Resolving the chemotactic wave paradox: A mathematical model for chemotaxis of Dictyostelium amoebae

The slime mould Dictyostelium discoideum is a widely studied paradigm for biological pattern formation. To provide an explanation for the apparently paradoxical behaviour of Dictyostelium amoebae in the symmetric chemoattractant waves which govern their aggregation, we extend the standard model for chemotaxis of a cell population by explicitly considering adaptation of the chemotactic signalling pathway. In the limiting cases of very fast and very slow adaptation kinetics the model equations reduce to the standard model which predicts cell movement opposite to the observed direction. Adaptation on an intermediate timescale, however, provides cells with a "short-term memory" of experienced chemoattractant concentrations which can fully account for the experimental observation of cell translocation opposite to the direction of propagation of the chemoattractant waves.