Initiation of slime mold aggregation viewed as an instability

The chemotactic interaction of amoebae, as mediated by acrasin, is evidenced in a variety of ways, the most dramatic of which is aggregation. In this paper we present a mathematical formulation of the general interaction, and provide a detailed analysis of the aggregation process. By analogy with many problems in the physical world, aggregation is viewed as a breakdown of stability caused by intrinsic changes in the basic parameters which characterize the system. This point of view provides a description of aggregation which does not require that any cells be distinguished, but rather assumes a homogeneous population.