A model for the contractility of the cytoskeleton including the effects of stress-fibre formation and dissociation

A model for the contractility of cells is presented that accounts for the dynamic reorganization of the cytoskeleton. It is motivated by three key biochemical processes: (i) an activation signal that triggers actin polymerization and myosin phosphorylation, (ii) the tension-dependent assembly of the actin and myosin into stress fibres, and (iii) the cross-bridge cycling between the actin and the myosin filaments that generates the tension. Simple relations are proposed to model these coupled phenomena and a constitutive law developed for the activation and response of a single stress fibre. This law is generalized to twoand three-dimensional cytoskeletal networks by employing a homogenization analysis and a finite strain continuum model is developed. The key features of the model are illustrated by considering: (i) a single stress fibre on a series of supports and (ii) a two-dimensional square cell on four supports. The model is shown to be capable of predicting a variety of key experimentally established characteristics including: (i) the decrease of the forces generated by the cell with increasing support compliance, (ii) the influence of cell shape and boundary conditions on the development of structural anisotropy, and (iii) the high concentration of the stress fibres both at the focal adhesions and at the sites of localized applied tension. Moreover, consistent with the experimental findings, the model predicts that multiple activation signals are more effective at developing stress fibres than a single prolonged signal.