Hawkes P.W., Spence J.C.H. (Eds.) Science of Microscopy. V.1 and 2

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1030 M. Amrein

In the following section, AFM and its elements are described. The

basics for preparing macromolecular and cellular samples are then

described. Finally, a few select examples highlight AFM experiments,

in which a combination of imaging with sample manipulation has been

used to understand macromolecular or cellular function. A compre-

hensive review all AFM applications in the life sciences is beyond the

scope of this chapter.

2 Instrumentation and Imaging

2.1 Introduction

In AFM, the topology of the sample is traced by a sharp stylus that is

scanned line by line over the sample. For most setups, the stylus is

sitting at the free end of a cantilever spring. Every elevation on the

sample causes the stylus to move up and bend the cantilever upward

and every depression makes the lever move down. Stylus and cantile-

ver are usually microfabricated from silicon or silicon nitrite. The can-

tilever is typically a fraction of a millimeter long and a few micrometers

thick. The softer the specimen, the softer the cantilever spring should

be for it to trace the sample surface rather than deform it. The shape of

the stylus is crucial too. It may be tetrahedral or extended, with a high

aspect ratio, depending on need. The radius of curvature at the apex

of the stylus may be as small as 2 nm (the apex of the stylus is also

referred to as the tip) (Figure 16–5).

Accurate measurement of the deﬂ ection of the cantilever is the basis

for accurate measurement of the sample topology. It also allows proper

control of the loading force of the stylus onto the sample. It turns out

that this latter aspect is particularly important in life science applica-

tions of AFM (see below). The ﬁ rst AFMs used an STM behind the

cantilever to measure the deﬂ ection. Deﬂ ection has also been mea-

sured by the change in electrical capacitance between the cantilever

and a reference electrode, or by means of a piezoresistor integrated

with the cantilever (Tortonese et al., 1993). Most AFMs now use an

Figure 16–5. The elements of

an AFM.

Chapter 16 Atomic Force Microscopy in the Life Sciences 1031

optical pointer to measure cantilever deﬂ ection. This detection system

is fully adequate as it poses no limitation to AFM resolution.

In the optical pointer detection, a laser beam is focused onto the back

of the free end of the cantilever (Figure 16–5). The laser beam is then

reﬂ ected off the cantilever onto a four-segment photodiode. Prior to

imaging, the four-segmented laser diode is moved until all four seg-

ments are equally illuminated. For imaging, the stylus is then loaded

onto the sample. This causes the free end of the cantilever to bend

upward and the laser beam now illuminates the two upper segments

more strongly. The signals from the two upper segments of the diode

are compared to the two lower segments [(A + B) − (C + D)] to derive

the amount of deﬂ ection of the lever in the z direction. The load is

preset by the user, depending on the application and is related to the

deﬂ ection of the cantilever:

F = c ⋅ ∆S

∆S is the deﬂ ection in the z direction and c is the spring constant of

the cantilever. The force is typically selected within the range of less

than 100 pN to a few nanonewtons, depending on the application.

In operation, the cantilever is deﬂ ected from the preset value by the

sample topology and the reﬂ ected laser beam is moved up or down.

The original deﬂ ection is then restored via a feedback loop by a motion

of the scanner perpendicular to the sample plane (referred to as the z

direction). The position of the scanner with respect to the tip is recorded

and used as the AFM topographical image.

Torsion of the cantilever may also occur during scanning, when the

tip is experiencing friction with the sample. When the cantilever is

becoming twisted, the laser beam is moved sideways. The amount of

torsion and, hence, friction is then derived from comparison of the

signals from the two right and two left segments of the photodiode

[(A + C) − (B + D)]. Maps of local friction are used to reveal materials

contrast in addition to the topographical image.

In dynamic AFM modes, the cantilever is oscillated and the ampli-

tude and phase of the oscillation are monitored using the laser signal

on the photodiode rather than a static deﬂ ection.

An AFM does not necessarily need to be based on a cantilever at all.

