traces showing
predominantly fast unfolding and some other slow unfolding.
This conformational heterogeneity was confirmed in subsequent observations by
Tan in 2003 on the natural form of the hairpin [50]. These experiments also revealed
that the system did not show a single unfolded but rather two rapidly interconverting
unfolded states. Transitions to the folded state occurred from the unfolded states
possessing the higher FRET efficiency, therefore called a “proximal” state. The
dynamics of conformational fluctuations depended strongly on Mg2þ concentrations. When the transitions were slow enough, it was possible to construct a
histogram of dwell times of the molecule in the proximal state (Figure 8.2a).
This histogram could be fitted with a monoexponential decay, with a decay time
characteristic of the transition between the proximal and the distal states
(Figure 8.2b). At low Mg2þ concentrations, however, the fluctuations became too
fast to be clearly directly measured from single-molecule traces (Figure 8.2c). Fast
smFRET dynamics may be more clearly resolved by cross-correlating the donor and
acceptor fluorescence intensity traces. Indeed, changes in FRET efficiency result in
anticorrelated intensity variations of the donor and acceptor fluorophores. The crosscorrelation function could then be fitted in turn with a monoexponential decay. In
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330
Figure 8.2 (a) SmFRET time trace showing
transitions between folded (F), proximal (Up),
and distal (Ud) states. When transitions are
clearly resolved, the histogram of dwell times in
state Up reveals the transition time constant
(here, 96 ms). (b–d) When transitions are faster,
cross-correlation of donor and acceptor traces
allows access to short transition time
constants, down to 1 ms. (Reproduced with
permission from Ref. [50]. Copyright 2003,
National Academy of Sciences, USA.)
this study, this analysis yielded transition rates of up to 1000s1 between the two
unfolded states (Figure 8.2d). Finally, cleavage reaction kinetics were examined on a
single hairpin basis from smFRET measurements and also showed a high
heterogeneity.
SmFRET data analysis must provide strong evidence that the molecule
immobilization on the substrate does not modify its conformational dynamics.
To test whether the previously observed heterogeneity could originate from nonspecific interactions between the immobilized hairpin and the substrate, these
experiments were reproduced on single hairpins encapsulated inside 100–200 nm
lipid vesicles [30]. This conformation is very different since the RNA is confined near
the surface but not attached to it. Again, 50-fold variations in the dwell times of
folded and unfolded states were observed. This confirmed that folding heterogeneity
was indeed intrinsic to the hairpin and possibly attributable to heterogeneity in the
conformation of the loop substructures, not to nonspecific interactions with the
surface.
While oligonucleotides present in general low levels of nonspecific interactions
with the substrate, possibly due to repulsive electrostatic interactions, proteins are
much more complex macromolecules that interact more strongly with the substrate
and its functionalization layer. For example, Rhoades had studied the folding
fluctuations of vesicle-encapsulated adenylate kinase (AK), a 214-amino acid protein
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8.2 Single-Molecule FRET of Immobilized Molecules
j 8 Single-Molecule Applications
[29]. To test whether AK proteins were interacting nonspecifically with the vesicle
walls, he first observed the fluorescence polarization values of AK labeled with the
donor fluorophore only. All observed molecules showed very low polarization values,
due to the fast rotational motion of the fluorophore that randomizes the polarization
of consecutive fluorescence photons. On the contrary, proteins adsorbed on glass
showed a much broader polarization distribution due to immobilization of the
protein. In addition, he found that the distribution of FRET values was significantly
different between vesicle-encapsulated and surface-immobilized proteins, suggesting a partial denaturation of the protein when adsorbed on the glass substrate and
emphasizing the importance of the immobilization strategy. Most of the observed
time traces showed single FRET values due to the folding transition being slower
than the average fluorophore lifetime (10–20 s due to photobleaching). However, in
smFRET traces showing at least one transition, histograms of FRET values showed
mainly two subpopulations corresponding to folded and unfolded states. Analyzing
the amplitude of changes in FRET values showed a large spread of the transitions,
indicating a large heterogeneity of the folding reaction, and the existence of several
intermediate folded states. In addition, the authors show that many molecules
exhibit slow transitions (>1 s). These slow transitions were interpreted as continuous directed conformational changes, possibly slowed down by local traps.
