Structure Determination and Analysis : X-ray Crystallography
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Source
X-rays
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Sample
Diffraction
Detector
Intensity of
diffracted beam
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Energy = hc
λ
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X-rays
• Unlike using a light microscope,
there is no way of re-focusing
diffracted x-rays.
• Instead we must collect a
diffraction pattern (spots).
•It is possible to translate information in the diffraction pattern
into atomic structure using Bragg’s law, which predicts the angle
of reflection of any diffracted beam from specific atomic planes
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A typical crystallography experiment
Pure protein
Grow crystal
Characterize crystals
Collect diffraction data
Solve phase problem
Calculate electron density map
Build/rebuild model
Refine model
Analyze structure
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The Beginning
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Principles of X-ray diffraction
What is a crystal?
•The unit cell is the basic building block of the crystal
•The unit cell can contain multiple copies of the same molecule
whose positions are governed by symmetry rules
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Proteins and crystallisation
•What type of protein is it? Has
anything similar been crystallized
before?
•Proteins must be pure (> 99%) & fully
folded Check the activity of your protein
if you have an assay Check folding by
other spectroscopic methods
•Proteins must be homogenous & monodispersed.
•Need large amount (mg quantities)
•Is it stable ( salt, pH, temp)
•Will modifications have to be made?
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•Crystallisation of proteins
protein.
‘controlled’ precipitation of the
•Protein aggregates associate & form intermolecular contacts
that resemble those found in the final crystal. Aggregates reach
the critical nuclear size, growth proceeds by addition of
molecules to the crystalline lattice.
•The processes of nucleation and crystal growth both occur in
supersaturated solutions.
Cover-slip
sealed with
Process controlled by: vacuum grease
Protein in
“Hanging drop”
•Temp
•pH
•Salt conc
Precipitant
•Precipitants (PEG, ethanol)
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Diffraction Apparatus
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Synchrotron radiation
More intense X-rays at shorter wavelengths mean higher
resolution & much quicker data collection
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Experimental setup
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Mounting crystals
Remove cover
slip and fish
out crystal with
a small nylon
loop
Surface tension
of the liquid in
the loop holds
crystal in place
Mount loop on
goniostat in a
stream of
nitrogen gas
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Diffraction
•Each image represents the
rotation of the crystal 1
degree in the X-ray beam.
•Each images gives us the
position of each spot relative
to all the others & there
intensity.
•Intensity
amplitude.
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=
square
of
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Diffraction Principles
nl = 2dsinq
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Diffraction Principles
A string of atoms
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Corresponding
Diffraction Pattern
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The reciprocal lattice and
the geometry of diffraction
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X-ray
detector
X-ray source
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Spacing between diffraction spots defines
unit cell
1/
b
1/
a
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Waves & the phase problem
X
l
Y
A
Z
The amplitudes of the diffracted X-rays can be experimentally
measured, but the phases cannot = phase problem.
i.e. we don’t know the
phase of each diffracted
ray relative to the
others!
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X
?
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The Phase Problem
• Diffraction data only records intensity, not phase
information (half the information is missing)
• To reconstruct the image properly you need to have
the phases (even approx.)
– molecular replacement
– direct methods
– isomorphous replacement
– anomolous dispersion
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Structure factors & Fourier transforms
unit cell
F (h,k,l) = Vx=0 y=0 z=0 (x,y,z).exp[2I(hx + ky + lz)].dxdydz
A reflection
electron density
All reflections
phase
(x,y,z) = 1/V hkl F (h,k,l)exp[2I(hx + ky + lz) + i(h,k,l)
Electron density
amplitude
At a point
• The vector (amplitude and phase) representing the overall
scattering from a particular set of Bragg planes is termed the
structure factor (F).
• Structure factors for various points on the crystal lattice
correspond to the Fourier transform of electron density within
the unit cell and vice-versa.
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Fourier Transform of a molecule
FT
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Fourier
Transform of a
crystal
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The Phase Problem
• Diffraction data only records intensity, not phase
information (half the information is missing)
• To reconstruct the image properly you need to have
the phases (even approx.)
