A constrained mixture approach to mechano-sensing and force generation in contractile cells

Biological tissues are very particular types of materials that have the ability to change their structure, properties and chemistry in response to external cues. Contractile cells, i.e. fibroblasts, are key players of tissue adaptivity as they are capable of reorganizing their surrounding extra-cellular matrix (ECM) by contracting and generating mechanical forces. This contractile behavior is attributed to the development of a stress-fiber (SF) network within the cell's cytoskeleton, a process that is known to be highly dependent of the nature of the mechanical environment (such as ECM stiffness or the presence of stress and strain). To describe these processes in a consistent manner, the present paper introduces a mutiphasic formulation (fluid/solid/solute mixture) that accounts for four major elements of cell contraction: cytoskeleton, cytosol, SF and actin monomers, as well as their interactions. The model represents the cross-talks between mechanics and chemistry through various means: (a) a mechano-sensitive formation and dissociation of an anisotropic SF network described by mass exchange between actin monomer and polymers, (b) a bio-mechanical model for SF contraction that captures the well-known length-tension and velocity-tension relation for muscles cells and (c) a convection/diffusion description for the transport of fluid and monomers within the cell. Numerical investigations show that the multiphasic model is able to capture the dependency of cell contraction on the stiffness of the mechanical environment and accurately describes the development of an oriented SF network observed in contracting fibroblasts.