Derivation of a General Matrix Method for the Calculation of Control Coefficients

Abstract

As our knowledge about metabolism and metabolic pathways increases, it is becoming more important to be able to describe these processes quantitatively in mathematical terms. This is desirable if we are to be able to get a better understanding of the behavior and to make predictions of the metabolic systems or if a system is to be optimized. Since a metabolic network is a very complex system, a mathematical description must be simplified and limited to special cases; for instance the steady state of the system. Two such simplified and related tools have been developed: metabolic control analysis (MCA), developed by Kacser and Burns¹ and by Heinrich and Rapoport² in the early 1970s (for a review see Kell and Westerhoff³) and biochemical systems analysis (BSA), developed by Savageau^4–6 in the late 1960s. MCA and BSA are based on the same mathematics, but whereas MCA is a pure steady-state model, BSA deals, to some extent, with dynamic behavior.