– molecular replacement
– direct methods
– isomorphous replacement
– anomolous dispersion
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Molecular replacement
• Requires a starting model for structure
• Can calculate back from structure to electron density to
structure factors
• Works if model is 30 to 40 % identical to correct answer
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Molecular Replacement
By determining the correct orientation and position of a molecule in
the unit cell using a previously solved structure as a ‘search model’.
This model can then be used to calculate phases
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Isomorphous replacement (IR)
• Provides indirect estimates of the protein phase angles
by observing the interference effects of the intensities
on scattered beams by a heavy atom marker.
• All the electrons in the heavy atom will scatter
essentially in the same phase.
• We can solve the positions of these heavy atoms
because they are few in number and strong in signal.
• Using this estimate we can deduce the positions of the
protein atoms and their phases
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Anomalous scattering
• Scattering information of an atom whose absorption frequency is
close to the wavelength of the source beam produces phase
information
• Resolved anomalous scattering requires intensity measurements
at one wavelength
• Multi-wavelength anomalous dispersion, requires intensity
measurements at several wavelengths
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•Using the structure factor calculation
we can produce electron density maps
for the whole protein.
•We then fit our protein model (coordinates X,Y,Z) inside the map.
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Resolution
1.2 Å
2Å
3Å
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Resolution
6Å: Outline of the model, feature
such as helices can be identified.
3Å: Can trace polypeptide chain
using sequence data, establish
folding
topology. Assign side
chains.
2Å:
Accurately
establish
mainchain conformation, assign
sidechains without sequence data,
I.d water molecules.
1.5Å : Individual atoms are almost
resolved, detailed discription of
water structure.
1.2Å: Hydrogen atoms may become
visible.
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Final Structure
But the work is not over yet!
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Refinement
• The process of building and rebuilding a model can cause
many errors in the structure.
1. Bond length,
2. Bond angle
3. Atomic clashes etc
• It is necessary to subject the structure to refinement in order
to remove these errors and produce a better structure.
• Minimization
• Thermal parameters
• In order to further improve the model, it is refined using a
simulated annealing protocol
• Refinement progress is monitored by following the agreement
between the the observed data ( data collected) and the
calculated data (data calculated from current model) = R
factor
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Quality of the structure?
• R-factor The agreement between the the observed data (data
collected)
and the calculated data (data calculated from
current model) the lower the number the better; typically
around 20%
• Resolution The higher the resolution the more detail that can
be seen 3.0Å is fairly low whilst 1.1Å is approaching atomic
resolution
• B-factor Measure of thermal motion. i.e. how much energy
each atom contains. Gives us information on mobility &
stability
• Rms deviation Deviation of bond lengths & angles from ideal
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Rms deviation of bond length & bond angle
Deviation of bond lengths &
angles from ideal. All based
on the geometry of small
molecules. Rms deviation for
bond lengths should be less
than 0.02Å and less than 4º
for bond angles
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Determined using a
Ramachandran plot.
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Absorption of Light
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Absorption in the UV and visible range
Protein chromophores:
•Peptide bond
•Amino acid side chains
•Prosthetic groups
Amino acid side chain absorbance:
• Asp, Glu, Asn, Gln, His and Arg have
transitions at the same wavelength where
peptide absorbs
Peptide bond absorbance:
• 210 nm due to n   transition
• 190 nm due to    transition
Protein concentration can be measured by measuring absorbance at 280 nm and
by assuming that 1 mg ml-1 solution of protein has absorbance of 1.0
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Absorption and emission spectra of individual tryptophan
residues, in the absence of energy transfer
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Fourth derivative absorption spectrum
• Fourth derivatives of the absorption spectra have been
documented as a valuable tool for studying structural
changes in proteins.
• Protein fourth derivative spectra have been shown to be
very sensitive to changes in the microenvironment (polarity,
hydration, hydrophobic interactions, packing density) of
tyrosine and tryptophan residues
Chauhan and Mande,
Biochem J, 2001
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Measurements of conformational properties
using optical activity
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Linearly polarised light
Right circular polarisation
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Left circular polarisation
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• Nearly all molecules of life are optically active
• There are four ways that an optically active sample
can alter the properties of transmitted light: optical
rotation, ellipticity, circular dichroism, circular
birefringence
Linear
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Circular
Elliptical
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After passing through an optically active absorbing sample, the
light is changed in two aspects:
1. The maximal amplitude E is no longer confined to a place,
instead it traces an ellipse
Ellipticity = tan-1 (minor/major axis)
2. The orientation of the ellipse is an indication of optical
activity. If the sample did not absorb any light, the ellipse
would such small axial ratio that it would be equivalent to a
plane-polarised light. In this case we will say that the plane
polarised light has been rotated.
