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Contents
ix
xi
1. Fundamentals and methods of atomic force microscopy for
biophysics
1.1 Background of atomic force microscopy for biophysics
1.2 Atomic force microscopy topographical imaging modes
1.3 Atomic force microscopy force spectroscopy techniques
1.4 High-speed atomic force microscopy
1.5 Topography and recognition imaging mode atomic force microcopy
References
2. Imaging and force detection of single deoxyribonucleic acid
molecules by atomic force microscopy
2.1 Background
2.2 Sample preparation methods
2.3 Topographical imaging of single DNA molecules and events
2.4 Time-lapse imaging of individual DNA molecular dynamics
2.5 Extracting the persistence length of DNA molecules from atomic force
microscopy images
2.6 Mechanically unzipping single DNA molecules by atomic force
microscopy force spectroscopy
2.7 Probing individual DNA behaviors on DNA origami nanostructures
2.8 Summary
References
3. High-resolution imaging and force spectroscopy of single
membrane proteins by atomic force microscopy
3.1 Background
3.2 Topographical imaging of single native membrane proteins
3.3 Unfolding mechanics of individual native membrane proteins
3.4 Observing the dynamics of single membrane proteins by high-speed
atomic force microscopy
3.5 Multiparametric atomic force microscopy imaging of single membrane
proteins
1
1
5
19
31
33
35
43
43
44
47
52
55
58
61
66
68
75
75
77
84
88
91
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Contents
3.6 Topography and recognition imaging of single membrane proteins
3.7 Summary
References
4. Characterizing the nanostructures and mechanical
properties of hydrogels by atomic force microscopy
94
97
99
105
4.1 Background
4.2 Nanostructures and nanomechanics of natural plant hydrogels
4.3 Characterizations of biopolymeric hydrogels inspired by carnivorous
plant mucilage
4.4 Imaging and mechanical analysis of peptide-assembled nanofibrillar hydrogel
4.5 Probing the mechanical cues in cellhydrogel interactions
4.6 Summary
References
105
108
116
122
127
130
131
5. Detecting the behaviors of single viruses by atomic force
microscopy
135
5.1 Background
5.2 Imaging the fine structures of single viruses
5.3 Nanoindentation for mechanical measurements and manipulations of
single viruses
5.4 Single-virus force spectroscopy for probing viral binding affinity
5.5 Multiparametric atomic force microscopy imaging of viruscell interactions
5.6 Visualizing individual viral dynamics by high-speed atomic force microscopy
5.7 Summary
References
143
147
150
153
155
156
6. Imaging and mechanical analysis of single native exosomes by
atomic force microscopy
161
6.1 Background
6.2 Exosome isolation and immobilization
6.3 Imaging single native exosomes in liquid
6.4 Measuring the mechanics of single native exosomes
6.5 Multiparametric imaging of single native exosomes
6.6 Single-molecule force spectroscopy on single exosomes
6.7 Summary
References
161
164
168
172
174
177
179
182
7. Nanoscale imaging and force probing of single microbial
cells by atomic force microscopy
187
7.1 Background
7.2 Immobilization methods of living microbial cells for atomic force
microscopy imaging
135
139
187
191
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7.3 Visualizing the nanostructures and their dynamics of living microbial
cells by atomic force microscopy
7.4 Measuring the mechanical properties of single living microbial cells by
atomic force microscopy
7.5 Single-molecule force spectroscopy and single-cell force spectroscopy of
microbial adhesion
7.6 Multiparametric atomic force microscopy imaging of single living
microbial cells
7.7 Atomic force microscopy cantilever as a nanomechanical sensor for
monitoring microbial activities
7.8 Summary
References
210
212
213
8. Investigating the structures and mechanics of single
animal cells by atomic force microscopy
219
8.1 Background
8.2 Imaging the surface structures and their dynamics of single living
adherent animal cells
8.3 Measuring the mechanical properties of single living adherent animal cells
8.4 Probing the molecular activities on the surface of single adherent cells
8.5 Visualizing the surface structures and their dynamics of single living
suspended animal cells
8.6 Detecting the mechanical cues involved in the activities of lymphoma cells
8.7 Probing the molecular activities on the surface of primary lymphoma cells
8.8 Summary
References
9. Characterizing the extracellular matrix for regulating cell
behaviors by atomic force microscopy
9.1 Background
9.2 Detecting the mechanical properties of decellularized extracellular matrix
9.3 Investigating the structures and mechanics of basement membranes
9.4 In situ imaging of cell culture medium-forming nanogranular surface
for cell growth
9.5 Hierarchical micro-/nanotopography of extracellular matrix for tuning
cellular structures and mechanics
9.6 Summary
References
193
200
203
207
219
222
229
241
246
248
258
261
262
269
269
272
275
279
281
284
285
10. Combining atomic force microscopy with complementary
techniques for biophysics
289
10.1 Background
10.2 Scanning near-field ultrasound holography
10.3 Fluidic force microscopy
289
291
293
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Contents
10.4 Combining atomic force microscopy with micropipette
10.5 Combining atomic force microscopy with fluidic environment
10.6 Summary
References
297
301
305
306
11. Future perspectives of atomic force microscopy for
biophysics
309
References
313
Index
315
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C H A P T E R
1
Fundamentals and methods of
atomic force microscopy for
biophysics
1.1 Background of atomic force microscopy for biophysics
Single-cell analysis is an emerging and promising area expected to
remarkably benefit unveiling the underlying mechanisms guiding life
activities. A cell is the fundamental structural and functional unit of living organisms. The study of the structure, function, and behavior of
cells is critical for seeking the answers to the questions of what life is
and how it works [1], which has been highlighted long ago by the pioneering cell biologist E. B. Wilson in his famous textbook The Cell in
Development and Heredity: “The key to every biological problem must
finally be sought in the cell, for every living organism is, or at some
time has been, a cell” [2,3]. So far much of our understanding of cellular
physiological and pathological activities has come from traditional
ensemble-averaged assays [4], which reflect the dominant biological
traits in a population and assume that an average response is representative of a typical cell within a population, whereas cell-to-cell differences are usually obscured [5,6]. Heterogeneity between individual cells
is an intrinsic feature of dynamic cellular processes, including signaling,
transcription, and cell fate [7]. Even for genetically identical cells that
have been cultured under the same conditions, cellular heterogeneity
can also be observed [8]. The basis of cellular heterogeneity is a field of
active investigation, and multiple mechanisms are thought to contribute
to this phenomenon, such as stochastic molecular interactions, phenotypic differences, stochastic transcriptional bursting, and so on [911].
Cellular heterogeneity represents one of the greatest challenges in tumor
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1. Fundamentals and methods of atomic force microscopy for biophysics
therapeutics [12,13]. For tumors, extensive genetic and phenotypic variations have been observed, including intertumoral heterogeneity (variations between tumors of different tissue and cell types), intratumoral
heterogeneity (subclonal diversity within a tumor), and intercellular heterogeneity (cellular variations within a subclonal population of tumor
cells) [14], which significantly add the complexity of tumors and have
been shown to be closely associated with the therapeutic responses and
drug resistance as well as disease relapse of tumors [15,16]. Single-cell
analysis is therefore essential to understand the causes and consequences of cellular heterogeneity and how it changes during the physiological or pathological processes [17]. In fact, there have been significant
advances in the development of single-cell biochemical analysis tools in
the past years, which are able to detect diverse components of individual cells, including DNAs, RNAs, proteins and metabolites [1820]. The
practical applications of single-cell biochemical analysis methods have
significantly promoted our understanding of tumor heterogeneity,
including the identification of metastasis-initiating cells [21], single-cell
pathology landscape of breast cancer [22], revealing heterogeneity of
intratumoral T cell states for cancer immunotherapy [23], discovering
novel cell types of tumor microenvironment [24], and so on, showing
the great potentials of single-cell analysis in addressing biological issues
from the perspective of individual cells.
It is increasingly evident in the communities of life sciences that
mechanical cues play a fundamental role in regulating cellular activities.
Cell life is not only a chemical process but also a mechanical one [25].
Cells generate, transmit and respond to forces through an intricate network of mechanical components, resulting in cell movement and shape
change, as well as altered signaling, modulated expression and even genomic damage [26]. The mechanical interactions between the cell and extracellular matrix (ECM) often yield unique biochemical and mechanical
properties of the cell [27]. For example, studies have shown that substrates
with a stiffness similar to that of the brain (0.11 kPa), muscle (817 kPa),
or bone tissues (2540 kPa) guide the stem cells to differentiate into neurons, myoblasts, and osteoblasts, respectively [28]. Particularly, changes in
the biomechanical and biophysical properties of cells and subcellular
structures influence, and are influenced by, the onset and progression of
human diseases such as cancer [29]. Numerous studies have shown that
cancerous cells are softer and more deformable than healthy cells due to a
disorganized and less filamentous cytoskeletal network, which helps the
malignant cells to squeeze through the narrow constrictions of the ECM
and the tight endothelial cellcell junctions [3032]. In malaria disease,
researchers have shown that progression through the parasite development stages (ring stage, trophozoite stage, schizont stage) leads to a considerable stiffening and decreased deformability of the host red blood
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1.1 Background of atomic force microscopy for biophysics
3
cells compared to healthy ones [3335]. The knowledge of cell mechanics,
combined with previously known biochemical cues, has greatly advanced
our understanding of related diseases [36] and has inspired new therapeutic approaches for practical applications. In recent years researchers have
been exploring targeting the mechanical cues involved in diverse human
diseases (cancer, fibrosis, and cardiovascular disease) as a therapeutic
intervention [37] and various agents that interfere with either the mechanical properties of the tissue or signaling responsive to changes in the tissue
mechanics have been developed for preclinical and clinical trials [38],
offering new opportunities for treating human diseases.
Biointerfaces are surfaces at which tissues, microorganisms, cells,
viruses or biomolecules make contact with other natural or synthetic
materials, and observing and manipulating the interactions that occur at
biointerfaces is critical for understanding the behaviors of biological systems nearly at all levels [39]. We know that in vivo cells are embedded
within the fibrous ECM to form tissues and then many tissues are organized together to constitute organs [40]. The ECM provides not only
essential physical scaffolding for the cellular constituents but also initiates crucial biochemical and biomechanical cues that are required for
tissue morphogenesis, differentiation and homeostasis [41]. The resident
cells of each tissue are responsible for and responsive to the ECM in a
process referred to as dynamic reciprocity: cells modify their secreted
ECM products in response to various stimuli (e.g., mechanical cues,
oxygen and nutrient concentration), and in turn, the ECM sends
mechanical and biochemical signals to resident cells through the
engagement of cell surface receptors (e.g., integrins, ion channels [42])
and the subsequent activation of intracellular signaling cascades and
ultimately the changes in gene expression and cell phenotype [43].
