Theory of steady-state control in complex metabolic networks

Based on the concept of control coefficients introduced by Kacser and Burns (Symp. Soc. Exp. Biol. 32 (1973) 65-104) and Heinrich and Rapoport (Eur. J. Biochem. 42 (1974) 83-95) a theoretical analysis of steady-state control in metabolic networks is presented. The control results from the kinetic properties of the reactions in the system, expressed by elasticity coefficients with respect to the intermediate signals, as well as from the stoichiometric structure of the system, expressed by pathway fractions of the pathway fluxes through the system. The intermediate signals and the pathway fluxes are defined as quantities which contain complete information about the patterns of the intermediates and fluxes in the steady-state without the constraints generated by the stoichiometric structure. Quantitative formulation leads to connectivity theorems relating the control coefficients with the kinetic properties of the reactions, and to pathway summation theorems relating the control coefficients with the stoichiometric structure. For larger systems a hierarchical substructure can be introduced; for the subsystems the term "functional compartment" is proposed. These compartments include several reactions but can be formally created as a single reaction. It is demonstrated that the control exerted by a reaction in the whole system is proportional to the control exerted in the isolated compartment if the compartment includes an unbranched flux structure, while this is not applicable in case of a branched structure.