Abstract
Two enzymes, cross-coupled through their respective products, are membrane-bound and thereby separated from each other. The cross-coupling is of opposite character and diffusion limited, i.e. an activation-inhibition couple with a diffusion-induced time-lag. In this paper an integral representation for the solutions of the dynamic equations is developed using the Green's function technique, and an application to morphological changes in the mitochrondrion is discussed.
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Literature
Edelstein, B. B. 1970. “Instabilities Associated with Dissipative Structure.”J. Theor. Biology,26, 227–241.
Glass, L. and S. A. Kauffman. 1972. “Co-operative Components Spatial Localization and Oscillatory Cellular Dynamics.”,34, 219–237.
Morse, P. M. and F. Feshbach. 1953.Methods of Theoretical Physics. New York: McGraw-Hill.
Schaeffer, G., P. Balde and W. Lamprecht. 1967. “Substrate Transformation Dependent on Respiratory States in Mitochondria.”Nature,214, 20–23.
Singer, T. P., E. B. Kearney and M. Gutman. 1972. “Regulation of Succinate Dehydrogenase in Mitochondria.” InBiochemical Regulatory Mechanisms in Eukaryote Cells, Kun, E. and S. Grisolia, eds. New York: Wiley-Interscience.
Thames, H. D., Jr. 1973. “Dependence of Stability on Interenzyme Distance in Cooperative Systems.”J. Theor. Biology,41, 331–345.
Utsumi, K. and L. Packer. 1967. “Oscillatory States of Mitochondria. II. Factors Controlling Period and Amplitude.”Arch. Biochem. Biophys.,120, 404–412.
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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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Thames, H.D. Stability and enzyme separation: Integral representation of the solutions. Bltn Mathcal Biology 36, 197–203 (1974). https://doi.org/10.1007/BF02458603
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DOI: https://doi.org/10.1007/BF02458603