NANOTECHNOLOGY
Spatially resolved force spectroscopy of
biological surfaces using the atomic force
microscope
William F. Heinz and Jan H. Hoh
The spatial distribution of intermolecular forces governs macromolecular interactions. The atomic force microscope, a
relatively new tool for investigating interaction forces between nanometer-scale objects, can be used to produce spatially
resolved maps of the surface or material properties of a sample; these include charge density, adhesion and stiffness,
as well as the force required to break specific ligand–receptor bonds. Maps such as these will provide fundamental
insights into biological structure and will become an important tool for characterizing technologically important biological
systems.
ong- and short-range interactions between macromolecules and macromolecular assemblies are central to the dynamic behavior of biological systems.
Many interactions have been examined in great detail
using thermodynamic and kinetic approaches. However, there is little direct information about how the
interaction energy between two structures is distributed
in space because it is difficult to measure explicitly the
interaction energy as a function of separation distance.
The most direct way to obtain this kind of data is to
measure the force (the derivative of energy with respect
to distance) between two structures.
A wide range of instruments and approaches has been
developed for measuring forces between small structures, including mechanical springs made from glass
fibers1,2, optical tweezers3, vesicle-based force transducers4 and the surface-forces apparatus (SFA)5. Other
approaches to investigating intermolecular forces
include optical or diffraction methods to monitor the
displacement of structures under a load resulting from
hydrodynamic6 or osmotic7 forces. Using optical methods, it is also possible to monitor the thermally driven
motion of particles in solution and from that motion
to infer interactions that particles have with the media
and nearby structures8,9.
The atomic force microscope (AFM)10 is a relatively
new tool for measuring intermolecular forces between
nanometer-scale objects. The AFM has many similarities to several of the force-sensing instruments. In one
view, the AFM is much like a miniature SFA in which
a mechanical spring is used to measure force as a function of distance between two structures; however,
because the AFM uses a probe with a radius of curvature typically on the order of 10–100 nm (compared
with the ~1 cm effective radius of curvature of the
SFA), the AFM can measure local interactions with a
high spatial resolution. Thus, it can be applied to highly
L
W. F. Heinz and J. H. Hoh ([email protected]) are at the
Department of Physiology, Johns Hopkins University School of
Medicine, Baltimore, MD 21205, USA.
TIBTECH APRIL 1999 (VOL 17)
heterogeneous surfaces, albeit at the expense of sensitivity. In another view, the AFM is a sophisticated
extension of the glass-fiber force-sensing technology.
This is, in part, borne out by the fact that glass fibers
have now been modified for use with commercial
AFMs11.
One reason the AFM is considered to be a separate
technology is because it was first developed as an imaging tool, something neither the SFA or glass fibers had
been used for at the time. The relative ease of use and
the commercial availability of the AFM make it one of
the most widely used instruments for measuring intermolecular forces. In this article, we review the use of
the AFM as a tool for force spectroscopy (measuring
forces as a function of distance) in biomolecular
systems. We will cover only DC-type force measurements; AC-based measurements, including thermalnoise-based approaches, are not included.
Basic elements of the AFM
A useful way to consider the AFM is the ‘small ball
on a weak spring’ model (Fig. 1a). In this model, a weak
mechanical spring is used to measure the forces
between a probe (the ball) and a sample whose position
may translate relative to the probe. In practice, the
spring is composed of a cantilever and the ball is a tip
at the free end of the cantilever. The tip and sample are
translated relative to each other using piezoelectric
ceramics, and movements of the spring are measured
using sensitive optical methods. The detailed implementation of AFM has been reviewed12 and a common
implementation is shown in Fig. 1b for reference.
Approximating the AFM tip as a sphere is reasonable
for many interaction forces. For some forces, analytical
expressions describing the tip as a cone or a pyramid
exist. In other cases (noted below), the specific geometry and area of the tip are key determinants of the
interaction force. The surface chemistry of the tip is
also critical to the interaction with the sample and there
is a great deal of ongoing research aimed at modifying
and characterizing tip chemistry13.
