Using a form-finding model to analyze the effect of actin bundles on the stiffness of a cytoskeleton network

Networks of actin filaments and bundles are ubiquitous in cellular cytoskeletons, but the elasticity of the network is not well understood. In this paper, a computational model based on form-finding analysis is proposed to investigate the stiffness of cytoskeleton networks consisting of actin filaments and bundles. The model shows that networks with parallel bundles aligned in the stretching direction are stiffer than those with randomly distributed bundles. The results provide a mechanical explanation for the experimental observation that cells primarily create parallel rather than disordered bundles during cell adhesion and cell motion. The effect of filament undulations on network stiffness is explored briefly. The results show that undulations can soften the network by increasing the bending-dominated deformations in filaments and bundles. Finally, we find that the effect of the relative density of bundles depends on their orientation. Increasing the density of randomly distributed bundles has no effect on the stiffness of cells, but softens the cytoskeleton network. In contrast, the stiffness of networks of parallel bundles first increases, then reduces as the relative density of bundles increases. The stiffest network is a mixture of actin filaments and bundles.