Coenzyme cycles and metabolic control analysis: the determination of the elasticity coefficients from the generalised connectivity theorem.

Metabolic control analysis allows one to express the elasticity coefficients (which describe the "local" kinetic features of enzymes) in terms of the control coefficients (quantitative indicators of the "global" control properties). However, when coenzymes (or metabolites linked by conservation constraints) are present in the pathway this procedure yields the "apparent" values of elasticity coefficients that correspond to the kinetic responses of the enzymes to such a simultaneous change of the coenzyme forms which leaves the total concentration of these forms unchanged (e.g., NAD+ + NADH in the glycolysis). We show that a generalised connectivity theorem (Kholodenko et al, Eur. J. Biochem. (1994) 225, 179-186) makes it possible to express the elasticity coefficients with respect to every coenzyme form separately. Such expressions include (i) the control coefficients and (ii) the responses to changes in the total concentrations of the coenzymes.