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.

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