Spiral waves of cyclic amp in a model of slime mold aggregation

Abstract 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 Martiel and Goldbeter to account for oscillations and signal 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 Keener and Tyson.

[1]  J. Keener,et al.  Spiral waves in the Belousov-Zhabotinskii reaction , 1986 .

[2]  James P. Keener,et al.  The dynamics of three-dimensional scroll waves in excitable media , 1988 .

[3]  J. Keener,et al.  The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent , 1988, Science.

[4]  James P. Keener,et al.  Diffusive effects on dispersion in excitable media , 1989 .

[5]  A Goldbeter,et al.  A mechanism for exact sensory adaptation based on receptor modification. , 1986, Journal of Theoretical Biology.

[6]  P. Fife.  Propagator-Controller Systems and Chemical Patterns , 1984 .

[7]  James P. Keener,et al.  Waves in Excitable Media , 1980 .

[8]  J. Gross,et al.  Signal emission and signal propagation during early aggregation in Dictyostelium discoideum. , 1976, Journal of cell science.

[9]  P. Devreotes,et al.  Adenosine 3',5'-monophosphate waves in Dictyostelium discoideum: a demonstration by isotope dilution--fluorography. , 1981, Science.

[10]  A. Winfree.  Spiral Waves of Chemical Activity , 1972, Science.

[11]  M. Allessie,et al.  Circus Movement in Rabbit Atrial Muscle as a Mechanism of Tachycardia , 1973, Circulation research.

[12]  P. Devreotes,et al.  Kinetics and concentration dependence of reversible cAMP-induced modification of the surface cAMP receptor in Dictyostelium. , 1985, The Journal of biological chemistry.

[13]  F. Alcântara,et al.  Signal propagation during aggregation in the slime mould Dictyostelium discoideum. , 1974, Journal of general microbiology.

[14]  H Parnas,et al.  Computer evidence concerning the chemotactic signal in Dictyostelium discoideum. , 1977, Journal of cell science.

[15]  A. Mikhailov,et al.  Rotating spiral waves in excitable media: The analytical results , 1983 .

[16]  J. Keener.  A geometrical theory for spiral waves in excitable media , 1986 .

[17]  A. B. Rovinskii.  Spiral waves in a model of the ferroin catalyzed Belousov-Zhabotinskii reaction , 1986 .

[18]  Arthur T. Winfree,et al.  Rotating Chemical Reactions , 1974 .

[19]  Demonstration of receptor heterogeneity and affinity modulation by nonequilibrium binding experiments. The cell surface cAMP receptor of Dictyostelium discoideum. , 1984 .

[20]  A Goldbeter,et al.  A Model Based on Receptor Desensitization for Cyclic AMP Signaling in Dictyostelium Cells. , 1987, Biophysical journal.

[21]  John J. Tyson,et al.  Spiral waves in a model of myocardium , 1987 .

[22]  Paul C. Fife,et al.  Pattern formation in reacting and diffusing systems , 1976 .

[23]  S A MacKay,et al.  Quantitative analysis of cyclic AMP waves mediating aggregation in Dictyostelium discoideum. , 1983, Developmental biology.

[24]  J. Tyson,et al.  Target patterns in a realistic model of the Belousov–Zhabotinskii reaction , 1980 .

[25]  Alexander V. Panfilov,et al.  Turbulent rings in 3-dimensional active media with diffusion by 2 components , 1986 .

[26]  S. A. MacKay.  Computer simulation of aggregation in Dictyostelium discoideum. , 1978, Journal of cell science.

[27]  M. Dworkin,et al.  Solubility and diffusion coefficient of adenosine 3':5'-monophosphate. , 1977, The Journal of biological chemistry.

[28]  J. Keener,et al.  Singular perturbation theory of traveling waves in excitable media (a review) , 1988 .

[29]  J Bures,et al.  Spiral waves of spreading depression in the isolated chicken retina. , 1983, Journal of neurobiology.