Abnormal interactions between cells and ECM are often accompanied
by pathological changes in living organisms such as tumors [44] which
leverages ECM remodeling to create a microenvironment that promotes
tumorigenesis and metastasis [45] (e.g., thickening and linearization of
ECM fibers are common in cancers, which facilitate the migration and
progression of tumor cells [46]). At the level of individual cells, cells
interact with their environments via their surfaces whose functions are
mediated by the structurally complex and dynamic assembly of specific
carbohydrates, proteins, lipids and other macromolecules distributed on
cell surfaces [47]. Cell surface molecules regulate many essential cellular
processes, including cell adhesion, tissue development, cellular communication, inflammation, tumor metastasis, and microbial infection [48],
and therefore probing the molecular activities and behaviors on the cell
surface is of remarkable significance for understanding the underlying
mechanisms guiding cellular processes. At the level of individual
viruses, in order to gain access to the cell interior to deliver the viral
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1. Fundamentals and methods of atomic force microscopy for biophysics
genome to the cell cytoplasm, viruses attach to the host cells via the specific binding interactions between molecules on the surface of the virus
and receptors (proteins, carbohydrates, or lipids) on the cell surface
[49]. Consequently, investigating the structures and properties as well
as functions of biointerfaces is particularly meaningful for revealing the
underpinnings of life processes.
The advent of atomic force microscopy (AFM) provides a revolutionary, powerful, and multifunctional tool for investigating the structures
and mechanics of living biological systems at biointerfaces under aqueous conditions with high resolution. AFM uses a sharp tip mounted at
the end of a soft cantilever to raster scan the surface of specimens
immobilized on stiff substrates, during which a laser beam is used to
detect the deflections of the cantilever to sense the interaction forces
between tip atoms and specimen surface atoms and a piezoelectric actuator drives the tip move vertically to maintain the interaction forces constant [50], yielding the three-dimensional topographical images of the
specimen surface. In essence, the spatial resolution of AFM is determined by the contact area between the AFM tip and sample surface,
which typically contains several factors, including probe geometry, tip
sharpness, sticking of sample to AFM tip, mobility of the sample (or the
substructures on the surface of the sample), mobility of substrate, and
so on, and historically the spatial resolution of AFM on biological samples in liquids is about 1 nm at best [51]. Recently, a new technique
called localization AFM (LAFM) is developed by Heath et al. [52],
which increases the spatial resolution of AFM to 0.1 nm on biomolecules
in a buffer solution. AFM is able to not only visualize the native structures of living specimens in near-physiological conditions without the
need for chemical treatments (e.g., fixation, staining, labeling) [53], but
also can measure the mechanical properties of specimens and quantify
the molecular forces at force spectroscopy mode [54,55], making AFM
particularly suited for applications in life sciences.
Compared with other typical high-resolution imaging and force measurement methods used in molecular and cell biology, AFM has unique
advantages. The spatial resolution of conventional optical microscopy is
limited to about 200300 nm due to the effect of Abbe diffraction, making
it impossible to visualize cellular structures and machineries as well as their
assembly dynamics in nanoscopic details [56]. The development of superresolution optical microscopy [e.g., stimulated emission microscopy (STED),
photoactivated localization microscopy (PALM), stochastic optical reconstruction microscopy (STORM)] shatters this limit and achieves the spatial
resolution of 20 nm [57], enabling visualization of previously invisible
molecular details in biological systems [58]. However, super-resolution optical microscopy requires the fluorescent labeling of target molecules, and
strictly speaking the results only reflect the behaviors of the fluorescein, not
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1.2 Atomic force microscopy topographical imaging modes
5
of the target molecules. Besides, fluorescent labeling inevitably reduces the
fidelity of the target molecules and may affect the physiological activities of
molecules and cells [59]. Electron microscopy [including scanning electron
microscopy (SEM) and transmission electron microscopy (TEM)] is able to
observe single molecules with high spatial resolution, but it requires the
dehydration of the samples which can cause damage to samples [60,61].
Though cryo-electron microscopy (cryo-EM) is able to resolve the structures
of proteins and macromolecular complexes at near-atomic resolution
(,0.4 nm) without the need for crystals [62], it only provides static snapshots of molecules and is unable to capture the dynamics of molecules.
Optical tweezers and magnetic tweezers are widely used methods for
single-cell and single-molecule force assays [6368], but they cannot obtain
the structural information of samples while AFM is able to simultaneously
perform topographical imaging and force measurements on samples. The
detailed comparisons between AFM and the other techniques described
above are summarized in Table 1.1. The excellent merits of AFM have
attracted the tremendous attention of researchers from various disciplines
(e.g., biology, chemistry, physics, and engineering) to utilize AFM to probe
cellular and molecular activities taking place at biointerfaces. In the past
decades, AFM has achieved great success in characterizing the structures
and mechanical cues of diverse biological systems with the unprecedented
spatiotemporal resolution, yielding numerous insights into how mechanical
forces regulate physiological and pathological behaviors at the single-cell
and single-molecule levels. Particularly, the instrumental performances and
functions of AFM have been being improved continuously since its invention, which has considerably promoted the wide applications of AFM, offering novel possibilities for unveiling the underlying mechanisms guiding life
processes and human diseases from the perspective of biomechanics and
biophysics.
1.2 Atomic force microscopy topographical imaging modes
1.2.1 Basic principles
In order to understand the principles of AFM imaging, we need to discard the notions of conventional microscopy (optical microscopy, electron
microscopy), since AFM does not have any lenses. Instead, AFM uses a tip
mounted on a soft cantilever to feel the sample surface, much like a blind
person feels a person’s face with their fingers and then forms a mental
image of the person’s face [69]. As shown in Fig. 1.1A, an AFM is commonly composed of five parts, including a soft microcantilever with a
sharp tip mounted at its end (the cantilever/tip assembly is often referred
to as the probe), a piezoelectric tube actuator, an optical lever system, a
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TABLE 1.1
biology.
Comparisons of representative high-resolution imaging and force measurement tools for applications in molecular and cell
Techniques/
features
Atomic force
microscopy
General
descriptions
The deflection of a
cantilever is measured
by a laser beam and a
position-sensing
detector to obtain force
and displacement for
both topographical
imaging and force
spectroscopy. For force
spectroscopy, ligand
molecules are attached
to the surface of AFM
tip which is then
controlled to touch the
receptors on the
substrate (or cell
surface) to form
receptorligand pairs
and mechanically
rupture the molecular
pairs.
Spatial
resolution
0.11 nm
Super-resolution
optical microscopy
(STED, PALM,
STORM)
Electron microscopy
(SEM, TEM, Cryo-EM)
Optical tweezers
Magnetic tweezers
Applying a focused
excitation beam with a
donut shape to create a
region of fluorescent
emission much smaller
than a typical focal spot
of conventional optical
microscopy (STED) or
stochastically turning
on individual
molecules within the
diffraction-limited
volume at different
time points (PALM,
STORM).
Using electrons to
penetrate a thin
specimen and then
image the transmitted
electrons (TEM), or
focusing electrons into
a small-diameter
electron probe to raster
scan the specimen and
then collect the
secondary electrons
released from each
local region of the
specimen (SEM). CryoEM is a type of TEM
capable of observing
samples at cryogenic
temperatures.
An optical trap is
created by focusing a
laser to a diffractionlimited spot with a
high numerical
aperture (NA)
microscope objective
to capture the
dielectric particles
(Bμm sized beads,
bacteria, organelles).
Polystyrene or silica
beads used as
“handles” attached to
biological samples
permit precise
measurements of force
and displacement.
A pair of permanent
magnets is placed
above the sample
holder of an inverted
microscope outfitted
with a charge-coupled
device (CCD) camera,
applying force and
rotation on magnetic
beads linked with
biological samples. The
three-dimensional
position of the bead is
obtained by video
tracking.
2050 nm
0.210 nm
B1 nm
110 nm
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Force range
10104 pN
N/A
N/A
0.1100 pN
0.01100 pN
Sample
preparation
and work
environment
Samples immobilized
on substrates in
physiological
conditions (cell growth
medium or buffer
solution, controllable
temperature and CO2).
Fluorescent labeling of
target molecules in
physiological
conditions
Dehydrated specimens
on grid in vacuum
(TEM); dehydrated and
gilding specimens in
vacuum (SEM); vitrified
specimens at cryogenic
temperatures (cryoEM).
Beads on living cells
or inside cells by
phagocytosis, or beads
coated with molecules
in physiological
conditions.
Magnetic beads on
living cells or inside
cells by phagocytosis,
or beads linked with
molecules in
physiological
conditions.
Advantages
Imaging living samples
and observing life
dynamics under native
conditions without the
need of staining,
labeling or fixation;
simple sample
preparation; high
signal-to-noise ratio;
assessment of multiple
physical, chemical and
biological parameters.
Access to threedimensional cellular
structures; high
spatiotemporal
resolution; monitoring
biomolecular processes
in living cells.
Solving atomic
structures of proteins;
conformational
snapshots of proteins
and complexes;
visualizing molecular
structures within the
cell; imaging the
surfaces of specimens
at nanometer
resolution.
High precision control
of torque and force,
parallel processing of
multiple beads, and
capable of altering the
trap position at high
frequencies (kHz).
Insensitive to drift and
low-frequency noise
(,1 Hz), inherently
providing
ultrastable operation,
no need of complex
designs, passive force
clamp.
Limitations
Restricted to the
surface of specimens
and unable to detect
intracellular structures.
Fluorescent labeling
decreases specimen
fidelity and could affect
life processes.
Providing only static
snapshots and
incapable of observing
life dynamics.
Photodamage and
sample heating.
Lower resolution and
no 3D trapping.
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1. Fundamentals and methods of atomic force microscopy for biophysics
FIGURE 1.1 Atomic force microscopy (AFM) configuration. (A) Schematic of AFM
principle. (B and C) Actual photographs of commercial AFMs. (B) A commercial Bioscope
Catalyst AFM (Bruker, Santa Barbara, CA, USA) is set on an inverted optical and fluorescence microscope. The inset shows the Petri dish. Cells are grown in dishes and the AFM
probe is immersed in the medium in the dish to probe the cells under the guidance of optical (fluorescence) microscopy. (C) A commercial Dimension Icon AFM (Bruker, Santa
Barbara, CA, USA) which has a lateral optical microscope for visual guidance of moving
AFM probe to target areas on the substrates. The inset is the optical image of the working
AFM probe in liquids in the dish. Source: (B) Reprinted with permission from M. Li, L. Liu, N.
Xi, Y. Wang, X. Xiao, W. Zhang, Nanoscale imaging and mechanical analysis of Fc receptormediated macrophage phagocytosis against cancer cells, Langmuir 30(6) (2014) 16091621.
