METHODS 20, 329 –340 (2000)
doi:10.1006/meth.1999.0926, available online at http://www.idealibrary.com on
Force Probe Measurements of
Antibody–Antigen Interactions
D. E. Leckband,* ,1 T. L. Kuhl,† H. K. Wang,‡ W. Müller,§
J. Herron,‡ and H. Ringsdorf§
*Department of Chemical Engineering and Center for Biophysics and Computational Biology, University of
Illinois at Urbana–Champaign, Urbana, Illinois 61801; †Department of Chemical Engineering,
University of California at Santa Barbara, Santa Barbara, California 93106; ‡Department
of Biomaterials, University of Utah, Salt Lake City, Utah 84112; and §Institute for
Organic Chemistry, Johannes Gutenberg University, Mainz, Germany
The surface force apparatus has been used to quantify directly
the forces that govern the interactions between proteins and
ligands. In this work, we describe the measured interactions
between the antigen fluorescein and the Fab⬘ fragment of the
monoclonal 4-4-20 anti-fluorescyl IgG antibody. Here we first
describe the use of the surface force apparatus to demonstrate
directly the impact of the charge composition in the region of the
antibody binding site on the antibody interactions. Several approaches are described for immobilizing antigens, antibodies, and
proteins in general for direct force measurements. The measured
force profiles presented are accompanied by an extensive discussion of protocols used to analyze the force– distance curves and to
interpret them in terms of the antibody structure. In addition to
long-range electrostatic forces, we also consider short-range
forces that can affect the strength of adhesion between the Fab⬘
and immobilized fluorescein. The latter investigations demonstrate the influence of interfacial properties on the recognition of
surface-bound antigens. © 2000 Academic Press
Antibody recognition of foreign molecules is a key
step in the immune response (1, 2). The high selectivity
and affinities of antibody–antigen interactions are
among the most finely tuned noncovalent bonds exhibited by proteins. Both the rapid, efficient binding and
the high binding affinities are the direct consequence of
the molecular forces that govern the net interaction.
Knowledge of the forces, and hence the potentials, that
control the associations between these species is therefore key to understanding antibody function. Moreover,
1
To whom correspondence should be addressed.
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determining relationships between antibody structures and the fields that govern the protein interactions with other molecules will facilitate the rational
design of high-affinity, high-selectivity proteins for a
variety of engineered functions.
No single force determines protein behavior, and
bimolecular interactions are mediated by the simultaneous action of several of different force fields, which
exhibit different magnitudes and distance dependences (3, 4). Because their ranges of action differ, the
forces similarly influence different stages of the binding event. For example, long-range electrostatic forces
modulate the rates of antibody–antigen binding prior
to antigen docking (5). At intermediate separations,
van der Waals and solvation forces operate in conjunction with the electrostatic force (3–5). Finally, at distances D ⬍ 1 nm, the antigen docks in the binding
pocket, and the resulting noncovalent bond is stabilized by the superposition of multiple, short-range hydrogen bonds, hydrophobic contacts, salt bridges, and
van der Waals contacts (6 – 8). The superposition of all
of these three-dimensional force fields together governs
both the rate and the strength of these highly selective
bimolecular interactions. It is also important to appreciate, however, that the structures of both the antigen
and the antibody determine the details of these interactions.
Molecular modeling, kinetic, and equilibrium measurements have provided avenues for elucidating the
relationship between antibody structure and the forces
that control function. The short-range potentials that
determine the strength of the contacts between the
antigen and antibody have been inferred from crystal
structures, equilibrium binding measurements, and
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LECKBAND ET AL.
site-directed mutagenesis (9 –12). These short-range
potentials do govern the slow rates of antigen dissociation. However, long-range, noncontact interactions
also impact the affinities by altering the association
rates (5, 13–17). Electrostatics, in particular, operate
at large distances and can enhance or impede bimolecular collision rates (13–15, 18, 19).
Because electrostatic forces guide ligand docking,
the calculation of protein electrostatic potentials has
been a prolific field of research (12, 13, 15, 17, 19 –29).
A variety of computational algorithms have been developed to calculate the electrostatic fields surrounding
complex protein structures (17, 22, 24, 26). Without
methods with which one can measure the spatial distribution of the electrostatic field or antibody interaction forces directly, indirect methods have been used to
test model predictions. Variations in measured kinetic
rates following site directed mutagenesis, for example,
are frequently used to test the influence of calculated
electrostatic double-layer forces on protein association
rates (17, 22). However, measured changes both in
binding rates and in isoelectric points often embed
several other parameters such as, for example, solvation energies and assumed dielectric constants for both
the protein interior and the solvent layer adjacent to
the surface of the macromolecule (22, 26). They do not,
therefore, give a direct measure of the electrostatic
potential field.
With the advent of scanning force probes, one can
now measure the forces that govern protein interactions directly (30 –33). In particular, hypotheses concerning the impact of topographical variations on the
protein electrostatics were tested recently by direct
measurements with the surface force apparatus (32,
34, 35). Both the surface force apparatus and the
atomic force microscope have also been used to quantify the tensile strengths of receptor–ligand bonds (31,
33, 36).
This work describes the use of the surface force apparatus (SFA) (i) to quantify the force fields that control antibody–antigen interactions with immobilized
antigens and (ii) to relate those force profiles both to
the antibody structure and to the composition of the
target membrane surface. This instrument is used to
quantify the electrostatic forces, the van der Waals
forces, and the adhesion energy density due to shortrange, specific bonds (4, 37, 38). The electrostatic
double-layer force is determined by the protein structure, and this force determines the long-range poten-
tial between the protein and the ligand-derivatized
surface (13–15, 17, 21–23, 34). While the relationship
between the tensile strength of receptor–ligand bonds
and their binding free energies is still not wellestablished, the changes in the measured adhesion
energy do reflect perturbations in the intermolecular
potentials. Thus, we also describe the use of this
method to probe forces that can impact antibody recognition of immobilized antigens.
The described studies focus on the measured interactions between the monoclonal 4-4-20 anti-fluorescyl
antibody and the negatively charged fluorescein (35).
The structure of the Fab⬘ fragment of the protein has
been determined, and the molecular contacts within
the antibody binding site are known from the crystal
structure (39 – 41). However, a ring of positive charge
outside the binding site is believed to guide the negatively charged antigen to the binding pocket (Fig. 1)
(39 – 41). Moreover, when the fluorescein is immobilized, additional interfacial forces can alter the net
intermolecular potential that governs the apparent affinity. The measurements described not only probe the
impact of the local charge cluster on the antibody–
antigen interaction, but also the impact of the interfacial forces on the apparent biological activity of
membrane-bound fluorescein.
