SUMMARY

Observed pulsatile aggregation of cellular slime mould amoebae is simulated on a computer. One spatial dimension is considered. In the simulation, attractant is rapidly secreted by the cells, after a delay period, when a superthreshold attractant concentration is sensed. Cells are refractory to further signals after secretion. Once secreted, the attractant diffuses and is hydrolysed. Movement results if a cell's extending pseudopods sense a supercritical increase of attractant; if increases are sensed on both sides, a sufficiently large difference can also initiate movement. The movement continues for a period independently of further signals, but then can be reversed by an attractant increase (at the back of the cell) that surpasses a high threshold. After 100s, motion stops and the threshold for movement reverts to normal. With the above rules, and with parameter values taken, as far as possible, from the literature, the simulation provides the observed pattern of aggregation. Outward moving waves of attractant and organized inward pulsatile ' steps ' of cell movement surround a cell that secretes autonomously every few minutes. Other rules fail to give this picture, or give it only for a relatively narrow range of parameter values. It appears that of the various possible signals for chemotaxis, the most likely to be used by the amoebae is a temporal increase of attractant as sensed by extending pseudopods. Nonetheless, we cannot rule out the ' classical ' hypothesis that cells directly sense concentration differences