Publisher's Note: Hexagonal, square, and stripe patterns of the ion channel density in biomembranes [Phys. Rev. E75, 016202 (2007)]

Abstract

Transmembrane ion flow through channel proteins undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane giving rise to electrophoresis of charged channels. A model for the dynamics of the channel density and the voltage drop across the membrane (cable equation) coupled to 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. Due to the binding release reaction spatially periodic modulations of the channel density with a finite wave number are favored at the onset of pattern formation, whereby the wave number decreases with the kinetic rate of the binding-release reaction. In a two-dimensional extended membrane hexagonal modulations of the ion channel density are preferred in a large range of parameters. The stability diagrams of the periodic patterns near threshold are calculated and in addition the equations of motion in the limit of a slow binding-release kinetics are derived.

Quantised transistor response to ion channels revealed by nonstationary noise analysis

“…Introduction. -Biomembranes on a solid support have been considered in connection with biophysical processes such as mechanical fluctuations [1], protein diffusion [2], pattern formation [3], cell adhesion [4], cell motion [5], synaptic transmission [6], and neuroelectronic interfacing [7]. The electrical features of a supported membrane are determined by the current of ion channels, which gives rise to a voltage in the narrow space between the membrane and the support (fig.…”