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Domain formation via phase separation for spherical biomembranes with small deformations

Published online by Cambridge University Press:  18 September 2020

C. M. ELLIOTT  and
L. HATCHER
C. M. ELLIOTT
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK emails: C.M.Elliott@warwick.ac.uk; L.Hatcher@warwick.ac.uk
L. HATCHER
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK emails: C.M.Elliott@warwick.ac.uk; L.Hatcher@warwick.ac.uk
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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 first 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 flow 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.

Keywords

spherical biomembraneslipid raftssurface phase-field equationsphase separationCanham-Helfrich energysurface Allen-Cahn equation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 6: Special issue featuring papers on Professor Sam Howison , December 2021 , pp. 1127 - 1152
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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