MEASURING PROTEIN INTERACTIONS WITH
THE SURFACE FORCE APPARATUS
Principles of the Technique
The surface force apparatus is used to measure directly the forces between materials as a function of the
distance between them (Fig. 2) (4, 37). Generally, the
samples are immobilized on cleaved mica sheets, which
are glued to transparent, silica lenses (38). Positioning
controls allow one to adjust the relative spacing between the materials over a range of 0.1 nm–1 cm. The
net force is then measured between the materials as
their separation distance D decreases.
The two parameters obtained from the measurements are the force and distance between the samples.
Multiple beam interferometry is used to determine the
intersurface spacing with a resolution of 0.1 nm (42). In
the apparatus, the two opposing mica sheets with reflecting silver mirrors, the deposited sample materials,
and intervening medium make up a Fabry–Perot in-
FIG. 1. Calculated electrostatic potential field surrounding the Fab⬘ fragment of the monoclonal 4-4-20 anti-fluorescein antibody. The
coordinates of the fragment were obtained from the Brookhaven Protein Data Bank. Calculations of the electrostatic potentials were done
with the commercial program Delphi and a bulk salt concentration of 5 mM. The charges on the ionizable groups used for the calculations
were determined by assuming the bulk pK’s of the different amino acid side chains. The yellow worm is the protein backbone. The negative
⫺kT potential surfaces are shown in green, and the positive ⫹kT potential surfaces are in blue. The red CPK structure is the bound
fluorescein. The biotinylation site is located on the lower surface of the protein.
FORCE PROBE MEASUREMENTS OF Ab–An INTERACTIONS
331
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LECKBAND ET AL.
terferometer (Fig. 2). When white light passes through
the sandwich, only wavelengths that interfere constructively exit the resonant cavity. The interference
fringes of equal chromatic order (FECO) are then separated with a spectrometer. Since the conditions for
constructive interference depend on the thicknesses
and indices of refraction of the intervening layers, the
transmitted wavelengths shift by an amount ⌬␭ as the
distance D between the sample changes (42). These
wavelength shifts can then be related to changes ⌬D
with an accuracy of 0.1 nm. In addition, the dependence of the transmitted wavelengths on the index of
refraction enables one to determine the refractive index of an intervening (e.g., protein) layer in situ (42).
The deflection in the leaf spring that supports the
lower disk determines the force acting between the
samples at each separation distance (Fig. 2). With
Hook’s law, one determines the force at each separation with a resolution of about 10 nN (37). While the
force transducer is not as sensitive as that used in
atomic force measurements, the area of contact between the lenses is ca. 5 ␮m 2. The measured force is
therefore due to ca. 300,000 molecular interactions (4).
This generates sufficient attraction or repulsion to
measure with the mechanical spring. This sensitivity
both in the distance and in the force determinations
allows one to measure, for example, the van der Waals
and electrostatic forces between proteins (32, 34, 35).
The lenses supporting the materials are cut in the
form of hemicylinders with radii of curvature R 1 and
R 2 . These contact at a point when oriented 90° relative
to each other (Fig. 2). The equivalent geometry is that
of a sphere of geometric average radius (R 1 R 2 ) 1/ 2 interacting with a flat plate [3]. Because the 2-cm radius
of curvature R is much greater than the ranges of the
forces (⬍20 nm), local curvature effects are negligible
(3, 5). The radius does, however, scale the size of the
effective contact area and therefore the magnitude of
the force (3, 5). For this reason, the data are reported in
terms of the force normalized by the radius of curvature, F/R. This allows one to compare directly the
measured normalized force profiles from different experiments, even though the local radii of curvature
might differ.
An additional advantage of the crossed cylindrical
geometry is that the normalized force between the
curved surfaces F c/R is directly proportional to the
interaction free energy between flat surfaces E f of identical composition: namely, (F c /R) ⫽ 2 ␲ E f (3, 5). This
relationship is known as the Derjaguin approximation,
and it applies for interactions between a sphere of
radius R and a flat surface where R Ⰷ D. It is well
known in colloid science and has been derived in several texts (3, 5). Importantly, the normalized forces
reported in surface force measurements are directly
proportional to the interaction energy.
The Immobilized Proteins Must Be Homogeneously
Oriented
FIG. 2. Schematic of the instrumental setup used for surface force
measurements. The force instrumentation comprises the main apparatus and optical components, which are used for the interferometric distance determinations. The main instrument chamber
houses the crossed cylindrical lenses (A). The lower disk is attached
to a position control stage via a sensitive leaf spring as indicated (A).
The sample sandwich consists of two mica sheets back-silvered with
reflecting silver films, sample materials on the front mica surfaces,
and the intervening liquid (B). The silvered, mica sheets are glued to
the surfaces of the silica lenses, and the supported lipid bilayers are
then coated on the exposed mica surfaces. The samples are mounted
in the apparatus, which is filled with buffered solution. White light
directed into the resonant cavity between the two silver mirrors (C)
interferes constructively within the cavity so that only certain wavelengths exit the interferometer. The transmitted light is then separated into the component interference fringes with a spectrometer
(D).
One of the objectives of the force probe studies with
proteins is to relate the measured force fields to the
protein structure. Because the net measured force is
due to multiple molecular interactions, all proteins on
each sample must be oriented uniformly. This ensures
that the same region of the bound macromolecules
contributes to the measured force. Additionally, when
measuring the receptor-mediated adhesion, all bonds
will be stressed along their axes in the same way (43).
Although the bonds distributed between the two
curved surfaces may experience different tensile
stresses at a particular surface separation, the average
force required to rupture them will be the same (43).
Finally, all of these samples are supported on atomically flat mica substrates. This prevents disordering of
the protein layers on account of the surface roughness.
Langmuir–Blodgett supporting films for protein attachment. To prepare homogeneously oriented protein monolayers, we use as supports planar, phospholipid bilayer membranes supported on atomically
smooth mica sheets (38, 44). These bilayers are excellent biocompatible substrates for protein immobilization. They do not normally induce protein denatur-
FORCE PROBE MEASUREMENTS OF Ab–An INTERACTIONS
ation, and one can control their composition at will. In
particular, the bilayers can be doped with commercially available lipids with chemically reactive headgroups (Northern Lipids, Vancouver, Canada; Avanti
Polar Lipids, Birmingham, AL) for covalent protein
attachment (45). Langmuir–Blodgett deposition techniques also generally allow good control both of the
lipid packing density and of the membrane composition
(44). The spreading of lipid vesicles on hydrophobic
supports has been used with some success to create
hybrid bilayers for biosensors (46, 47). This is not advisable for SFA studies, due to the uncontrolled residual adherence of some vesicles, which will interfere
with the force measurements. Additionally, the resulting bilayers tend to contain a higher density of defects.
