Dynamics of a stochastically driven Brownian particle in one dimension

TL;DR

This paper analyzes the stochastic dynamics of two hardcore particles with different diffusion rates, revealing a crossover from diffusion to drift and an intermediate subdiffusive regime, with implications for biological membrane processes.

Contribution

It introduces a detailed model of two diffusing particles with different rates, highlighting a novel crossover behavior and subdiffusive intermediate regime.

Findings

Positional fluctuation of M shows a crossover from diffusion to drift.

Intermediate subdiffusive regime can be significantly large.

Model relates to biological membrane protrusions and actin filament dynamics.

Abstract

We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses slowly towards the second particle, labeled M. The displacements of particle M exhibits a crossover from diffusion to drift at a characteristic time which depends on the rate constants. We show that the positional fluctuation of M exhibits an intermediate crossover regime of subdiffusion separating initial and asymptotic diffusive behavior; this is in agreement with the complete set of Master Equations that describe the stochastic evolution of the model. The intermediate crossover regime can be considerably large depending on the hopping probabilities of the two particles. This is in contrast to the known crossover from diffusive to subdiffusive behavior of a tagged particle that is in the interior of a large single-file system on an unbound real line. We discuss our model with respect to the biological phenomena of membrane protrusions where polymerizing actin filaments (F) push the cell membrane (M).