A Model for Pattern Formation in Gap-Junction Coupled Cells

A general mechanism of biochemical pattern formation, based on a bisubstrate kinetics with substrate inhibition, is presented. The substrates are able to cross the cell membrane via gap-junction (GJ) protein channels, thus enabling substrate flow between adjacent cells. A one-dimensional system of two coupled cells, as well as coupled cells in a two-dimensional array are considered to study the evolution of the homogenous steady state towards structure formation. Since diffusion through gap junctions can be regulated under physiological conditions, attention is focused on the influence of regulation on the resulting patterns, which turn out to be highly dynamic. Both, in the one- and two-dimensional case, damped as well as limit cycle oscillations of the substrate concentration are possible in absence of diffusion. Patterns formed under diffusive conditions (Turing structures) behave differently upon chemical regulation. While the situation does not change qualitatively in the one-dimensional case, two-dimensional patterns are sensitively affected by chemical regulation. Since bisubstrate kinetic reactions are most frequently encountered in metabolism, the present model can be used to explain zonation of metabolic function in histologically homogenous tissues.