Intermolecular, not only intramolecular, interactions between DNA, RNA, and
proteins may also be probed by smFRET to examine reaction pathways and kinetics.
Ha et al. have, for example, examined DNA unwinding by the Rep helicase [21]. DNA
probes were composed of an acceptor strand attached to a polymer-coated surface
and a complementary donor strand. The two strands form a junction between singlestranded and double-stranded DNA (dsDNA). Unwinding of the dsDNA portion by
helicases increased the separation between the dyes and thus reduced FRET
interactions. Some time traces showed complete unwinding with a complete
suppression of FRET due to fast diffusion of the donor strand away from the
immobilized acceptor strand. However, some time traces show stalls in the DNA
unwinding, with occasional rewinding. These transient events could not have been
detected in ensemble experiments. Further experiments examining the kinetics of
helicase binding and DNA unwinding under different concentration of Rep helicases were able to show that DNA unwinding must involve the interaction of more
than one Rep protein.
In the preceding example, only one of the interacting partners, the dsDNA, was
labeled with fluorophores. This allowed tracking conformational changes of a few
DNA molecules in the presence of a high concentration of Rep helicases (up to
100 nM) to increase the probability of Rep–DNA intermolecular interactions.
However, situations where the molecules do not undergo drastic conformational
changes upon interaction require labeling of both interacting molecules to follow
their binding and unbinding kinetics. In that case, one is confronted with two
seemingly incompatible constraints: the need for a low concentration to ensure
detection of isolated FRET pairs (typically <0.1 nM) and the need for a high
concentration to ensure efficient interaction (>1 mM depending on association–
dissociation constants). Vesicle co-encapsulation provides a way to reconcile these
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332
Figure 8.3 (a) Schematics showing two
interacting proteins trapped inside a lipid
nanovesicle. (b) Model for the protein
interactions with one unbound and two distinct
bound states. (c–e) Histograms of dwell times
with the corresponding derived transition rates.
(Adapted with permission from Ref. [31].
Copyright 2009, American Chemical Society.)
two aspects [34]. The effective concentration inside the nanovesicle may be as high
as tens of mM due to the confined space (1 molecule complex in a 100 nm sphere).
Vesicles may, however, be immobilized on a substrate with a sufficient spatial
separation to allow visualization of single vesicles. This experimental setup is thus
particularly interesting to study weakly interacting molecules. Benitez et al., for
example, have studied interactions between two copper-binding proteins, Hah1 and
WDP, encapsulated in lipid nanovesicles (Figure 8.3a) [31]. Each protein was labeled
at a C-terminal cysteine residue with a donor or acceptor fluorophore. The presence
of only one protein pair was verified by examining photobleaching steps. FRET
traces showed three distinct FRET states attributed to one unbound state and two
different bound states. Transition rates (binding, dissociation, and conformational
change) for each state were then derived from histograms of the different dwell
times (Figure 8.3b). In another study, Cisse et al. developed methods to introduce
nanometer-sized pores into the vesicle walls [32]. These pores were created either by
incorporation of bacterial toxins or by bringing the vesicle at the lipid phase
transition temperature, triggering lipid packing defects. These pores were
impermeable to large molecules and maintained confinement of the studied
DNA and protein molecules, but allowed modulating the concentration of ATP.
The authors could then follow the interaction dynamics of the same interacting
molecules under different ATP conditions. The change in the chemical environment indeed induced an observable change in the interaction between proteins and
DNA. Finally, it should be noted that the vesicle lipid membrane constitutes a
promising platform to study membrane-anchored proteins [34].
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8.2 Single-Molecule FRET of Immobilized Molecules
j 8 Single-Molecule Applications
8.2.4
Analyzing Complex FRET Trajectories
In most of the above examples, FRET trajectories were decomposed into two or three
distinguishable FRET states and corresponding macromolecular conformations.
