A model for cellular mechanotransduction and contractility at finite strain

In this work we introduce a theoretical and computational modeling framework for the contractile response of single cells triggered by external mechanical stimuli. The structural response due to the formation and dissociation of stress fibers is modeled following isotropic anisotropic contractile phases with an orientation that evolves with time and strain. The passive and active structural components are postulated to act in parallel, and the re-orientation process drives the anisotropic phase of stress fiber orientation to align with the direction of the maximum principal stretch. A reduced form of the Hai-Murphy model is used to follow kinetics of myosin states considering the combined effect of "latch"- and "cross"-bridge states. The introduction of distinct isotropic and anisotropic activation allows modeling of the contractile intensity of each phase. Tractions on the cell surface initiate bio-chemical signaling through the RhoA pathway, which in turn controls both myosin contraction and F-actin polymerization. A signaling model is introduced to effectively connect intracellular events with the tractions on the cell surface. The overall model is defined by a free energy density function that couples the deformation and the activation, and associated equilibrium and kinetic models for evolution. Features of the model are highlighted via implementation in a finite element model and application to benchmark problems. The model captures the dynamic contractile responses of cells and stress fiber re-alignment under complex load histories. For example, physiologically relevant scenario such as relaxation of cells to their initial state upon removal of applied loads can be simulated.