Peter Ronny, Zimmermann Walter
Theoretische Physik, Universität Bayreuth, D-95440 Bayreuth, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 2):016206. doi: 10.1103/PhysRevE.74.016206. Epub 2006 Jul 18.
A model of mobile, charged ion channels embedded in a biomembrane is investigated. The ion channels fluctuate between an opened and a closed state according to a simple two-state reaction scheme whereas the total number of ion channels is a conserved quantity. Local transport mechanisms suggest that the ion channel densities are governed by electrodiffusionlike equations that have to be supplemented by a cable-type equation describing the dynamics of the transmembrane voltage. It is shown that the homogeneous distribution of ion channels may become unstable to either a stationary or an oscillatory instability. The nonlinear behavior immediately above threshold of an oscillatory bifurcation occurring at finite wave number is analyzed in terms of amplitude equations. Due to the conservation law imposed on ion channels, large-scale modes couple to the finite-wave-number instability and have thus to be included in the asymptotic analysis near the onset of pattern formation. A modified Ginzburg-Landau equation extended by long-wavelength stationary excitations is established, and it is highlighted how the global conservation law affects the stability of traveling ion channel density waves.
本文研究了嵌入生物膜中的可移动带电离子通道模型。离子通道根据简单的双态反应方案在开放态和关闭态之间波动，而离子通道的总数是一个守恒量。局部传输机制表明，离子通道密度由类电扩散方程控制，这些方程必须由描述跨膜电压动态的电缆型方程补充。结果表明，离子通道的均匀分布可能会对静态或振荡不稳定性变得不稳定。根据振幅方程分析了在有限波数处发生的振荡分岔阈值以上的非线性行为。由于对离子通道施加了守恒定律，大规模模式与有限波数不稳定性耦合，因此必须包含在图案形成开始附近的渐近分析中。建立了一个由长波长静态激发扩展的修正金兹堡 - 朗道方程，并强调了全局守恒定律如何影响移动离子通道密度波的稳定性。
