Revisiting the entropic force between fluctuating biological membranes

TL;DR

This study critically reexamines the entropic force between biological membranes, revealing a different scaling law at small separations than previously accepted, with implications for understanding membrane interactions.

Contribution

The paper provides an analytical and simulation-based reassessment of the entropic membrane force, challenging the traditional $1/d^3$ scaling at small separations.

Findings

At small separations, pressure scales as 1/d, not 1/d^3.

At intermediate separations, results agree with Helfrich.

At large separations, pressure decays exponentially.

Abstract

The complex interplay between the various attractive and repulsive forces that mediate between biological membranes governs an astounding array of biological functions: cell adhesion, membrane fusion, self-assembly, binding-unbinding transition among others. In this work, the entropic repulsive force between membranes---which originates due to thermally excited fluctuations---is critically reexamined both analytically and through systematic Monte Carlo simulations. A recent work by Freund \cite {Freund13} has questioned the validity of a well-accepted result derived by Helfrich \cite{Helfrich78}. We find that, in agreement with Freund, for small inter-membrane separations ($d$), the entropic pressure scales as $p\sim 1/d $, in contrast to Helfrich's result: $p\sim 1/d^3$. For intermediate separations, our calculations agree with that of Helfrich and finally, for large inter-membrane separations, we observe an exponentially decaying behavior.