A Chemomechanical Model of Matrix and Nuclear Rigidity Regulation of Focal Adhesion Size

In this work, a chemomechanical model describing the growth dynamics of cell-matrix adhesion structures (i.e., focal adhesions (FAs)) is developed. We show that there are three regimes for FA evolution depending on their size. Specifically, nascent adhesions with initial lengths below a critical value that are yet to engage in actin fibers will dissolve, whereas bigger ones will grow into mature FAs with a steady state size. In adhesions where growth surpasses the steady state size, disassembly will occur until their sizes are reduced to the equilibrium state. This finding arises from the fact that polymerization of adhesion proteins is force-dependent. Under actomyosin contraction, individual integrin bonds within small FAs (i.e., nascent adhesions or focal complexes) must transmit higher loads while the phenomenon of stress concentration occurs at the edge of large adhesion patches. As such, an effective stiffness of the FA-extracellular matrix complex that is either too small or too large will be relatively low, resulting in a limited actomyosin pulling force developed at the edge that is insufficient to prevent disassembly. Furthermore, it is found that a stiffer extracellular matrix and/or nucleus, as well as a stronger chemomechanical feedback, will induce larger adhesions along with a higher level of contraction force. Interestingly, switching the extracellular side from an elastic half-space, corresponding to some widely used in vitro gel substrates, to a one-dimensional fiber (as in the case of cells anchoring to a fibrous scaffold in vivo) does not qualitative change these conclusions. Our model predictions are in good agreement with a variety of experimental observations obtained in this study as well as those reported in the literature. Furthermore, this new model, to our knowledge, provides a framework with which to understand how both intracellular and extracellular perturbations lead to changes in adhesion structure number and size.