3. Orientation of the ellipse is the optical rotation. Optical
rotation as a function of wavelength is called the optical
rotatory dispersion (ORD).
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Circular Dichroism
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CD spectrum of a protein
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Where can Circular Dichroism be used?
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Measurements of conformational properties
using fluorescence
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Fluorescence
• Chromophores are components of
molecules which absorb light
• They are generally aromatic rings
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Fluorescence
Jablonski Diagram
Singlet States
Triplet States
Vibrational energy levels
Rotational energy levels
Electronic energy levels
S2
ENERGY
T2
S1
IsC
ABS
FL
I.C.
T1
PH
IsC
S0
[Vibrational sublevels]
ABS - Absorbance
FL - Fluorescence
I.C.- Nonradiative Internal Conversion
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S 0.1.2 - Singlet Electronic Energy Levels
T 1,2 - Corresponding Triplet States
IsC
- Intersystem Crossing
PH - Phosphorescence
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Simplified Jablonski Diagram
S’
1
S
1
hvex
hvem
S
0
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Fluorescence
The longer the wavelength the lower the energy
The shorter the wavelength the higher the energy
eg. UV light from sun causes the sunburn
not the red visible light
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Fluorescence Excitation
Spectra
Intensity
related to the probability of the event
Wavelength
the energy of the light absorbed or emitted
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Corrected excitation spectra (corrected for source output and monochromator throughput) can be obtained
by using a reference channel equipped with a "quantum counter". This is a concentrated dye solution
(typically 3 mg/mL rhodamine B in ethylene glycol). A tiny fraction of the excitation beam is diverted to the
reference detector. The quantum counter absorbs all of this light, and converts it (with 100% efficiency to
fluorescence), the intensity of which is independent of wavelength between 220 and 580 nm. Any changes in
lamp output or monochromator throughput will cause corresponding alterations in the output of the
reference channel. By dividing the fluorescence signal by the reference signal, these wavelength-dependent
variations are cancelled out.
Unfortunately, the quantum counter will not entirely correct the emission spectrum. However, instrument
manufacturers supply correction factors for their monochromators. Application of these will give an
approximately correct spectrum. If more accuracy is needed, the spectrum of a known standard compound
(fluorescing in the region of interest) can be compared to published standards.
j. Biological fluorophores
1) Intrinsic fluorophores
a) Proteins
Tryptophan dominates protein
fluorescence spectra
- high molar absorptivity
- moderate quantum yield
- ability to quench tyrosine
and phenylalanine
emission
by energy transfer.
Free tyrosine has a relatively high fluorescent output, but
is strongly quenched by trptophan in native proteins.
Unless tyrosine and tryptophan are absent, emission from
phenylalanine is not observed in protein fluorescent
spectra.
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Tryptophan is a good fluorophore
6000
300000
fluorescence
extinction coefficient
5000
250000
4000
200000
3000
150000
2000
100000
1000
50000
0
200
250
300
350
400
wavelength (nm)
450
0
500
fluorescence emission
absorption
note that this
fluorescence expt
used an excitation
l of 270nm
note that the
fluorescence looks
like a mirror
image of the
280nm absorption
peak (and not the
220nm peak)
we can consider solvent effects on its emission
wavelength in the same way we did for absorption...
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Absorption vs Emission for Trp
comparing our diagrams for absorption and emission –
and assuming that protein interiors behave like organic
solvents(!) – we predict:
in water
buried in protein
absorption
emission
Abs.
DEabs
DEabs
DEem
DEem
l
Em.
protein water
protein water
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l
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Effect of Ca2+ on Intrinsic Trp-fluorescence and on
Fluorescence Anisotropy
Blue shift and intensity enhancement upon
addition of Ca2+
▼ Wild type
• Dome loop mutant
Change in anisotropy upon titration in the wild
type, but not in the mutant
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Raman Scatter
• A molecule may undergo a vibrational
transition (not an electronic shift) at exactly
the same time as scattering occurs
• This results in a photon emission of a
photon differing in energy from the energy
of the incident photon by the amount of the
above energy - this is Raman scattering.