Copyright 2014 American Chemical Society. (C) Reprinted with permission from M. Li, N. Xi, Y.
Wang, L. Liu, In situ high-resolution AFM imaging and force probing of cell culture mediumforming nanogranular surfaces for cell growth, IEEE Trans. Nanobiosci. 19(3) (2020) 385393.
Copyright 2020 IEEE.
signal processing module and a feedback control electronics. The piezoelectric actuator acts as an electromechanical transducer that is able to convert electrical potentials into mechanical movements or vice versa. When a
potential difference is applied on the opposite faces of a piezoelectric structure, the shape of the piezoelectric structure changes, and normally the
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1.2 Atomic force microscopy topographical imaging modes
9
expansion coefficient for a single piezoelectric shape is on the order of
0.1 nm/V applied [70]. The piezoelectric materials used in AFM are commonly lead zirconate titanate (PZT). The piezoelectric scanner of AFM integrates independently operated electrodes for X, Y, and Z directions into a
single tube, which allows the nanopositioning of the AFM probe in threedimensional directions (XYZ) on the surface of the sample being probed.
Notably in the early days of scanning probe microscopy, the shape of the
piezoelectric scanner is like a tripod, which has been totally superseded by
tubes of piezoelectric ceramic materials now. Piezoelectric tube has many
advantages over tripod arrangement and the principal one is that larger
scan ranges are possible with the compact and symmetrical geometry of
the tube scanner [71]. In essence, the piezoelectric material does not
respond linearly to the applied voltage, and there are two prevailing methods in current commercial AFM to address this issue: one is adding XYZ
position sensors to monitor the actual movements of the piezoelectric tube
and then correcting the nonlinearity through a feedback loop (usually
called close loop), and the other one is firstly modeling the nonlinearity
and then using nonlinear voltage to drive the tube to obtain linear movements (usually called open loop) [72]. For AFM imaging, the AFM probe is
driven by the piezoelectric tube to raster scan the surface of the sample in
the horizontal plane (XY directions), during which the piezoelectric tube
simultaneously drives the probe to move vertically (Z direction) to maintain the constant interaction forces between tip surface atoms and sample
surface atoms. The interaction forces between the AFM probe and sample
are sensed by the optical lever system. A laser beam is focused onto
the backside of the cantilever and is reflected via a mirror to a fourquadrant position sensitive detector (PSD). Any cantilever deflections
caused by the changes of tip-sample interaction forces will result in slight
alterations in the direction of the reflected beam, which is tracked by the
PSD. The PSD signals are analyzed by the signal processing module and
then the feedback system will control the piezoelectric tube to move vertically according to the topography of the sample to maintain the tip-sample
interaction forces constant. The displacements in the XYZ directions of the
piezoelectric tube are recorded during scanning, which yields a threedimensional topographical image of the specimen being scanned. A
computer is linked to the controller to set up AFM imaging parameters
and collect data from the controller. In practice, an optical microscopy
system is commonly integrated with the commercial AFM to facilitate the
manipulator to visually move the AFM probe to the specimens [73,74], as
shown in Fig. 1.1B and C.
AFM imaging depends on monitoring the interaction forces between
tip surface atoms and sample surface atoms. It is now well-known that
there are four distinct forces in nature, two of which are the strong and
weak interactions that act between neutrons, protons, electrons, and
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1. Fundamentals and methods of atomic force microscopy for biophysics
other elementary particles and have a very short range of action
(less than 1025 nm) [75]. The other two types of forces are the electromagnetic and gravitational interactions that act between atoms and
molecules. For the interaction forces between tip surface atoms and
sample surface atoms involved in AFM imaging, the gravitational force
is completely insignificant compared to electromagnetic force (e.g., the
gravitational force between two ions 1 nm apart is 32 orders of magnitude weaker than the electrostatic force) [76]. Electromagnetic forces are
the source of all intermolecular interactions which determine the properties of solids, liquids, and gases, the behaviors of particles in solution,
chemical reactions, and the organization of biological structures [75].
We know that electrons within an atom are in continual motion and
travel extremely fast. For a given atom, it may appear electrically
neutral over conventional periods of time, but for a very short period of
time (saying a snapshot), the distribution of electric charges due to the
electron motions is not perfectly symmetrical and this gives rise to subtle charge imbalances referred to as dipoles. Each molecule, therefore,
exhibits a slightly different distribution of charge within a given snapshot and the charge imbalance in one molecule can electrically induce a
similar imbalance in a neighbor molecule, causing that the slightly positive end of one molecule will be attracted to the negative end of another
neighboring molecule and this is the origin of the van der Waals force
[71]. For simplicity, we can consider the interactions between an atom at
the tip apex and another atom on the sample surface, which can be
characterized by the LennardJones potential function [77]:
EðrÞ 5 4ε
σ 12 σ6
2
r
r
(1.1)
where r is the separation between the two atoms, ε is the depth of the
potential well (associated with interaction strength), and σ is the interatomic distance where the potential is zero. ε and σ are two constants
that depend on the materials and need to be experimentally determined
to describe the specific molecular interaction. Normally, σ is approximately equal to the diameter of the atom involved (typically a few
Angstroms [77]), and is sometimes called the hard sphere diameter [71].
Plotting the LennardJones function gives the interaction forces
between the AFM tip atom and sample surface atom, as shown in
Fig. 1.2. When the tip atom is far away from the sample atom, there is
no interaction force between the two atoms (stage ①). When the tip
atom approaches the sample atom gradually, the van der Waals attractive force arises which pulls the tip atom toward the surface, causing
the downward deflection of the AFM cantilever (stage ②). As the tip
atom further contacts and compresses the sample atom, repulsive forces
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1.2 Atomic force microscopy topographical imaging modes
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FIGURE 1.2 Schematic showing the interactions between atomic force microscopy tip
atom and sample surface atom modeled by LennardJones function.
due to Pauli exclusion principle and electrostatic (Coulombic) interactions dominate the interaction forces between tip atom and sample
atom, causing the upward deflection of the AFM cantilever (stage ③).
Depending on the types of interaction forces (attractive force or repulsive force) between the AFM tip and sample sensed by the AFM cantilever, different AFM imaging modes are obtained (as denoted in Fig. 1.2),
which will be described in the following paragraphs. It should be noted
that the interaction forces between the AFM tip and sample surface are
highly complicated and many other types of forces are involved in different imaging environments, for example, meniscus force arises from
capillary condensation around the contact sites between the AFM tip
and sample surface for AFM imaging under ambient conditions,
whereas double-layer and hydrodynamic force emerge when imaging
in liquids [78]. Readers are referred to the references [76,78] for more
descriptions of the AFM tip-sample interaction forces.
1.2.2 Contact mode
Contact mode is the first imaging mode developed for AFM, and it is
the basis for AFM techniques. In the contact mode, the AFM probe tip
is in continuous physical contact with the sample surface and the repulsive forces between the probe tip and sample surface are sensed by the
AFM probe cantilever (Fig. 1.2). For contact mode AFM imaging, the
piezoelectric tube drives the probe to raster scan the sample in the horizontal plane, during which the probe is dragged across the sample surface (Fig. 1.3A) and the topographical changes of the sample surface in
the vertical direction will result in the alterations of the deflection of
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1. Fundamentals and methods of atomic force microscopy for biophysics
FIGURE 1.3 Typical types of atomic force microscopy (AFM) imaging modes. (A)
Contact mode and tapping mode. (I) Schematic diagram of AFM imaging of biological specimens (an example of a cell membrane is shown) attached on the substrate. (II) Contact
mode AFM imaging. In contact mode, AFM tip is scanned over the specimen surface,
while the deflection of the cantilever is maintained constant. (III) Tapping mode AFM
imaging. In tapping mode, commonly the amplitude of the oscillating cantilever is maintained constant. (B) PFT mode. (I) Schematic diagram of AFM imaging at PFT mode. The
vibrating tip indents the specimen in the vertical direction (z) at each sampling point to
record force curves during raster scanning (the movement trajectory of the AFM tip is
denoted by the dashed yellow line) at the horizontal plane (xy). (II) Schematic diagram of
the force curve. Each force curve is composed of two portions, including an approach
curve and a retract curve. By analyzing the different parts of the force curve, various
mechanical parameters of the specimen are obtained, including Young’s modulus, deformation, adhesion force, and energy dissipation. Young’s modulus and adhesion forces are
obtained from the retract curve, deformation is obtained from the approach curve, and
the energy dissipation represents the area (orange shaded area) between the approach
curve and retract curve.
AFM probe. The AFM signal processing and feedback module then compare the current cantilever deflection (called the feedback parameter) with
a preset threshold (called the setpoint). The difference between the current
cantilever deflection and the setpoint is called the error signal. If the current cantilever deflection is not equal to the setpoint, specific voltage is
then applied to control the piezoelectric tube to move up or down to make
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1.2 Atomic force microscopy topographical imaging modes
13
the error signal back to zero. By recording the movements of the piezoelectric tube in three-dimension directions, we get the three-dimensional topographical image of the sample being scanned. The setpoint of the
cantilever deflection in contact mode is preset by the user before AFM
scanning and this parameter determines how hard the AFM tip pushes
against the surface of the sample (called the scan force), which is important
for utilizing contact mode AFM imaging to observe fragile biological samples. Notably, the contact mode AFM imaging described here operates in a
way of constant force mode. Constant force mode is by far the most widely
used mode, and generally any references to contact mode AFM mean constant force mode [79]. Contact mode can also work in constant height
mode, in which the probe maintains a fixed height above the sample and
there is no feedback loop in this mode. In constant height mode, the image
signal comes entirely from the cantilever deflection and the deflection force
on the cantilever is directly used to calculate the separation between the tip
and sample surface. Constant height mode is appropriate for quick scans of
samples with small height differences (if height differences are large, the tip
will very likely crash onto the surface, causing either the tip to be destroyed
or the tip to damage the sample) [80] and this mode has specific biomedical
applications (e.g., observing the behaviors of biomolecules firmly attached
to the smooth substrate with high-speed AFM [81,82]).
A notable point for contact mode AFM is the selection of the probe.
