Relaxation and curvature-induced molecular flows within multicomponent membranes

Richard G Morris

doi:10.1103/physreve.89.062704

Abstract

The quantitative understanding of membranes is still rooted in work performed in the 1970s by Helfrich and others, concerning amphiphilic bilayers. However, most biological membranes contain a wide variety of nonamphiphilic molecules too. Drawing analogy with the physics of nematic-non-nematic mixtures, we present a dynamical (out-of-equilibrium) description of such multicomponent membranes. The approach combines nematohydrodynamics in the linear regime and a proper use of (differential-) geometry. The main result is to demonstrate that one can obtain equations describing a cross-diffusion effect (similar to the Soret and Dufour effects) between curvature and the (in-membrane) flow of amphiphilic molecules relative to nonamphiphilic ones. Surprisingly, the shape of a membrane relaxes according to a simple heat equation in the mean curvature, a process that is accompanied by a simultaneous boost to the diffusion of amphiphiles away from regions of high curvature. The model also predicts the inverse process, by which the forced bending of a membrane induces a flow of amphiphilic molecules towards areas of high curvature. In principle, numerical values for the relevant diffusion coefficients should be verifiable by experiment.

Highlights

The behavior of the cell membrane is crucially important to a wide variety of processes in biology [1]
Since the underlying construction of almost all biological membranes is that of an amphiphilic bilayer, much of the physics literature has so far focused on understanding simple bilayers and their closed-form counterparts, vesicles [2,3]
The result was obtained by combining nematohydrodynamics and geometry under the important assumption (18), which is equivalent to the statement that

Summary

INTRODUCTION

The behavior of the cell membrane is crucially important to a wide variety of processes in biology [1]. Recently have attempts been made to write nonequilibrium descriptions of membrane dynamics, but so far the focus has been solely on vesicles [18,19,20,21,22] Taking inspiration from such studies, this article goes back to the original model of Helfrich and demonstrates that it can be extended by analogy with nematohydrodynamics in the linear regime. As we show, such an approach permits the incorporation of additional nonamphiphilic components and leads to a membrane description in terms of both curvature and in-membrane molecular flows

FREE ENERGY OF THE MEMBRANE

Elastic description of amphiphilic interactions

Gaussian curvature

RECIPROCAL LINEAR RELATIONS AND CROSS-DIFFUSION

DISCUSSION