Entanglement Density Tunes Microscale Nonlinear Response of Entangled Actin

We optically drive a microsphere at constant speed through entangled actin networks of 0.2 - 1.4 mg/ml at rates faster than the critical rate controlling the onset of a nonlinear response. By measuring the resistive force exerted on the microsphere during and following strain we reveal a critical concentration \(c^{*}\simeq0.4\) mg/ml for nonlinear features to emerge. For \(c>c^{*}\), entangled actin stiffens at short times with the degree of stiffening \(S\) and corresponding timescale \(t_{stiff}\) scaling with the entanglement tube density, i.e. \(S\sim t_{stiff}\sim d_t^{-1}\sim c^{3/5}\). The network subsequently yields to a viscous regime with the yield distance \(d_y\) scaling linearly with yield force \(f_y\) and inversely with the entanglement length (\(f_y\sim d_y\sim l_{e}^{-1} \sim c^{2/5}\)). Stiffening and yielding dynamics are consistent with recent theoretical predictions for nonlinear cohesive breakdown of entanglements. We further show that above \(c^{*}\) force relaxation proceeds via slow filament disengagement from dilated tubes coupled with \(\sim\)10x faster lateral hopping, with the corresponding concentration dependences in agreement with recent theoretical predictions for entangled rigid rods.