How constrained is metabolic control?

The response of metabolic variables to small rate changes is quantitatively described by the control coefficients (Kacser & Burns, 1973; Heinrich & Rapoport, 1974). Owing to the existence of structural and kinetic constraints in metabolism, the control coefficients are not all independent. Two quantities are defined to evaluate how constrained metabolic control is: the fraction of independent control coefficients (fw) and the number of independent control coeffcients per independent variable [N(C/V)]. It is shown that fw can be expressed in terms of the fraction of independent metabolite concentrations, the fraction of independent fluxes and the average fraction of independent metabolites affecting each rate. N(C/V) is equal to the average number of metabolite concentrations affecting each rate. The estimation of these quantities using experimental information available leads to the following conclusions concerning cellular metabolism: (i) only a small fraction of the control coefficients are independent; (ii) the number of rates (in average) that independently controls each independent variable is much smaller than its theoretical maximum; and (iii) the kinetic constraints are the main cause of the low value showed by fw and N(C/V). Finally, some arguments are given that could explain why living organisms do not evolve to less constrained metabolic responses.