Effective free energy for pinned membranes

TL;DR

This paper derives an upper bound for the free energy of pinned membranes, maps the interactions onto a lattice gas model, and finds that adhesion sites do not condense solely due to membrane-induced interactions.

Contribution

It introduces a systematic expansion to derive membrane adhesion interactions and maps the problem onto a lattice gas model, providing new insights into membrane adhesion behavior.

Findings

Induced interactions are too weak for adhesion site condensation.

Thermal roughness inversely relates to the square root of adhesion site density.

Theoretical results agree with previous computer simulations.

Abstract

We consider membranes adhered through specific receptor-ligand bonds. Thermal undulations of the membrane induce effective interactions between adhesion sites. We derive an upper bound to the free energy that is independent of interaction details. To lowest order in a systematic expansion we obtain two-body interactions which allow to map the free energy onto a lattice gas with constant density. The induced interactions alone are not strong enough to lead to a condensation of individual adhesion sites. A measure of the thermal roughness is shown to depend on the inverse square root of the density of adhesion sites, which is in good agreement with previous computer simulations.