By Hans Meinhardt (auth.)
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Additional resources for The Algorithmic Beauty of Sea Shells
So far, it has been assumed that the rate of activator production is inversely proportional to inhibitor concentration. This is a simplification since, of course, the production rate remains finite even if no inhibitor is present. 1, must be considered. If either the Michaelis-Menten constant sb or the basic inhibitor production bb is high, but the basic activator production ba is low, a spontaneous trigger may not occur since the effective inhibition remains too high. Such a system will no longer oscillate but will remain arrested in an excited state.
Pattern regulation due to growth. (a) Natural patterns. Bifurcation of existing lines, insertion of new lines, or a wedge-like widening of existing lines occurs. (b)-(d) Computer simulations of an activator-inhibitor model. Growth is simulated by the insertion of two new cells, one in each half after a certain time interval. (b) If activator production saturates, the broader maxima become still broader until a split and shift occurs. (c) New maxima become inserted if the distance between existing maxima becomes too large.
The net exchange of molecules by diffusion is, of course, zero if all cells have the same concentration. e. in the case of a linear concentration gradient. In this case each cell obtains the same amount of substance from its higher neighbour as it loses to its lower neighbour. In other words, it is not the change of concentrations but the change of concentration changes in space that is decisive in loss or ga in by diffusion. ba Basic activator production. A small activator-independent activator production can initiate the system at low activator concentrations.
The Algorithmic Beauty of Sea Shells by Hans Meinhardt (auth.)