Specific Adhesion of Soft Elastic Materials - Structural Interfaces and Attachments in Biology - page 149

Fig. 8.1 Model of an
adhesive patch of molecular
bonds between two elastic
bodies subject to an applied
tensile load
experiments for activated a 5 b 1 -integrin binding to fibronectin under low loading
rates have indicated that the characteristic time scale for ligand-receptor binding/
dissociation is on the order of 100 s (e.g., Li et al. [ 31 ]). Although a single bond has
only a limited lifetime, a cluster of bonds can survive for much longer due to
collective effects in a stochastic ensemble. A common assumption of the existing
models on molecular cluster adhesion is equally sharing of applied load among
all closed bonds. Based on this assumption, Erdmann and Schwarz [ 32 ] predict that
the cluster lifetime monotonically increases as the cluster size grows: the larger
the cluster, the more stable it is. When the cluster becomes large enough, constant
adhesion strength will be reached. This finding is similar to FXs that are subject
to frequent turnover, and large clusters tend to have a much longer lifetime
similar to FAs.
It seems that the theories of classical contact mechanics and molecular clusters
suggest two opposite tendencies for the adhesion strength as a function of adhesion
size. In cell adhesion, both the cell and ECM can be regarded as elastic media in a
relative limited time scale, while the molecular bonds are subject to frequent
rupture and rebinding. Such a system couples the elastic deformation of contacting
media and stochastic processes of binder molecules. It is expected that the optimal
strength will be achieved at a finite size. As an implication, experimental
observations have shown in general that focal adhesion size is limited to around a
few microns [ 33 ].
In order to provide unification of the elasticity description of adhesive contact at
large scales and the statistical description of single-bond behavior at small scales,
we developed an idealized model [ 34 - 41 ] of an adhesive patch of molecular bonds
between two elastic bodies subject to an applied tensile load to realize the coupling
between elasticity of the adhesion system and statistical behaviors of molecular
bonds. In this model, one side of the adhesion is an elastic medium and can be
viewed as the body of a cell (actin cytoskeleton), and the other side is an elastic