Dynamics of a stochastically driven Brownian particle in one dimension

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).

Crawling of a driven adherent membrane

“…In fact, for the special case M = 1 and p 1 the velocity has a linear relationship v ∼ p, which is in variance with classical two-particles theories. 9,10,32,45 The saturation of vM ≈ 0.785 for ε = 0 and pM 1 has a similar origin as the saturation of L/M (compare Fig. 4(a)): for large drag pM 1 and large membranes M 1, the cortex-driven front part near the leading edge of the membrane, which is short ranged, becomes less important as compared to the trailing part of the membrane, which is dragged behind.…”

“…(1) Our current theoretical understanding of membrane protrusion is based on two-particle approximations, 9,10,31,32,45 which do not take into account the size of the cell membrane. It is conceivable, however, that the mass M of the cell membrane must play a role.…”