This is easily achieved when the number of states is low and when FRET values can
be clearly separated by a manually set threshold to discriminate between FRET
states. This method is, however, ill adapted to situations with a higher number of
states, or when it becomes difficult to discriminate the effects of noise or photophysical changes from a true conformational transition. These more complex FRET
trajectories may be instead analyzed using hidden Markov modeling (HMM). This
algorithm has been used in various applications such as speech recognition,
cryptanalysis, and biophysics, including single-molecule FRET [51–53]. Its parameters consist of the emission probability functions and the transition probability
matrix. The emission probability functions epA(B . . . )(g) describe the probability of a
specific FRET ratio value g being detected when the system is in state A (B . . . ).
Gaussian functions are generally used to include effects of real (conformational,
photophysical) and noise-induced fluctuations. The transition probability matrix tp
describes the probability of the system changing from a FRET state to another in the
subsequent step and is directly related to the different transition monoexponential
rates. The cumulated probability that a given FRET ratio sequence {g1, g2, g3}
corresponds to a specific conformation trajectory {A ! A ! B} is then determined
from the product of all corresponding emission and transition probabilities: epA(g1)
epA(g2)epB(g3)tp(A ! A)tp(A ! B). Similar probabilities are calculated for all
possible trajectories to determine the most probable trajectory. The Viterbi algorithm may help here to reduce computation costs [51,54]. In most experimental
cases, neither the emission probability functions nor the transition matrix is known
beforehand. These parameters are thus varied and optimized over a set of many
different single-molecule FRET trajectories to obtain a maximized total probability.
This finally yields the most probable emission probability functions for each state
and the corresponding transition probability matrix. Several publicly available
programs have been developed that allow application of HMM to single-molecule
FRET data, such as HaMMy [51] (http://bio.physics.illinois.edu/HaMMy.html),
QuB [52] (http://www.qub.buffalo.edu/wiki/index.php/Main_Page), and vb-FRET
[55] (http://vbfret.sourceforge.net/).
Hidden Markov modeling has been used, for example, by McKinney et al. to
analyze binding of RecA proteins to single DNA molecules [51]. Since several RecA
proteins can bind to a single DNA strand, different FRET states are observed,
corresponding to different RecA:DNA ratios. While the high number of states
precluded analysis using manually set thresholds between the different FRET states,
HMM revealed the existence of five different states (0, 1, 2, 3, and 4 associated RecA
proteins). Transition probabilities were high only between neighboring states,
suggesting that RecA proteins bind and dissociate one by one to the DNA strand.
Further analysis showed that association rates increased with RecA concentration,
while dissociation rates were independent.
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334
In another report, Abelson et al. study the conformational changes of a small
mRNA strand during in vitro splicing [56]. This complex multistep reaction involves
an ensemble of small ribonucleoproteins and leads to the removal of specific intron
sequences from the RNA strand. Figure 8.4a shows a typical fluorescence and FRET
ratio time trace and the corresponding most probable sequence of FRET states.
Figure 8.4b shows the transition density plot, representing the number of transitions observed from an initial FRET state (horizontal axis) to a particular final FRET
state (vertical axis) in a collection of single-molecule FRET trajectories. This plot is
used as a visual representation of the different observed transitions. Sometimes,
however, a small number of molecules exhibit an unusually high number of fast
transitions, which become therefore strongly emphasized in this representation,
while slow transitions may be underrepresented. To avoid this problem, another
representation may be used with population-weighted and kinetically indexed
transition density (POKIT) plots. POKIT plots represent as concentric circles the
fraction of molecules undergoing a specific transition at least once. This avoids
giving too much importance to a small number of molecules exhibiting a large
number of transitions. The average dwell time in an initial state before undergoing a
specific transition is coded with different colors (e.g., red corresponding to fast
transitions, green to slower ones, and so on). In the particular example shown in
Figure 8.4c, these graphs summarize several important characteristics of the studied
Figure 8.4 (a) Typical donor and acceptor
fluorescence and FRET time traces in the
splicing buffer, with the corresponding HMMderived traces; corresponding TDP (b) and
POKIT (c) plots; (d) POKIT plot in ATP-depleted
buffer. (Reproduced with permission from Ref.