To prepare planar, lipid bilayers by Langmuir–
Blodgett deposition (Fig. 3), one first spreads a
chloroform/methanol solution of lipid on the water surface of a computer-controlled Langmuir trough (NIMA,
Coventry, England). The amphiphilic molecules orient
at the liquid–vapor interface with their headgroups in
the aqueous subphase and their alkane chains in the
vapor phase. The composition of the chloroform lipid
mixture determines the monolayer composition, and
sweeping the Teflon barrier across the water surface
controls the molecular packing. The barrier corrals the
lipids in a defined area on the water surface. Upon
achieving the desired area per lipid, as determined
from the measured surface pressure of the film, the
monolayer is then transferred onto a solid hydrophilic
support, i.e., mica by pulling the substrate vertically
through the air–water interface (Fig. 3).
Lipid bilayers are prepared by two successive passes
of the substrate through the water surface. As the mica
sheet is withdrawn vertically from the subphase, the
first lipid layer deposits onto the hydrophilic support
FIG. 3. Illustration of the Langmuir trough and preparation of
supported lipid bilayers. Lipid monomers are spread on the water
surface and then confined to a smaller region with a movable Teflon
barrier. A sensor records the surface pressure of the lipid film.
Dipping the hydrophobic substrates into the water or pulling hydrophilic substrates up through the interface transfers the lipid film
onto the support. Once prepared, the supported bilayers must be
kept under water while transferring the disks to and mounting them
in the apparatus.
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with the headgroups adjacent to the mica. The exposed
alkane chains render the surface hydrophobic, and the
lipid-coated mica emerges from the water dry. The
second, outer lipid monolayer is deposited by then lowering the hydrophobic mica through a second lipid film.
The second monolayer deposits on the first lipid layer
with the lipid headgroups exposed to the solution. The
thus prepared supported, lipid bilayer membrane is
then used as a protein support. The bilayers are not
robust, however, and must be kept under water during
all subsequent manipulations (48). To prevent desorption of the lipids, the bathing solution is also saturated
with the lipid monomers.
Because the force measurements average interactions over 5- to 10-␮m 2 areas, the lipid films should be
laterally homogeneous. First, the matrix and reactive
lipids must be well-mixed in the two-dimensional
monolayer films. Second, since the underlying monolayer can influence both the homogeneity and the fluidity of the outer lipid layer, the choice of lipid in the
proximal layer is important. Crystalline dipalmitoylphosphatidylethanolamine (DPPE) on mica at a
packing density of 0.43 nm 2/lipid gives the best results
(49). The tightly packed, exposed hydrocarbon tails
form a dense, hydrophobic surface that is relatively
free of defects. As a result, the mobile fraction of lipids
in the distal layer is close to 0.95, and the lipid diffusivity is 10 ⫺10 cm 2/s (49). By contrast, the mobile lipid
fraction on amorphous supporting monolayers is only
0.67 ⫾ 0.02, and the lipids exhibit substantially lower
diffusivities (49). For this reason, the crystalline phospholipids give the best primary layers.
When the monolayers of proteins and ligands first
come into contact, the opposing molecules may not be
in mutual registry and therefore cannot bind (32). To
promote lateral rearrangements that facilitate such
mutual alignment, the supporting lipids in the outer
bilayer leaflet must also be laterally mobile. The melting temperature of the lipids T m relative to the temperature of the experiment determines the fluidity (32,
38). For example, at room temperature, the synthetic
phospholipids ditridecanoylphosphocholine (T m ⫽
⫺14°C), dilaurylphosphocholine (T m ⫽ ⫺1°C), and
dioleoylphosphocholine (T m ⫽ ⫺20°C) will all yield
fluid monolayers. Measured lipid diffusivities in such
supported films are ca. 10 ⫺10 cm 2/s (49). By contrast,
lipid mobility is negligible (⬍10 ⫺14 cm 2/s) with monolayers of dimyristoylphosphatidylethanolamine (T m ⫽
29°C) or dipalmitoylphosphocholine (T m ⫽ 41°C) at
room temperature. Therefore, matrix lipids are generally chosen with melting temperatures below the experimental temperature.
Chemistries for the immobilization of proteins on
planar lipid bilayers. The chemical reactivity and reactive site density of the supported bilayer surface are
determined by the composition of the outer monolayer
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LECKBAND ET AL.
(45). To bind proteins via surface accessible sulfhydryls, one can incorporate lipids with the following
reactive groups attached to the headgroup: maleimido-,
iodoacetyl-, or (2-pyridyldithio)propionyl- (Northern
Lipids). These lipid derivatives can be obtained with
different spacers between the phospholipid headgroup
and the reactive moiety. Additionally, when chelated
with copper ions, the iduronic acid moiety of
1-N,N-dicarboxymethylamino-3,6-dioxaoxtyl)-2,3-stearoylglyceryl ether (IDA-TRIG-DSGE, Northern Lipids)
binds polyhistidine epitope tags on engineered proteins
(50, 51).
Depending on the desired anchoring chemistry, the
outer, reactive lipid monolayer will comprise one of the
above-mentioned lipid derivatives and a neutral phospholipid at a defined mole fraction. The reactive site
density on the membrane is therefore determined by
the average area per lipid (ca. 0.60 nm 2/lipid) divided
by the mole fraction of reactive lipid in the matrix.
Alternatively, biotinylated proteins can be immobilized and oriented on crystalline streptavidin monolayers. Two-dimensional streptavidin crystals form on
supported lipid monolayers that contain 5 mol%
of a biotin–lipid conjugate N-((6-(biotinoyl)amino)hexanoyl)-1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine (biotin-X-DHPE, Molecular Probes, Eugene, OR) in a neutral, fluid phospholipid matrix (49).
Streptavidin binds to the membrane-anchored biotin
through two of its four biotin binding sites, and the two
unoccupied sites are exposed to the solution (52, 53). A
second protein, biotinylated at a single surfaceaccessible amino acid, will then bind to the exposed
pockets of streptavidin and self-assemble into a uni-
FIG. 4. Illustration of the immobilized, oriented Fab⬘ layer and
opposing fluorescein–lipid bilayer as used in the described force
measurements.
formly oriented monolayer (Fig. 4) (54). The density of
binding sites on the streptavidin film is 1/15 nm 2 or
twice the area occupied by each streptavidin molecule.
However, the distance between the two biotin pockets
is approximately 3 nm, so that the stoichiometry of
biotinylated protein/streptavidin is limited by the excluded volume of the bound proteins.
