Chemotaxis and the early stages of aggregation in cellular slime molds

We consider here the effect of aggregative movement on organizing wave propagation in the cellular slime molds. We start by formulating chemotactic response in a way that is susceptible to quantitative treatment. Next we report a series of quantitative results on chemotactic aggregative movements obtained from observations and subsequent theoretical analysis. Perhaps the most important of these are that the chemotactic signal is impulsive, i.e. short compared to the duration of the response, that the response is of the all-or-none variety, and that differences in period between Dictyostelium discoideum and Polysphondylium violaceum are compensated by differences of chemotactic response to give comparable aggregation territories. An explicit formula is derived for the density changes produced by the chemotactic response to the periodic signals and their effect on the wave propagation discussed. The most startling effect is an appreciable Doppler shift of the apparent frequency of the signal as seen by those amebae having a chemotactic response different from the average. The shift may be important for understanding the efficiency of entrainment by the center of all amebae in its territory.