[56]. Copyright 2010, Macmillan Publishers
Ltd.)
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8.2 Single-Molecule FRET of Immobilized Molecules
j 8 Single-Molecule Applications
molecular system. It allows a quick evaluation of the number of distinct FRET states.
HMM analysis of this system revealed the existence of up to 10 or 11 states but
transitions occur predominantly between 5 distinct states. One can also immediately
see that transitions occur mostly between neighboring FRET states, implying a stepby-step reaction. Finally, the graph is symmetric with respect to the diagonal, which
means that most transitions work in both directions and that they are reversible.
These graphs also facilitate comparisons of different reaction conditions. For
example, Figure 8.4d shows the POKIT plot under ATP-depleted conditions: both
the nature and the dynamics of the observed transitions are modified.
8.3
Single-Molecule FRET of Freely Diffusing Molecules
This section presents the second family of single-molecule FRET techniques,
consisting in the detection of freely diffusing molecules in solution. We present
the experimental techniques, along with a few examples to illustrate what can be
achieved with solution smFRET experiments. Finally, we present advanced techniques that take advantage of the large volume of data available with solution
smFRET to perform more refined data analysis.
8.3.1
Experimental Setup
Detecting single molecules freely diffusing in solution presents several advantages
and drawbacks. It is both simpler and more robust than imaging immobilized
molecules. This is due in part to the absence of any substrate surface susceptible to
interfere with the conformation of the molecule of interest, which greatly simplifies
sample preparation and reduces possible sample-to-sample variations. On the other
hand, the need to isolate the fluorescence signal of an individual molecule from its
neighbors puts strong constraints on the detection scheme and chromophore
concentration. The detection volume must indeed be sufficiently small to contain
at most one molecule at a time. This is usually realized by confocal or two-photon
excited fluorescence microscopy. Typically, an excitation laser is focused by a high
numerical aperture objective into the sample solution a few microns above a glass
coverslip. Fluorescence photons are collected through the same objective and
separated from the excitation beam by a dichroic mirror and emission filters.
Donor and acceptor photons are then separated by a second dichroic mirror, passed
through additional emission filters, and finally detected on avalanche photodiode
detectors (APDs). Appropriate pinholes are placed in the excitation and detection
path at the image conjugate planes to ensure confocality. All detected fluorescence
photons originate from molecules located inside the small (few femtoliters)
diffraction-limited confocal volume. Alternatively, the sample solution may be
introduced in a small glass capillary and flowed through the confocal observation
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336
volume. This capillary may be integrated into a microfluidic device to probe, for
example, chemical reactions at different times after mixing or the effects of heating
by changing the location of the detection spot along a microfluidic channel [57].
Finally, zero-mode waveguides present an interesting alternative to isolate fluorescence signals from single molecules [58,59]. This technique uses nanometer-scale
apertures fabricated in thin metal films on a transparent substrate. Light intensity
decays very rapidly at the entrance of the apertures, creating effective detection
volumes that are three orders of magnitude smaller than diffraction-limited confocal
volumes. In practice, this enables to probe more concentrated solutions but reduces
the time spent by the molecule in the detection spot.