To measure forces between antigens and antibodies,
the antigen must also be linked covalently to a second
lipid bilayer (Fig. 5), which is supported on the surface
opposite the protein monolayer in the force apparatus
(Figs. 2 and 4) (35, 55–58). Several phospholipid conjugates with haptens such as fluorescein and dinitrophenol are commercially available (Molecular Probes).
Alternatively, the antigen derivatives of phospholipids
can be synthesized. The latter is more challenging with
small ligands, but proteins such as hen egg lysozyme,
for example, can be immobilized directly onto planar
bilayers using the reactive lipids described above.
Oriented Monolayers of Fab⬘ Fragments and
Fluorescein–Lipids for Force Measurements
Materials and methods. Surface force measurements were conducted with the Fab⬘ fragments of the
murine monoclonal anti-fluorescyl 4-4-20 IgG 2a(␬) antibody isolated from ascites fluid (35, 56 –58). The Fab⬘
was prepared by papain hydrolysis and then biotinylated with N-[6-(biotinamido)hexyl]-3⬘-(2⬘-pyridyldithio)propionamide (biotin-HPDP, Pierce, Rockford, IL) at a
single cysteine in the hinge region. Scatchard analysis
of the thus modified Fab⬘ indicated that 75% of the
derivatized protein was active (56).
The biotinylated Fab⬘ was immobilized (Fig. 4) on
streptavidin monolayers supported on membranes containing 5 mol% biotin-X-DHPE (Molecular Probes) and
95 mol% dilaurylphosphatidylethanolamine (Avanti
Polar Lipids) (35). Centrifugation of the Fab⬘ solution
in an Eppendorf benchtop microcentrifuge followed by
filtration through a 0.1␮m Durapore filter (Millipore,
FIG. 5. Illustration of the DODA(EO) 2FITC headgroup and the
effect of surface hydration on the effective tether length.
FORCE PROBE MEASUREMENTS OF Ab–An INTERACTIONS
Bedford, MA) removed the majority of contaminating
particulates. When biotinylated Fab⬘ was then incubated with the streptavidin crystals, the proteins
bound in a 1:1 stoichiometry, such that the effective
surface density of the antibody fragment was 1 Fab⬘/15
nm 2. The attachment at the hinge region distal from
the antibody binding site ensured that the
complementarity-determining region was exposed to
the opposed fluorescein-functionalized membrane (54).
To prepare antigen-derivatized bilayers, fluorescein
was conjugated to the double-chain surfactant according to published procedures to form
1,1-[(N,N-dioctadecylamido)carboxy]-19-(5⬘-fluoresceinthioureoyl)-4-carboxy-5-oxa-2,8,22,-14,17-pentaoxanonadecane (DODA(EO) 2FITC) and the -trioxanonadecane (DODA(EO) 4FITC) derivative (56 –58). These
conjugates were designed to allow one to investigate
interactions between anti-fluorescyl monoclonal antibodies and fluorescein-presenting membranes. Because the depth of the antibody binding pocket is ca.
1.8 nm (39, 40, 59), the antigen was attached to the
membrane by either a 1.8- or a 2.2-nm hydrophilic,
ethyleneoxide (EO) n spacer (Fig. 5). The different
tether lengths also allowed us to quantify the range of
additional surface steric barriers due to, for example,
surface hydration that might impede the antibody
binding (Fig. 5). The fluorescein–lipid was then mixed
at 5 and 2 mol% with palmitoyloleoylphosphatidylethanolamine (POPE, T m ⫽ 25°C, Avanti Polar Lipids) and used to prepare the antigen-derivatized membranes.
335
the point of adhesive contact between the protein and
ligand. These experiments were carried out at 25°C
and pH 7.2 in a solution containing either 3 or 30 mM
phosphate buffer. Measurements at low ionic strength
(3 mM) are indicated by the filled circles in Fig. 6.
At large distances, the force is attractive, but at a
separation distance D ⬍ 1–2 nm, the intersurface
attraction increases significantly on account of the formation of specific bonds between the fluorescein and
Fab⬘ molecules. The tensile force required to pull apart
the membranes gives strength of intersurface adhesion
and defines the depth of the minimum in the curve. At
the higher salt concentration, the range of the force
decreased substantially, but the force profile remained
overall attractive. The magnitude of the adhesion was
lower by ca. 40%. The origin of the latter change will be
discussed below.
Analysis of the Force Profiles
Determination of the electrostatic surface potentials
of the antibody and antigen monolayers. From these
measurements, one seeks to quantify molecular origins
of the force curves and to relate them both to the
structure of the macromolecule and to the composition
of the target membrane. The overall force– distance
profiles between proteins and hapten-derivatized surfaces will, in general, be a superposition of electrostatic, van der Waals, and steric forces, together with
specific binding (3, 5). The objective is to then quantify
FORCES BETWEEN 4-4-20 Fab⬘ FRAGMENTS
AND CHARGED FLUORESCEINFUNCTIONALIZED MEMBRANES
Force Measurements
Definition of D ⫽ 0. In these measurements, the
reference position, or D ⫽ 0, refers to the equilibrium
separation of the two samples or the position of the
adhesive minimum. The thickness of the Fab⬘ layer T F
is obtained from the total measured thickness of the
organic layers between the two mica sheets ⌬ and the
known membrane bilayer thicknesses T b (38, 60), and
the known 4.5-nm (61) thickness of the supporting
streptavidin monolayer T s: namely, T F ⫽ ⌬ ⫺ 2T b ⫺
T s. The total thickness of both assemblies ⌬ is determined from the difference in the distance of closest
interlayer approach following the UV destruction of
the organic films (38, 60).
Measured force profiles. Figure 6 shows the measured normalized force F/R between the 4-4-20 Fab⬘
monolayer and the 5 mol% fluorescein–lipid-containing
membrane as a function of the distance D relative to
FIG. 6. Force versus the distance between a Fab⬘ monolayer and a
5 mol% DODA(EO) 2FITC membrane. Forces profiles were measured
between the Fab⬘ and FITC membranes in 3 mM (filled circles, N ⫽
3) and 50 mM (open circles, N ⫽ 3) sodium phosphate buffer at pH
7.2 and 25°C. The solid lines through the curves are the best visual
fits of the data to solutions of the one-dimensional, nonlinear
Poisson–Boltzmann equation. The best fit parameters are given in
the text. The dashed lines are merely to guide the eye. The error bars
indicate the error in the force measurement. The pull-off force, which
gives the adhesive strength, is indicated by the outward-directed
arrows. The data show the impact of the ionic strength on the
apparent strength of the interaction between the fluorescein and
antibody fragment.
