Mathematical analysis of multienzyme systems. II. Steady state and transient control.

The control theory of steady states, previously presented for linear enzymatic systems (Heinrich and Rapoport, 1974) is extended to nonlinear systems. On the basis of three theorems a new procedure for the calculation of the control strength and of the control matrix is developed. The theory is applied to the extended model of glycolysis of erythrocytes, which includes also ATP-consuming processes. Also in this model the glycolytic flux is mainly controlled by the hexokinase-phosphofructokinase-system. The control strengths of the pyruvate kinase and of the enzymes of the 2.3 P2G-bypass are negligibly small. The control strength of the ATPase is negative, i.e. an activation of this enzyme leads to a decrease of the flux. For transition states of multienzyme systems definitions are given for the mean time required for the transition of the metabolites and for the "transient control" of enzymes. Enzymes with a pronounced influence on the transition time are called time-limiting enzymes. Enzymes which excert strong control on the time-dependent processes may have little influence under steady state conditions and vice versa. The transition times of ATP have been calculated for transient states of glycolysis.