Normally, there is a contradiction between the force sensitivity and the
stability of the probe. A softer cantilever (with a lower spring constant)
deforms more under the same load and thus has better force detection
sensitivity. However, a softer cantilever is more susceptible to the thermal drift caused by the environmental temperature variation (e.g., the
heat generated by the AFM laser or optical microscope illumination
often results in significant drift in deflection of the cantilever with a
spring constant lower than 0.01 N/m, in the range of a few volts in the
PSD output signals [72]), which conversely influences the quality of
AFM imaging. In practice, cantilevers with a spring constant between
0.01 and 0.1 N/m are usually good for living cell imaging by contact
mode AFM [72]. Besides, commercial AFM probes are commonly fabricated with the use of silicon or silicon nitride. In order to increase the
reflectivity, a thin layer of gold is often coated on the backside of the
cantilever, or a ferromagnetic coating may be applied if magnetic sensitivity is required [71]. Obviously, due to the fact that the thermal expansion coefficient of the coated material is different from the cantilever
material (silicon/silico nitride), coating only one side of the cantilever
will lead to a substantial thermal drift of the cantilever in response to
the changes of environmental temperature. In 2012, Churnside et al. [83]
have shown that even coating AFM cantilevers on both sides has thermal drift effects on the probe, whereas removing the coating layers of
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1. Fundamentals and methods of atomic force microscopy for biophysics
the AFM probes significantly increases the force stability and precision.
As an alternative way, we can perform gold coating only at the end of
the probe cantilever for increasing laser reflectivity while the rest of the
cantilever is uncoated (this type of probe has been commercially available [72]), which will produce the probe that is insensitive to environmental temperature alterations and at the same time has adequate force
detection precision.
Since contact mode AFM imaging senses the repulsive forces between
AFM tip atoms and sample surface atoms to obtain the topographical
image of the sample, and the repulsive forces are highly localized
(the repulsive force between the tip atom and a target atom on the sample is not susceptible by the neighbor atoms of the target atom), contact
mode has a high spatial resolution. In fact, contact mode has long been
used to obtain the high-quality topographical image of single membrane
proteins (which will be described in Chapter 3) immobilized on substrates in near-physiological buffer solutions in the past decades [84,85]
and so far contact mode AFM is still the preferred method to obtain the
high-resolution topography of single native membrane proteins under
aqueous conditions [52]. Besides, contact mode is suited for imaging the
fine structures of single living cells [86,87], which usually requires
applying the adequate scan force on living cells depending on which
cellular parts are to be visualized (e.g., cell surface structures, cytoskeletons beneath cell surface, and so on). Applications of AFM topographical imaging on single membrane proteins (Chapter 3) and living cells
(Chapters 7 and 8) will be described in detail in the subsequent chapters
of the book. Notably, the drawback of contact mode is that the lateral
dragging of the probe tip across the sample surface can cause mechanical deformation or even damage to the sample, which is detrimental for
observing soft and fragile biological samples which are loosely adsorbed
onto the substrate.
1.2.3 Noncontact mode
Noncontact AFM (NC-AFM) is the only one AFM mode which is able to
detect the behaviors of single atoms (including true atomic resolution, control of atomic forces, measurement of atomic forces, measurement of atomic
response, observing atomic defects, mechanical manipulation of individual
atoms, and mechanical assembly atom by atom) [88]. Atomic imaging of
molecules by NC-AFM is commonly performed in frequency-modulated
NC-AFM, in which the cantilever is actively oscillated at constant amplitude
at its resonance frequency by a feedback circuit and interaction of the tip
with the sample surface causing the resonance frequency to shift by Δf
which is the key measurement signal in NC-AFM [89]. In the limit of small
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1.2 Atomic force microscopy topographical imaging modes
15
amplitudes, the frequency shift (Δf) is proportional to the gradient of the
interaction force between tip and sample and therefore the tip-sample interaction forces can be measured by monitoring the frequency shift of the cantilever. NC-AFM usually works in constant height mode, in which the tip is
scanned in a fixed plane above the sample surface while the frequency shift
of the cantilever is recorded (typically, for atomic imaging, the height of the
scanning tip above the sample is a few Angstroms [90]). A notable point is
that atomic imaging by NC-AFM usually requires the use of a specific sensor called qPlus [91] which is based on the concept of piezoelectric quartz
tuning forks similar to those used as timekeeping elements in wristwatches,
allowing AFM operation at oscillation amplitudes down to a few Angstrom.
A standard qPlus sensor is created by attaching one of the prongs of the
tuning fork to a substrate and attaching a tip to the other prong which acts
as a probe with the capability of self-sensing. For more descriptions of
qPlus sensors, readers are referred to the recent review of literature by
Giessibl [91]. An alternative to the self-sensing piezoelectric quartz sensor is
the length extensional resonator or the so-called Kolibri sensor and the performance comparison between qPlus and Kolibri sensors is still under
debate in the community [90]. Besides, utilizing NC-AFM to visualize the
atomic structures of single molecules often requires tip functionalization
[92]. For imaging single molecules, the AFM probe tip should be rather inert
to prevent the target molecule from being picked up or moved by the tip,
whereas the bare metal tips are often with high reactivity which could lead
to the picking up of the target molecule before obtaining an atomic image.
So far, the most popular functionalization for high-resolution NC-AFM is
the CO tip [92], which is made by picking up a CO molecule with a metal
tip (often copper [89]). Notably, NC-AFM is mainly applied in the fields of
surface chemistry [93] for single molecular characterization with atomic resolution and requires substantial instrumentation as well as the harsh work
environments (often in ultra-high vacuum (UHV) conditions [94]), which
are uncommon for other applications, particularly for biomedical applications. The purpose of the brief description of NC-AFM here is to help readers understand AFM imaging techniques.
1.2.4 Tapping mode
Tapping mode is also known as intermittent contact mode, dynamic
force mode, oscillation mode, or AC mode. In tapping mode (Fig. 1.3A),
the probe cantilever vibrates near its resonance frequency while raster
scanning the sample surface and the probe tip intermittently touches
the sample at its downward movement. When the probe is brought to the
sample surface, the interactions between the tip and sample cause changes
in both cantilever amplitude and resonance frequency. Either amplitude
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1. Fundamentals and methods of atomic force microscopy for biophysics
or resonance frequency of the cantilever can be used as the feedback
parameter for tapping mode imaging, but using the amplitude as feedback is technically simpler because it requires only one feedback loop
compared with using frequency as feedback which requires three such
loops [61]. Hence, so far tapping mode AFM is commonly based on
amplitude modulation. However, it should be noted that compared with
amplitude modulation, the resonance frequency shift is more sensitive to
the forces acting on the tip at the closest approach to the sample surface
during the oscillation cycle [50], and frequency modulation is particularly
suited for high-resolution imaging AFM such as in NC-AFM described
above. During the raster scanning, the amplitudes of the cantilever are
detected by the lock-in amplifier in the AFM controller and the piezoelectric tube drives the probe to move vertically to maintain the constant
amplitude of the cantilever, yielding the three-dimensional topography of
the sample by recording the XYZ displacements of the piezoelectric tube.
The amplitude setpoint defines the amplitude of the cantilever oscillation
signal to be maintained by the feedback loop and the setpoint reflects the
tapping force exerted on the sample. In practice the amplitude setpoint is
often chosen at about 80% of the free cantilever amplitude [72]. However,
the adequate setpoint should be determined during experiments and it is
associated with various factors, including specimen and probe as well as
the imaging conditions. Generally, a larger tapping force often means better imaging quality, but also means more likely to cause tip damage (e.g.,
tip wear, tip break, and tip contamination) which could influence the life
of the tip. A feasible way is starting the scanning with a lower tapping
force and then increasing it slowly until the imaging quality does not
improve anymore. Since tapping mode eliminates the lateral force
between tip and sample, tapping mode is good at imaging loosely
adsorbed and soft samples (e.g., biomolecules [50] and cellsurface fine
structures [95]) which are often challenging for contact mode AFM.
Incidentally, tapping mode AFM achieves great success in imaging DNA
molecules, which will be described in Chapter 2. Nevertheless, one drawback of tapping mode is that it is unable to directly measure the interaction forces between tip and sample, as the lock-in amplifier only monitors
the amplitude changes of the vibrating cantilever, making users unable to
quantitatively characterize the interactions between tip and sample.
Tapping mode AFM offers a powerful method for mapping the material and mechanical properties of the sample, which is called phase
imaging [96]. Depending on the properties of the surface being probed
(e.g., composition, friction, viscoelasticity, and adhesion), in addition to
the amplitude changes, the interactions between tip and sample surface
will also cause the phase changes of cantilever oscillation (called phase
lag or phase shift), which can be recorded by the lock-in amplifier of
AFM as well. Therefore, the cantilever’s vibration amplitude is used as
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1.2 Atomic force microscopy topographical imaging modes
17
the feedback parameter to move the piezoelectric tube vertically to generate the topography of the sample while the cantilever’s vibration
phase lag is used to simultaneously generate the material properties
map of the sample. Phase lag is caused by the energy dissipation during
each contact between the tip and sample, which includes several factors
(the inelastic deformation of the sample caused by the tip during the
approaching stage, the van der Waals attractive force (Fig. 1.2) and
adhesion force needing to overcome by the tip during retracting stage)
[72] and are associated with the properties of the sample. The dissipated
energy due to the inelastic tipsample interactions can be mathematically described as follows [97]:
E5
kω AA0 sinϕ 2 A2
2Q
(1.2)
where E is the dissipated energy, k is the spring constant of the cantilever, Q is the quality factor, A is the cantilever vibration amplitude during scanning, A0 is the free cantilever vibration amplitude without the
tipsample contact, ω is the driving frequency, and ϕ is the phage lag
compared to driver. We can see that, since the cantilever vibration
amplitude is maintained constant during scanning, the energy dissipation is directly linked to the phase lag and therefore the phage images
reflect the mechanical properties of the sample. Tapping mode phase
imaging is undoubtedly useful for investigating the material properties
and readers are referred to Ref. [96] for more descriptions of the phase
imaging theory. Nevertheless, as described above, the force curves are
not recorded during tapping mode imaging and thus information on
the sample provided by tapping mode phase imaging is limited.
Particularly, there has been a new AFM technique called peak force tapping (PFT) mode which provides powerful capabilities to quantitatively
characterize the diverse material properties of samples and will be
described in the following.
1.2.5 Peak force tapping mode
PFT mode originates from the AFM-based force spectroscopy techniques [50,98]. Traditionally, for AFM-based force spectroscopy assays, the
AFM tip is controlled to vertically indent the specimens, during which the
force curves are recorded. The mechanical properties of the specimens can
be extracted from the obtained force curves, which will be described in
detail in the following contents. However, traditional force spectroscopy is
time-consuming and inefficient with a poor spatiotemporal resolution, and
recent developments in AFM techniques allow fast obtaining force curves
on each sampling point on the specimen while simultaneously recording
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1. Fundamentals and methods of atomic force microscopy for biophysics
topographic images of the specimen [61,99,100], and this technique is
called PFT. The principle of PFT is shown in Fig. 1.3B. During AFM’s raster scanning along the xy horizontal plane (the movement trajectory of the
AFM tip is denoted by the dashed yellow line in Fig. 1.3BI), the vibrating
tip performs approachretract cycle in the vertical direction (z) on the
specimen at each sampling point (each tiny grid in Fig. 1.3BI is equal to a
sampling point). During the approach-retract movement, the changes in
the deflection of the cantilever and the vertical displacements of the piezoelectric tube are recorded, which yield the so-called forcedistance curves.
