Membrane fluctuations near a plane rigid surface

TL;DR

This study combines analytical and simulation methods to analyze how a rigid surface influences the thermal fluctuations of a nearby membrane, modeling the effect as a weak quadratic confinement that mainly affects large-scale bending modes.

Contribution

It introduces a simplified quadratic potential model to describe surface effects on membrane fluctuations, supported by analytical calculations and Monte Carlo simulations.

Findings

Surface influence is modeled as a quadratic confining potential.

Maximum confinement occurs when membrane corners are a few nanometers from the surface.

Confinement mainly affects the amplitude of large bending modes.

Abstract

We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance $d$ above a plane rigid surface. Our analysis shows that the surface influence on the bilayer fluctuations can be effectively described in terms of a uniform confining potential that grows quadratically with the height of the membrane $h$ relative to the surface: $V=(1/2)\gamma h^2$. The strength $\gamma$ of the harmonic confining potential vanishes when the corners of the membrane patch are placed directly on the surface ($d=0$), and achieves its maximum value when $d$ is of the order of a few nanometers. However, even at maximum strength the confinement effect is quite small and has noticeable impact only on the amplitude of the largest bending mode.