Garcke, Harald and Kampmann, Johannes and Raetz, Andreas and Roeger, Matthias (2016) A coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 26 (6). pp. 1149-1189. ISSN 0218-2025, 1793-6314
Full text not available from this repository. (Request a copy)Abstract
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 behavior of the model and its parameter dependence. Both the mathematical analysis and the numerical simulations show the emergence of raft-like structures in the nonequilibrium case whereas in the equilibrium case only macrodomains survive in the long-time evolution.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PARTIAL-DIFFERENTIAL-EQUATIONS; BLOCK-COPOLYMERS; MICROPHASE SEPARATION; BIOLOGICAL-MEMBRANES; SIGNALING NETWORKS; INTERFACE APPROACH; PATTERN-FORMATION; PHASE BOUNDARIES; DOMAIN APPROACH; PDES; Partial differential equations on surfaces; phase separation; Cahn-Hilliard equation; Ohta-Kawasaki energy; reaction-diffusion systems; singular limit |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Mar 2019 08:50 |
| Last Modified: | 15 Mar 2019 08:50 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2769 |
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