Cross-link-governed dynamics of biopolymer networks

Recent experiments show that networks of stiff biopolymers cross-linked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by cross-links in such networks. We show that a single microscopic time scale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times and a shear modulus G ∼ ω(1/2) for low frequencies ω. This model quantitatively describes the measured rheology of actin networks cross-linked with α-actinin-4 over more than four decades in frequency.