Dictyostelium discoideum, a cellular slime mold, is a widely studied model system from which basic insights into signal transduction, cell movement, chemotaxis and pattern formation have been gained. Shortly after starvation, randomly spaced pacemakers begin to periodically release cAMP which nearby cells detect via surface receptors. These cells amplify the signal by producing more cAMP and relay it by secreting cAMP. Aggregation results from the chemotactic response of dispersed amoeba to the resulting traveling wave of cAMP. In this talk we will describe a model in which the cells are treated as discrete entities that detect and respond to the continuum field of the chemoattractant. The model comprises a mechanism for signal transduction and cAMP production to describe relay, as well as cell movement rules. We will discuss a split-time-step `particle-in-cell' computational algorithm to solve the reaction-diffusion equations for the chemoattractant, together with the governing equations for the individual cell dynamics.
We show that this model gives insight into the origin of target patterns vs. spiral waves and into the mechanism of stream formation. In particular we show that spiral waves can arise spontaneously when the intial cell distribution is random and we give computational evidence that stream formation is the result of a finite-amplitude instability. We also show how aggregation is affected by different movement rules and discuss techniques for incorporating microscopic movement rules into macroscopic continuum descriptions of the aggregation field.