Band-Type Dissipative Structure in Ion Transport Systems with Cylindrical Shape

Abstract

A theory is presented for an appearance of band-type pattern of electric potential accompanied with electric current surrounding a unit or many-cell system of a cylindrical shape. A flux continuity at the membrane is reduced to a nonlinear equation composed of passive and active fluxes through a diffusion equation for protons. Another equation concerns the concentration of a diffusive substance weakening the pump activity. It is shown that, when an external parameter is varied from the homogeneous state, a symmetry breaking along a longitudinal axis usually appears before the one along a circumferential direction. A TDGL equation for spatial modes, which can describe both normally and invertedly bifurcating cases, is derived. An observation of hysteretic bands of chloroplasts in the green alga Acetabularia is discussed within the present theoretical scheme.