Vol. 8, No. 1, 2020

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Equilibrium theory for a lipid bilayer with a conforming cytoskeletal membrane

Brett Hendrickson, Milad Shirani and David J. Steigmann

Vol. 8 (2020), No. 1, 69–99
Abstract

We discuss the mechanics of a lipid bilayer with a conforming cytoskeletal membrane in which the bilayer has the structure of a nematic liquid crystal and the cytoskeleton that of a simple elastic solid. Under certain conditions the cytoskeletal membrane mimics the effects of the so-called spontaneous curvature of the conventional theory of lipid membranes. The model is used to predict the classical biconcave discoid shape of red-blood cells in equilibrium.

Keywords
lipid bilayers, membrane cytoskeleton, differential geometry.
Mathematical Subject Classification 2010
Primary: 53B50, 74K25
Milestones
Received: 24 October 2019
Revised: 27 February 2020
Accepted: 4 April 2020
Published: 11 May 2020

Communicated by Francesco dell'Isola
Authors
Brett Hendrickson
Department of Mechanical Engineering
University of California, Berkeley
6112 Etcheverry Hall
Berkeley, CA 94720-1740
United States
Milad Shirani
Department of Mechanical Engineering
University of California, Berkeley
6112 Etcheverry Hall
Berkeley, CA 94720-1740
United States
David J. Steigmann
Department of Mechanical Engineering
University of California, Berkeley
6133 Etcheverry Hall
MSPBSTART1-10-7-27-MSPESTART<p class = "indent">We discuss the mechanics of a lipid bilayer with a conforming cytoskeletal membrane in which the bilayer has the structure of a nematic liquid crystal and the cytoskeleton that of a simple elastic solid. Under certain conditions the cytoskeletal membrane mimics the effects of the so-called spontaneous curvature of the conventional theory of lipid membranes. The model is used to predict the classical biconcave discoid shape of red-blood cells in equilibrium.</p>
Berkeley, CA 94720-1740
United States