Kinks in two-phase lipid bilayer membranes

Abstract

Common models for two-phase lipid bilayer membranes are based on an energy that consists of an elastic term for each lipid phase and a line energy at interfaces. Although such an energy controls only the length of interfaces, the membrane surface is usually assumed to be at least $C^1$ across phase boundaries. We consider the spontaneous curvature model for closed rotationally symmetric two-phase membranes without excluding tangent discontinuities at interfaces a priorily. We introduce a family of energies for smooth surfaces and phase fields for the lipid phases and derive a sharp interface limit that coincides with the $\Gamma$-limit on all reasonable membranes and extends the classical model by assigning a bending energy also to tangent discontinuities. The theoretical result is illustrated by numerical examples.

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References in corpus (3)

• Lipid membranes with free edges
• Convergence of an approximation for rotationally symmetric two-phase lipid bilayer membranes
• Snapping elastic curves as a one-dimensional analogue of two-component lipid bilayers

Cited by in corpus (7)

• Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes
• Convergence of an approximation for rotationally symmetric two-phase lipid bilayer membranes
• Thermodynamic equilibrium of binary mixtures on curved surfaces
• Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation
• Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds
• Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes
• Lower regularity assumption for an Euler-Lagrange equation on the contact line of the phase dependent Helfrich energy