Out-of-phase oscillations and traveling waves with unusual properties: the use of three-component systems in biology

Pattern formation requires the interaction of a self-enhancing component and its long-ranging antogonist. If once established maxima are quenched by a second local-acting antagonist, three-component systems result that allow the generation of highly dynamic patterns. Either out-of-phase oscillations in groups of cells, traveling waves with a soliton-like behavior or a regular flashing up of signals at displaced positions are possible. By comparison with the pole-to-pole oscillations in E. coli, with pigment pattern on tropical sea shells, with the orientation of chemotactic cells and with the signaling for the initiation of new leaves on a growing shoot (phyllotaxis) it is shown that three-component systems are appropriate to account for a wide class of biological phenomena. Even when triggered by random fluctuations, these pattern-forming systems obtain rapidly their characteristic properties although they never reach a stable steady state.