Effective elasticity and persistence of strain in active filament-motor assemblies

The spatial extent to which elastic deformations of cross-linked filaments persist in noisy active environments and the associated decay length plays a fundamental role in many biological settings. Here, we study the mechanical response of an active ordered composite comprised of elastic filaments sheared by active motors. We compare results from Brownian multi-particle collision dynamics-based numerical simulations for actively driven deformations of noisy and moderately soft composites with theoretical predictions from a mean-field theory valid in the noiseless and weakly elastic limit. Surprisingly, several qualitative features predicted by the noise-less mean field model are seen even in strongly noisy simulations. We find, from both theory and simulations, that even when extensibility is negligible locally, it cannot be ignored when considering global deformation fields. This is because the length scale over which extensional deformations persist is controlled by the competition between passive elasticity of the filament and active effective shear stiffening due to attached motors and other crosslinks. Specifically, for fixed motor kinetics and properties, the decay length of extensional deformations is controlled by the ratio of the passive elastic modulus of the composite to an effective active, motor generated shear modulus. For steady strains, the length scale is surprisingly independent of motor activity except when motors are in a state of rigor. For oscillatory strains, the persistence length may be varied strongly by changing the frequency of forcing. When the effect of noise is dominant, the strain fields on the filament becomes uncorrelated. Our study demonstrates how correlated activity in natural ordered active matter possesses a finite range of influence with testable experimental implications.