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Measuring a mitotic oscillator: The ARC discontinuity

  • Paper from the Dissipative Structures Section of the Tenth Symposium on Biomathematics and Computer Science in the Life Sciences, University of Texas, Houston. March 29–31, 1973
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Abstract

Mitosis occurs synchronously in up to 108 nuclei in the syncytial plasmodium ofPhysarum polycephalum. Any two phases of the mitotic cycle may be mixed by fusing plasmodial pairs. A topological property of the synchronized phase of the fused pair as a function of parental phases, the arc discontinuity, characterizes the underlying oscillator, and indicates mitosis is controlled by a moderate relaxation oscillator which rotates more rapidly near its singularity than its limit cycle. A model oscillator is briefly described.

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Literature

  • Cohen, M. 1972. “Clocks and Maps in Developing Organisms. Lectures in Mathematics in the Life Sciences.”Some Mathematical Questions in Biology: II, Cowan, J., ed. Providence, R.I.: American Mathematical Society, Vol. 3, pp. 1–32.

    Google Scholar 

  • Ghosh, A. K., B. Chance and E. K. Pye. 1971. “Metabolic Coupling and Synchronization of NADH Oscillations in Yeast Cell Population.”Arch. Biochem. Biophys.,145, 319–331.

    Article  Google Scholar 

  • Glansdorf, P. and I. Prigogine. 1971.Structure, Stability and Fluctuations. New York: Interscience.

    Google Scholar 

  • Kauffman, S. and J. J. Wille. 1974. “The Mitotic Oscillation Physarum polycephalum.” Submitted for publication.

  • Landahl, H. D. and V. Licko. 1970. “On Coupled Biological Oscillations.”Biophys. J. Soc. Abstracts,10.

  • Rusch, H. P., W. Sachsenmaier, K. Berens and U. J. Gnuter. 1966. “Synchronization of Mitosis by the Fusion of the Plasmodia ofPhysarum polycephalum.”J. Cell. Biology,31, 204–209.

    Article  Google Scholar 

  • Sachsenmaier, W., U. Remy and R. Plattner-Schobel. 1972. “Initiation of Synchronous Mitosis inPhysarum polycephalum.”Exp. Cell. Res.,73, 41–48.

    Article  Google Scholar 

  • Sel'Kov, E. E. 1968. “Self-Oscillations in Glycolysis.”European J. Biochem.,4, 79–86.

    Article  Google Scholar 

  • Tyson, J. and S. Kauffman. 1974. “Continuous Biochemical Control of Mitosis: I.” Submitted for publication.

  • Westerveld, A. and M. A. Freeke. 1971. “Cell Cycle of Multinucleate Cells after Cell Fusion.”Exp. Cell. Res.,65, 140–144.

    Article  Google Scholar 

  • Winfree, A. 1972. “Oscillator Glycolysis in Yeast: The Pattern of Phase Resetting by Oxygen.”Arch. Biochem. Biophys.,149, 388–401.

    Article  Google Scholar 

  • Winfree, A. 1974. “Compromise in Biological Cycles.”J. Math. Biol. In press.

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Authors and Affiliations

  1. Department of Theoretical Biology, University of Chicago, 60637, Chicago, Illinois

    S. Kauffman

Authors
  1. S. Kauffman
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Proceedings article from the Dissipative Structures Section of the Tenth Symposium on Biomathematics and Computer Science in the Life Sciences, University of Texas, Houston. March 29–31, 1973. Symposium Chairman: Stuart O. Zimmerman. Session Chairman and Proceedings Editors: Charles Walter and Hugo M. Martinez.

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Kauffman, S. Measuring a mitotic oscillator: The ARC discontinuity. Bltn Mathcal Biology 36, 171–182 (1974). https://doi.org/10.1007/BF02458601

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  • DOI: https://doi.org/10.1007/BF02458601

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