Simplest Kinetic Schemes for Biochemical Oscillators

G. L. Ermakov^* and B. N. Goldstein

Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, 142290 Russia; fax: (7-0967) 79-0553; E-mail: ermakov@venus.iteb.serpukhov.su

^* To whom correspondence should be addressed.

Received March 19, 2001; Revision received May 17, 2001

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The topological structure of the simplest critical fragments in biochemical systems has been characterized. The conditions are considered where the critical fragments induce oscillations of the concentrations of the system participants. To illustrate, three biochemical systems (transport of ions through a membrane, protein phosphorylation, and two-substrate reaction) are discussed. The kinetic schemes of these systems contain one of the discovered critical fragments. Relaxation oscillations of the concentrations of the system participants were demonstrated using the numerical integration method.

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KEY WORDS: graph, critical fragment, mathematical modeling

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