Analysis of cyclic enzyme reaction schemes by the graph-theoretic method.

The development of the graph-theoretic method is proposed particularly for the analysis of closed cycles of elementary stages in enzyme reaction schemes. Some simplifications of the graph structure may be based on the application of Kirchhoff's laws to enzyme reaction graphs in the steady-state. The importance of the cyclic processes for enzyme regulations and a principle non-equilibrium of this phenomenon are emphasized. As an example of the regulatory role of cycles "the liberation" from substrate inhibition by substrate analogues is considered. The modification of the graph-theoretic method in the pre-steady-state kinetics for arbitrary initial conditions (for pre-mixing procedures) is also discussed. The necessary and sufficient conditions for damped oscillations in the pre-steady state are formulated which are the equality conditions for some of the rate constants along the cycle (both for reversible and irreversible stages).