0167-7799/99/$ – see front matter © 1999 Elsevier Science. All rights reserved. PII: S0167-7799(99)01304-9
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NANOTECHNOLOGY
b
a
Diode
laser
Optical
detector
Ball
Cantilever
and tip
Computer and
feedback control
Sample
Sample
Piezoelectric ceramic
tube scanner
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Spring
Figure 1
(a) ‘Small ball on weak spring’ model of an atomic force microscope (AFM). This model highlights the central features of the AFM as a mechanical sensor for probing interaction forces. (b) Schematic diagram of a common implementation of an AFM. The sample is mounted on
a stage that can move in the x, y and z directions, typically using a piezoelectric actuator. The deflection of the cantilever in response to
interactions at the tip is detected by an optical lever, in which the movements of a laser reflected off the cantilever are detected by a splitsegment photodiode. The deflection data are passed to a computer controller that provides appropriate feedback to the stage and collects
data. The essential elements of an AFM are: a probe (tip) attached to a spring (cantilever); a means of measuring deflections of the spring
(optical lever and split-segment photodiode); a sample; and a means for moving the sample and probe relative to each other (piezoelectric
tubes). Deflections of the spring are then used to measure interactions of the probe tip with the sample.
Force curves
Force is measured in an AFM by collecting a force
curve, which is a plot of cantilever deflection, dc, as a
function of sample position along the z-axis (i.e.
towards or away from the probe tip; the z-piezo position) (Fig. 2a). It assumes a simple relationship (i.e.
Hooke’s Law) between the force, F, and the cantilever
deflection (Eqn 1):
F 5 2k dc
(1)
where k is the spring constant of the cantilever.
The interpretation of AFM force curves relies almost
entirely on established force laws, particularly those
determined using the SFA14,15. These force laws
describe force as a function of the probe–sample separation distance (D) rather than as a function of the
z-piezo position. Thus, to be useful, the force curves
must be transformed into descriptions of force as a
function of distance, F(D).
However, current AFMs do not have an independent
measure of D. Instead, the transformation to D is
achieved by subtracting the cantilever deflection from
the z-piezo movement (Fig. 2b)16 . For a very hard surface, zero separation is defined as the region in the force
curve in which the cantilever deflection is coupled 1:1
with the sample movement; this appears in the force
curve as a straight line of unit slope. A corrected curve
is called a force–distance curve. Notice that determining D by this approach requires that the tip make contact with the sample. In practice, there are two factors
(long-range forces and sample elasticity) that can make
determining the point of contact very difficult.
A complete force curve includes the forces measured
as the probe approaches the sample and is retracted to
its starting position. Because the forces on the tip can
vary as it is moved toward or away from the sample, for
the purposes of presentation, we will divide the force
144
curve into approach and retraction portions and
consider them separately.
Approach
For a simple approach between two hard surfaces in
the absence of any long-range interactions, van der
Waals forces will dominate. The attractive van der Waals
force varies with separation distance as D22 for a (large)
sphere approaching a flat surface. As the tip dimensions
decrease to those of a single atom, the D22 dependence
becomes a D24 dependence14. This force appears in the
approaching force curve as small downward deflection
just prior to contact (Fig. 3a). The downward deflection is often very steep and is sometimes associated with
a jump-to-contact event. The jump results when the
force gradient between the tip and the sample exceeds
the stiffness of the cantilever, causing instability in the
position of the cantilever17. The force also depends on
the tip, sample and medium composition.
Two long-range forces that give rise to force curves
with a similar morphology (a smooth, exponentially
increasing repulsive force) are electrostatic (for like
charges) and polymer-brush forces. Quantitative electrostatic measurements with the AFM are based on
forces produced from overlapping electrical double
layers, and the associated ion gradients, as a charged
probe is brought near a charged sample surface
(Fig. 3b). SFA work has shown that the Gouy–
Chapman theory [the electrostatic part of Derjaguin,
Landau, Verwey and Overbeek (DLVO) theory] can
relate force measurements to surface charge and potential5,14,18. Ducker and colleagues showed that this also
holds for AFM measurements19. Subsequently, a number of groups have measured surface-charge density and
Debye length as a function of pH, electrolyte type and
concentration with the AFM, and found agreement
TIBTECH APRIL 1999 (VOL 17)
NANOTECHNOLOGY
Cantilever deflection/force
a
Force curve
iii
ii
i
iv
Piezo/sample position
Force–distance curve
iii
ii
i
iv
Tip–sample separation distance
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Cantilever deflection/force
b
Figure 2
Components of a force curve. (a) Uncorrected force curve. (b)
Corrected force curve. (a,b) As the stage extends and retracts, the
tip–sample separation distance decreases and then increases, and
the tip–sample interaction force changes accordingly. A complete
force curve contains both the approaching (solid) and retracting
(dashed) portions. There are five regions of interest in a typical force
curve. At the beginning of the curve (i), the tip is far from the sample, and there is no interaction and no cantilever deflection (zerodeflection line). As the stage extends and brings the sample closer
to the tip, long- and short-range tip–sample interactions cause the
cantilever to deflect (ii); here, a long-range repulsive interaction is
shown. When the tip contacts the surface, the stage movement and
cantilever deflection become coupled, which appears in the curve
as a straight line (iii); this is sometimes called the contact line. At
maximal deflection, the stage stops advancing and begins to retract.
