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

Cross-linked, elastic, filamentous networks that are deformed by active molecular motors feature in several natural and synthetic settings. The effective active elasticity of these composite systems determines the length scale over which active deformations persist in fluctuating environments. This fundamental quantity has been studied in passive systems; however mechanisms determining and modulating this length-scale in active systems has not been clarified. Here, focusing on active arrayed filament-motor assemblies, we propose and analyze a minimal model in order to estimate the length scale over which imposed or emergent elastic deformations or stresses persist. We combine a mean-field continuum theory valid for weakly elastic assemblies with high dimensional Multi-Particle Collision (MPC) based Brownian simulations valid for moderate to strongly elastic and noisy systems. Integrating analytical and numerical results, we show that localized strains - steady or oscillatory - persist over well-defined length scales that dependent on motor activity, effective shear elasticity and filament extensibility. Extensibility is key even in very stiff filaments, and cannot be ignored when global deformations are considered. We clarify mechanisms by which motor derived active elasticity and passive shear elasticity of the filamentous backbone combine to effectively soften filaments. Surprisingly, the predictions of the mean-field theory agree qualitatively with results from stochastic discrete filament-motor model, even for moderately strong noise. We also find that athermal motor noise impacts the overall duty ratio of the motors and thereby the persistence length in these driven assemblies. Our study demonstrates how correlated activity in natural ordered active matter possesses a finite range of influence with clear testable experimental implications.