Lifetime and Strength of Periodic Bond Clusters between Elastic Media under Inclined Loading

Abstract

Focal adhesions are clusters of specific receptor-ligand bonds that link an animal cell to an extracellular matrix. To understand the mechanical responses of focal adhesions, here we develop a stochastic-elasticity model of a periodic array of adhesion clusters between two dissimilar elastic media subjected to an inclined tensile stress, in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction are unified in a single modeling framework. We first establish a fundamental scaling law of interfacial traction distribution and derive a stress concentration index that governs the transition between uniform and cracklike singular distributions of the interfacial traction within molecular bonds. Guided by this scaling law, we then perform Monte Carlo simulations to investigate the effects of cluster size, cell/extracellular matrix modulus, and loading direction on lifetime and strength of the adhesion clusters. The results show that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, and low-angle pulling are factors that contribute to the stability of focal adhesions. The predictions of our model provide feasible explanations for a wide range of experimental observations and suggest possible mechanisms by which cells can modulate adhesion and deadhesion via cytoskeletal contractile machinery and sense mechanical properties of their surroundings.

Effects of contact surface shape on lifetime of cellular focal adhesion

“…Comparing the focal adhesion lifetimes between E * = 200 kPa and E * = 100 kPa shows that the adhesion lifetimes are much smaller for the softer system. This is concurrent to the results shown in other studies of system stiffness and adhesion lifetime [Qian et al 2008;2009]. Besides this difference in magnitude of adhesion lifetime, the behavior of the data in the case of E * = 100 kPa seems to differ when compared to the results shown in Figure 3, top left.…”

“…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.…”

“…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].…”