The retracting curve can display hysteresis (iv) owing to a variety of
tip–sample interactions, the most common of which is an adhesive
force before the sample pulls away from the tip. The tip may then
experience long-range interactions before the tip–sample separation
distance is large enough for the cantilever to return to zero
deflection.
with standard DLVO theory for measurements over
hard surfaces17,20–22.
Polymers grafted onto a surface can, by virtue of their
thermally driven (Brownian) motion, exert a repulsive
force on a particle moving through their space23. A
polymer attached by one end to a surface will diffuse
thermally within a volume defined primarily by its
monomer size, the number of monomers, the temperature and the strength of the interaction between
monomers in a given solvent. A particle attempting to
TIBTECH APRIL 1999 (VOL 17)
move through this volume will experience a repulsive
force arising from the reduction the polymer’s entropy.
Thus, a grafted polymer acts as an entropic spring,
which can be examined with an AFM24,25. For a
densely grafted polymer in an appropriate solvent, the
force on a spherical probe can be described by the
Alexander deGennes’ theory (Fig. 3c).
The material properties of samples can be investigated with AFM force curves by relating the applied
force to the depth of indentation as the tip is pushed
against the sample. Although this is not an interaction
force per se, we include it because it is a widely used
application of AFM force spectroscopy and because
sample elasticity is often convolved with real interaction forces. AFM force curves have been used to examine the viscoelastic properties of a wide range of biological structures (for a recent review, see Ref. 26),
including cartilage27, lysozyme molecules28, gelatin
gels29, glial cells30, epithelial cells31,32 and mast cells33.
Temporal changes in cellular mechanics have also been
monitored34,35, which involves the technically challenging problem of maintaining the tip at a single point
for long periods of time. One of the simplest and most
widely used models for mechanical deformation that
has been applied to AFM-force-curve data is the Hertz
model, which gives the force on a spherical probe as a
function of the elastic properties of the material, the
radius of the probe and the indentation depth36
(Fig. 3d). However, when investigating viscoelastic
samples, careful consideration must be given to the
time-dependent viscous contributions, which strongly
affect the rate of approach.
Retraction
The retracting portion of the force curve sometimes
follows the approach curve; however, there is often
hysteresis. The most common type of hysteresis is due
to some sort of adhesion, which appears in the force
curve as a deflection below the zero-deflection line.
The source of the adhesion can vary depending on the
sample. In the ideal case of a sphere interacting with a
flat surface, the adhesion force can be related to the
radius of the sphere and the surface energies (Fig. 3e)
of the two surfaces14.
Under ambient conditions, the main source of adhesion is the formation of a capillary bridge between the
tip and the sample (Fig. 3f). In air, most samples have
several nanometers of water adsorbed to the surface;
this water layer wicks up the tip and forms a ‘bridge’
between the tip and the sample. Pulling the tip out of
that bridge requires a large force to overcome the surface tension37. In fluid, the adhesive force depends on
the interfacial energies between the tip and sample surfaces, and the solution14; varying the solution can thus
change the force of adhesion38.
A different form of ‘adhesion’ occurs when a polymer is captured between the AFM tip and the substrate.