The peak force (as shown in Fig. 1.3BII, the peak force is the force from the
cantilever at its maximum deflection during approach stage) of the
obtained force curve is then used as the feedback parameter for controlling
the piezoelectric tube to move vertically to maintain the peak force constant, which subsequently constructs the topography image of the specimen as the tip horizontally raster scans the specimen. As described above,
contact mode AFM and tapping mode AFM record the deflection or the
oscillation amplitude (frequency) of the cantilever as the feedback parameter during the scanning, which cannot sense the contact processes between
the tip and sample during imaging. On the contrary, PFT records the force
curves and uses the peak force of the force curves as the feedback parameter for imaging, and thus the tipsample contact processes during imaging
are available from the force curves (e.g., the contact point between the tip
and sample is discernible from the force curve and can be used to determine when the tip contacts the sample), facilitating integrating AFM with
other complementary techniques to realize the simultaneous multimodal
probing (such as combining PFT imaging and infrared imaging [101]) with
high controllability and precision, which is quite meaningful for comprehensively understanding life activities.
PFT imaging is able to display the multiple properties of the sample
as colored maps by analyzing the force curves, which are correlated
with the topography of the sample. The force curve contains various
physical properties of the sample, as shown in Fig. 1.3BII. For example,
the adhesion force reflects the adhesive capabilities of the sample surface. When using a bare tip (without functionalization) to perform PFT
imaging, the adhesion force map reflects the nonspecific adhesive features of the sample surface. When using the functionalized tip to perform PFT imaging [102], the adhesion force map reflects the specific
adhesive interactions between the target molecules on the sample surface and the antibody molecules on the tip surface, which is meaningful
for revealing the molecular behaviors of cells. Particularly, viruses can
also be directly attached to the surface of the AFM tip via linker molecules [103], which is useful for probing viruscell interactions at the
single-virus level. Detailed descriptions of AFM-based force spectroscopy with the use of functionalized tip will be presented in the
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1.3 Atomic force microscopy force spectroscopy techniques
19
following texts. By fitting the force curve with mechanical models,
Young’s modulus of the sample can be obtained. Notably, the commercially AFM produced by Bruker Company (Santa Barbara, CA, USA)
uses DerjaguinMullerToporov (DMT) to extract Young’s modulus of
samples. Some other theoretical models, such as HertzSneddon model
(this mode will be described in detail in the following sections) and
JohnsonKendallRoberts (JKR) [78], have also been widely used to
analyze the force curves to obtain Young’s modulus of samples. The
deformation of the sample can be obtained by analyzing the approach
curve after the contact point, and the energy dissipation can be obtained
by analyzing the area between the approach curve and the retraction
curve. Since multiple properties maps of the specimen are generated
simultaneously with the topographical image of the specimen during
PFT imaging, PFT-based AFM imaging is also called multiparametric
AFM [99,102]. The biomedical applications of PFT-based multiparametric imaging will be included in the subsequent chapters. Notably,
for utilizing PFT-based AFM to investigate the mechanical properties of
the specimens, we need to use appropriate AFM probes based on the
characteristics of the specimens. Stiffer cantilevers can cause larger
deformation on the specimen, while softer cantilevers have better detection sensitivity, and thus compromises are required for the specimens
being probed. Generally, the cantilever spring constant should be comparable with the stiffness of the specimens being probed [104].
1.3 Atomic force microscopy force spectroscopy techniques
1.3.1 Single-cell mechanical measurement
AFM achieves great success in measuring the mechanical properties
(e.g., elasticity, viscoelasticity) of single living cells in the past decades
and now AFM indentation assay has become a standard method for
characterizing the mechanics of cells. Both cellular elasticity and viscoelasticity can be simultaneously measured by applying an AFM probe
to vertically perform approach-dwell-retract movements on the cell surface [50]. The process of the AFM approach-dwell-retract cycle is shown
in Fig. 1.4A. Firstly, the AFM probe, which is far away from the cell, is
controlled by the piezoelectric tube to gradually touch and indent
the cell in the vertical direction (stage ①). The contact between the tip
and cell will result in the deflection of the AFM cantilever (x) which is
detected by the PSD of AFM (Fig. 1.1A). According to Hooke’s law:
F 5 kx
(1.3)
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1. Fundamentals and methods of atomic force microscopy for biophysics
FIGURE 1.4 Measuring cellular viscoelastic properties by atomic force microscopy
(AFM) approach-dwell-retract experiments. (A) Schematic diagram of controlling AFM tip
to vertically perform approach-dwell-retract movement on the cells. (B) A typical FD curve
(I) and FT curve (II) obtained during the approach-dwell-retract process. (I) According to
the contact point, the approach curve is converted into the indentation curve and the
indentation curve is then fitted by the HertzSneddon model to extract cellular Young’s
modulus (the inset). (II) The FT curve is fitted by the two-order Maxwell model to extract
the cellular relaxation times (the inset). Source: Reprinted with permission from M. Li, N. Xi,
Y. Wang, L. Liu, Nanotopographical surfaces for regulating cellular mechanical behaviors investigated by atomic force microscopy, ACS Biomater. Sci. Eng. 5(10) (2019) 50365050. Copyright
2019 American Chemical Society.
where k is the spring constant of the cantilever and x is the deflection of
the cantilever, the interaction force between probe and cell is obtained
(also called the loading force of probe cantilever). Notably, in order to
exactly obtain the loading force exerted by the cantilever, the spring
constant of the cantilever needs to be accurately calibrated in advance.
Diverse methods have been developed to calibrate the spring constant
of cantilever [105], including the static mass hanging method, reference
cantilever method, dynamic mass attachment method, resonant frequency method, and thermal noise method. In practice, commonly,
force curves are firstly obtained on the stiff substrate to calibrate the
deflection sensitivity of the cantilever, and then the spring constant of
the cantilever is calibrated by the thermal noise [106] module of AFM.
When the loading force of the cantilever achieves the preset value during the approach process, AFM probe stops approaching and dwells on
the cell surface for a period of time (stage ②). The purpose of dwelling
is to observe the relaxation process of the cell. Subsequently, the AFM
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1.3 Atomic force microscopy force spectroscopy techniques
21
probe retracts from the cell surface to its original position (stage ③).
During the approach-dwell-retract cycle, the vertical displacements of
the AFM piezoelectric tube and the deflections of the AFM cantilever
are obtained by AFM, which yields the forcedistance (FD) curve (also
called force curve), as shown in Fig. 1.4BI. Each force curve is composed
of two portions, an approach curve and a retract curve. Due to the
dwelling of the AFM tip on the cell surface, the endpoint of the
approach curve does not coincide with the start point of the retract
curve. Generally, the approach curve is used for calculating the cellular
elastic properties (such as Young’s modulus) [107], whereas the retract
curve is used for probing adhesive interactions which usually requires
using functionalized tips [47]. By linking an oscilloscope to the output
signal of AFM, the PSD signal changes of AFM cantilever versus time
are recorded [108,109], which yield the forcetime (FT) curves (also
called relaxation curve). The FT curves obtained during the dwelling
process of AFM tip on cells reflect the relaxation dynamics of cells, as
shown in Fig. 1.4BII. By analyzing the FT curves, cellular viscoelastic
properties (such as relaxation time) are obtained. The detailed processes
of extracting cellular Young’s modulus from FD curve and relaxation
time from FT curve are described in the following, respectively.
Cellular Young’s modulus is obtained by fitting the FD curve with theoretical models. Several models have been presented for analyzing the indentation process of AFM tip, including HertzSneddon model, JKR model,
DMT model, and OliverPharr model [40]. HertzSneddon model neglects
the adhesion forces between the AFM tip and specimen, while JKR and
DMT models consider the adhesion forces between the AFM tip and specimen (the JKR model considers the adhesion forces inside the contact area
between tip and specimen, while the DMT model considers the adhesion
forces outside the contact area) [110]. Thus, strictly speaking, HertzSneddon
is applicable when the adhesion force is much smaller than the loading force,
the JKR model is applicable in the case of large tips and soft samples with a
large adhesion, and the DMT model is applicable in the case of small tips
and stiff samples with a small adhesion [78]. The OliverPharr model is
mainly used for determining the mechanical properties of thin films [111].
Nevertheless, for practical reasons, the HertzSneddon model is the most
widely used one for calculating cellular Young’s modulus from FD curves
[104,112114]. Hertz model is applicable to spherical tip and Sneddon
extended the Hertz model to conical tip:
pffiffiffiffi
4Eδ1:5 R
Fspherical 5
(1.4)
3ð1 2 υ2 Þ
Fconical 5
2Eδ2 tanθ
πð1 2 υ2 Þ
(1.5)
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1. Fundamentals and methods of atomic force microscopy for biophysics
where υ is the Poisson ratio of cell (cells are often considered as incompressible materials and thus υ 5 0.5), F is the loading force of the AFM
probe, δ is the indentation depth, E is the cellular Young’s modulus, θ is
the half-opening angle of the conical tip, and R is the radius of the
spherical tip. For applying the HertzSneddon model to analyze the FD
curves, the FD curve needs to be converted into the indentation curve
according to the contact point in the FD curve (the indentation δ is equal
to the difference between the vertical displacement change of AFM piezoelectric driver and the deflection of the cantilever). We can imagine that if
the specimen being indented is extremely stiff and there is no deformation
on the sample during the indentation process, the vertical displacement of
the piezoelectric tube is therefore equal to the deflection of the cantilever
and the indentation depth is zero. For the soft specimens such as cells,
there is a deformation of the specimen during indentation, and therefore
the vertical displacement of the piezoelectric tube is the sum of the
indentation depth and cantilever deflection. The HertzSneddon model is
then used to fit the indentation curve. The inset in Fig. 1.4BI is an example
showing the comparison of the HertzSneddon fitting curve and experimental indentation curve. The fitting gives the cellular Young’s modulus
E. Notably, the HertzSneddon model assumes that the sample is infinitely thick, but it works well when the indentation into the sample by the
tip is less than 10% of the sample thickness [115]. In 2012, Gavara and
Chadwick [116] improved the HertzSneddon model to make it applicable
for thin samples by introducing a bottom effect correction factor, significantly facilitating probing of the mechanical properties of cellular lamellar
structures such as pseudopodia. However, this method requires measuring
the thickness of the cell and is more complex than the HertzSneddon
model. It should be noted that cellular Young’s modulus measured by
AFM is influenced by experimental conditions, such as tip shape, probe
loading rate, cellular positions being indented, environmental temperature
and measurement medium [117], and thus these conditions should be
maintained identical during experiments to eliminate artificial errors and
make the results comparable with each other. Besides, cells are highly heterogeneous, and the elastic properties of different intracellular structures
are included in the different parts of the recorded force curves. With smaller indentations, the AFM tip senses the stiff cellular cortex which is composed of actin proteins. With larger indentations, the AFM tip senses the
softer structures beneath the cellular cortex, such as cytoplasm. When further increasing the loading force to indent the cells, the cell nuclei may be
probed by AFM. Another notable point regarding AFM-based cellular
mechanical measurement is the geometry of the probe tip. Studies have
shown that cellular Young’s modulus measured by the conical tip is significantly larger than that measured by the same cantilever modified with a
spherical tip [118], and this is due to the fact that different intracellular
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1.3 Atomic force microscopy force spectroscopy techniques
23
structures are probed by the different tips. The spherical tip has a much
larger contact area than the conical tip. The conical tip primarily probes
the stiff cell cortex, whereas the spherical tip probes both the cell cortex
and the softer underlying cytoplasm.
