Brownian motion near an elastic cell membrane: A theoretical study

TL;DR

This paper provides a theoretical analysis of Brownian motion near elastic cell membranes, revealing how membrane elasticity influences particle transport and diffusion behavior, with validation through simulations.

Contribution

It introduces an analytical framework for understanding Brownian motion near elastic membranes, incorporating frequency-dependent mobility and memory effects, which was not previously detailed.

Findings

Elastic membranes induce long-lived subdiffusive regimes.

Diffusion near elastic membranes approaches no-slip wall behavior in steady state.

Analytical results are validated with boundary-integral simulations.

Abstract

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.