In this case, there is a very distinctive ‘adhesive’ force
as the tip is pulled away. Typically, these curves initially
retrace the approach curve near the surface but, away
from the surface, exhibit a smooth negative deflection
as the polymer is stretched until it breaks or detaches
from the tip or the substrate, and the cantilever returns
to the zero-deflection line (Fig. 3g). If multiple
polymer molecules attach to the tip and substrate, a
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NANOTECHNOLOGY
Approach
Retraction
e Adhesion
a van der Waals
F(D) =
AR
F = – 3πR γ
12D 2
b Electrostatic
f Capillary force
F(D ) =
4πR λσRσS
ε
e–D/λ
c Brush
F = 4πR γLcosθ
g Polymer extension
F(D ) ≈
50LkT
s3
F(x ) =
e–2πD/L
x 
L* 

a
Na 
kT
0.2 ø D/2L ø 0.9
d Elastic
h Binding
F(δ) =
4E
R
3(1–ν2)
F=
δ3/2
U – kT ln(τ/τ0)
Λ
A
a
D
E
k
L
L*
N
R
s
Hamaker constant
Monomer length
Probe – sample separation distance
Elastic modulus
Boltzmann’s constant
Brush thickness in a good solvent
Inverse Langevin function
Number of units in polymer
Radius of probe sphere
Mean distance between polymers
T
U
x
Absolute temperature
Bond energy
Elongation of polymer
Λ
λ
θ
δ
ε
γ
Indentation depth
Dielectric of the medium
Surface energy between tip
and sample
Surface energy of the liquid
Poisson ratio
σR
σS
τ
γL
ν
τ0
Characteristic length of bond
Debye length of the medium
Angle related to the geometry of
the tip–sample contact
Surface-charge density of sphere
Surface-charge density of sample
Period over which the bond will
rupture
Reciprocal of the natural bond
frequency
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Definitions
Figure 3
Examples of atomic force microscope (AFM) force curves and the force laws used to interpret them. Notice that the curves are
shown as force versus sample-position curves, which is the most common way they are displayed in the literature; however, the force laws
are all functions of the separation distance, D. (a–d) Approach curves. (e–h) Retraction curves. (a) An ideal, attractive, van der Waals force
in the absence of other forces14. (b) Repulsive electrostatic double-layer force in solution16,17. (c) Polymer-brushing forces that result from
the thermally driven motion of polymers grafted onto a solid surface in solution14. (d) Indentation curve on an elastic sample; notice that, in
this case, the true contact is near the point at which the cantilever begins to deflect29. (e) Adhesion between a sphere and a plane in the
absence of contaminating adsorbates (typically in a vacuum)14. (f) Capillary adhesion (very common under ambient conditions, under which
many surfaces have thin layers of water) results from the formation of a water bridge between the tip and sample14. (g) Polymer-extension
force curves show a characteristic negative deflection far from the surface and a jump back to zero deflection as the polymer breaks or
detaches from one of the surfaces40,50. (h) The unbinding of specific receptor–ligand pairs sometimes produces a stepwise return to zero
deflection from the point of maximal adhesion. This is thought to be due to the sequential unbinding of multiple receptor–ligand pairs46–49.
In some experiments, the binding partners are attached at the ends of polymers and the unbinding curve is combined with the polymerextension curve45.
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Special cases and artefacts in force–distance curves
In addition to the force curves described above, many
other types of event can be observed, although it is
beyond the scope of this review to cover all of them.
One notable special case is the ‘punch through’ that
occurs when a force curve is collected on a surfactantcovered surface51. These curves have a short, smooth
repulsive component, which is followed by a clear
4–5 nm downward deflection (depending on the type
of surfactant) as the tip penetrates with surfactant.
There is also an interesting prediction for the ‘escape’
of a polymer from beneath an AFM tip during the
approach part of a force curve52, where there is
expected to be a smooth repulsive force as the polymer
is compressed and a sharp downward deflection as the
polymer escapes.
There are several types of artefact in AFM force
curves. An offset between the lines of the non-contact
(zero-deflection) parts of the curves usually results from
viscous drag on the cantilever and can be eliminated by
reducing the scan rate or the viscosity of the solution53.
Periodic oscillations in the non-contact portion of the
curve are common and typically arise from optical
interference between reflections of the diode laser from
the cantilever and the substrate54. It is also common to
see an offset between the lines that define contact; this
can have two causes.
TIBTECH APRIL 1999 (VOL 17)
a
Force-volume imaging
z
y
x
b
Isoforce imaging
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saw-tooth pattern can be observed as individual
polymers detach.