In an instrument combining AFM topographical imaging with near-

ﬁ eld optical imaging (the scanning near-ﬁ eld optical microscope,

SNOM or NSOM), a tapered optical ﬁ ber is used as the stylus in most

current instruments. It is oscillated parallel to the sample. Dampening

of this oscillation is used as the feedback signal. In another alternative

setup to the cantilever-based AFM, the sample is mounted on the

membrane of an electret microphone and the output of this micro-

phone is used for feedback. This setup performs equally well as the

more traditional cantilever setup (Figure 16–6).

In addition to a highly sensitive probe, AFM depends on a precise

scanner. The scanner is attached either to the probe or the sample. It

allows the sample to be scanned with respect to the stylus in the plane

of the sample (referred to as the x,y plane) and adjusting the relative

height of the sample and the probe (referred to as the z direction) with

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subatomic precision (Amrein et al., 1997). AFM scanners are made of

voltage-driven piezoceramic elements.

AFM imaging is a mechanical process, usually operated in a closed

feedback loop. Even an apparently crisp, high-resolution topographical

image need not necessarily reﬂ ect the true sample topography. The

faithfulness of the topographical images depends on the properties of

the feedback loop, the tip and sample geometries, and on how much

the sample deforms upon imaging. Eventually, the accuracy of the

topographical images is limited by noise (Figure 16–7). Each of these

aspects is discussed below. Also discussed is how development of

AFM technology might lead to improved instrument performance.

Figure 16–6. Actin ﬁ laments (left) and an archebacterial S-layer (HPI-layer, right) imaged with an

AFM based on an electret sensor, rather than a cantilever sensor (Schenk et al., 1994, 1996).

Figure 16–7. The faithfulness of an AFM topographical image depends on the

sample and tip geometries, the sample deformation, the quality of the mechan-

ical feedback loop of the instrument, and noise.

Chapter 16 Atomic Force Microscopy in the Life Sciences 1033

2.2 Geometry of the Stylus

When the stylus moves over a sample, the effective point of contact of

the tip with the sample also changes. The topographical image is, col-

loquially speaking, convoluted with the tip geometry. The early days

of AFM (and STM) were plagued by ill-characterized tips. Multiple

whiskers created images that contained the same object multiple times

(Figure 16–8). For a blunt stylus, each prominent object of the sample

resulted in a local image of the tip itself rather than the local sample

topology, and the overall appearance of such images has been cloudy.

Because both the tip geometry and the sample topology matter, high-

resolution images were sometimes obtained with an apparent blunt tip

for very ﬂ at samples. This is because even the bluntest of tips has a

rough surface, being covered with ﬁ ne asperities.

Commercially available cantilevers now come with a well-

characterized stylus and the apex may have a very small radius of cur-

vature. The shape of the stylus needs to be selected with the sample in

mind. Biological membranes or two-dimensional arrays of proteins with

little overall height variations, for example, are well imaged by a pyramid-

shaped stylus that ends in an apex of small radius of curvature, whereas

a sample with prominent topology with steep ﬂ anks needs to be scanned

by an elongated, needle-like stylus of high aspect ratio. During imaging,

even a well-characterized, sharp stylus may become mechanically

damaged or may pick up contaminate that renders it blunt. In these

cases, the probe needs to be cleaned (e.g., by washing in ultrapure water,

containing a detergent). If not successful, it has to be replaced.

When selecting an appropriate stylus, not only the expected sample

topology must be considered. The sample compliance is an equally

important aspect as a sharp tip may strongly deform a soft sample.

This aspect is described below.

2.3 Tip–Sample Interaction

The tip–sample interactions need to be considered carefully, because

they inﬂ uence critically the success of the experiments. In AFM, most

of the time the stylus is loaded onto the sample either intermittently

(referred to as intermittent contact mode or tapping mode) or con-

Figure 16–8. A single active ﬁ lament, imaged with a single tip (left) and after

the tip has become a triple tip (right).

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stantly (contact mode; see below). This is achieved by approaching the

probe and sample and bending the cantilever until the desired loading

force is achieved.

