Vol. 9, No. 2, 2021

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On the equations of equilibrium for asymmetric tilted lipid bilayers

Brett Hendrickson, Milad Shirani and David J. Steigmann

Vol. 9 (2021), No. 2, 153–166
Abstract

Several competing two-dimensional models of the mechanical response of tilted lipid bilayers have been proposed in the biophysics literature. Following an idea due to Helfrich, in the present work we seek to settle this subject by deriving a two-dimensional model via asymptotic analysis of three-dimensional liquid-crystal theory in which lipid length plays the role of the small parameter. Our model emerges as an example of Cosserat shell theory featuring independent sets of director fields for each of the two leaves constituting the bilayer.

Keywords
lipid tilt, asymmetric bilayers
Mathematical Subject Classification
Primary: 53B50
Secondary: 74K25
Milestones
Received: 9 January 2021
Accepted: 11 March 2021
Published: 17 April 2021

Communicated by Francesco dell'Isola
Authors
Brett Hendrickson
Department of Mechanical Engineering
University of California, Berkeley
Berkeley, CA
United States
Milad Shirani
Department of Mechanical Engineering
University of California, Berkeley
Berkeley, CA
United States
David J. Steigmann
Department of Mechanical Engineering
University of California, Berkeley
Berkeley, CA
United States