• The dominant effect in flow cytometry is
the stretch of the O-H bonds of water. At
488 nm excitation this would give
emission at 575-595 nm
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Rayleigh Scatter
• Molecules and very small
particles do not absorb, but
scatter light in the visible region
(same freq as excitation)
• Rayleigh scattering is directly
proportional to the electric
dipole and inversely proportional
to the 4th power of the
wavelength of the incident light
the sky looks blue because the gas molecules scatter more
light at shorter (blue) rather than longer wavelengths (red)
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Probes for Proteins
Probe
FITC
PE
APC
PerCP™
Cascade Blue
Coumerin-phalloidin
Texas Red™
Tetramethylrhodamine-amines
CY3 (indotrimethinecyanines)
CY5 (indopentamethinecyanines)
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Excitation
488
488
630
488
360
350
610
550
540
640
Emission
525
575
650
680
450
450
630
575
575
670
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Probes for Nucleic Acids
•
•
•
•
•
•
•
•
•
•
•
Hoechst 33342 (AT rich) (uv)
DAPI (uv)
POPO-1
YOYO-1
Acridine Orange (RNA)
Acridine Orange (DNA)
Thiazole Orange (vis)
TOTO-1
Ethidium Bromide
PI (uv/vis)
7-Aminoactinomycin D (7AAD)
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346
359
434
491
460
502
509
514
526
536
555
460
461
456
509
650
536
525
533
604
620
655
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DNA Probes
• AO
– Metachromatic dye
• concentration dependent emission
• double stranded NA - Green
• single stranded NA - Red
• AT/GC binding dyes
– AT rich: DAPI, Hoechst, quinacrine
– GC rich: antibiotics bleomycin, chromamycin
A3,
mithramycin, olivomycin,
rhodamine 800
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Probes for Ions
•
•
•
•
INDO-1
QUIN-2
Fluo-3
Fura -2
Ex350
Ex350
Ex488
Ex330/360
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Em405/480
Em490
Em525
Em510
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pH Sensitive Indicators
Probe
Excitation
Emission
• SNARF-1
488
575
• BCECF
488
440/488
525/620
525
[2’,7’-bis-(carboxyethyl)-5,6-carboxyfluorescein]
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Probes for Oxidation States
Probe
Oxidant
• DCFH-DA
• HE
• DHR 123
(H2O2)
(O2-)
(H2O2)
DCFH-DA
HE
DHR-123
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Excitation
488
488
488
Emission
525
590
525
- dichlorofluorescin diacetate
- hydroethidine
- dihydrorhodamine 123
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Specific Organelle Probes
Probe
BODIPY
NBD
DPH
TMA-DPH
Rhodamine 123
DiO
diI-Cn-(5)
diO-Cn-(3)
Site
Golgi
Golgi
Lipid
Lipid
Excitation
505
488
350
350
Mitochondria 488
Lipid
488
Lipid
550
Lipid
488
Emission
511
525
420
420
525
500
565
500
BODIPY - borate-dipyrromethene complexes
NBD - nitrobenzoxadiazole
DPH - diphenylhexatriene
TMA - trimethylammonium
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Other Probes of Interest
• GFP - Green Fluorescent Protein
– GFP is from the chemiluminescent jellyfish Aequorea
victoria
– excitation maxima at 395 and 470 nm (quantum efficiency
is 0.8) Peak emission at 509 nm
– contains a p-hydroxybenzylidene-imidazolone
chromophore generated by oxidation of the Ser-Tyr-Gly at
positions 65-67 of the primary sequence
– Major application is as a reporter gene for assay of
promoter activity
– requires no added substrates
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Energy transfer
transfer
excitation
A
B
emission
phycoerythrin-Texas Red ECD
phycoerythrin-cyanine5
PC5
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Energy Transfer
• Effective between 10-100 Å only
• Emission and excitation spectrum must significantly
overlap
• Donor transfers non-radiatively to the acceptor
Molecule 1
Molecule 2
Fluorescence
Fluorescence
ACCEPTOR
DONOR
Absorbance
Absorbance
Wavelength
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