Nonequilibrium diffusion of active particles bound to a semiflexible polymer network: Simulations and fractional Langevin equation

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question concerns quantitatively explaining how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semiflexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays superdiffusive and subdiffusive a thermal motion with a time-dependent anomalous exponent alpha. In such viscoelastic feedback, the active particle always exhibits superdiffusion with alpha = 3/2 at times shorter than the self-propulsion time (tau(A)). At times greater than tau(A), the subdiffusive motion emerges with alpha bounded between 1/2 and 3/4. Remarkably, active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high Pe limit, athermal fluctuation in the stiff filament eventually leads to alpha = 1/2, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semiflexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe (Pe *) and crossover times (t* and t dagger) above which active viscoelastic dynamics emerge on timescales of tau* less than or similar to t less than or similar to tau dagger. Our study may provide theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments. Published under an exclusive license by AIP Publishing.