In concentrated solutions, Brownian motion and flow induce fluctuations in the
detected fluorescence signals, which may be analyzed using fluorescence correlation
spectroscopy (FCS) [60,61]. However, when the observed solution is dilute enough
(typically a few tens of pM for confocal detection schemes), most of the time the
confined observation volume does not contain any fluorophore, and for brief periods
it contains a single biomolecule. The resulting traces thus present long periods of
background noise interrupted by fluorescence bursts. The duration of these bursts
corresponds to the time necessary for the biomolecule to diffuse out of the
observation volume. Their intensity depends on the intrinsic fluorescence parameters described in Equations 8.3 and 8.4 for the observation of single immobilized
molecules (excitation cross sections, fluorescence quantum yields, FRET efficiency,
etc.). APD signals are collected by counting boards and time traces are then
registered, which can be binned using different time resolutions. Fluorescence
bursts above a predefined threshold value are then selected from the background
noise and corrected from detection efficiencies and spectral cross-talks as described
in Equations 8.1 and 8.2. The most simple and straightforward analysis of singlemolecule FRET data consists in displaying histograms of the number or population
fraction of bursts as a function of the emission ratio g ¼ IA/(IA þ cID), where IA and
ID are the acceptor and donor burst intensities, respectively, and c ¼ WA/WD is the
correction factor already described above (Figure 8.5). The emission ratio g is closely
related to the FRET efficiency provided all corrections are properly performed
(Equation 8.5). It is, however, difficult to ensure that each fluorescence burst is
appropriately corrected, due to the possible heterogeneity in the environment and
photophysical properties of each fluorophore pair, and the emission ratio is often
referred to in practice as the apparent FRET efficiency, Eapp.
8.3.2
Applications
The first ratiometric measurements of single freely diffusing biomolecule FRET
were developed practically simultaneously to those on surface-bound molecules
[63–65]. Immediate advantages of solution measurements were to eliminate possible artifacts due to nonspecific interactions with the surface and to rapidly measure a
large number of events to enable statistical analysis. Solution smFRET was rapidly
applied to identify subpopulations in a heterogeneous ensemble. In particular,
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8.3 Single-Molecule FRET of Freely Diffusing Molecules
j 8 Single-Molecule Applications
100
Counts
80
Sample
Obj
60
40
20
0
320
Dichroic 1
Notch filter
Dichroic 2
LP filter
APDD
APDA
321
322
323
324
325
Time (s)
Population fraction
Excitation
laser
0.1
U
0.08
0.06
D
F
0.04
0.02
0
-0.2
0
0.2 0.4 0.6 0.8
1
1.2
Emission ratio
Figure 8.5 Typical solution smFRET optical
setup and experimental fluorescence burst time
traces. Bursts are selected (arrows) when the
sum of their donor and acceptor photons is
larger than the predefined threshold (dashed
line). The donor and acceptor burst intensities
are then analyzed to provide a FRET histogram,
showing, for example, donor-only (D), unfolded
(U), and folded (F) species. (Adapted with
permission from Ref. [62]. Copyright 2006,
American Chemical Society.)
biomolecule labeling with donor and acceptor fluorophores is often incomplete. In
addition, a portion of the acceptor dyes may be nonfluorescent and/or nonabsorbing
due to photobleaching and blinking. This often leads to a nonnegligible population
of donor-only biomolecules. These donors are not quenched by FRET, and this may
lead to underestimate FRET efficiencies in ensemble measurements. Solution
smFRET allows an easy identification of those donor-only molecules as a zerocentered peak in apparent FRET efficiency histograms. Deniz et al. demonstrated in
1999 that they were able to isolate this population and take into account only signals
from dual-labeled DNA double strands for sufficiently high average Eapp (>0.4)
[64]. In addition, they varied the distance between the donor and acceptor dyes and
observed a progressive decrease in FRET efficiency for larger separation distances.
They showed that they were able to separate two dsDNA populations corresponding
to different interdye distances. The sequence with the longer separation distance,
DNA17, contained an enzyme target sequence between the donor and acceptor
fluorophores, while the other, DNA7, did not. Cleavage of the DNA strands by the
enzyme led to the separation of the fluorophores in the DNA17 population. The
authors showed that the DNA17 peak in the Eapp histogram indeed disappeared
while the peak around zero, corresponding to isolated donor molecules, increased
accordingly. The peak corresponding to the DNA7 sequence remained unchanged
in the process.
