Lifetime and Strength of Adhesive Molecular Bond Clusters between Elastic Media

Abstract

With a long-term objective toward a quantitative understanding of cell adhesion, we consider an idealized theoretical model of a cluster of molecular bonds between two dissimilar elastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to obey classical elastic equations whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. Monte Carlo simulations that combine the elastic and stochastic equations are conducted to investigate the lifetime of the bond cluster as a function of the applied load. We show that the interfacial traction is generally nonuniform and for a given adhesion size the average cluster lifetime asymptotically approaches infinity as the applied load is reduced to below a critical value, defined as the strength of the cluster. The effects of elastic moduli, adhesion size, and rebinding rate on the cluster lifetime and strength are studied under strongly nonuniform distributions of interfacial traction. Although overly simplified in a number of aspects, our model seems to give predictions that are consistent with relevant experimental observations on focal adhesion dynamics.

Effects of contact surface shape on lifetime of cellular focal adhesion

“…For the model we chose a rebinding factor γ = 100 which is representative of highly favorable rebinding conditions [Qian et al 2008;2009], and a load factor ϕ = 0.46 which corresponds to the applied tensile load on the system being ρ = 1.78 kPa where ρ = F/2ab and F = ϕ F b N . The model is defined to represent a focal adhesion being experimented on at room temperature, corresponding to a value of k B T = 4.1 pN · nm.…”

“…This difference in lifetime increases more drastically as the adhesion continues to grow in size. This drastic reduction in adhesion lifetime for larger bonds with varying adhesion surface geometry from the optimal shape can be understood by the fact that generally stress concentrations are more severe as the focal adhesion increases in size [Qian et al 2008;2009]. What the optimal shape does for adhesion lifetime is to remove the preexisting stress concentrations from the bond cluster at its initial state.…”

“…Once the separation length δ has reached a value of roughly 2l b , rebinding of the ligand/receptor becomes almost impossible no matter how great the rebinding factor is [Qian et al 2008]. In our model we consider both stochastic rebinding and rupturing of all bonds within a focal adhesion.…”

“…Their model showed that the larger the focal adhesion becomes the longer adhesion lifetime it can experience. Qian et al [2008;2009] were the first to model focal adhesions between cell and substrate in terms of clusters of ligand/receptor bonds between two dissimilar continuous elastic media, showing the effects of varying adhesion size and system stiffness on focal adhesion strength and lifetime. According to their results, a possible explanation for the characteristic micron-size scale of focal adhesions is that small adhesion size leads to single-molecule-like behavior of limited lifetime because of statistical effects whereas large adhesion also leads to single-molecule-like behavior because of the focusing effect of stress concentration that confines the bond dissociation events to a smaller number of bonds near the adhesion edges.…”

“…However, due to the elasticity effects of the system, there is an upper limit in size of a focal adhesion in order for it to avoid stress concentration effect [Qian et al 2008;2009]. It has also been shown that stiffness of cell and substrate is a factor in controlling the stability of focal adhesions, and cells have a preference towards stiffer substrates potentially due to the increased focal adhesion lifetime [Qian et al 2008;2009].…”