The Non-Equilibrium Thermodynamics and Kinetics Governing Coupled Stress Fiber and Focal Adhesion Dynamics

Abstract

We consider the coupled mechano-chemistry governing the cytoskeletal force in cells with stress fibers and focal adhesions. Our studies include published experimental work in which we monitor the cytoskeletal forces in cells on elastomeric substrates of micron-sized posts. These experiments demonstrate complex dynamics involving substrate strain as well as the binding/unbinding of cytoskeletal and focal adhesion proteins. Our model explains these dynamics, which underlie force generation and motility of, especially, mesenchymal cells. The broader motivation for this research comes from our ongoing work on cancer cell motility and invasion. Guided by our experiments, our model considers a single stress fiber, the focal adhesion by which it is attached to a micropost, the cell reservoir of cytoskeletal and focal adhesion proteins, the deforming micropost and underlying substrate. The complex mechano-chemistry that controls these sub-systems' interaction is itself governed by non-equilibrium thermodynamics: The binding/unbinding of proteins is driven by free energy changes due to chemistry, elasticity and mechanical work done. The stress fibers' mechanical response has viscoelastic and active contributions, the latter due to myosin contractility. Our model, an extension of our recently published work, generates a very rich range of responses depending on the mechanical and chemical boundary conditions, and parameter values (which are obtained from our experiments, and well-established estimates from the literature). This range of model responses includes every case observed in our experiments. We find that while applied strain and acto-myosin contractility dictate the increase of force in stress fibers over the short to medium time scale (∼600 sec.), the longer time scale response (∼1000-10000 sec) is dominated by the growth and disassembly of focal adhesions. These findings have direct implications for published and ongoing work on cancer cell locomotion in our group.