Protein folding studies have benefited from smFRET as a tool to separate folded
from unfolded species. The cold shock protein, for example, has served as an
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338
excellent model system for protein folding due to its simple structure and its twostate behavior [66,67]. Under normal conditions, FRET efficiency histograms of
dual-labeled protein solutions show the usual donor-only peak around zero and a
peak at high FRET efficiency, corresponding to the compact folded state. Under
denaturating conditions, this peak disappears while a new peak arises at lower FRET
efficiencies, corresponding to unfolded states (Figure 8.6a) [68]. In addition, this
second peak shifts toward lower FRET efficiencies as the concentration of denaturant increases, indicating that the protein further unfolds. Revealing this type of
complex behavior is a unique force of single-molecule studies and would have been
very difficult to extract from FRET ensemble measurements. In this simple solution
experiment, one observes the equilibrium of folded and unfolded populations, but
does not have access to out-of-equilibrium conditions such as transient states or the
underlying folding and unfolding dynamics. This may be achieved using microfluidic devices in which different solvents, proteins, and molecules may be flowed in
channels and mixed where the channels merge under controlled conditions of flow.
Locating the detection volume at different points of the output channel allows
probing different times after mixing of the reactants, depending on the flow speed
and the distance between the detection volume and the mixer. Lipman et al. used this
Figure 8.6 (a) Histograms of measured FRET
efficiencies at various denaturant
concentrations for labeled cold shock protein.
(Reproduced with permission from Ref. [68].
Copyright 2002, Macmillan Publishers Ltd.) (b)
Varying the distance between the mixing point
of the microfluidic channel and the laser
confocal volume allows probing different times
after mixing. FRET histograms obtained for
different times after mixing. (Reproduced with
permission from Ref. [57]. Copyright 2003,
American Association for the Advancement of
Science.)
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8.3 Single-Molecule FRET of Freely Diffusing Molecules
j 8 Single-Molecule Applications
principle to probe cold shock protein folding kinetics by smFRET [57]. They induced
an abrupt drop of denaturant concentration in the protein solution by dilution. They
observed that the unfolded proteins rapidly switch to a more compact (higher FRET)
unfolded state before slowly reaching the new equilibrium between folded and
unfolded states (Figure 8.6b). This experiment thus gives access to transient species
that are not strongly represented under equilibrium conditions.
The ability to eliminate artifacts due to imperfect biomolecule labeling and
measure FRET efficiencies with a good precision was used, for example, to revisit
polyproline peptides as rigid spectroscopic rulers. These studies provide a good
illustration of what information can be extracted from smFRET measurements in
terms of subpopulations and dynamics, and of the possible caveats. Polyprolines
adopt a type II helix in aqueous solution [69] and have been used as rigid spacers to
verify the distance dependence of FRET in the range of 1–12 prolines per peptide,
corresponding to a 20–45 A range [70]. Schuler examined polyprolines in a larger
size range, from 6 to 40 proline residues using a FRET pair with a larger R0 distance
(54 A instead of 35 A in the earlier work) [71]. He found that solution of longer
peptides contained a nonnegligible fraction of donor-only molecules, which could
lead to errors in ensemble measurements. However, the authors observed a
significant discrepancy between the observed FRET efficiencies, Eapp, and those
theoretically predicted assuming a rigid peptide conformation. Shorter peptides
showed lower Eapp than predicted; this discrepancy has been attributed to failure of
the point-dipole FRET model at short interdye distances and to the absence of fast
orientational averaging, and consequently an error in the estimation of the k2 factor.
This was supported by polarization measurements. Long peptides showed a low
residual steady-state polarization value of 0.05, corresponding to a near total
reorientation of the dipole between excitation and emission. However, for shorter
peptides, the donor decay was significantly accelerated due to FRET and became
comparable to the reorientation speed, as shown by the increase of steady-state
polarization value to 0.11. Replacing the usual k2 ¼ 2/3 value corresponding to the
rapid orientational averaging by an approximation of random, but static orientations, the authors found theoretical FRET efficiencies compatible with the observed
values.
Longer peptides, on the contrary, showed higher FRET efficiencies than expected.