Cellular relaxation time is obtained by analyzing the FT curves recorded
on cells. Young’s modulus only reflects the elastic properties of cells, while
in fact living cells are intrinsically viscoelastic materials and the rheological
behavior of cells is closely connected to the fundamental functions of cells.
Hence, characterizing the viscoelastic properties of cells is quite meaningful
for understanding cell behaviors from the perspective of biomechanics. By
the way, AFM is a type of active method for characterizing cellular rheological properties, and passive methods (using the thermal fluctuations of
embedded colloidal probes to measure cellular rheology) [119] have also
been developed to characterize the rheology of cells. Generally, the FT
curve can be fitted by a two-order Maxwell spring-dashpot model to
obtain cellular relaxation time [108,109]:
FðtÞ 5 A0 1 Ai
2
X
e2t=τ i
(1.6)
i51
τi 5
ηi
; i 5 1; 2
Ei
(1.7)
where F is the loading force of the AFM probe, A0 is the instantaneous
(purely elastic) response, Ai are the ith force amplitudes, τ i is the ith cellular relaxation time, ηi is the ith cellular viscosity, and Ei is the ith cellular
Young’s modulus. The cellular relaxation time (τ) is the ratio of cellular
viscosity (η) to cellular Young’s modulus (E), and thus cellular relaxation
time indicates the viscoelastic properties of cells. In practice, the one-order
Maxwell model often does not fit the FT curve well, while the two-order
Maxwell model matches the FT curve well [108,109,120,121]. The inset in
Fig. 1.4BII is an example showing the comparison of the two-order
Maxwell fitting curve and experimental relaxation curve and we can see
that the two curves are considerably consistent with each other. Fitting the
relaxation curve with a two-order Maxwell model gives two cellular relaxation times (τ 1 and τ 2). During the AFM indentation process, the AFM tip
successively probes the cell membrane and cytoskeleton. The first-order
cellular relaxation time τ 1 (the fast relaxation time) originates from the
rapid deformations of the cell membrane, while the second-order cellular
relaxation time τ 2 (the slow relaxation time) originates from the relatively
slow reorganizations of cytoskeletons. A notable point is that cellular relaxation times measured by AFM are dependent on the measurement parameters, such as surface dwell time and ramp rate [122], and thus
experimental conditions should be identical to make the obtained results
comparable.
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1. Fundamentals and methods of atomic force microscopy for biophysics
Modifying the AFM cantilever with an individual sphere to form a
spherical tip is particularly useful for characterizing cell mechanics since
the spherical tip has a defined geometry which facilitates theoretical
modeling and the spherical tip could also better represent the mechanical
properties of the whole cell compared with a conical tip which only detects
the mechanical properties of local areas of cells. We have conveniently fabricated an AFM probe with spherical tips based on AFM micromanipulations [120,121] and the protocol is in the following as a reference to the
readers (Fig. 1.5). First, a regular AFM probe is mounted onto the AFM
head and the laser signal reflected on the cantilever is adjusted (for some
commercial AFMs, such as the Dimension 3100 AFM used here, we need
to adjust the laser signal of the cantilever to beyond a certain value and
then the AFM head can be moved). Subsequently, a drop of the polystyrene sphere solution (the sphere diameter is B20 μm here and readers can
use spheres with different sizes according to their experimental requirements) is placed on a fresh glass slide and a drop of mixed two-part epoxy
adhesive (Araldite, USA) is placed on another position of the same glass
slide by using a toothpick. The glass slide is then placed onto the specimen
stage of AFM. Under the guidance of optical microscopy, the AFM cantilever is controlled to slightly touch the epoxy adhesive and then retract
immediately. The AFM cantilever is then moved to contact a single sphere
for 10 s and then retract from the glass slide. Fig. 1.5A shows the optical
FIGURE 1.5 Fabricating spherical tip for single-cell mechanical analysis. (A) Under the
guidance of optical microscopy, a sphere is glued to the end of the atomic force microscopy (AFM) cantilever. Optical images obtained before (I) and after (II) gluing a sphere to
the AFM cantilever. (B and C) SEM images of the fabricated spherical tips. (B) Triangular
cantilever glued with a sphere. (C) Rectangular cantilever glued with a sphere. Source: (A)
Reprinted with permission from M. Li, L. Liu, X. Xiao, N. Xi, Y. Wang, Effects of methotrexate on
the viscoelastic properties of single cells probed by atomic force microscopy, J. Biol. Phys. 42(4)
(2016) 551569. Copyright 2016 Springer Nature. (B and C) Reprinted with permission from M.
Li, L. Liu, N. Xi, Y. Wang, Atomic force microscopy studies on cellular elastic and viscoelastic
properties, Sci. China Life Sci. 61(1) (2018) 5767. Copyright 2017 Science China Press and
Springer-Verlag GmbH Germany.
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1.3 Atomic force microscopy force spectroscopy techniques
25
images before (Fig. 1.5AI) and after (Fig. 1.5AII) gluing a sphere to the cantilever of the AFM probe. The prepared probes with spherical tips are
placed in a probe box for 24 h at room temperature for the hardening of
epoxy adhesive and then the probe can be used for single-cell mechanical
measurement experiments. Experimental results have shown that either triangular or rectangular cantilevers can be easily modified with spherical
tips by this method (Fig. 1.5B and C).
1.3.2 Single-cell force spectroscopy
AFM-based single-cell force spectroscopy (SCFS) is able to quantify the
adhesive interactions of individual cells. Cell adhesion, commonly defined
as the binding of a cell to a substrate (the substrate can be another cell, a
surface or an organic matrix), is broadly connected to physiological and
pathological processes, including embryonic development, assembly of tissues, cellular communication, inflammation, wound healing, tumor metastasis, cell growth, and viral and bacterial infection [123]. AFM-based SCFS
offers novel possibilities for seeking answers to the fundamental issues in
cell adhesion. The prerequisite of SCFS is functionalizing the AFM cantilever to allow firmly attachment of individual living cells onto the cantilever
to prepare single-cell probe. For single-cell probes, weak adsorption of the
cell onto the cantilever may cause the sliding of cells during measurements,
which results in the failure of the experiments. Commonly, AFM cantilevers
are coated with concanavalin A (ConA) to adsorb single cells [124,125]. For
doing so, AFM cantilever is firstly incubated with biotin-conjugated bovine
serum albumin (BSA) at 37 C overnight, after which the cantilever is
washed with phosphate buffered saline (PBS) to remove the unbound
molecules. The cantilever is then incubated in streptavidin solution for
30 min at room temperature. After the incubation, the cantilever is washed
with PBS again and then is incubated in biotin-conjugated ConA solution
for 30 min at room temperature. After the incubation, the ConAfunctionalized cantilever can be stored in PBS for up to 1 week at 4 C.
Individual living cells can be tightly attached to the ConA-functionalized
cantilever by AFM micromanipulations for SCFS experiments, as shown in
Fig. 1.6A. Under the guidance of optical microscopy, the ConAfunctionalized cantilever is moved to gradually approach individual living
cells on the substrate (I in Fig. 1.6A). When the cantilever contacts the cell
with adequate forces, the cantilever dwells on the cell for about 30 s to
allow the formation of firm binding between the cell and cantilever (II in
Fig. 1.6A), after which the cantilever retracts from the cell and usually a
single-cell probe is prepared (III in Fig. 1.6A). A notable point is that after
attaching the cell to the cantilever, the cell needs to recover for at least
10 min, during which the cell will form firm contacts with the cantilever
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1. Fundamentals and methods of atomic force microscopy for biophysics
FIGURE 1.6 Atomic force microscopy (AFM)-based single-cell force spectroscopy
(SCFS). (A) Attaching single living cell to the ConA-coated cantilever by AFM micromanipulations. (I) The ConA-coated cantilever is approaching a cell on the substrate under the
guidance of optical microscopy. (II) The cantilever contacts the cell and dwells on the cell
for 30 s to allow the binding of the cell to the cantilever. (III) The cantilever retracts from
the substrate and the cell is attached to the cantilever. (IV) Staining the cell probe with
CFDA SE confirms the viability of the cell. (B) Schematic of SCFS for measuring the adhesive interactions between cell and surface. The single-cell cantilever is lowered toward the
collagen substrate (I) until a preset force is reached (II). After a given contact time, the cantilever is retracted from the surface (III) until cell and substrate are completely separated
(IV). (C) A typical FD curve showing steps (I, II, III, IV) corresponding to those outlined in
(B). The maximum force required to separate the cell from the surface is referred to the
detachment force (F). Source: (A) Reprinted with permission from D. Dang, R. Xiang, B. Liu, X.
Liu, M. Li, Quantifying the adhesion forces of lymphoma cells by AFM single-cell force spectroscopy, Prog. Biochem. Biophys. 46(1) (2019) 8998. (B and C) are reprinted with permission from
J. Friedrichs, J. Helenius, D. J. Muller, Quantifying cellular adhesion to extracellular matrix components by single-cell force spectroscopy, Nat. Protoc. 5(7) (2010) 13531361. Copyright 2010
Nature America, Inc.
surface [125]. In order to examine the viability of the cell on the cantilever,
the live/dead reagent CFSE DA is used to stain the cell on the cantilever,
and we can see that cells exhibit bright fluorescence after the staining of
CFSE DA (IV in Fig. 1.6A), indicating that the cell on the cantilever is alive.
