Interactions between Membrane Inclusions on Fluctuating Membranes

TL;DR

This paper models membrane protein interactions on fluctuating membranes, revealing various anisotropic and symmetry-dependent forces that could drive protein aggregation.

Contribution

It introduces a field theoretic approach to quantify membrane protein interactions considering anisotropy and symmetry, extending previous models.

Findings

Identifies non-entropic $1/R^{4}$ interactions for certain proteins.

Finds anisotropic $1/R^{2}$ interactions for reflection-symmetry-conserving proteins.

Predicts interactions that could lead to protein aggregation.

Abstract

We model membrane proteins as anisotropic objects characterized by symmetric-traceless tensors and determine the coupling between these order-parameters and membrane curvature. We consider the interactions between transmembrane proteins that respect up-down (reflection) symmetry of bilayer membranes and that have circular or non-circular cross-sectional areas in the tangent-plane of membranes. Using a field theoretic approach, we find non-entropic $1/R^{4}$ interactions between reflection-symmetry-breaking transmembrane proteins with circular cross-sectional area and entropic $1/R^{4}$ interactions between transmembrane proteins with circular cross-section that do not break up-down symmetry in agreement with previous calculations. We also find anisotropic $1/R^{4}$ interactions between reflection-symmetry-conserving transmembrane proteins with non-circular cross-section, anisotropic $1/R^{2}$ interactions between reflection-symmetry-breaking transmembrane proteins with non-circular cross-section, and non-entropic $1/R^{4}$ many-particle interactions among non-transmembrane proteins. For large $R$, these interactions might provide the dominant force inducing aggregation of the membrane proteins.