Observations in diverse biological systems that appear overtly completely unrelated can be accounted for by a common mechanism: patterns become locally destabilized shortly after their generation. Typical patterns generated in this way are out-of-phase oscillations in groups of adjacent cells, traveling waves and flashing up of signals at displaced positions. The pigmentation pattern on some tropical sea shells, the orientation of chemotactic cells by minute external signals, the helical arrangement of new leaves in phyllotaxis, the pole-to-pole oscillation in E.coli for the positioning of the division plane, and the separation of barbs (hairs) in avian feather formation will be discussed as examples. It will be shown that these systems can be described by coupling of one self-enhancing reaction with two antagonistic reactions. One antagonist has a long range and a short time constant. It is responsible for the formation of the pattern. A second antagonist has opposite properties; it acts locally but persists longer. It causes a quenching of a maximum shortly after its generation. Depending on parameters, peaks can disappear and reappear at displaced positions or they become continuously shifted into adjacent positions. In the latter case travelling waves can arise that have unusual properties, e.g., they can penetrate each other without annihilation. These waves can arise spontaneously without a pacemaker region. Even when triggered by random fluctuations, these systems obtain rapidly their characteristic properties although they never reach a stable steady state. Such systems allow, for instance, a sensitive adaptation to changing conditions although non-linear reactions have normally a substantial hysteresis.
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