In addition to the loading force, exerted by the cantilever spring,

there are additional forces F

StSa

acting between the sample and the

stylus (see below). They may be repulsive or attractive. An attractive

force makes the effective load of the tip onto the sample greater than

what would be assumed from the bending of the cantilever. A repul-

sive force that acts prior to physical contact reduces the effective load

of the tip onto the sample. The total loading force of the tip onto the

sample becomes

F = c ⋅ ∆S + F

StSa

where ∆S is the deﬂ ection of the cantilever and c is the spring constant

of the cantilever.

Evaluating these interactions may be pursued by acquiring force-

versus-distance curves (referred to also as “force spectroscopy”).

Thereby, the tip is approached to the sample and the deﬂ ection of the

cantilever recorded as a function of the vertical position of the scanner

with respect to the sample. The deﬂ ection of the cantilever can then be

converted into a force using the spring constant of the lever (Figure

16–9).

2.3.1 Sample Deformation

When physical contact of the tip and the sample is established, the

sample will deform until the contact area has sufﬁ ciently increased

such that the load is accommodated (Figure 16–10).

The deformation strongly determines the resolution and trustwor-

thiness of AFM imaging and must therefore be considered carefully.

Figure 16–9. Force versus distance curve. For the example shown here, the tip ﬁ rst experiences a

long-range repulsive force upon approaching the sample, even before the tip and sample are in physi-

cal contact. Close to the sample, the tip becomes strongly attracted by the van der Waals force. In this

instance, the attractive force gradient becomes greater than the force gradient by the cantilever spring.

This causes the tip to snap into physical contact with the sample (the perpendicular part of the

approach curve). Once physical contact has been made, the cantilever is deﬂ ected linearly by the

approaching scanner. On the way back, the tip may stick to the sample by adhesion until the pull by

the cantilever forces it out of contact.

Chapter 16 Atomic Force Microscopy in the Life Sciences 1035

There are a number of models that relate the deformation of a solid

body to the loading force of a stylus. According to Sneddon (Heuberger

et al., 1996), for example, the repulsive force F for a stylus being loaded

onto a solid, homogeneous body is

−

(

)

−

(

)

−









−













ηln

where E

is the Young’s modulus, ν

is the Poisson’s ratio of the sample,

and R is the apex radius of the stylus (the deformation of the stylus is

neglected). With increasing loading force, the radius η of the contact

area between the tip and the sample increases. The penetration

depth σ of the tip and the radius of the contact area η are related as

(Heuberger et al., 1996):

ση

−









Hence, for highest resolution, macromolecular samples need to be

imaged at minimal load. Under optimal conditions, subnanometer

scale resolution has been obtained on protein samples (Schabert and

Engel, 1994); for a review, see Engel and Müller (2000). Müller et al.

found on a two-dimensional regular array of the protein bacteriorho-

dopsin that at a load exceeding about 100 pN, the resolution dropped

and the molecules became deformed vertically and laterally (Müller

and Büldt, 1995). Because the atomic structure of bacteriorhodopsin

is known, the change in topography could be assigned to a distinct

Figure 16–10. Parameter plot of the loading force F versus the penetration

depth σ for three different radii of curvature of the apex R and for two types

of differently stiff samples. A Young’s modulus of 0.1 GPa might reﬂ ect a living

cell; 1 GPa could be ascribed to a protein structure. The plot shows that even

at a very low force, a sharp stylus dives right into the softer sample. It is there-

fore crucial to select the right kind of an apex radius for each application.

1036 M. Amrein

conformational change of the protein upon the higher load (Figure

16–11).

A convenient way to detect sample deformation upon too high a load

comes from comparison of images from trace and retrace (Hoh et al.,

1993; Müller et al., 1996; Schabert and Engel, 1994). Trace and retrace

refer to the line-by-line motion of the scanner. All commercial AFMs

allow two individual images to be acquired, one using the line traces

when the stylus moves from left to right and the other one using the

traces on the way back.

