Self-reinforcing directionality generates truncated Levy walks without the power-law assumption

We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Levy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)]. We derive the nonhomogeneous in space and time, hyperbolic partial differential equation for the probability density function (PDF) of particle position. This PDF exhibits a bimodal density (aggregation phenomena) in the superdiffusive regime, which is not observed in classical linear hyperbolic and Levy walk models. We find the exact solutions for the first and second moments and criteria for the transition to superdiffusion.

Automated summary

This study introduces a persistent random walk model to explain how exponentially distributed runs self-organize into truncated Levy walks observed in active intracellular transport. The PDF of particle position derived in the study shows bimodal density in the superdiffusive regime, which is not observed in classical linear hyperbolic and Levy walk models. Exact solutions for the first and second moments, as well as criteria for the transition to superdiffusion, are also found.