Abstract
Atomic force microscopy (AFM)1, 2 has been used to measure the strength of bonds between biological receptor molecules and their ligands3, 4, 5, 6. But for weak noncovalent bonds, a dynamic spectrum of bond strengths is predicted as the loading rate is altered, with the measured strength being governed by the prominent barriers traversed in the energy landscape along the force-driven bond-dissociation pathway7. In other words, the pioneering early AFM measurements represent only a single point in a continuous spectrum of bond strengths, because theory predicts that these will depend on the rate at which the load is applied. Here we report the strength spectra for the bonds between streptavidin (oravidin) and biotin8—the prototype of receptor–ligand interactions used in earlier AFM studies3, 4, 5, and which have been modelled by molecular dynamics9, 10. We have probed bond formation over six orders of magnitude in loading rate, and find that the bond survival time diminished from about 1 min to 0.001 s with increasing loading rate over this range. The bond strength, meanwhile, increased from about 5 pN to 170 pN. Thus, although they are among the strongest noncovalent linkages in biology (affinity of 1013 to 1015 M-1)8, 11, these bonds in fact appear strong or weak depending on how fast they are loaded. We are also able to relate the activation barriers derived from our strength spectra to the shape of the energy landscape derived from simulations of the biotin–avidin complex.
To measure strengths, we used two modes of a biomembrane force probe (BFP)12 as described in Fig. 1 legend: a vertical mode with high resolution in position and force (2–5 nm and 0.2–0.5 pN) for testing weak bonds under slow loading (Fig. 2a); and a horizontal mode with modest resolution (8–10 nm and 1–10 pN) for testing strong bonds under fast loading (Fig. 2b). The BFP tip and test surface were prepared with a paucity of reactive sites to limit the frequency of bond formation to 1 per 7–10 touches in the tests (see Methods). As such, the likelihood of forming and breaking single bonds was expected to be greater than 0.9. To obtain sufficient numbers (50–100) of rupture forces at each loading rate, several hundred cycles of approach–touch–separation were performed by computer-controlled piezo displacement of either the transducer or the test surface. The nominal loading rate kfv t was preselected by setting the BFP force constant kf in the range 0.1–3 pN nm-1 and piezo retraction speed vt in the range 1–20,000 nm s -1 . Force histograms were compiled at 11 and 8 loading rates between 0.05 to 60,000 pN s-1 for biotin–avidin and biotin–streptavidin, respectively. A montage of histograms is shown in Fig. 3a for biotin–streptavidin. Complete spectra of the most frequent rupture forces f* versus log rf (where rf = loading rate) are plotted in Fig. 3b.
Figure 1: The spring in the biomembrane force probe BFP is a pressurized membrane capsule12.

Membrane tension sets the force constant kf (force/capsule
extension) and is controlled by micropipette suction P and radius
Rp, kf
PR
p. Using a red blood cell as the transducer, the BFP stiffness was
tuned between 0.1 and 3 pN nm-1 to measure
forces from 0.5 to 1,000 pN. As the BFP tip, a glass microbead of 1–2
m
diameter was chemically glued to the membrane (see Methods). a, Operated
on the stage of an inverted microscope, the BFP (on the left) in the horizontal
mode was kept stationary and the microbead test surface (on the right) was
translated to/from contact with the BFP tip by precision piezo control. With
fast video (
1,000 frames per s) processing, a simulated cursor was required
to track the image of the bead as shown, which yielded a resolution of 8–10 nm
for transducer deflection. b, Reflection interference contrast image
of the BFP tip translated along the optical axis by piezo control to/from
a coverglass test surface in the vertical mode. Standard video (30 frames
per s) processing of the circular interference pattern was used to track elevation
of the tip at a resolution of 2–5 nm. Transducer deflection was
obtained from the difference between piezo translation and bead displacement.
Figure 2: BFP tip–substrate distance and force versus time for cycles of approach–touch–separation with formation and rupture of a bond.
![Figure 2 : BFP tip|[ndash]|substrate distance and force versus time for cycles of
approach|[ndash]|touch|[ndash]|separation with formation and rupture of a bond.
Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com](/nature/journal/v397/n6714/images/397050ab.eps.0.gif)
a, Loaded at extremely slow rate, a bond held the tip to the surface
for
24 s and broke at
3 pN as the piezo retracted
the transducer (dashed trajectory). The fluctuations in tip position were
due to thermal excitations of the BFP (mean square displacement
k
BT/kf). Stretch of the PEG polymers that
linked the bond to the glass surfaces is shown by the slight upward movement
(
15 nm) under force before detachment. Because of polymer compliance,
the true loading rate felt by a bond at nominal rates (kf
vt) below 10 pN s-1 had
to be obtained from the force versus time. b, Loaded at extremely fast
rate, a bond held the tip to the surface for
0.003 s (spike in
force) and broke at
170 pN as the piezo retracted the test surface
(dashed trajectory). The force fluctuations were due to position uncertainties
BFP stiffness.
Figure 3: Biotin–streptavidin bond strengths.
![Figure 3 : Biotin|[ndash]|streptavidin bond strengths. Unfortunately we are unable to provide accessible alternative text for this. If you require assistance to access this image, or to obtain a text description, please contact npg@nature.com](/nature/journal/v397/n6714/images/397050ac.eps.0.gif)
a, Force histograms from tests of single biotin–streptavidin
bonds demonstrate shift in peak location and increase in width with increase
in loading rate. Gaussian fits used to determine the most frequent rupture
force or bond strength are shown. Governed ideally by the thermal force
f
, standard deviations
f of the distributions
also reflected uncertainties in position
x and video sampling
time
tv, that is,
f
[
f
2 + (kf
x)2 + (rf
t
v)2]1/2. As
f
increased from
1 pN at the slowest rate to
60 pN at the fastest
rate, the standard error in mean force (the statistical measure for error
in strength) ranged from
0.3 pN to
5 pN. b, Dynamic
strength spectra for biotin–streptavidin (circles) and biotin-avidin
(triangles) bonds. Defined as thermal energy kB
T ÷ distance x
, the slopes (f
) of the solid lines in the biotin–streptavidin spectrum
map activation barriers at x
0.5 nm
and 0.12 nm along the direction of force based on values of 8 pN
and 34 pN. Merging with biotin–streptavidin above 85 pN,
the high-strength regime for biotin–avidin also maps an inner barrier
at x
0.12 nm but the
slope f
13–14 pN
of the intermediate strength regime (dashed line) between 38 pN and
85 pN indicates that the next barrier maps to x
0.3 nm. Slight curvature and reduction in slope
between 38 pN and 11 pN suggests that the barrier extends to
0.5 nm.
Below 11 pN, the biotin–avidin spectrum exhibits a low-strength
regime (dashed line) with a slope of f
1.4 pN that maps to x
3 nm. Consistent with the high-strength regime is the biotin–streptavidin
strength (
AFM) measured recently by atomic-force microscopy
(AFM) using a carbon nanotube as the tip24 and the biotin–avidin
strength (not shown) measured previously4 by AFM.
To understand why strength depends on loading rate, it is important to
recognize that the lifetime of a bond sustained by weak noncovalent interactions
diminishes rapidly when subjected to force because of thermal activation.
Conceptually, the energy landscape is tilted by force (Fig.
4a), which lowers energy barriers, decreases the likelihood of bond
survival, and speeds up dissociation. So, we might expect the form of a strength
spectrum obtained under rising force in probe tests to be complicated and
difficult to interpret. However, when linear regimes appear over many orders
of magnitude of loading rate as in Fig. 3b, interpretation
of the spectrum is simple: each regime produces an image of a sharp energy
barrier at a fixed location along the unbinding pathway7. The
energy contour in configuration space local to a sharp barrier (called the
transition state) is highly curved and therefore does not change shape as
the barrier height falls under rising force f (Fig.
