Nonequilibrium as a source of unmixing

The intermediates, U and V, of a simple model reaction system (the so-called Brusselator) are shown to have both uniform and patterned steady states in a membrane. The patterned distribution of U and V has the symmetry of hexagons in the plane and is stable for B #62; B_m, B being the controlled concentration of one of the parametric species. The uniform solution is stable for B < B_c, and, since B_c #62; B_m, the increase and subsequent decrease of B over an interval that includes (B_m,B_c) can produce a hysteresis in which the transitions from mixed (i.e. uniform) to unmixed (i.e. hexagonlly patterned) states happen quite suddenly at the two critical values. Since the transfer or reactive properties of the membrane might be different in the two states, this model provides a bistable membrane element that might have prototypical value in a theory of biochemical control.