Hybrid simulations of lateral diffusion in fluctuating membranes

TL;DR

This paper presents a new numerical simulation method for lateral diffusion of particles in fluctuating membranes, accounting for membrane height fluctuations and particle dynamics, and compares results with analytical approximations.

Contribution

The authors introduce a coupled dynamic simulation approach for membrane fluctuations and particle diffusion, validating it against analytical preaveraging approximations.

Findings

The simulation accurately reproduces diffusion behavior in fluctuating membranes.

The preaveraging approximation is valid over a surprisingly large parameter range.

Results provide insights into the relationship between projected and intramembrane diffusion coefficients.

Abstract

In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.