A Variational Approach to Particles in Lipid Membranes

TL;DR

This paper reviews and unifies various models of particle interactions in lipid membranes using a variational framework, providing mathematical consistency, relating different approaches, and demonstrating numerical applicability.

Contribution

It introduces a mathematically rigorous variational formulation for membrane-particle interactions, linking diverse models and enabling effective numerical methods.

Findings

Unified variational formulations for membrane models

Proved existence and uniqueness of solutions

Numerical methods successfully applied to new formulations

Abstract

A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a variational framework, relate apparently different modelling approaches in terms of successive approximation, and investigate existence and uniqueness. Numerical computations illustrate that the new variational formulations are directly accessible to effective numerical methods.