4a). The thermally averaged displacement in configuration space needed
to reach the top of the barrier does not shift with force and the displacement
maps to a constant position x
along the direction
of force. First postulated intuitively by Bell13, lowering thebarrier
by the mechanical potential fx
leads to exponential
amplification of the dissociation kinetics, that is, off rate
v
v0 exp (fx
/kBT). Hence,
the relevant force scale f
=
kBT/x
for thermally activated rupture is thermal energy (k
BT
4.1
10-21 J or
4.1 pN nm
at room temperature) divided by the projected bond displacement, not the maximum
gradient in an energy landscape. The force statistics in probe tests are predicted
by a first-order kinetic process where dissociation rate increases rapidly
with the rising force7. For a single barrier, the peak f
* in the force distribution shifts to higher force in proportion to log
e (loading rate) with a slope f
. Much less trivial,
complex macromolecular bonds involve many interactions that create a mountainous
terrain of barriers in the energy landscape. Assuming a cascade of sharp barriers,
the strength spectrum is predicted to follow a piece-wise continuous sequence
of linear regimes with ascending slopes7. The abrupt increase
in slope from one regime to the next signifies that an outer barrier has been
suppressed by force and that an inner barrier becomes the dominant kinetic
impedance, as shown in Fig. 4a. The regime governed
by a particular barrier spans a range of loge (loading rate) determined
by its height relative to adjacent barriers (see Methods). The off rate rises
as a staircase of exponentials in force that amplify off rate less and less
from one to the next.
Figure 4: Conceptual and real (MD) energy landscapes traversed along a molecular reaction coordinate under force.

a, Oriented at an angle
to the molecular coordinate
x, external force f adds a mechanical potential, -(f cos
)
x, that tilts the landscape and lowers barriers. The inner barrier emerges
to dominate kinetics when the outer barrier falls to a level
k
BT below it under force. For sharp barriers, the local energy
contours, called transition states, are highly curved and change little in
shape or location under force. Even though the unbinding pathway may be tortuous
and the orientation fluctuates wildly, the energy weighted locations of sharp
barriers can project as constant distances x
=
xts cos 
along
the direction of force. b, Instantaneous interaction energy between
biotin and avidin computed along a half-nanosecond extraction from the binding
pocket in the simulations of Israilev et al.10 (kindly
provided to us by K.Schulten and co-workers, University of Illinois). Bordered
by regions of rapid intense fluctuations, locations of rarified statistics
reveal transition states expected in a thermally averaged free energy landscape7. Arrows mark barrier locations derived from the strength spectrum
for biotin–avidin in Fig. 3b.
Applying these concepts to the spectra plotted in Fig. 3b
, we derive locations of prominent energy barriers that govern strength
of biotin–streptavidin and biotin–avidin bonds. How does this
one-dimensional map along the direction of probe force compare with detailed
molecular dynamics (MD) simulations of biotin–(strept)avidin interactions?
In separate simulations, biotin was extracted from a binding pocket of streptavidin9 and avidin10 by pulling on the outer end with a pseudo-mechanical
spring. Chemically and structurally, the binding pockets in avidin and streptavidin
are very similar except biotin forms an additional nonpolar interaction and
three additional hydrogen bonds in avidin14, 15.
Also, the longer '3–4' loop in avidin seems to close more
tightly behind biotin in the bound state14, 15, 16. Revealing
the inherent molecular complexity, the simulations yield a dynamic superposition
of many polar (hydrogen bonds and water bridges) and nonpolar (to aromatic
residues) interactions along the unbinding trajectories, which are emphasized
quite differently in each report9, 10. Even so,
common qualitative features are described that provide important clues to
the thermally averaged free energy landscape relevant on laboratory timescales.
First, within an initial displacement of less than 0.2 nm, unbinding
began with detachment of the 'head' (ureido ring) of biotin from
a nest of hydrogen bonds, water bridges and nonpolar interactions deep in
the binding pocket. Next, forces reached maximal values followed by sudden
displacements of biotin at a distance of
0.5 nm in the biotin–streptavidin
simulation (attributed to rupture in a transient network of water bridges
and hydrogen bonds) and at
0.4 nm in the biotin–avidin simulation
(attributed both to polar and to nonpolar interactions). Finally, as biotin
left the pocket, a prominent jump occurred with lower forces at
1 nm
in both simulations (attributed to hydrogen bonds) and biotin was observed
still to cling to peripheral polar groups at
1.4 nm in avidin
simulations. To show this behaviour clearly, we have plotted a record of the
instantaneous interaction energies between biotin and avidin calculated over
a half-nanosecond time course of extraction in the simulations of Israilev
et al.10 (Fig. 4b). Transition states
are readily identified by regions with a paucity of states where biotin passes
quickly. Marked in Fig. 4b, the activation barriers
derived from the high and intermediate strength regimes in
Fig. 3b correlate with regions of rarified statistics and the qualitative
appearance of the energy landscape. The interpretation is that the transition
states implied by these features persist on long timescales and that the molecular
reaction coordinate perhaps deviates by
40–45° from the direction
of force local to the second transition state. But surprisingly, the outer
barrier indicated by the low-strength regime in Fig. 3b
is 2–3-fold more distant than the last transition state seen in the
MD simulation.
