On the orientation of plane tensegrity cytoskeletons under biaxial substrate stretching

Two different simple cases of plane tensegrity cytoskeleton geometries are presented and investigated in terms of stability. The tensegrity frames are used to model adherent cell cytoskeletal behaviour under the application of plane substrate stretching and describe thoroughly the experimentally observed reorientation phenomenon. Both models comprise two elastic bars (microtubules), four elastic strings (actin filaments) and are attached on an elastic substrate. In the absence of external loading shape stability of the cytoskeleton is dominated by its prestress. Upon application of external loading, the cytoskeleton is reorganized in a new direction such that its total potential energy is rendered a global minimum. Considering linear constitutive relations, yet large deformations, it is revealed that the reorientation phenomenon can be successfully treated as a problem of ma- thematical stability. It is found that apart from the magnitude of contractile prestress and the magnitude of extracellular stretching, the reorientation is strongly shape–dependent as well. Numerical applications not only justify laboratory data reported in literature but such experimental evidence as the concurrent appearance of two distinct and symmetric directions of orientation, indicating the cellular coexistence of phases phenomenon, are clearly detected and incorporated in the proposed mathematical treatment.