Wave propagation in the early stages of aggregation of cellular slime molds

A detailed theory of the velocity of propagation of the acrasin pulse responsible for the aggregation of some of the cellular slime molds is presented. The ingredients are diffusion of acrasin, triggering after a threshold concentration is reached, an intracellular delay between the reaching of threshold and subsequent release of acrasin, the destruction of acrasin by acrasinase, and an intracellular refractory period. It is suggested that the rate limiting factor in the velocity of propagation is probably the intracellular delay and not intercellular diffusion. It is shown that there is a critical density of amebae below which the waves cannot propagate. The number of neighboring amebae triggered simultaneously by the propagating wave, and therefore the spatial width of the pulse tends to increase with density. Rough estimates are given for the number of acrasin molecules per pulse and for its threshold concentration.