Diffusion on Ruffled Membrane Surfaces

TL;DR

This paper develops a Langevin equation and a Brownian Dynamics algorithm to study particle diffusion on rough and fluctuating surfaces, revealing how surface properties influence effective diffusivity.

Contribution

It introduces a position Langevin equation for overdamped particles on rough surfaces and demonstrates a numerical method to predict effective diffusion coefficients.

Findings

Area-scaling prediction matches numerical results for static rough surfaces.

Surface fluctuations increase effective diffusivity, approaching a limit.

Protein motion on cell surfaces involves multiple physical regimes.

Abstract

We present a position Langevin equation for overdamped particle motion on rough two-dimensional surfaces. A Brownian Dynamics algorithm is suggested to evolve this equation numerically, allowing for the prediction of effective (projected) diffusion coefficients over corrugated surfaces. In the case of static surface roughness, we find that a simple area-scaling prediction for the projected diffusion coefficient leads to seemingly quantitative agreement with numerical results. To study the effect of dynamic surface evolution on the diffusive process, we consider particle diffusion over a thermally fluctuating elastic membrane. Surface fluctuation has the effect of increasing the effective diffusivity toward a limiting annealed-surface value discussed previously. We argue that protein motion over cell surfaces spans a variety of physical regimes, making it impossible to identify a single approximation scheme appropriate to all measurements of interest.