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LECKBAND ET AL.
the ranges and magnitudes of these different contributions to the interaction (3–5, 34, 35, 38, 62).
In Fig. 6 (filled circles), the long-range attractive
force is due to electrostatic interactions between the
materials. The Debye length, which scales the distance
dependence of the double-layer force in 1:1 electrolytes
such as NaCl is (3) ␭ D ⫽ (0.304 nm/ 公C) where C is the
molar concentration of salt. The long-range attraction
in Fig. 6 (filled circles) decays with a characteristic
length of 3.4 nm, compared with the predicted Debye
length of 3.1 nm. One can therefore confirm the electrostatic origin of the long-range force from the change
in the decay length with the ionic strength (3, 5). Consistent with this, Fig. 6 shows that increasing the salt
concentration by an order of magnitude decreased the
range of the force and the Debye length (Fig. 6, open
circles), as expected.
To quantify the magnitudes and signs of the electrostatic surface potentials of the interacting materials,
one fits the measured long-range electrostatic force to
numerical solutions of the one-dimensional, nonlinear
Poisson–Boltzmann (PB) equation (3, 5). In a recent
study of the pH dependence of the surface charge density of oriented streptavidin monolayers, we demonstrated that the electrostatic potentials of protein films
thus obtained are governed by the charge composition
of the exposed surface of the protein (34). The fitted
electrostatic potential of the immobilized Fab⬘ monolayers will therefore reflect the charge composition of
the exposed surface of the protein.
Fits of the force profile measured at low salt to the
superposition of the calculated double-layer potential
at pH 7.2 and the van der Waals energy is shown in
Fig. 6. The best visual fits to the data were obtained
with an effective surface potential for the antibody
monolayer of ⫹5 ⫾ 2 mV (35). The Hamaker constant,
which scales the van der Waals energy, was 10 ⫺21 J. In
the fitting procedure, we used as fixed input parameters for the fluorescein–membrane the measured surface charge density of ⫺6 mC/m 2, the constant charge
boundary condition, and a 3.4-nm Debye length. The
constant potential boundary condition and a surface
potential of 5 ⫾ 2 mV for the Fab⬘ monolayer gave the
best fit to the data. In 30 mM buffer, the surface potential was similar at 5 ⫾ 2 mV, and the experimental
Debye length was 1.1 nm. The Grahame equation,
which relates the surface charge density to the Debye
length and electrostatic surface potential [3], predicts
that the potential should also have decreased to 2 ⫾ 2
mV. However, within experimental error, we could not
distinguish these two values.
The effective charge density of the protein monolayer
is net positive, in spite of the fact the net negative
charge on the protein at pH 7.2 (pI 6.8). This suggested
that the ring of positive charge surrounding the CDR
dominates the measured electrostatic potential of the
exposed surface of the Fab⬘ fragment (Fig. 1) (39, 40,
59). The long-range electrostatic attraction between
the fluorescein and the positively charged mouth of the
binding site of 4-4-20 Fab⬘ further indicates that the
latter charge cluster will steer the binding trajectory of
the soluble, negatively charged fluorescein (14, 15, 17,
39, 40, 59).
To demonstrate that the fitted electrostatic potential
was indeed due to the charge cluster, similar measurements were done with thermally denatured Fab⬘ fragments. We reasoned that the more disordered inactivated protein would exhibit electrostatic properties
that were similar to the overall macromolecule. Indeed,
measurements with inactive Fab⬘ exhibited no adhesion, and the fitted charge density of the resulting Fab⬘
monolayer was ⫺1 charge/10 nm 2. This confirmed that
the attractive electrostatic potential was indeed a consequence of the ring of charges surrounding the exposed binding site of the folded protein.
Methods used to fit the electrostatic double-layer
force. The unique determination of the charge densities and electrostatic surface potentials of the interacting samples requires the independent characterization
of the surface charge density of at least one of them.
The double-layer force between two dissimilar materials depends on the charge densities of each of the two
surfaces. Additionally, two independent boundary conditions must be specified, to account for the charge
regulation of the interacting materials in the presence
of their respective electrostatic double layers. Fits that
allow variations in all of these four parameters do not
yield unique solutions.
For this reason, we determined the charge density of
⫺1 charge/14 nm 2 (⫺6 mC/m 2) for the fluorescein–lipid
membrane independently, by measuring the force profile between identical bilayer membranes containing 5
mol% fluorescein–lipid. The symmetrical arrangement
of the samples in this experiment simplifies the data
analysis, which yields a unique value for the surface
charge density, and determines the charge regulation
boundary condition. The sign of the electrostatic potential is inferred from the known properties of the “test”
material. For example, the carboxylic acid of the fluorescein moiety generates a net negative charge, so that
the sign of the electrostatic membrane potential is
negative.
Two methods can be used to determine the electrostatic properties of the protein monolayer. First, fits of
the double-layer force between identical protein films
will give this information. The advantage of this approach is the relative simplicity of the data analysis.
However, it is not possible to also determine the sign of
the electrostatic potential, since the double-layer force
between similar materials is always repulsive. Alternatively, from the electrostatic force between the protein layer and a second, ligand-functionalized sub-
337
FORCE PROBE MEASUREMENTS OF Ab–An INTERACTIONS
strate, one can determine the charge density, its sign,
and the charge regulation boundary condition. If both
the sign and the charge density of, for example, the
hapten-displaying membrane are known, then one determines the electrostatic potential of the antibody
monolayer uniquely from fits to the force curves. Additionally, the specific binding between, for example, the
4-4-20 Fab⬘ and fluorescein can only be measured with
this asymmetric sample configuration.
Importantly, these fitted surface charge densities or
potentials represent the surface-averaged values at a
defined plane relative to the protein surface (34). For
convenience, we set the effective outer Helmholtz plane
or plane of charge tangent to the outer van der Waals
surface of the protein. The latter plane defines the
distance of closest surface approach in the force measurements. The fitted potential and charge density
thus reflect the net charge projected onto the tangent
plane (34, 45). Lateral heterogeneities in the electrostatic potential distribution over the protein surface
are averaged to give the effective Guoy–Chapman potential for the entire monolayer. The charged residues
on the outer protein surface near the charge plane
nevertheless largely govern the measured electrostatic
potential.
