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

Cross-linked composite filaments animated by molecular motors are ubiquitous in biology. An important length scale that controls the range of force transmission in these filament-motor assemblies is the distance over which elastic strain fields persist. Previous studies have identified this persistence or decay length in passive networks, and recently, in random elastic networks with embedded elements generating constant forces or stresses. Yet, the range over which strains persist in assembles comprised of motors attaching stochastically to nearly inextensible filaments remains unclear. Here, we analyze the intrinsic decay length for extensional strain in a minimal model - ordered composite assemblies comprised of cross-linked filaments interacting with arrayed motors. We explores three related concepts: the effective active elasticity of these assembles, the length scale over which localized elastic strains persist in these systems, and its dependence on motor kinetics for static and oscillatory deformations. By combining mean-field theory for noiseless weakly extensible systems with Multi-Particle Collision Brownian simulations for noisy systems we are able to additionally investigate the effects of motor noise. For steady strains, we find that the persistence length is independent of motor kinetics and dependent on the passive elasticity of the composite. For oscillatory strains, the persistence length is frequency dependent and depends on passive elasticity and on motor kinetics. For strong motor activity, the decay length is significantly modulated by extensional softening resulting from attached motors. Theoretical predictions agree qualitatively with our simulations, even at low motor numbers or moderately strong motor noise. Taken together, our results highlight how extensional strain and correlated dynamics in possess a finite range of influence even in active networks comprised of nearly inextensible filaments.