The actual load leading to high-resolution images might be even

smaller than expected from the force setting of the microscope. Yang

and co-workers (1996) proposed that short-range interactions with a

local asperity give rise to high-resolution contrast while longer-range

interactions with blunter parts of the tip help support the load of the

tip in contact with the sample. Muller et al. (1997) have argued that in

solution, the long-range force required for repulsion of the body of the

tip is electrostatic. They adjust the supporting electrolyte so that the

asperity just touches the sample lightly.

To obtain details of living cells and tissues by AFM, a meaningful

image is often obtained only after a loading force of a few nanonew-

tons has been applied. Such high loads lead to deformation of the cell

up to several hundred nanometers (Hoh and Schoenenberger, 1994).

The cell membrane is then pressed onto intracellular structures such

Figure 16–11. Force-dependent surface topography of bacteriorhodopsin

(scale bar represents 10 nm) demonstrating the effect of force variations on the

topography of the cytoplasmic purple membrane surface. The initial force of

300 pN (bottom of image) was decreased during the scan to 100 pN (top of

image). A conformational change is distinct: donut-shaped bacteriorhodopsin

trimers transform into units with three pronounced protrusions at their

periphery. Inset: noise reduced image at higher magniﬁ cation (scale bar rep-

resents 4 nm). (Courtesy of Müller and Büldt, 1995).

Chapter 16 Atomic Force Microscopy in the Life Sciences 1037

as the nucleus, cytoskeletal elements, and vesicles, which in conse-

quence become visible (Chang et al., 1993; Fritz et al., 1994; Hoh and

Schoenenberger, 1994). In these cases, the AFM images reﬂ ect the local

plasticity of the living cells more than their true surface topography.

2.3.2 Forces between the Apex of the Stylus and the Sample

A van der Waals force F

vdW

is always present between the tip and

the sample. The main contribution to F

vdW

is the dispersion force,

caused by the dipole-induced dipole interaction and is present

between all kinds of materials. The Lifshitz theory, a combination of

quantum electrodynamics theory and spectroscopic data allows

the forces between two geometrically shaped surfaces to be calculated.

In the case of a ﬂ at surface (representing the sample) and a sphere

(being used as an approximation for the apex of the stylus) F

vdW

(Israelachvili, 1991)

vdW

−

where R is the radius of the tip (radius of the tip apex) and d is the

distance between apex and sample. H

represents the Hamaker con-

stant, which characterizes the interaction of the two surfaces (media)

across a third medium. For example, for two mica surfaces in water H

is 2.2 × 10

−20

J and for two silicon oxide surfaces in water H

is 8.3 × 10

−21

(Israelachvili, 1991). For hydrocarbons in water, H

lies between (0.2 − 1)

× 10

−20

J (Butt, 1992). The van der Waals force between particles is

always attractive in air and attractive for most situations in an aqueous

solution.

When imaging in aqueous solution, additional interactions between

the apex of the stylus and the sample need to be taken into account.

Many of the commonly used supports and probes as well as most bio-

logical samples are charged in an aqueous environment. This is because

they usually carry weak acidic and basic functional groups. They dis-

sociate in an aqueous solution, according to their equilibrium con-

stants. The net charge density of a surface in water depends on the

density of the functional groups, their pK values, and the pH of the

buffer solution.

The DLVO (Derjaguin, Landau, Verwey, Overbeek) theory quantita-

tively describes the total force between charged interfaces in aqueous

solution. It considers the electrostatic double-layer interaction caused

by surface charges and the van der Waals forces and neglects entropic

or steric contributions. Unlike the van der Waals interaction, the electri-

cal double-layer repulsion depends on the sign and magnitude of the

surface charge density, the ion concentration, and the pH. A charged

surface attracts counterions in the water. At the solid–liquid interface,

a charge cloud on the order of molecular dimensions is created as a

transition region. In this so-called electrical double layer (EDL) the

counterions balance the charge of the surface. The density of the

charges surrounding the surface falls off exponentially with distance

z from the surface (Debye–Hückel approximation):

ψ = ψ

−z/λ

1038 M. Amrein

represents the potential at the surface. The Debye length λ

is the

thickness of the EDL:

εε

∑

ecq

where ε

represents the vacuum permittivity, ε

the dielectric permit-

tivity of the electrolyte, k the Boltzmann constant, T the absolute tem-

perature, e the unit charge, and c

the concentration and q

the ionic

charge of the ith component of the liquid. Note the strong dependence

of the double layer thickness on the valence of the ions.

