The sensitivity of initial conditions in the aggregation pattern of Dictyostelium discoideum

The simulation of the aggregation phase of the development of Dictyostelium discoideum with mathematical and physical methods, has been an important topic in the researching of biological pattern formation for a long time. The aggregation is mediated by cyclic adenosine monophosphate (cAMP). Some experiments have shown that the cells respond primarily to the leading edge of the camp wave. That is, the role of camp is just as an "inducing switch". In this paper, based on the concept of inducing switch, we present a discrete model to simulate the aggregation pattern in Dictyostelium discoideum with the method of cellular automata. An important result is that the aggregation patterns evidently depend on the initial response interphases of the cells. This is good illustration of the sensitivity of initial conditions in the complex evolution of nonlinear biological system.