A Minimum Mechanism to Generate Oscillating Polar Patterns
Destabilization of an activator maximum occurs if, in addition to the primary long ranging antagonist, a second antagonist exists that acts locally and has a long time constant. Polar patterns generated in a small field start to oscillate. An activator maximum forms but then disappears after some time because of the slowly accumulating second antagonist (pink). After a maximum breaks down, a new one emerges rapidly at the previously nonactivated side. The following simulation uses two inhibitors as antagonistic components, one with a short time constant and a long range (red) and one with a long time constant but a short range (pink; see equation) :
The use of such dynamic patterns is widespread in nature. For example, essentially the same mechanism as described above is involved in the ability of cells to maintain a permanent sensitivity to minute external signals as well as in the positioning of new leaves at displaced positions behind a growing shoot meristem (see Meinhardt, H. (1999) J. Cell. Sci. 112, 2867-2874 and Meinhardt, H., Koch, A. J. & Bernasconi, G. (1998) in Symmetry in Plants, eds., Barabe, D. & Jean, R. V. (World Scientific, Singapore), pp. 723-758; see also http://www.eb.tuebingen.mpg.de/abt.4/meinhardt/theory.html).