If the tip and the sample are approaching each other, the electrical

double layers of the two interfaces become perturbed when they begin

to overlap (Figure 16–12). This results in a force that is known as the

double layer force F

. F

decreases exponentially with distance d

between the two surfaces. For a stylus with an apex radius of curvature

of R and a planar sample (at a surface potential <50 mV) (Butt, 1992):

−

πσσλ

εε

where σ

and σ

represent the surface charge density of the stylus and

the specimen, respectively, ε

is the vacuum permittivity, ε

the dielec-

tric permittivity of the electrolyte, and d the distance between the two

surfaces. This equation is a simpliﬁ cation of any real situation. At a

distance much below λ

, it is necessary to resort to numerical solutions

for which there are no simple expressions.

In addition, when the two charged surfaces approach each other, the

local ion concentration also changes. This means a shift in the equilibrium

conditions of the charged groups with the ions in solution. Hence, the ion-

izable functional groups of the surface may become neutralized for ﬁ nite

dissociation constants, according to the new equilibrium conditions, and

the surface charge density is decreased. This phenomenon is called charge

regulation and causes a less strong repulsive force for surfaces charged

with similar sign than would occur without charge regulation. F

can even

become attractive at very small distances (Israelachvili, 1991).

Figure 16–12. Speciﬁ c interaction of ions at solid–liquid interfaces. The sur-

faces are negatively charged. (Left) The ions produce an interfacial region of

excess solute concentration, the electrical double layer, which consists of the

Debye layer and the counterions bound at the surface (Helmholtz layer).

(Right) Two negatively charged surfaces at very small separation. The ion

clouds of the electrical double layer overlap and cause a repulsive force

(Amrein and Müller, 1999). (From Mueller et al., 1997a, reprinted with

permission.)

Chapter 16 Atomic Force Microscopy in the Life Sciences 1039

To evaluate the overall force that is relevant for the interaction

between the stylus and the sample, the electrical double-layer force and

the van der Waals force are summed up to the total DLVO force (F

DLVO

)

(Figure 16–13).

DLVO

−

πσσλ

εε

For high-resolution imaging, the electrical double-layer repulsion

may have to be reduced such that the stylus can effectively come in

physical contact with the sample rather than “riding” on the electrical

double layer. This can be achieved by increasing the (bivalent) ion

concentration (Butt 1991, 1992; Butt et al., 1995; Ducker et al., 1991).

There are a number of interactions that need to be considered in

addition to the above-mentioned DLVO force, including steric, hydro-

phobic, and hydrophilic interactions.

When the microscopy is performed in air, there is often a water

bridge occurring between stylus and sample. This is because under

ambient conditions, most surfaces are covered by a thin water layer.

The resulting meniscus force may be quite strong (e.g., in the order of

−7

N) and may pull the tip effectively onto the sample. This will result

in poor resolution and may even cause damage to the sample and

stylus. It is notable that the van der Waals interaction in air is usually

about an order of magnitude stronger than in an aqueous environment.

The detrimental effects occurring in air through these forces may par-

Figure 16–13. Force versus distance curves showing the DVLO force between

a silicon nitride cantilever and a mica surface under varying pH conditions

and at ﬁ xed ion concentration. Mica is naturally negatively charged at neutral

pH, less charged at low pH, and increasingly charged at higher pH. At low

surface charge, the van der Waals attraction dominates and causes the tip to

snap onto the sample. At higher charge, the van der Waals attraction becomes

increasingly screened by the repulsive electrical double layer repulsion. (From

Butt, 1992, reprinted with permission).