With the use of single-cell probe, the adhesive interactions between cell and
substrate can then be probed by controlling the probe to vertically perform
approach-retract cycle on the substrate, as shown in Fig. 1.6B. Incidentally,
Fig. 1.6B only shows an example of adhesive interactions between cell and
surface (collagen), and the surface can be replaced with a cell grown on a
substrate and in that case the adhesive interactions between two cells are
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1.3 Atomic force microscopy force spectroscopy techniques
27
measured. Firstly, the cell probe, which is originally far away from the surface, is controlled to vertically approach the surface. After the cell probe
contacts the surface, the probe compresses the surface until the preset force
is achieved (II in Fig. 1.6B) and the probe dwells on the surface for a period
of time (called the contact time). Subsequently, the cell probe withdraws
from the surface, during which the adhesion between the cell and surface
could cause the downward deflection of the cantilever (III in Fig. 1.6B).
When the pulling force is larger than the adhesion forces between the cell
and surface, the cellsurface adhesive bonds rupture and the cell probe
return to its original position (IV in Fig. 1.6B). By analyzing the force curves
recorded during the approach-retract cycle (Fig. 1.6C) [123,125], the detachment force of the cell (denoted by F in Fig. 1.6C) is obtained. Particularly,
studies have shown that two types of smaller unbinding events are often
contained in the obtained force curves which are frequently named rupture
(denoted by r in Fig. 1.6C) and tether (denoted by t in Fig. 1.6C) events,
respectively [126]. In rupture events, the receptor remains anchored in the
cell cortex and unbinds as the loading force increases, causing the shrinking
of the contact area and subsequently the detaching of the cell body from
the substrate. In tether events, receptor anchoring is lost and the membrane
tethers are pulled out of the cell, causing the staircase-like manner of the
force curve.
1.3.3 Single-molecule force spectroscopy
AFM can probe the specific interaction force of single receptorligand pair by the technique called single-molecule force spectroscopy (SMFS). For doing so, ligands are attached to the surface of the
AFM tip and then the functionalized tip is controlled to vertically perform approach-retract cycles on the cell surface. The ligands attached to
the surface of the AFM tip can specifically bind to the particular
receptors on the cell surface. As shown in Fig. 1.7A, the ligandconjugated tip, which is originally far away from the cell, gradually
approaches the cell surface (I in Fig. 1.7A). The tip contacts and compresses the cell surface until the loading force achieves the preset maximum value (II in Fig. 1.7A). Subsequently, the tip retracts from the cell
surface (III in Fig. 1.7A). If the receptorligand binding occurs during
the contact between the AFM tip and cell, the receptorligand pair is
stretched by the AFM tip (III in Fig. 1.7A) during the retract process.
When the pulling force exerted by the AFM cantilever is larger than the
bond strength of the receptorligand pair, the receptorligand pair
ruptures and then the AFM tip returns back to its original position (IV
in Fig. 1.7A). By analyzing the force curves (Fig. 1.7C) recorded during
the approach-retract cycle, the rupture force of the individual
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1. Fundamentals and methods of atomic force microscopy for biophysics
FIGURE 1.7 Atomic force microscopy (AFM)-based single-molecule force spectroscopy
(SMFS). (A) Schematic diagram of probing single receptors on cell surface by AFM-based
SMFS. (I) AFM tip carrying ligands begins approaching cell surface. (II) AFM tip contacts
the cell surface, allowing the binding of ligands and receptors. (III) AFM tip retracts from
cell surface, which stretches the receptorligand pair. (IV) Receptorligand ruptures
when the pulling force exerted by AFM cantilever is larger than the strength of receptorligand bond. (B) Schematic diagram of tip functionalization for SMFS. Not only various biomolecules (I), but also virus (II) can be attached to the AFM tip. (C) A typical force
curve recorded during AFM-based SMFS experiments. The denoted steps (I, II, III, IV) correspond to those outlined in (A). Source: (B) Reprinted with permission from D. J. Muller, Y. F.
Dufrene, Force nanoscopy of living cells, Curr. Biol. 21(6) (2011) R212R216. Copyright 2011
Elsevier Ltd. (C) is reprinted with permission from M. Li, X. Xiao, L. Liu, N. Xi, Y. Wang, Z.
Dong, et al., Nanoscale mapping and organization analysis of target proteins on cancer cells from
B-cell lymphoma patients, Exp. Cell Res. 319(18) (2013) 28122821. Copyright 2013 Elsevier Inc.
receptorligand pair is obtained. Fig. 1.7C shows a practical force curve
obtained during SMFS experiments [127]. The stretching of the receptorligand pair (III in Fig. 1.7C) yields an unbinding force peak in the
retract portion of the curve (denoted by the black arrow in Fig. 1.7C)
and the magnitude of this peak is equal to the rupture force of the
receptorligand pair. When the density of ligands linked to the AFM
tip is adjusted to an appropriate level that only one receptorligand
pair is formed between the tip-cell contact area, the unbinding peak
then corresponds to single receptorligand pair and thus the unbinding
force of single molecular pair is measured.
A critical point for AFM-based SMFS is linking biomolecules (which
can specifically bind to the target receptors on the cell surface) onto the
surface of AFM tips, and this process is commonly called tip functionalization (Fig. 1.7B) [128]. Originally, researchers attach biomolecules
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1.3 Atomic force microscopy force spectroscopy techniques
29
onto the surface with the use of short rigid linker [129132] (typically
avidinbiotin system), and the drawback of this method is that high
coverage of ligands increases the risk of probing multiple binding
events and increases steric hindrance, which can interfere with the binding process [55]. Besides, ligands linked to the AFM tip have weak conformational mobility. In order to overcome these defects, researchers have
used long, flexible and distensible linkers such as polyethylene glycol
(PEG) to attach ligands onto AFM tip [133]. For doing so, the PEG linker
molecules typically carry two different functional ends. One end of the
PEG linker molecule covalently reacts with the amine-functionalized tip
surface, and the other end covalently reacts with the ligands. The use of
heterobifunctional PEG crosslinker has several advantages. First, the binding strength of covalent bonds (12 nN) is about ten times stronger than
typical receptorligand bonds [134], which ensures that the receptorligand pair ruptures during the SMFS process. Second, the ligands at
the end of the PEG linker can freely orient in the solution to recognize the
receptors on the cell surface, which facilitates the receptorligand binding
interactions. Third, during the retract process, stretching the PEG linker will
often cause a nonlinear shape of force peak in the force curve (denoted by
the green arrow in Fig. 1.7C), which can be used to discriminate the specific
receptorligand rupture events and nonspecific rupture events. Hence, so
far PEG covalent coupling has been the predominant tip functionalization
method for SMFS. Notably, in practice, one end of the PEG linker is commonly NHS, and the other end of the PEG linker is diverse depending on
the types of ligands to be attached. In brief, amino-functionalization is
firstly performed to coat the AFM probe with a layer of NH2. The NH2
group is able to form covalent bonds with the NHS group of the PEG
linker, allowing attachment of the PEG linker to the AFM tip. The last step
is attaching ligands to the reactive groups at the other end of the PEG
linker, and various strategies (e.g., NHS-PEG-aldehyde, NSH-PEG-maleimide) have been presented to attach a wide range of ligands (e.g., protein,
antibody, virus) [135]. Besides, methods based on the affinity between tetravalent nickel and histidine have also been developed for the attachment of
His6-tagged ligands, which achieve tip functionalization in a controlled
orientation of the ligands.
There are several points which should be noted for practical SMFS
experiments. Before applying AFM force spectroscopy to probe the target receptors on the cell surface, the expression levels of the receptor on
the cell surface need to be confirmed, which can be performed by staining the target receptors with fluorescein and the subsequent recording
of the fluorescent images [136]. For AFM force spectroscopy experiments, due to the fact that membrane proteins are often heterogeneously distributed on the cell surface, force curves are commonly
recorded at different surface points of multiple cells (at least 10 cells) to
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1. Fundamentals and methods of atomic force microscopy for biophysics
obtain statistical results and the probability of finding specific molecular
unbinding events usually ranges from 10% to 30% [137]. Besides, blocking experiments are often required to demonstrate the specific receptorligand binding interactions, during which free ligands are added to
block the receptors on the cell surface and then the functionalized tip is
applied to record force curves on the cell surface. For the force curves
obtained on cells after blocking, there should be no, or few specific
unbinding force peaks. Since receptorligand interactions are closely
related to the cell states, one should carefully monitor cell morphology
and cell viability during SMFS experiments and only force curves
obtained from the same cell morphology/viability can be compared
with each other [55]. In addition, the rupture force of receptorligand
pair measured by AFM is dependent on the loading rate (retraction
velocity multiplied by the spring constant of the cantilever) of the AFM
cantilever, which is theoretically described by the BellEvans model
[138]:
F5
kB T
rxβ
ln
xβ
koff kB T
(1.8)
where F is the rupture force, r is the loading rate, koff is the kinetic dissociation rate at zero force, xβ is the distance to the transition state along the
projection of the applied force, kB is the Boltzmann’s constant, and T is the
temperature. The formula (1.8) indicates the linear relationship between
the measured receptorligand rupture force and the logarithm of the loading rate. Hence, in practice, rupture forces are measured at different
pulling velocities to investigate the dissociation dynamics of the molecular
interactions and at least 1000 force curves [55] are required to record one
pulling velocity.
AFM-based SMFS also allows the revealing of the unfolding dynamics
of single membrane proteins. Most proteins have to acquire an adequate
three-dimensional structure to perform biological functions. The folding of
proteins into their compact three-dimensional structures is one of the most
fundamental examples of biological self-assembly. Protein misfolding is
associated with many human diseases, including neurodegenerative diseases (e.g., Alzheimer’s disease, spongiform encephalopathies, Parkinson’s
disease), nonneuropathic systemic amyloidosis (e.g., amyloid A (AA) amyloidosis), and nonneuropathic localized amyloidosis (e.g., type II diabetes)
[139]. Hence, understanding the protein folding process significantly benefits understanding the underlying mechanisms guiding protein functions
and behaviors. Utilizing AFM-based SMFS to mechanically unfold single
proteins provides unique insights into the mechanics of proteins. For doing
this, AFM tip does not require tip functionalization. After immobilizing
membrane protein patches, either natural membranes containing highly
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1.4 High-speed atomic force microscopy
31
ordered proteins (e.g., purple membrane) or artificial membranes containing reconstituted proteins [140], onto the substrate, the AFM tip is moved
to above single membrane proteins based on high-resolution AFM imaging
of single membrane proteins [141]. AFM tip is then controlled to approach
and touch a single membrane protein with a contact force of B0.51 nN
for B1 s, which results in firm adsorption of the protein to the AFM tip in
about 15% of all cases [85]. Subsequently, the AFM tip retracts from the
membrane, which mechanically unfolds the membrane protein. Force
curves are recorded during the approach-retract cycle of the tip. Notably, if
the polypeptide adsorbed to the AFM tip is the C- or N-terminal end of the
protein, the force curves will exhibit a length corresponding to that of the
entirely stretched protein. If the protein attaches with a polypeptide loop or
slips off the tip before being completely unfolded, the force curves will be
shorter and thus difficult to interpret. Therefore, only force curves representing the entirely unfolded and stretched protein should be used for analysis [142]. The force curve with a fully membrane protein unfolding
process shows the sawtooth-like pattern of force peaks, each of which corresponds to the unfolding of a segment of membrane protein. The force curve
is fitted by the worm-like chain (WLC) model to analyze the unfolding
pathway of the protein [55,84]:
"
#
kB T 1
x 22
x
1
12
1
2
(1.9)
FðxÞ 5
lp 4
Lc
L0
4
where F(x) is the force, Lc is the contour length of the peptide, lp is the
persistence length of the peptide which describes the rigidity of the
polymer, x is the extension of peptide, kB is the Boltzmann’s constant,
and T is the temperature. Fitting each sawtooth-like peak with WLC
model gives the number of amino acids of the stretched segment and
thus the unfolding pathway of the protein is generated after fitting all
the peaks.
