Stability of Adhesion Clusters and Cell Reorientation under Lateral Cyclic Tension

Abstract

This work is motivated by experimental observations that cells on stretched substrate exhibit different responses to static and dynamic loads. A model of focal adhesion that can consider the mechanics of stress fiber, adhesion bonds, and substrate was developed at the molecular level by treating the focal adhesion as an adhesion cluster. The stability of the cluster under dynamic load was studied by applying cyclic external strain on the substrate. We show that a threshold value of external strain amplitude exists beyond which the adhesion cluster disrupts quickly. In addition, our results show that the adhesion cluster is prone to losing stability under high-frequency loading, because the receptors and ligands cannot get enough contact time to form bonds due to the high-speed deformation of the substrate. At the same time, the viscoelastic stress fiber becomes rigid at high frequency, which leads to significant deformation of the bonds. Furthermore, we find that the stiffness and relaxation time of stress fibers play important roles in the stability of the adhesion cluster. The essence of this work is to connect the dynamics of the adhesion bonds (molecular level) with the cell's behavior during reorientation (cell level) through the mechanics of stress fiber. The predictions of the cluster model are consistent with experimental observations.

Frequency-Dependent Focal Adhesion Instability and Cell Reorientation Under Cyclic Substrate Stretching

“…However, we expected that the force for inducing the rupture of focal adhesions should be much larger than the force that triggering the catch bond, and we focused our attention on the effects of the force of larger scale by adopting the simple view of the Bell model. To consider the bond formation, the forward rate k on can be described as, 21,36 k on ¼ k where k 0 on is the forward rate constant for an immobile contact, s c is the contact time and s b is the association time of integrin-ligand bonds. The contact time s c is defined as the time during which the free end of the bond is exposed to a contact area that moves with respect to the bond, given by…”

“…17,34 In addition, the threshold value of external loading for cell reorientation can be predicted by assuming a limiting anchoring strength of the FAs. 12,36,37 Cell reorientation is cell's responses to the external load via the interplay of dynamic responses of FAs and those of actin cytoskeleton. The mechanical properties (elastic and viscoelastic) of cells are mainly determined by the stability of FAs, the mechanical properties of cytoskeleton, and the loading modes of the stimuli.…”

“…Their model captured the exponential relationship of the loading frequency vs. cell reorientation time. Inspired by the force dipole model, Kong et al 30,36 developed a mesoscopic model that not only considered the dynamics of adhesion molecules, but also accounted for the mechanical properties of stress fiber. They showed that the loading frequency affected FA's stability that consequently affected the cell reorientation.…”

A discrete approach for modeling cell–matrix adhesions

“…Olberding et al [28] proposed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. Kong et al [21] treated the focal adhesion as an adhesion cluster and studied the stability of this cluster under dynamic load by applying cyclic external strain on the substrate. There are also other works that were not specifically conceived for cell adhesions, but their methodology can be applied to model them.…”

Adhesion of a gas-filled membrane on a stretched substrate

“…In microscopic views, cell-cell and cell-substrate adhesion was studied with statistical physics method, such as the well-known Bell's model (Bell, 1978). In order to interpret cell reorientation in experiments, Kong et al (2008) established a stochastic model to investigate the stability of focal adhesion under a dynamic load by applying an externally cyclical strain on substrates, and found that a threshold of the external strain amplitude exists beyond which the adhesion cluster disrupts quickly. Combining the statistical physics and the elastic contact theory, series of theoretical models were proposed in order to characterize cell-substrate adhesion (Gao et al, 2011;Qian and Gao, 2010;Zhang et al, 2013Zhang et al, , 2012, in which the effect of matrix stiffness (Qian and Gao, 2010), anisotropy of matrix material (Zhang et al, 2013), graded modulus of substrates (Zhang et al, 2012) and the pulling angle of external forces (Gao et al, 2011) were considered.…”