These longer peptides must thus adopt different conformations, bringing the two
dyes closer to each other, and allow for higher FRET rates. Molecular dynamics
showed that the timescale of these fluctuations (0.1–10 ns) was much shorter than
the fluorescence burst duration (1 ms). In this regime, the effect of conformational
fluctuations on the apparent FRET efficiency depends on the comparison between
the dynamics of the peptide conformation, the rotational correlation time of the
fluorophores, and their fluorescence lifetime. In this study, fluorescence and
anisotropy decay measurements showed that the dye rotation (0.3 ns) was faster
than both the fluorescence lifetime (1–10 ns) and the expected conformational
fluctuations (0.1–10 ns). The obtained theoretical estimations of FRET efficiencies
were in the same range as the experimental values, confirming that these peptides
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340
indeed adopt flexible conformations and showing the importance of considering
dynamics for extracting structural information.
Another regime exists when conformational fluctuations change slowly compared
to the duration of fluorescence burst, that is, the time spent by the biomolecule in the
detection spot before diffusing away. In that case, each molecule presents a different,
static conformation when passing through the confocal volume. This results in a
broadening of the FRET histograms. The width of FRET histogram peaks thus
contains information about dynamics of conformational changes. Its analysis is,
however, complicated by additional contributions from shot noise and photophysical
effects. The shot noise standard deviation s sn arises from the finite number of
photons in each time bin and provides a fundamental statistical lower limit to the
width of the histogram peaks. It is defined by
EÞ=ðn
s2sn ¼ Eð1
A þ nD Þ;
ð8:9Þ
is the average FRETefficiency and nA þ nD is the total number of photons in
where E
the donor and acceptor channel. A limit on this number is provided by considering
the threshold value below which fluorescence bursts are rejected. Additional effects
of dye molecular fluctuations are difficult to isolate and characterize. A reference
molecule with the same fluorophores but no conformational fluctuations slower
than the time bins considered may be used to estimate a standard width s 0. Any
excess width, defined by s 2 s 20, may then be attributed to slow conformational
fluctuations. Theoretical FRET histogram widths have been derived by Gopich and
Szabo as a function of fluctuation dynamics and acquisition speed [72,73]. Schuler
et al. used this method to examine the folding kinetics of cold shock protein. They
analyzed FRET histograms obtained under different denaturing conditions, where
the protein fluctuated between unfolded and folded configurations (Figure 8.6a).
They then observed that the FRET peak widths were not much larger than those for a
short rigid polyproline peptide [67,68]. This allowed them to put an upper limit of
30 ms to the protein reconfiguration time. This conformational dynamics can be
used to obtain information about the free energy barrier for folding, as discussed in
Refs [67,68].
Best et al. have further used the distributions in FRET histograms to obtain
information about conformational flexibility of long polyprolines [74]. They have
used a pulsed excitation source and recorded the arrival time of each photon after the
corresponding excitation pulse. Interestingly, the authors were able to rule out
possible contributions to the distribution widths from acceptor photobleaching, by
observing that histograms constructed from the first and second halves of the time
bins were identical. If photobleaching had any influence, histograms from the
second half of the bins would have been shifted to lower FRET values. They also
ruled out contributions from acceptor random blinking by examining the statistics
of strings of consecutive donor or acceptor photons. If there is no blinking, the
probability of observing a sequence of n consecutive donor photons varies as
(1 Eapp)n. In contrast, blinking of the acceptor would give rise to a higher
probability of observing long strings of donor photons. The distributions of
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8.3 Single-Molecule FRET of Freely Diffusing Molecules
j 8 Single-Molecule Applications
Figure 8.7 SmFRET results for polyproline-20
in TFE (a) and water (b). The yellow dashed line
indicates shot noise-limited width of the
distribution. Insets: The donor fluorescence
decays for donor photons from the
subpopulations with corresponding colors in
the efficiency histograms. (Reproduced with
permission from Ref. [74]. Copyright 2007,
National Academy of Sciences, USA.)
consecutive sequences of donor photons perfectly matched theoretical predictions
in the absence of blinking.
