A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes

By Harald Garcke, J. Kampmann, A. Ratz, M. Roger. 2015

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We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. To account for cholesterol exchange between cytosol and cell membrane we couple a bulk-diffusion to an evolution equation on the membrane. The latter describes the relaxation dynamics for an energy which takes lipid–phase separation and lipid–cholesterol interaction energy into account. It takes the form of an (extended) Cahn–Hilliard equation. Different laws for the exchange term represent equilibrium and nonequilibrium models. We present a thermodynamic justification, analyze the respective qualitative behavior and derive asymptotic reductions of the model. In particular we present a formal asymptotic expansion near the sharp interface limit, where the membrane is separated into two pure phases of saturated and unsaturated lipids, respectively. Finally we perform numerical simulations and investigate the long-time...

Subfields: Computational Theory and Mathematics, Materials Chemistry, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/424141c4f5cccb4e6729cfc1ae40abef0ccfae74