  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.