There are several models, such as the worm-like39 or
freely-jointed40 chain models, that can be used to
describe the force–distance relationships for extending
polymers. Extension measurements of high molecular
weight dextrans show force–distance relationships in
agreement with the freely-jointed-chain model40.
Similar results have been described for proteoglycans41.
Examining the interaction forces between specific
biological receptor–ligand systems is an application that
has generated enormous interest42. At present, only the
unbinding force (adhesion) of a receptor–ligand pair
has been examined. Here, a ligand-functionalized AFM
tip is brought into contact with the receptor-coated
surface (or vice versa); the receptor and ligand bind,
and the tip is retracted. In the simplest case, the magnitude of the adhesion ‘spike’ is a direct measure of the
binding force. For a small number of discrete binding
events per force curve, statistical analysis of many adhesion measurements can be used to estimate single bond
strengths43,44. This measure of bond strength is related
to the depth of the potential well holding the two molecules together. In some cases, the resultant retraction
force curves have a jagged appearance (Fig. 3h), which
is thought to correspond to multiple pairs unbinding
at different times. Controls include competition with
excess free ligand/receptor to occupy all available sites
and the use of nonspecific ligands.
Force-curve studies have focused on several antibody–antigen systems45–47, avidin–biotin and their
analogues48,49, and complementary DNA strands50.
Because the effects of loading force, loading rate and
tip geometry contribute to the unbinding force
measured, these types of experiments are very difficult
to perform and interpret, and the analytical framework
for the data is still being developed.
Figure 4
Approaches to producing spatially resolved force measurements.
(a) Force-volume imaging is based on collecting arrays of force
curves. Individual curves are transformed into force–distance curves
and all the curves are assembled into a three-dimensional force volume. (b) Isoforce imaging is based on a surface of equal force collected over (or below) the sample surface. By collecting a stack of
such isoforce surfaces at different forces, it is in principle possible
to reconstruct a force volume. However, this is not possible in
practice with current instruments.
In the first case, the contact lines are separated but converge to the point at which the scanning reverses direction and starts the retract part of the curve. This form of
contact-line hysteresis results from nonlinearities in the
piezoelectric ceramics used to move the sample55. In the
second and more-common case, the contact lines are
parallel and exhibit a distinct ‘jump’ at the turnaround
point. This type of behavior results from friction on the
tip as it slides across a surface and the associated anomalous bending of the cantilever53. Offsets in contact lines
can be a serious problem because they make it difficult
to determine true separation distances.
The anomalous bending of the cantilever caused by
frictional effects is a special case of the general endslope
problem, which results from the optical detection
method used for measuring cantilever deflections.
Because the deflection of the cantilever is inferred from
the change of slope at one point on the cantilever,
anomalous bending of the cantilever (i.e. bending in a
way other than the way the cantilever bends during calibration) can give rise to erroneous measurements56,57.
This is a serious limitation of most current AFMs for
quantitative force measurements.
Force-curve feedback
Although not yet widely applied, feedback in AFM
force measurements can be extremely useful. The set
point for force-curve feedback is sometimes referred to
as a trigger. Two simple types of trigger are an absolute
trigger, in which the tip and sample are brought
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Figure 5
Examples of surface maps produced by spatially resolved force
spectroscopy. (a–d) Electrostatic maps of phospholipid bilayers.
(Reproduced with permission from Ref. 67.) (a) Topographic image
of a dipalmitoylphosphatidylcholine (DPPC) bilayer on a mica surface.
Light regions in the image are the DPPC bilayer and dark regions
are the mica substrate. (b) The corresponding electrostatic map produced by D–D mapping; the mica is highly charged relative to the
DPPC. (c) Topographic image of a dipalmitoylphosphatidylserine
(DPPS) bilayer. The mica surface is almost entirely covered (small
defects can be seen) and the DPPS patch in the image sits on top
of a DPPS bilayer. (d) The electrostatic map shows no differences
in charge, as would be expected. (e–h) Adhesion maps of a patterned streptavidin surface. (Reproduced with permission from
Ref. 62.) (e) Topographic image of the patterned surface; streptavidin is bound on the lines between the squares. (f) An adhesion
map using a biotinylated tip shows contrast on the lines. (g) Topographic image in the presence of soluble biotin. (h) An adhesion map
using a biotinylated tip in the presence of competing biotin shows
no contrast. (i,j) Elasticity map. (i) Topographic image of mitotic
epithelial cells. (j) The corresponding elasticity map produced by
force integration to equal limits (FIEL) mapping shows distinct differences in the hardness of the centers (tall parts) of two of the cells.
