PROBING CELLULAR ADHESION AT THE SINGLE-MOLECULE LEVEL - Life at the Nanoscale: Atomic Force Microscopy of Live Cells - page 238

tether, with membrane proteins and the underlying cytoskeleton. 41,60 Thus,
varying the pulling speed will lead to different levels of the force plateau. It is
important to emphasize that this force ( Fig. 11.4d ) is not the force required
to rupture the bond at the applied loading rate, since this is virtually zero
given the zero slope of the plateaus. In contrast, this tether force is the force
supported by the bond, which binds the receptor on the membrane to the
ligand on the opposing substrate. Thus, the lifetime of the tethers, i.e. the
lifetime of the force plateau, is a direct measure of the lifetime of the bond at
the applied force. Therefore, measuring tether lifetimes at different pulling
speeds (different force plateau values) is a physiological alternative to force
clamp measurements. This approach has been recently applied using the
micropipette aspiration technique 61 and the AFM 44 on different cell adhesion
complexes.

11.3.3 Theorecal Framework

Biological interactions are speciic interactions mediated by a complex and
dynamic combination of hydrogen bonding, van der Waals, hydrophobic,
steric and electrostatic interactions. 10 This combination of forces leads to an
equilibrium state that is normally simpliied by a one-dimensional free energy
landscape with a deep minimum and a barrier along the reaction coordinate
( ) ( Fig. 11.6 ) . The mechanical strength of the interaction is then determined

by bringing the system out of equilibrium by applying a pulling force that
distorts the energy landscape. The most established theoretical description
of forced unbinding of biological bonds originated with the classical work by
Bell. 50 Bell's approach was later reformulated by Evans and Ritchie and based
on the reaction rate theory developed by Kramers. 48,57 The model assumes
an intermolecular potential in which the dissociation dynamics is described
as a diffusive process with an intrinsic dissociation lifetime τ 0 , which is
determined by a dissipative term (

x

), two length scales related to local
curvatures of the energy landscape at the minimum and top of the barrier (

D

l c

$ G ‡ of the dominant energy barrier. 10,49,57

and l ts , respectively) and the height

l c l ts

_____

τ 0 =

D

e Δ G ‡ / k B T (11.1)

The multiplicative term before the exponential is known as the diffusive
relaxation time ( t D ), the inverse of the attempt frequency, which is governed

by molecular damping ζ = k B T / D . For biological molecules in liquid this

relaxation time is very short, seconds. However, given the

exponential dependence of the bond lifetime on the barrier height, it leads
to relatively slow intrinsic dissociation rates, τ 0 ~ 1 second, for a bond with
a barrier of

t D ~ 10

10

to 10

9

$ G ‡ ~ 21

k B T . The application of a force deforms the energy