Control analysis of unbranched enzymatic chains in states of maximal activity

It is shown that optimized states of metabolic systems are characterized by special distributions of control coefficients. Maximization of the steady-state flux through unbranched chains leads, under the constraint of fixed total amount of enzymes within the pathway, to a proportionality between control coefficients and enzyme concentrations. A detailed analysis is presented for two types of systems involving (a) reactions with linear kinetics and (b) reactions with Michaelis kinetics, respectively. In the first case one obtains for reactions with equilibrium constants larger than unity a monotonic decrease of enzyme concentrations and of control coefficients from the upper end to the lower end of the chain. In the second case optimization is performed by optimizing the intrinsic parameters (elementary rate constants) as well as the amounts of the enzymes. In contrast to systems with linear kinetics the results for reactions with Michaelis-Menten kinetics are dependent on the concentrations of the external reactants.