Nonlinear molecular deformations give rise to stress stiffening, yielding and non-uniform stress propagation in actin networks

Abstract

We use optical tweezers microrheology and fluorescence microscopy to apply nonlinear microscale strains to entangled and crosslinked actin networks, and measure the resulting stress and actin filament deformations. We couple nonlinear stress response and subsequent relaxation to the velocity profiles of individual fluorescent-labeled actin segments at varying times throughout the strain and varying distances from the strain path to determine the underlying molecular dynamics that give rise to the debated nonlinear response and stress propagation of crosslinked and entangled actin networks at the microscale. We show that initial stress stiffening arises from acceleration of strained filaments due to molecular extension along the strain, while softening and yielding is coupled to filament deceleration, halting and recoil. We demonstrate a surprising non-monotonic dependence of velocity profiles on crosslinker concentration. Namely, networks with no crosslinks or substantial crosslinks both exhibit fast initial filament velocities and reduced molecular recoil while intermediate crosslinker concentrations display reduced velocities and increased recoil. We show that these collective results are due to a balance of network elasticity and transient crosslinker unbinding and rebinding. We further show that elasticity and relaxation timescales display an exponential dependence on crosslinker concentration that reveal that crosslinks dominate entanglement dynamics when the length between crosslinkers becomes smaller than the length between entanglements. In accord with recent simulations, our relaxation dynamics demonstrate that post-strain stress can be long-lived in crosslinked networks by distributing stress to a small fraction of highly-strained connected filaments that span the network and sustain the load, thereby allowing the rest of the network to recoil and relax.