Dissipative structure in the Characea: Spatial pattern of proton flux as a dissipative structure in characean cells

Abstract

To clarify an essential mechanism on the formation of alternating alignment of acid and alkali bands along cell walls of Characean algae as Nitella and Chara, the behaviour of proton transport in a simplified model system is investigated theoretically from the viewpoint of nonequilibrium thermodynamics. The present model system is described by a linear diffusion equation for proton concentration with a nonlinear boundary condition on the flux continuity across the cell membrane under an integral constraint on the total flux connected with the light intensity. It is confirmed by numerical calculations that the present model can reproduce band-type spatial patterns of proton concentration above a critical light intensity, as has been observed experimentally. An expression for the pattern of proton flux with a characteristic M-shape is also derived analytically. It is shown that a formation of the spatial patterns can be described analogously to the occurrence of a phase separation if a local potential proposed in this paper is used in place of a chemical potential. An essential mechanism on the formation of spatial patterns in the Characean algae as a kind of dissipative structure is discussed with the aid of a kinetic equation of reaction-diffusion type derived from the local potential near the bifurcation point of the present system.