We develop a mathematical model of cell-to-cell-signaling in Dictyostelium discoideum that predicts the cAMP signal seen by individual cells in early aggregation. The model employs two cells on a plane and is designed to predict the space-time characteristics of both the extracellular cAMP signal seen by one cell when a nearby cell relays, and the intracellular cAMP response produced by the stimulus in the receiving cell. The effect of membrane bound phosphodiesterase is studied and it is shown that cells can orient effectively even in its absence. Our results give a detailed picture of how the spatio-temporal characteristics of the extracellular signal can be transduced into a time- and space-dependent intracellular gradient, and they suggest a plausible mechanism for orientation in a natural chemotactic wave. (C) 1998 Academic Press
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