A Theoretical Graph Method for Search and Analysis of Critical Phenomena in Biochemical Systems. II. Kinetic Models of Biochemical Oscillators Including Two and Three Substances

G. L. Ermakov

Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino 142292, Moscow Region, Russia; fax: (7-0967) 790-553; E-mail: ermakov-gennady@rambler.ru

Received January 21, 2003

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Four kinetic models of hypothetical complex reactions containing minimal two-substance or three-substance oscillators were constructed on the basis of the graphical rules suggested in the preceding work. The kinetic models are thought to be a part of one of four general biochemical systems: 1) system of mutual protein phosphorylation/dephosphorylation; 2) autophosphorylation of multisubunit protein; 3) association/dissociation of proteins or protein-containing structures during protein-protein or protein-ligand interaction; and 4) two-substrate enzymatic reaction with substrate inhibition by one substrate. Graphical rules of oscillator association with surrounding medium were considered. The graphical criteria of the oscillation generator elimination and criteria of oscillation damping were obtained. Both damped and undamped oscillations of reaction components were obtained by numerical integration of the mathematical models of these reactions. The areas of changes of model parameters and variables, within which the oscillations exist, were found.

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KEY WORDS: graph, oscillations, mathematical simulation

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