Dresden 2006 – wissenschaftliches Programm

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SYSS: Structure Formation and Self-Organization in non-equilibrium Systems

SYSS 3: Structure Formation and Self-Organization in non-equilibrium Systems - Poster

SYSS 3.24: Poster

Donnerstag, 30. März 2006, 16:00–18:00, P1

On hexagonal, square and stripe pattern of the ion-channel density in biomembranes — •Markus Hilt and Walter Zimmermann — Theoretische Physik Ia, Universität Bayreuth

Ion flow through channels in a membrane undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane which give rise to electrophoresis of charged channels. A model for the coupled dynamics of the channel density and the voltage drop across the membrane (cable equation), including a binding-release reaction with the cell skeleton (P. Fromherz and W. Zimmerman, Phys. Rev. E 51, R1659 (1995)) is analyzed in one and two spatial dimensions. This coupled dynamics may give rise to spatial periodic modulations of the channel density, where the wavenumber decreases with the kinetic rate of the binding release reaction. In a two-dimensional extended membrane hexagonal modulations of channel density are preferred in a large range of parameters. The stability diagrams of the periodic patterns near threshold and the anharmonic shape of the solutions far beyond threshold are calculated as well as the equations of motion in the limit of a slow binding release kinetics are derived.