Elasticities and stabilities: lipid membranes vs cell membranes

TL;DR

This paper explores the mechanical properties and stability of cell membranes, integrating lipid bilayer elasticity, cytoskeleton effects, and osmotic pressures, and extends static models to dynamic cell structure behavior.

Contribution

It introduces a comprehensive mechanical model of cell membranes that includes elastic, curvature, and cytoskeleton effects, and proposes a dynamic extension involving tensegrity and fluid dynamics.

Findings

Critical pressure for spherical cell membrane stability is significantly higher with cytoskeleton.

The free energy of cell membranes combines in-plane strain and Helfrich curvature energy.

A set of coupling equations for cell structure dynamics is proposed.

Abstract

A cell membrane can be simply regarded as composite material consisting of lipid bilayer, membrane cytoskeleton beneath lipid bilayer, and proteins embedded in lipid bilayer and linked with membrane cytoskeleton if one only concerns its mechanical properties. In this Chapter, above all, the authors give a brief introduction to some important work on mechanical properties of lipid bilayers following Helfrich's seminal work on spontaneous curvature energy of lipid bilayers. Next, the entropy of a polymer confined in a curved surface and the free energy of membrane cytoskeleton are obtained by scaling analysis. It is found that the free energy of cell membranes has the form of the in-plane strain energy plus Helfrich's curvature energy. The equations to describe equilibrium shapes and in-plane strains of cell membranes by osmotic pressures are obtained by taking the first order variation of the total free energy containing the elastic free energy, the surface tension energy and the term induced by osmotic pressure. The stability of spherical cell membrane is discussed and the critical pressure is found to be much larger than that of spherical lipid bilayer without membrane cytoskeleton. Lastly, the authors try to extend the present static mechanical model of cell membranes to the cell structure dynamics by proposing a group of coupling equations involving tensegrity architecture of cytoskeleton, fluid dynamics of cytoplasm and elasticities of cell membranes.