The FIEL map was produced as described in Ref. 74. Scale bars:
(a,b) 1 mm, (c,d) 500 nm, (e–j) 10 mm.
of force through which a probe moves. There are two
basic approaches to examining the spatial distribution
of forces within that volume using an AFM. The first
is to collect an array of force curves over the surface
and assemble these into a ‘force volume’ (FV) (Fig. 4a).
The second is to reconstruct the same force volume by
collecting a series of isoforce images, at increasing or
decreasing forces, across the x–y plane and assembling
these (Fig. 4b). Because, as described below, the latter
approach is currently not practical except in very limited ways, we use the term ‘force-volume imaging’ to
refer to arrays of force curves.
together until a predetermined cantilever deflection is
reached and the tip is retracted, and a relative trigger,
in which a deflection relative to the undeflected cantilever (beginning of the curve) is used as the turnaround
point. The latter is particularly useful, because it compensates for cantilever drift during the course of an
experiment, allows the examination of a specific range
of forces and minimizes possible damage to the sample
and contamination of the tip.
Spatially resolved force measurements
For a heterogeneous biological sample, the space
above the sample surface can be thought of as a volume
148
Force-volume imaging
A force-volume data set (FVDS) contains an array of
force curves and a so-called height image. Each force
curve is collected as described above, except that the
sample is also translated in the x–y plane. The forcevolume height image (FVH) is an array of z-piezo positions at the turnaround points (points of maximal
deflection) of the force curves. Typically, the force
curves making up a FV are collected using a relative
deflection trigger, and so the FVH is a surface of equal
force, not necessarily a height image in the sense of a
topograph. Together, the FVH and the FV provide a
three-dimensional, laterally resolved description of the
forces over and within a sample. For a sufficiently dense
collection of force curves, the lateral resolution
of force-volume imaging is related to the distance
dependence of the interaction. Thus, the lateral resolution varies within the volume and is not easily
defined.
The size of most FVs is limited by the data-acquisition
times. Because the acquisition time for a single force
curve is typically between 0.1 and 10 sec, the time to
acquire a force volume of, say, 64 3 64 curves is on the
order of 10 min to 10 h. There is no particular limit to
data collection in the z direction, although most
commercial instruments have data-acquisition rates of
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,100 kHz. A FVDS contains a great deal of information about the sample and this information can be
extracted and displayed in multiple ways. Distributions
of forces at different z positions, isoforce surfaces and
maps of the surface and material properties of the sample can all be constructed from the information in the
FVDS. Analytical methods include fitting individual
force curves to appropriate force laws and mapping the
differences between isoforce surfaces, force curves or
properties derived from isoforce surfaces and force
curves.
Isoforce imaging
Constant-force imaging is the main method for
determining sample topography by AFM. For this
application, the tip is typically in contact with the sample and the feedback loop is set to maintain a constant
cantilever deflection. However, in the presence of longrange forces, it is also possible to produce isoforce
surfaces in a non-contact regime58,59. As the sample
moves beneath the tip and forces of varying magnitude
interact with the tip, the feedback loop repositions the
stage so that the cantilever deflection remains constant.
The isoforce surface is the surface defined by the stage’s
positions during the scan. By collecting a set of isoforce
surfaces at different forces, it is in principle possible to
describe the full force volume above the sample. However, in practice, this is essentially impossible with current technology because of cantilever drift. Because
current AFM cantilevers are extremely sensitive to
temperature changes, the cantilever bends slightly with
time60 and any drift of the cantilever would make it
impossible to assemble the volume. Drift is not a problem when collecting arrays of force curves, so long as
a relative trigger is used.
Adhesion maps
Adhesion maps are typically produced by taking the
most negative force detected during the retraction
curve as the value for adhesion and plotting that value
against the x–y position of each curve. Several types of
spatially resolved adhesion map have been produced.