Quantification and Interpretation of the Short-RangeSpecific Attractive Force
Theory and results. While the long-range electrostatic force depends on the antibody structure, the
antigen–antibody binding determines primarily the
magnitude of the strong, short-range receptor–ligand
attraction F R-L at D ⬍ 1 nm (Fig. 6). The relationship
between the critical force to rupture a receptor–ligand
bond and the binding free energy is not yet wellestablished (7, 63, 64). Nevertheless, the bond force is
expected to reflect the bond distribution and the activation energy for unbinding (36, 43). Thus, changes in
F R-L reflect changes in the antigen identity, the solution
conditions, the receptor–ligand interaction potential,
or the ligand density.
The specific binding contribution F R-L to the measured adhesion is simply the difference between the
total force F T and the other nonspecific forces present.
In Fig. 6, the net force at the minimum in the force
curve D min is the result of a superposition both of the
nonspecific double-layer attraction and of the specific
protein–ligand adhesion. The magnitude of F R-L is,
therefore, the difference between the net force F T and
the double-layer force F es extrapolated to D min, or
F R-L(D min) ⫽ F T(D min) ⫺ F es(D min) (Fig. 6).
The measured adhesion between the Fab⬘ and
DODA(EO) 2FITC monolayers (1.8-nm spacer) at low
salt was ⫺5 mN/m 2 in 1 mM buffer. Since the extrapolated double-layer force at D min was ⫺0.7 mN/m, the
contribution of specific bonds to the overall adhesion
was ⫺5 ⫺ (⫺0.7) ⫽ ⫺4.3 mN/m (Table 1). Similarly, in
30 mM buffer, the adhesion was ⫺3 mN/m, and the
nonspecific double-layer force was ⫺0.3 mN/m. Therefore, the specific attractive force was ⫺2.7mN/m (Table
1). On the basis of these measurements, the strength of
the antibody–antigen interaction appears to be ionic
strength dependent, in contrast with the soluble species. The reason for the apparent ionic strength dependence of the binding is discussed below.
The average adhesion energy per area between deformable solids can be estimated from the normalized
adhesive force between a sphere and a flat surface by
E ⫽ (2F/3 ␲ R) (3, 65). Dividing E by the average
protein surface density thereby gives an estimate of
the average work to rupture the bonds. The absolute
value obtained is expected to reflect the activation energy for unbinding rather than the free energy of the
bond, however, and should be interpreted with caution
(7, 36, 63). With this force– energy relationship and a
site density of 40 nm 2/Fab⬘, the estimated adhesion
energy with the 1.8 and 2.2 nm tether is, respectively,
8kT and 14kT. These values are of the right order of
magnitude for this antibody–antigen pair. The difference between them, however, reflects perturbations to
the antibody–antigen interaction at the membrane
surface.
With these membrane-anchored proteins and ligands, it is important to establish that the cross-bridge
failure occurs via bond rupture rather than by pulling
lipid anchors out of the membrane (65, 66). We established with streptavidin and a series of biotin analogues that preferential bond rupture should occur for
receptor–ligand affinities below 10 6 M ⫺1 (65). This will,
in general, be the case, as long as the speed at which
the bonds are ruptured exceeds the intrinsic relaxation
time of the bond (63).
Verification that attractive forces are due to specific
antigen–antibody binding. That the short-range attraction is due to specific antibody–antigen bonds can
be verified by several methods. First, one can abolish
specific binding by blocking the receptor binding sites
with the corresponding soluble ligand. One can also
show that the adhesion varies in proportion to the
concentration of ligands or receptors on the membrane
TABLE 1
Effect of Steric Barriers on Antibody–Antigen
Binding at Surfaces
Tether length
(nm)
Steric barrier
thickness (nm)
Effective tether
length (nm)
Adhesion
(nM/m)
1.8
1.8
2.2
0.7 ⫾ 0.1
0.4 ⫾ 0.1
0.4 ⫾ 0.1
1.1
1.4
1.8
2.7
4.3
7.2
338
LECKBAND ET AL.
(43). Finally, one can inactivate the receptors by denaturation, as described in this work.
A signature of specific lock-and-key bonds is the
roughly linear dependence of the adhesion on the number of bonds between the two surfaces (43). Changing
the antigen surface coverage, in order to determine
how F R-L varies with the cross-bridge density can similarly alter the electrostatic potential of the antigenderivatized surface (35). This will be the case if the
antigen is also charged, as is fluorescein. To determine
how changes in the density affect the specific receptor–
ligand adhesion, one must first calculate the magnitude of the nonspecific electrostatic double-layer force
F es(D min) for each ligand density. Then changes in F T
can be properly interpreted in terms of changes in F R-L.
This approach was, in fact, used to show that, at excess
ligand densities, changes in the fluorescein coverage
altered the electrostatic double-layer force, but not the
number of cross-bridges formed or the adhesion (35).
The analysis of the nonbonding forces is necessary
when the chemical contrast between the receptor–
ligand and the nonspecific background forces is low.
For example, in Fig. 6 the double-layer contribution is
ca. 16% of the total adhesion, and F R-L was determined
by subtracting the double-layer force. By contrast, in
measurements between streptavidin and biotin–lipid
membranes, the nonspecific forces contributed ⬍5% to
the overall adhesion at D min, and the error incurred by
neglecting the latter forces was negligible (32). Importantly, force measurements between antibodies and
antigens will always involve both specific and nonspecific terms. The relative contributions of the latter
should be considered in order to quantify accurately
the adhesive strength of the protein–ligand interactions.
4-4-20 antibody to bind fluorescein immobilized on a
flat, inert surface (39, 40, 59). This minimum length is
defined by the distance of the carboxyl tail of the bound
fluorescein to the outer van der Waals surface of the
Fab⬘ (Fig. 5). However, the roughness of the membrane
and the steric barriers due to adsorbed water will decrease the effective linker length (Fig. 5). The 0.4-nm
tether length difference between DODA(EO) 2FITC and
DODA(EO) 4FITC thereby allowed us to determine the
range over which the such interfacial features alter the
antigen–antibody potential. The spacers were therefore used as molecular rulers to estimate the range of
influence of such colloidal surface forces.
RESULTS AND DISCUSSION
The force profile measured between the Fab⬘ and
membranes containing DODA(EO) 4FITC (2.2-nm
spacer) is shown in Fig. 7. At large separations, the
curve is very similar to that measured with
DODA(EO) 2FITC (Fig. 6). This is expected because the
ethylene oxide spacer is uncharged. Despite the fact
that the 1.8-nm tether should have been sufficient to
permit unrestricted binding, the adhesion measured
with the 2.2-nm tether was 60% higher at ⫺8 mN/m.
Since the double-layer force at D min is ⫺0.8 mN/m in
both cases, the relative normalized receptor–ligand attractive forces are ⫺4.3 and ⫺7.2 mN/m for the short
and long tether, respectively (Table 1). This difference
is due solely to the lengths of the two linkers.
