Optimal kinetic design of enzymes in a linear metabolic pathway

The rate equations for a sequence of enzymic reactions conforming to Michaelis-Menten kinetics have been analyzed in order to establish what kinetic design optimizes the steady-state reaction flux for a given total concentration of enzymes and a given average magnitude of true and apparent first-order rate constants in the reaction system. Analytical solutions are presented which have been derived with the assumptions that the concentration of the first substrate in the pathway represents a fixed parameter and that no diffusional constraints come into operation. The solutions prescribe that reaction flux in the examined system becomes optimal when all of the enzymes are present at equal active-site concentrations. The optimal kinetic design of each enzyme reaction is characterized by forward (true or apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. This means that the optimal kinetic design of the examined pathway is highly uniform, individual enzymes being likely to exhibit optimal V values differing by a factor less than 5 and optimal Km/[S] values falling within the range 0.3-2.