2001/08/10 by Stephan C. Kramer, Reiner Kree
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Lipid Membrane Structure and Behavior #Nonlinear Dynamics and Pattern Formation #cond-mat.soft #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.65.051920
10 pages, 7 figures, will be submitted to Phys. Rev. E
arxiv created 2001/08/10 · openalex publication_date 2002/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A model of mobile, charged ion channels in a fluid membrane is studied. The channels may switch between an open and a closed state according to a simple two-state kinetics with constant rates. The effective electrophoretic charge and the diffusion constant of the channels may be different in the closed and in the open state. The system is modeled by densities of channel species, obeying simple equations of electrodiffusion. The lateral transmembrane voltage profile is determined from a cable-type equation. Bifurcations from the homogeneous, stationary state appear as hard-mode, soft-mode, or hard-mode oscillatory transitions within physiologically reasonable ranges of model parameters. We study the dynamics beyond linear stability analysis and derive nonlinear evolution equations near the transitions to stationary patterns.