A theory of ordering of elongated and curved proteins on membranes driven by density and curvature

TL;DR

This paper develops a mean-field density functional theory to predict how elongated and curved proteins on membranes transition between isotropic and nematic order, influenced by density and membrane curvature.

Contribution

It extends previous models by incorporating microscopic properties to explain density-dependent orientational transitions on curved membranes.

Findings

Predicts density-dependent isotropic-nematic transition

Explains how membrane curvature modifies protein ordering

Analyzes coexistence of different orientational phases

Abstract

Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the work of [Nascimento et. al, Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientational order and evaluate the free-energy of ensembles of elongated and curved objects on curved membranes. This theory depends on the microscopic properties of the particles and explains how a density-dependent isotropic-to-nematic transition is modified by anisotropic curvature. We also examine the coexistence of isotropic and nematic phases. This theory lays the ground to understand the interplay between membrane reshaping by BAR proteins and molecular order, examined in [Le Roux et. al, Submitted, 2020].