Control Analysis in Terms of Generalized Variables Characterizing Metabolic Systems

Metabolic Control Analysis had originally been devised to quantify the effects of changes in enzyme concentrations onsteady-state fluxesandmetabolite concentrations. In many situations, fluxes and concentrations are not the only relevant variables. A formalism is presented by which the control of generalized variables characterizing biochemical systems can be described. The concepts of “state variables” and “response variables” are introduced. Formulae linking generalized control coefficients to generalized elasticities are established. From these, unified summation and connectivity theorems are derived. These formulae result in some of the well-known equations of Metabolic Control Analysis as special cases when the variables are specified to concentrations or fluxes. It is shown that if the response variables only depend on the state variables or the reaction rates or both, control coefficients do not depend on the special choice of the perturbation parameters. This is no longer the case if the response variables do depend on the parameters directly. The formalism provides a framework for dealing with proton-motive force, energy charge and many other variables as special cases. We illustrate the analysis by specifying it to the control analysis of concentration ratios, free-energy differences, transition times, and growth rate.