The ability to record the arrival times of photons after each excitation pulse
allowed them to reconstruct fluorescence decay curves from selected molecular
subpopulations [74,75]. They were able to show that, for polyproline peptides in
water, photons from molecules showing up in the higher side of the FRET
histogram peak yielded a faster decay curve compared to photons from molecules
showing lower FRET values (Figure 8.7). This indicated that FRET value heterogeneity indeed originated from differences in FRET rates, that is, to (slow) conformational fluctuations, not from noise. In contrast, fluorescence decay curves were
identical throughout the smFRET histogram measured in trifluoroethanol (TFE),
indicating that conformational fluctuations were smaller in this solvent compared to
water. The authors were further able to use fluorescence decay data as an additional
tool to evaluate FRET efficiencies. To construct the fluorescence decay of donor-only
species, they used photons from bursts showing a near-zero emission ratio. They
then calculated from molecular simulations the predicted fluorescence decay curves
taking into account FRET processes corresponding to different peptide conformations. This analysis, together with NMR measurements, allowed them to identify
different peptide conformations in TFE and water due to isomerization of proline
residues.
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8.3.3
Advanced Solution smFRET Methods
Single-molecule FRET methods described above are powerful tools to study heterogeneous populations but suffer from several limitations, due to sample preparation
and complex fluorophore photophysics. For example, smFRET cannot distinguish
between donor-only species and dual-labeled species with low FRET efficiencies: in
both cases, only the donor fluorophore is detected. More generally, it cannot detect
acceptor-only species, which limits studies of the interactions of a donor-labeled
molecule A with an acceptor-labeled molecule B. To overcome these limitations,
several techniques were introduced, based on alternate laser excitation (ALEX) and
multiparameter fluorescence detection (MFD). These schemes may also be applied
to surface-immobilized molecules, but are more adapted to solution diffusing
probes, thanks to the large volume of data accessible in solution measurements.
8.3.3.1 Alternate Laser Excitation
The ALEX method has been developed by Kapanidis et al. as an extension of
smFRET, in which the excitation consists of interleaved pulses of two different
wavelengths: one for donor excitation and the other for acceptor excitation [76,77].
The excitation wavelength switches more rapidly than the average fluorescence burst
duration, so that many excitation pulses are used for each single diffusing molecule.
Photon detection is synchronized with the excitation pattern providing four sets of
data after cross-talk and background corrections. Two of these fluorescence time
Aem
traces correspond to standard smFRET measurements, denoted F Dem
Dexc and F Dexc ,
respectively, for the donor and acceptor emissions under excitation of the donor. The
other fluorescence time traces correspond to the emission of the donor and the
Aem
Dem
acceptor under direct acceptor excitation, F Dem
Aexc and F Aexc (in practice, F Aexc 0).
The first two signals provide the usual apparent FRET efficiency, Eapp, using
Equation 8.7. In addition, the sum of all donor and acceptor emissions under
Aem
donor excitation,F Dexc ¼ cF Dem
Dexc þ F Dexc , and that under acceptor excitation,
Aem
F Aexc ¼ cF Dem
Aexc þ F Aexc , are calculated. One can now also define a stoichiometry
ratio, S, as
S¼
F Dexc
:
F Dexc þ F Aexc
ð8:10Þ
This ratio is independent of FRET efficiency, since F Dexc sums all photons emitted
after donor excitation and is corrected for the difference in quantum yields and
detection efficiency between the two fluorophores. The laser excitation intensities
are usually adjusted to yield F Dexc F Aexc . In that case, donor-only species display
S 1, acceptor-only species display S 0, and dual-labeled molecules assume
intermediate values. Kapanidis et al. demonstrated that this method enabled
separation of subpopulations based on apparent FRET efficiency and stoichiometry
[77]. They were, for example, able to correctly take into account acceptor-only species,
and also the presence of dimers (e.g., two donor–one acceptor macromolecules).
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8.3 Single-Molecule FRET of Freely Diffusing Molecules
j 8 Single-Molecule Applications
Figure 8.8 Typical example of an ALEX
smFRET experiment, with two dsDNA strands
with different interdye distances. The S versus E
plot reveals donor-only species (upper left),
acceptor-only species (bottom right), and
differe