Stress relaxation through crosslink unbinding in cytoskeletal networks

The mechanical properties of cells are dominated by the cytoskeleton, an interconnected network of long elastic filaments. The connections between the filaments are provided by crosslinking proteins, which constitute, next to the filaments, the second important mechanical element of the network. An important aspect of cytoskeletal assemblies is their dynamic nature, which allows remodeling in response to external cues. The reversible nature of crosslink binding is an important mechanism that underlies these dynamical processes. Here, we develop a theoretical model that provides us insight into how the mechanical properties of cytoskeletal networks may depend on their underlying constituting elements. We incorporate three important ingredients: non-affine filament deformations in response to network strain; the interplay between filament and crosslink mechanical properties; and reversible crosslink (un) binding in response to the imposed stress. With this we are able to self-consistently calculate the nonlinear modulus of the network as a function of deformation amplitude and crosslink as well as filament stiffnesses. During loading, crosslink unbinding processes lead to a relaxation of stress and therefore to a reduction of the network modulus and eventually to network failure, when all crosslinks are unbound. This softening due to crosslink unbinding generically competes with an inherent stiffening response, which may be due to either filament or crosslink nonlinear elasticity.