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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 insight into how the mechanical properties of cytoskeletal networks may depend on their underlying constituting elements. We incorporate three important ingredients: nonaffine filament deformations in response to network strain; interplay between filament and crosslink mechanical properties; reversible crosslink (un)binding in response to 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 crosslink are unbound. This softening due to crosslink unbinding generically competes with an inherent stiffening response, which may either be due to filament or crosslink nonlinear elasticity.