Wave propagation in aggregation fields of the cellular slime mould Dictyostelium discoideum

A mathematical model developed earlier to describe adaptation, relay and oscillation in the cellular slime mould Dictyostelium discoideum is used here to study various aspects of wave propagation in aggregation fields. We first show that travelling waves of cyclic AMP do not result from Turing (diffusive) instabilities. We then display the numerically computed dispersion relation for travelling periodic waves in one space dimension, and compare the results with the experimentally measured relation. Numerical results on phase locking in axisymmetric fields are also presented and the failure of propagation at low cell densities is discussed. Finally, we demonstrate that this model supports spiral waves whose wavelength and speed agree well with the experimental observations.