A Theoretical Graph Method for Search and Analysis of Critical Phenomena in Biochemical Systems. I. Graphical Rules for Detecting Oscillators

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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Sufficient conditions for existence of concentration oscillations of components of complex reactions are considered on the basis of graph theory. Graphical rules were developed for detecting oscillators in kinetic schemes of complex biochemical systems. The main types of topology and principles of construction of kinetic schemes of oscillators containing two, three, and four substances are considered. The resulting oscillators might be a part of the biochemical systems of the n-th order. Under certain conditions they were found to be capable of generating oscillations of the system components.

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KEY WORDS: graph, oscillations, mathematical simulation

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