Entangled F-actin displays a unique crossover to microscale nonlinearity dominated by entanglement segment dynamics

We drive optically trapped microspheres through entangled F-actin at constant speeds and distances well beyond the linear regime, and measure the microscale force response of the entangled filaments during and following strain. Our results reveal a unique crossover to appreciable nonlinearity at a strain rate of [small gamma, Greek, dot above]c ≈ 3 s(-1) which corresponds remarkably well with the theoretical rate of relaxation of entanglement length deformations 1/τent. Above [small gamma, Greek, dot above]c, we observe stress stiffening which occurs over very short time scales comparable to the predicted timescale over which mesh size deformations relax. Stress softening then takes over, yielding to an effectively viscous regime over a timescale comparable to the entanglement length relaxation time, τent. The viscous regime displays shear thinning but with a less pronounced viscosity scaling with strain rate compared to flexible polymers. The relaxation of induced force on filaments following strain shows that the relative relaxation proceeds more quickly for increasing strain rates; and for rates greater than [small gamma, Greek, dot above]c, the relaxation displays a complex power-law dependence on time. Our collective results reveal that molecular-level nonlinear viscoelasticity is driven by non-classical dynamics of individual entanglement segments that are unique to semiflexible polymers.