Guided by the MD simulation, we expect the outer barrier to emanate from
molecular interactions with the flexible '3–4' loop, which
closes behind biotin in crystallographic images14, 15, 16 of
the bound state and was set in an open conformation in MD simulations. Consistent
with this expectation, mutations that delete the '3–4' loop
in streptavidin result in major reductions in magnitude of binding enthalpy16 17. Interestingly, in the absence of biotin, the
'3–4' loop disappears in crystallographic images indicating
that the loop becomes disordered and flexible. Moreover, although not currently
implicated in biotin–avidin binding, other longer loops also border
the channel that leads to the binding pocket. Thus, our speculation is that
the outer barrier at
3 nm represents interactions on laboratory
timescales of the spacer-linked biotin with soft, flexible elements well beyond
the binding pocket. Even though biotin–(strept)avidin bonds can break
under very small forces, the location of the outer barrier at
3 nm
leads to a significant difference in energy between the outer and nearby inner
barriers as indicated by the difference in log(loading rate) intercepts of
the low and intermediate strength regimes.
The profound effect of thermal activation on strength of noncovalent linkages in biology has been recognized by researchers studying cell adhesion dynamics in shear flow18 19 and recently also in the unfolding of tandem immunoglobulin-like domains in long proteins20 21. What is not well known, however, is that thermal activation in a complex biomolecular assembly is likely to be governed by a rugged energy landscape with more than one kinetic barrier. We have shown here that to explore such a landscape with force probes, experiments have to be performed over an enormous range of loading rates.
Methods
Chemical preparation of BFP tips and test surfaces. First, amino silane (AEAPTMS, United Chemical Technologies, PA) groups were covalently bound to glass microbeads and coverslips. Next, amine-reactive polyethylene oxide polyethylene glycol (PEG) polymers with and without biotin end groups (mixture of NHS-PEG3400-VS and NHS-PEG3400-biotin, Shearwater Polymers, AL) were covalently linked to the silanized surfaces. Finally, the biotinylated beads and coverglasses were exposed to excess (strept)avidin and then washed. Even though almost completely saturated with (strept)avidin, the surfaces still had a number of free biotin groups. Thus, bonds formed very infrequently when identically prepared tip and test surfaces were touched together. (No bonding was detected when the PEG polymers on the test surface were terminated with methyl groups or when free biotin was blown at the tip and test surface by an auxiliary micropipette before touch.) A red cell covalently linked with PEG–biotin polymers was pushed together with an avidinated microbead to construct the probe as shown in Fig. 1a.
Analysis of strength spectra. Slopes of linear regimes in strength
versus loge (loading rate) map energy barriers to fixed
distances x
along the direction of force7.
Each slope is the force scale f
=
kBT/x
for e-fold amplification of dissociation rate impeded by a particular barrier.
Barriers emerge in succession from outer to inner positions to dominate kinetics.
Reflecting the Arrhenius dependence in the off rate, v
0 = (1/tD)exp(-E
b/kBT), differences
in logarithmic intercept loge (rf)f* = 0
and slope f
of regimes in Fig.
3b expose differences in barrier heights,
E
b
kBT{
log
e[f
/tD] -
loge (rf)f* = 0}, within
an unknown variation in a diffusive relaxation time tD.
Worked out by Kramers22, 23, thefrequency 1/
tD in liquids is governed by viscous friction
f and a productof length scales lalts
(la
confinement length in
the bound state andlts
impedance
width of the transition state), that is, 1/tD
kBT/(
fl
alts) and kBT/
f defines a diffusivity. From MD simulations9, values
of
f
2
10-8 pN s nm
-1 and xbx
ts
0.01–0.1 nm2 imply that 1/t
D is
109 –1010 s
-1 and that loge (f
/t
D) is
21–25 for a rate scale in pN s-1
.
