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Domain formation via phase separation for spherical biomembranes with small deformations

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Elliott, Charles M. and Hatcher, L. (2021) Domain formation via phase separation for spherical biomembranes with small deformations. European Journal of Applied Mathematics, 32 (6). pp. 1127-1152. doi:10.1017/S0956792520000297

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Official URL: https://doi.org/10.1017/S0956792520000297

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Abstract

We derive and analyse an energy to model lipid raft formation on biological membranes involving a coupling between the local mean curvature and the local composition. We apply a perturbation method recently introduced by Fritz, Hobbs and the rst author to describe the geometry of the surface as a graph over an undeformed Helfrich energy minimising surface. The result is a surface Cahn-Hilliard functional coupled with a small deformation energy. We show that suitable minimisers of this energy exist and consider a gradient ow with conserved Allen-Cahn dynamics, for which existence and uniqueness results are proven. Finally, numerical simulations show that for the long time behaviour raft-like structures can emerge and stabilise, and their parameter dependence is further explored.

Item Type: Journal Article
Subjects: Q Science > Q Science (General)
Q Science > QH Natural history
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Membranes (Biology) -- Mathematical models, Lipid membranes -- Mathematical models, Curvature
Journal or Publication Title: European Journal of Applied Mathematics
Publisher: Cambridge University Press
ISSN: 0956-7925
Official Date: December 2021
Dates:
DateEvent
December 2021Published
18 September 2020Available
11 August 2020Accepted
Volume: 32
Number: 6
Page Range: pp. 1127-1152
DOI: 10.1017/S0956792520000297
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: This article has been published in a revised form in European Journal of Applied Mathematics http://doi.org/10.1017/S0956792520000297. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © copyright holder.
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © The Author(s), 2020. Published by Cambridge University Press
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
Wolfson Research Merit AwardRoyal Societyhttp://dx.doi.org/10.13039/501100000288
EP/H023364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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