1.4 High-speed atomic force microscopy
The developments of high-speed AFM enable capturing the dynamics
of biomolecular activities at work with unprecedented temporal resolution. Life is dynamic and the functions of biological systems depend on
the dynamic processes that occur in biomolecules, organelles, and cells
[143]. Observing the real-time dynamics of single biomolecules at work
is considerably meaningful for uncovering the underpinnings of biological processes. AFM is the only technique which is able to visualize the
structure of single native biomolecules with nanometer spatial resolution under aqueous conditions. However, the topographical imaging
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1. Fundamentals and methods of atomic force microscopy for biophysics
speed of AFM has long been slow. It often takes minutes to acquire a
topographical image of biological specimens by conventional AFM,
which is much greater than the time scale at which dynamic processes
usually occur in biology [144]. Therefore, strong demand of AFM for
biomedical applications is the ability to rapidly acquire successive
high-resolution images of individual biomolecules in action. In 2001,
Ando et al. [145] developed a high-speed AFM for studying biomolecules based on tapping mode, which is able to capture a 100 3 100
pixel2 image within 80 Ms and the experimental results exhibit the
exciting capabilities of the high-speed AFM to capture the Brownian
motions of single myosin V molecules in solution. Since then, highspeed AFM techniques has been continuously advanced and now
high-speed AFM is coming of age [146] for biomedical applications.
High-speed AFM is able to not only watch single biomolecules in
action in real-time [147], but also can visualize the morphological
dynamics of single living cells [148], contributing much to molecular
and cell biology. High-speed AFM typically operates in tapping mode
[149], in which the cantilever is excited to vibrate near its resonance
frequency to intermittently contact the sample surface. The highest
possible imaging rate of tapping mode AFM is determined by the
bandwidth of feedback control to maintain the tapping amplitude constant during scanning as well as by scan parameters and the sample
itself [146]. The details of the basic principles of high-speed AFM are
beyond the scope of this book and readers are referred to the references [143,146,149] for more descriptions of the quantitative relationship between the feedback bandwidth and the various factors involved
in AFM and the scanning conditions. Briefly, in the high-speed AFM
system (Fig. 1.8A), various devices, including cantilevers (Fig. 1.8B),
electronic circuits, the sample-stage scanner (Fig. 1.8C), and the cantilever deflection detection system, are optimized for achieving highspeed performance [150,151]. For example, cantilevers are miniaturized to achieve high resonant frequencies and small spring constants,
while a new feedback control technique capable of maintaining weak
tip-sample interactions and active camping techniques to suppress the
scanner’s mechanical vibrations have been implemented. Notably,
Fig. 1.8C shows a narrow-area scanner for high-speed AFM.
Researchers have also developed a wide-area scanner for high-speed
AFM [152] which has a maximum XY scan range of 46 3 46 μm2 and is
able to capture the dynamic processes of single living bacterial and
eukaryotic cells. High-speed AFM has now become an important
method for observing the real-time dynamics of life processes and the
practical applications of utilizing high-speed AFM to address biological issues will be presented in the subsequent chapters.
Microscopy for Nanoscale Biophysics
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1.5 Topography and recognition imaging mode atomic force microcopy
33
FIGURE 1.8 High-speed atomic force microscopy (AFM). (A) Schematic diagram of the
configuration of the high-speed system. (B) SEM image of a small cantilever for highspeed AFM. The inset shows an electron beam deposited amorphous carbon tip grown on
the original tip. (C) Structure of a high-speed AFM scanner for narrow area imaging
( , 1 μm 3 4 μm). Source: (A) Reprinted with permission from T. Uchihashi, N. Kodera, T. Ando,
Guide to video recording of structure dynamics and dynamic processes of proteins by high-speed
atomic force microscopy, Nat. Protoc. 7(6) (2012) 11931206. Copyright 2012 Nature America,
Inc. (B and C) Reprinted with permission from T. Ando, High-speed AFM imaging, Curr. Opin.
Struct. Biol. 28 (2014) 6368. Copyright 2014 Elsevier Ltd.
1.5 Topography and recognition imaging mode atomic force
microcopy
The advent of simultaneous topography and recognition imaging
(TREC) mode AFM offers novel opportunities for detecting molecular
behaviors. Traditionally, in order to apply AFM force spectroscopy techniques to map the spatial distributions of particular receptors on single
cells, the functionalized probes are used to obtain arrays of force curves
at the small local areas on the cell surface [153]. For an array of force
curves, the unbinding force of each force curve is calculated from the
force peak in the retract curve (as denoted by the black arrow in
Fig. 1.7C). If there are no unbinding force peaks, the unbinding force is
set to zero. After normalizing the unbinding forces into gray colors
(0255), a force map is constructed by using imaging processing
software and the brightness of the pixel reflects the magnitude of
unbinding forces. This method is called force volume mode which is
time-consuming and inefficient. In 2004, Stroh et al. [154] developed a
new molecular recognition mode based on AFM, which is called TREC.
TREC is able to simultaneously obtain a topography image and a recognition image on the cell surface and the imaging time is comparable to
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1. Fundamentals and methods of atomic force microscopy for biophysics
conventional AFM imaging. TREC mode is based on tapping mode
AFM imaging. In TREC mode (Fig. 1.9A), the oscillating tip which carries ligands raster scans the cell surface. Both the maxima and minima
of the oscillation periods are recorded. During scanning, if the ligand
FIGURE 1.9 Topography and recognition imaging (TREC) mode atomic force microscopy (AFM). (A) Schematic diagram of the principle of detecting cell surface receptors by
TREC mode AFM. An oscillating AFM tip tethered with a ligand molecule scans across
the cell surface to elucidate the nanoscale organization of receptor molecules. The cantilever oscillation amplitude is split into lower and upper parts, resulting in simultaneously
acquired topography and recognition images. The topography image is generated from the
lower part and the corresponding recognition map is constructed from the upper part of
the oscillation amplitude. The recognition events originate from the PEG linker stretching
which results in a damping of the upper part of the oscillation. (B) Amplitude signals of
cantilever oscillations. The maxima signals of the cantilever oscillation amplitudes
(denoted by red arrows) keep constant when scanning with a bare tip (I). Scanning with a
functionalized tip results in significant changes in the maxima signals (denoted by blue
arrows) while the topographical information is also contained in the minima signals (II).
(C) Topography image (I) and corresponding recognition map (II) of thrombin protein
molecules deposited on mica. The circles indicate those protein molecules that were recognized, whereas the square indicates the protein that was not recognized. (D) Topography
image (I) and corresponding recognition map (II) of receptors on mica surface. In the recognition map, dark spots indicate the regions where the antibody on the tip is bound to
the target receptors on surface. The white arrows indicate the interactions with large
aggregates. Source: (A) Reprinted with permission from L.A. Chtcheglova, P. Hinterdorfer,
Simultaneous AFM topography and recognition imaging at the plasma membrane of mammalian
cells, Semin. Cell Dev. Biol. 73 (2018) 4556. Copyright 2017 Elsevier Ltd. (B) Reprinted with
permission from C. M. Stroh, A. Ebner, M. Geretschlager, G. Freudenthaler, F. Kienberger, A. S.
M. Kamruzzahan, et al., Simultaneous topography and recognition imaging using force microscopy, Biophys. J. 87(3) (2004) 19811990. Copyright 2004 The Biophysical Society. (C) Reprinted
with permission from S. Senapati, S. Manna, S. Lindsay, P. Zhang, Application of catalyst-free
click reactions in attaching affinity molecules to tips of atomic force microscopy for detection of protein biomarkers, Langmuir 29(47) (2013) 1462214630. Copyright 2013 American Chemical
Society. (D) Reprinted with permission from P. Kaur, Q. Fu, A. Fuhrmann, R. Ros, L.O. Kutner,
L.A. Schneeweis, et al., Antibody-unfolding and metastable-state binding in force spectroscopy and
recognition imaging, Biophys. J. 100(1) (2011) 243250. Copyright 2011 the Biophysical Society.
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References
35
molecules on the tip do not bind to the receptors on the cell surface, the
tip vibrates like imaging with a nonfunctionalized tip. When the ligand
molecules bind to the receptors on the cell surface, the subsequent
unbinding events of receptorligand pairs will result in changes in the
upper part of the vibration amplitude signal (maxima) but does not
influence the lower part of the vibration amplitude signal (minima)
(Fig. 1.9B) [155]. When using a bare tip (nonfunctionalized tip) to scan
the surface of specimen, the maxima signals of cantilever oscillations
keep constant while the topographical information is contained in the
minima of the cantilever oscillations (I in Fig. 1.9B). When using a functionalized tip to perform scanning, not only the topographical information is contained in the minima of the cantilever oscillations, but also the
specific molecular unbinding events are contained in the maxima of cantilever oscillations (II in Fig. 1.9B). By using a special electronic circuit
called TREC box, the recognition image is generated simultaneously with
the topographical image [156], therefore allowing correlating receptor distribution with cell surface structures. For TREC mode AFM, the cantilever
oscillation amplitude should be slightly smaller than the extended PEG
linker length, so that the ligand remains bound while passing a binding site
and the reduction of the maxima of cantilever oscillations is of sufficient
significance compared to the thermal noise. With TREC mode AFM, not
only the purified biomolecules deposited on the substrate can be recognized
[157159] (Fig. 1.9C and D), but also the proteins reconstituted in the artificial lipid bilayer membranes [160] and even the receptors on the cell surface
[136,156,161,162] can be recognized, which provide novel insights into the
molecular interactions and practical applications of TREC mode AFM will
be presented in the subsequent chapters. Notably, TREC does not record
force curves during imaging, and thus quantitative force information about
molecular binding events is missing.
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