INTERFACIAL FORCES ALSO IMPEDE
ANTIBODY BINDING TO IMMOBILIZED
ANTIGENS
Rationale for Antigen Immobilization
In surface force measurements of antibody–antigen
binding, as well as in several antibody-based technologies, antigens are tethered to a surface. This complicates antibody binding on account both of the steric
constraints imposed by the surface and of the force
fields at the interface. In particular, binding is sterically impeded. Tethering small haptens via long, hydrophilic spacers generally avoids this.
We demonstrated directly the impact of the interfacial environment on the Fab⬘ recognition of immobilized fluorescein in measurements with the antigen
anchored via spacers of different lengths. A minimum
spacer length of 1.8 nm would be required for the
FIG. 7. Force versus the distance between the 4-4-20 Fab⬘ and a 5
mol% DODA(EO) 4FITC monolayer. Forces profiles were measured
between the Fab⬘ monolayer and fluorescein anchored to the membrane surface via a 2.2-nm spacer. Measurements were carrier out in
1mM sodium phosphate buffer at pH 7.2 and 25°C. The solid line
through the data is the best visual fit of the data to the nonlinear
Poisson–Boltzmann equation with best fit parameters given in the
text. The dashed lines are merely to guide the eye. The force required
to detach the surfaces is indicated by the arrow. (Reprinted with
permission [Leckband et al., Biochemistry 34, 11467–11478]. Copyright 1995 American Chemical Society.)
FORCE PROBE MEASUREMENTS OF Ab–An INTERACTIONS
The large effect of this small 0.4-nm change in tether
length demonstrates clearly that short-ranged, surface
hydration and the roughness of the membrane generate additional steric impediments that the antibody
must overcome in order to bind to the antigen (38, 48,
60, 67– 69). In a separate experiment, the measured
steric thickness of the membrane hydration/fluctuation
barrier for these bilayers was 0.4 ⫾ 0.1 nm (Table 1).
This would reduce the effective tether length by the
same amount, and the linker would have to be at least
2.2 nm, in order to allow for unimpeded antibody binding. Consistent with this, increasing the linker length
indeed increased the adhesion strength. Extending the
antigen beyond the surface hydration layer lowered the
activation energy for binding, increased the population
of bound species, and thereby increased the resultant
adhesion (35).
The ionic strength reduction in the receptor–ligand
adhesion (Fig. 6) is attributed to similar interfacial
phenomena. In concentrated salt solutions, the electrical double layer near the surface becomes highly compressed. Although the ions may not actually bind to the
surface, their local concentration can be high, and their
excluded volumes also present an additional steric barrier to binding (Fig. 5) (67–70).
In 30 mM phosphate, the measured “hydration
layer” thickness increased to 0.7 nm adjacent to the
membrane. Consistent with this model, the hydrated
diameter of sodium ions, the principal counterion
present, is 0.7 nm (Table 1) (3). Thus, we can attribute
the lowered antibody binding at elevated salt concentrations to the “adsorbed” ions at the interface.
These findings show the remarkable sensitivity of
biological recognition to the surface microenvironment.
While they demonstrate the impact of short-range
steric repulsive forces on binding, they also show that
local surface forces interfere with specific binding in
proportion to range relative to the range of the intermolecular forces that govern receptor–ligand binding
(45).
CONCLUSION
This paper describes how one can use direct surface
force measurements both to probe the electrostatic
forces that control antibody–antigen interactions and
to investigate their structural origins. In addition,
measurements of the short-range adhesive interactions, while not a direct probe of the free energy of the
bond energy, can be used to investigate the impact of
changes in intermolecular potentials due to changes in
the antibody, antigen, or interfacial properties.
339
ACKNOWLEDGMENT
This study was supported by NIH R29 GM51338.
REFERENCES
1. Davies, D. R., and Cohen, G. (1996) Proc. Natl. Acad. Sci. 93,
7–12.
2. Davies, D. R., and Padlan, E. A. (1990) Annu. Rev. Biochem. 59,
439 – 473.
3. Israelachvili, J. (1992) Intermolecular and Surface Forces, 2nd
ed., Academic Press, New York.
4. Leckband, D. (1995) Nature 376, 617– 618.
5. Hunter, R. (1989) Foundations of Colloid Science, Vol. 1, Oxford
Univ. Press, Oxford.
6. Creighton, T. (1993) Proteins: Structures and Molecular Properties, 2nd ed., Freeman, New York.
7. Balsera, M., Stepaniants, S., Izrailev, S., Oono, Y., and Schulten,
K. (1997) Biophys. J. 73, 1281–1287.
8. Israelev, S., Stepaniants, S., Balsera, M., Oono, Y., and Schulten,
K. (1997) Biophys. J. 72, 1568 –1581.
9. Whitlow, M., and Teeter, M. M. (1986) J. Am. Chem. Soc. 108,
7163–7172.
10. Hao, H., and Scheraga, H. A. (1996) Proc. Natl. Acad. Sci. USA
14, 4984 – 4989.
11. Allen, S. C., Palmer, K. A., Shapiro, R., Vallee, B. L., and Scheraga, H. A. (1994) J. Protein Chem. 13, 649 – 658.
12. McCammon, J. A., and Harvey, S. C. (1987) Dynamics of Proteins and Nucleic Acids, Cambridge Univ. Press, New York.
13. Northrup, S. H., Boles, Jeffrey, O., and Reynolds, J. C. L. (1987)
J. Phys. Chem. 91, 5991–5998.
14. Kozak, R., d’Mello, M. J., and Subramaniam, S. (1995) Biophys.
J. 68, 807– 814.
15. Viswanathan, M., Anchin, J. M., Droupadi, P. R., Mandal, C.,
Linthicum, D. S., and Subramaniam, S. (1995) Biophys. J. 69,
741–753.
16. Warshel, A. (1981) Biochemistry 20, 3167–3177.
17. Sharp, K. A., and Honig, B. (1990) Annu. Rev. Biophys. Biophys.
Chem. 19, 302–332.
18. Getzoff, E., Cabelli, D., Fisher, C., Parge, H., Viezzoli, M., Banci,
L., and Hallewell, R. (1992) Nature 358, 347–351.
19. Northrup, S. H., Allison, S. A., and McCammon, J. A. (1984)
J. Chem. Phys. 80, 1517–1524.
20. Gibas, C., Subramaniam, S., McCammon, J. A., Braden, B., and
Poljak, R. J. (1997) Biochemistry 36, 15599 –15614.
21. Getzoff, E., Tainer, J., Weiner, P., Kollman, P., Richardson, J.,
and Richardson, D. (1983) Nature 306, 286 –290.
