Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics

TL;DR

This paper analyzes a complex diffuse interface model for cell blebbing, focusing on mathematical convergence and boundary layer behavior, with implications for understanding cellular mechanics involving membrane and cortex interactions.

Contribution

It provides a rigorous mathematical analysis of a diffuse interface model for cell blebbing, addressing boundary layer behavior and high-order differential equations.

Findings

Proved non-singularity of pressure at boundary layers

Derived high-order asymptotic series equations

Addressed coupling of complex differential equations

Abstract

We investigate the convergence of solutions of a recently proposed diffuse interface/phase field model for cell blebbing by means of matched asymptotic expansions. It is a biological phenomenon that increasingly attracts attention by both experimental and theoretical communities. Key to understanding the process of cell blebbing mechanically are proteins that link the cell cortex and the cell membrane. Another important model component is the bending energy of the cell membrane and cell cortex which accounts for differential equations up to sixth order. Both aspects pose interesting mathematical challenges that will be addressed in this work like showing non-singularity formation for the pressure at boundary layers, deriving equations for asymptotic series coefficients of uncommonly high order, and dealing with a highly coupled system of equations.