Spiral waves of cyclic AMP in a model of slime mold aggregation
During the aggregation phase of their life cycle, Dictyostelium discoideum amoebae communicate with each other by traveling waves of cyclic AMP (cAMP). These waves often have the geometry of rotating spirals. We calculate the properties of these spiral waves, their rotation period, wavespeed, and shape, from a model of the synthesis and degradation of cAMP by Dictyostelium cells. Our model is based on kinetic rate laws developed by \textit{J. L. Martiel} and \textit{A. Goldbeter} [Biophys. J. 52, 807-828 (1987)] to account for oscillations and string relaying by Dictyostelium amoebae in well-stirred cell suspensions. We show that the model also describes in quantitative detail experimental observations of rotating spiral waves of cAMP in fields of amoebae distributed over an agar surface. Furthermore, our numerically calculated spiral waves agree quantitatively with the singular perturbation theory of rotating spirals developed by \textit{A. Keener} and the first author [see e.g. Physica D 21, 307-324 (1986; Zbl 0611.35041)].
scientific article; zbMATH DE number 4091249