Co-entangled actin-microtubule composites exhibit tunable stiffening and power-law stress relaxation

We use optical tweezers microrheology and fluorescence microscopy to characterize the nonlinear mesoscale mechanics and mobility of in vitro co-entangled actin-microtubule composites. We create a suite of randomly-oriented, well-mixed networks of actin and microtubules by co-polymerizing varying ratios of actin and tubulin in situ. To perturb each composite far from equilibrium, we use optical tweezers to displace an embedded microsphere a distance greater than the lengths of the filaments at a speed much faster than their intrinsic relaxation rates. We simultaneously measure the resistive force the filaments exert and the subsequent force relaxation. We find that the presence of a large fraction of microtubules (>0.7) is needed to substantially increase the resistive force, which is accompanied by large heterogeneities in force response. Actin minimizes these heterogeneities by reducing the mesh size of the composites and supporting microtubules against buckling. Composites also undergo a sharp transition from stress-softening to stiffening when the fraction of microtubules ({phi}T) exceeds 0.5, by microtubules suppressing actin bending fluctuations. The induced force following strain relaxes via two time-dependent power-law decays. The first decay phase, with scaling exponents that increase proportionally with the fraction of actin, signifies actin bending fluctuations. Alternatively, the second phase, with a{phi} T-independent scaling exponent of ~0.4, is indicative of filaments reptating out of deformed entanglement constraints. Corresponding mobility measurements of steady-state actin and microtubules show that both filaments are more mobile in equimolar composites ({phi}T=0.5) compared to networks of primarily actin or microtubules. This non-monotonic dependence of mobility on{phi} T, which further demonstrates the important role mesh size plays in composites, highlights the surprising emergent properties that can arise in composites.