22. McCammon, A. J. (1998) Curr. Opin. Struct. Biol. 8, 245–249.
23. Nicholls, A., Sharp, K., and Honig, B. (1991) Proteins 11, 281–
296.
24. Warshel, A., Russell, S. G., and Churg, A. K. (1984) Proc. Natl.
Acad. Sci. USA 81, 4785– 4789.
25. Warshel, A., and Åqvist, J. (1991) Annu. Rev. Biophys. Biophys.
Chem. 19, 267–298.
26. Warshel, A., and Papazyan, A. (1998) Curr. Opin. Struct. Biol. 8,
211–217.
27. Yoon, B.-J., and Lenhoff, A. (1992) J. Phys. Chem. 96, 3130 –
3134.
28. Brooks, B., Bruccoleric, R., Olafson, B., States, D., Swaminathan, S., and Karplus, M. (1983) J. Comp. Chem. 4, 187–217.
340
LECKBAND ET AL.
29. Slagle, S. P., Kozack, R. E., and Subramaniam, S. (1994) J.
Biomol. Struct. Dynam. 12, 439 – 456.
30. Müller, D. J., and Engel, A. (1997) Biophys. J. 73, 1633–1644.
31. Florin, E.-L., Moy, V. T., and Gaub, H. E. (1994) Science 264,
415– 417.
32. Leckband, D., Schmitt, F.-J., Israelachvili, J., and Knoll, W.
(1994) Biochemistry 33, 4611– 4624.
33. Moy, V. T., Florin, E.-L., and Gaub, H. E. (1994) Science 266,
257–259.
34. Sivasankar, S., Subramaniam, S., and Leckband, D. (1998) Proc.
Natl. Acad. Sci 95, 12961–12966.
35. Leckband, D. E., Kuhl, T. L., Wang, H. K., Müller, W., and
Ringsdorf, H. (1995) Biochemistry 34, 11467–11478.
36. Chilkoti, A., Boland, T., Ratner, B. D., and Stayton, P. S. (1995)
Biophys. J. 69, 2125–2130.
37. Israelachvili, J. (1992) Surface Sci. Rep. 14, 110 –159.
38. Marra, J., and Israelachvili, J. (1985) Biochemistry 24, 4608 – 4618.
39. Voss, E. (1993) J. Mol. Recogn. 6, 51–58.
40. Kranz, D., Herron, J. N., and Voss, E. W. (1982) J. Biol. Chem.
257, 6987– 6995.
41. Herron, J., He, X.-M., Mason, M. L., Voss, E. W., and Edmundson, A. B. (1989) Proteins 5, 271–280.
42. Israelachvili, J. (1973) J. Colloid Interface Sci. 44, 259 –272.
43. Vijayendran, R., Hammer, D., and Leckband, D. (1998) J. Chem.
Phys. 108.
44. Tamm, L., and McConnell, H. (1985) Biophys. J. 47, 105–113.
45. Yeung, C., and Leckband, D. (1997) Langmuir 13, 6746 – 6754.
46. Plant, A. L. (1993) Langmuir 9, 2764 –2767.
47. Plant, A. L., Brighamburke, M., Petrella, E. C., and Oshannessy,
D. J. (1995) Anal. Biochem. 226, 342–348.
48. Israelachvili, J., and Marra, J. (1986) Methods Enzymol. 127,
353–361.
49. Calvert, T., and Leckband, D. (1997) Langmuir 13, 6737– 6745.
50. Frey, W., Schief, W. R., Pack, D., Chen, C.-T., Chilkoti, A.,
Stayton, P., Viola, V., and Arnold, F. H. (1996) Proc. Natl. Acad.
Sci. USA 93, 4937– 4941.
51. Pack, D., and Arnold, F. H. (1997) Chem. Phys. Lipids 86, 135–152.
52. Blankenburg, R., Meller, P., Ringsdorf, H., and Salesse, C. (1989)
Biochemistry 28, 8214 – 8221.
53. Darst, S. A., Ahlers, M., Meller, P. H., Kubalek, E. W., Blankenburg, R., Ribi, H. O., Ringsdorf, H., and Kornberg, R. D. (1991)
Biophys. J. 59, 387–396.
54. Spinke, J., Liley, M., Schmitt, F.-J., Guder, H.-J., Angermaier,
L., and Knoll, W. (1993) J. Chem. Phys. 99, 7012–7019.
55. Muller, W., Ringsdorf, H., Rump, E, Wildburg, G., Zhang, X.,
Angermaier, L., Knoll, W., Liley, M., and Spinke, J. (1993) Science 262, 1706 –1708.
56. Ahlers, M., Grainger, D. W., Herron, J. N., Lim, K., Ringsdorf,
H., and Salesse, C. (1992) Biophys. J. 632, 823– 838.
57. Ebato, H., Herron, J. N., Müller, W., Okahata, Y., Suci, P., and
Ringsdorf, H. (1992) Angew. Chem. Int. Engl. Ed. 31, 1087–1090.
58. Ebato, H., Gentry, C. A., Herron, J. N., Müller, W., Okahata, Y.,
Ringsdorf, H., and Suci, P. A. (1994) Anal. Biochem. 66, 1683–
1689.
59. Bedzyk, W., Herron, J. N., Edmundson, A. B., and Voss, E. W.
(1990) J. Biol. Chem. 265, 133–138.
60. Leckband, D. E., Helm, C. A., and Israelachvili, J. (1993) Biochemistry 32, 1127–1140.
61. Weber, P. C., Ohlendorf, D. H., Wendoloski, J. J., and Salemme,
F. R. (1989) Science 243, 85– 88.
62. Leckband, D. E. (1997) Adv. Biophys. 34, 173–190.
63. Evans, E., and Ritchie, K. (1997) Biophys. J. 72, 1541–1555.
64. Dembo, M., Torney, D. C., Saxman, K., and Hammer, D. (1988)
Proc. R. Soc. Lond. B 234, 55– 83.
65. Leckband, D., Müller, W., Schmitt, F.-J., and Ringsdorf, H.
(1995) Biophys. J. 69, 1162–1169.
66. Bell, G. I. (1978) Science 200, 618 – 627.
67. Leikin, S., Parsegian, V. A., and Rau, D. C. (1993) Annu. Rev.
Phys. Chem. 44, 369 –395.
68. Leikin, S., Rau, D. C., and Parsegian, V. A. (1994) Proc. Natl.
Acad. Sci. 91, 276 –280.
69. Israelachvili, J., and Wennerström, H. (1996) Nature 379, 219 –
225.
70. Pashley, R. (1981) J. Colloid Interface Sci. 80, 153–162.