The aggregation of Dictyostelium amoebae via cell streaming has been the subject of a number of mechanistic modelling approaches. Both models based on a continuum description of cell density and models employing particle-like cells have achieved quite detailed agreement with experimental observations. However, a theoretical understanding of the streaming phenomenon is lacking. Based on the hypothesis of a pivotal role of the cell-density dependence of the cAMP wave speed, an analytically tractable model of the onset of aggregation is developed. The cAMP waves are represented by a geometrical description in terms of wave front contours, to which cell movement is coupled by means of a movement rule and a density-wave speed relation. Comparing the predictions of this analysis in detail with numerical simulations, we conclude that a specific form of a small-amplitude chemotactic instability underlies the onset of cell streaming.

Joint work with Philip K. Maini.

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1998-1999 Mathematics in Biology