For example, Hlady and colleagues have examined the
spatial distribution of adhesion in grafted-polymer systems61. In a more biologically relevant system, the
distribution of streptavidin on a patterned surface was
visualized using a biotinylated AFM tip62 (Fig. 5). Similar experiments have used antibodies or ligands to map
the distribution of binding partners over purified components63. There has been considerable interest in using
adhesion mapping to produce spatially resolved maps
of the distribution of specific proteins on the
surfaces of living cells and some reports of these types
of experiments have appeared64. This is an extremely
challenging problem that will require a great deal
of work before its limitations and utility are fully
understood.
Electrostatic maps
The surface-charge density of bacteriorhodopsin
(BR) membranes was measured by Butt65 by comparing force curves collected over a BR membrane with
curves from the adjacent alumina substrate (which also
acted as a charge-density standard). Fitting the force
curves to the electrostatic part of DLVO theory and
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using the known surface-charge density of alumina
enabled him to extract charge information about the
BR membrane. Rotsch and Radmacher expanded on
this work by collecting a FVDS over BR adsorbed to
mica and constructing maps of the surface-charge
density66.
As noted above, fitting the force curves to DLVO
theory requires that the absolute separation between tip
and sample be known. However, it is sometimes desirable to minimize or prevent contact between the tip
and sample in order not to damage the sample or contaminate the tip. To address this problem, an approach
called D–D mapping was recently described for producing relative charge-density maps without the need
for an absolute measurement of D (and thus not requiring tip–sample contact)67. In this approach, isoforce
surfaces are collected, using FV imaging, at two different salt concentrations. The difference between these
isoforce surfaces is independent of topography and can
be quantitatively related to differences in local charge
density (or surface potential). Using this technique,
relative charge-density maps were produced of lipid
bilayers and BR membranes on mica (Fig. 5).
Polymer-brush maps
Recently, Brown and Hoh used AFM force volumes
to investigate neurofilaments and found that proteinacous projections (side arms) from the center of the
filament acted as grafted polymers68. These side arms
give rise to a long-range (.50 nm) repulsive force that
is absent on the mica substrate or on neurofilaments
that lack the side arms. Isoforce difference maps were
also used to show qualitatively the distribution of the
long-range forces.
Elasticity maps
Maps of cellular mechanical properties have been
produced for a range of systems. Radmacher et al.69
used the Hertz model to analyse FV images of platelets
and to construct one of the first AFM-based maps of
cellular mechanical properties. A similar approach was
applied to examine the contribution of the actin
cytoskeleton to the local mechanical properties of cardiac myocytes70 and macrophages71 using pharmacological agents such as cytochalasin B. The lack of
vinculin was shown in a murine carcinoma cell line to
reduce stiffness by approximately 20%72. Laney et al.73
applied the FV technique to map the elastic properties
of cholinergic synaptic vesicles as a function of buffer
composition.
One problem with fitting force curves to the Hertz
model is that the tip–sample contact point must be
determined, and this is extremely difficult for soft samples. The realization that the work done by the cantilever (area under the force–distance curve) can be
related to the local mechanical properties has provided
one way to circumvent this problem74 (Fig. 5). However, this approach is still subject to the limitations of
the Hertz model and questions of its applicability to
highly anisotropic cellular systems remain. There are a
number of more-sophisticated analytical frameworks
that can be applied, but it is not yet clear which of the
different approaches will prove to be useful. One view
is that truly quantitative measures of quantities such as
the Young’s modulus are not meaningful for living cells
149
NANOTECHNOLOGY
and what is really of interest are the spatial and temporal changes in mechanical properties. In that context,
the Hertz model may well be sufficient.
Future prospects
As AFM-based force spectroscopy continues to
develop, it will become increasingly sophisticated and
widely used. An obviously useful near-term application
is mapping the distribution of specific molecules on
various surfaces. More fundamentally, the current view
of biological structures as being delimited by their van
der Waals surface will be expanded to include forces
that surround the structures, a representation one might
call an interaction surface. These interaction surfaces
will provide important insight into macromolecular
assembly and the use of biological structures as construction elements in novel devices.
Acknowledgments
The authors’ research was supported by the Whitaker
Foundation for Biomedical Engineering, the Muscular Dystrophy Association and the Council for Tobacco
Research.
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