On stress fibre reorientation under plane substrate stretching

It is well documented in literature that under plane substrate stretching adherent cells reorganize their actin cytoskeleton by reorienting their stress fibres in one or two distinct directions, depending upon the magnitude of the substrate strain and the contractile mechanism of the cell. Since the cell is a quite deformable body, previous theoretical modelling according to the principles of linear elasticity theory is not adequate. Experimental evidence such as the concurrent appearance of two distinct and symmetric directions of orientation of the stress fibres in the same cell indicates the presence of a coexistence of phases nonlinear elastic phenomenon. Moreover, the aforementioned evidence supports the assumption that the strain energy density function of the stress fibres should be nonconvex. In the present study, following finite elasticity principles, the reorientation phenomenon is treated as a nonlinear elastic stability problem adopting the global (Maxwell's) criterion. In this way, apart from explaining thoroughly the coexistence of phases phenomenon, the contribution of other key elements, such as prestress and substrate strain, is stressed out. Further, the nonconvexity factor is correlated to the influence of the small GTPase Rho, regulator of the formation of the actin stress fibres. The predominant final stress fibres configuration, that is transverse to the maximum extracellular strain direction and appears after the coexistence of phases placement, is also clarified. The mathematical model that is proposed here for the description of adherent cell behaviour under plane substrate stretching is an extension of previous work by the authors, where the orientation of stress fibres under uniaxial substrate stretching was studied.