The dependence of flux, sensitivity and response of the flux on the concentrations of substrate and modifiers for cooperative enzymes

The sensitivity (change of flux per unit change in the concentration of substrate) and response (change of flux per unit change in the concentration of modifier) are studied for a two-site Adair model in which cooperativity arises from both binding and catalytic interactions. For positive cooperativity, the sensitivity is weakly dependent on the Hill coefficient for the binding case, but can increase without limit for the catalytic case. Negatively cooperative enzymes (binding only) give very large sensitivities compared with positively or non-interacting systems, but the sensitivity rapidly decreases as the saturation increases above 25%. Modifiers greatly enhance the sensitivity; large changes in flux can be obtained for small changes in the concentrations of substrates and modifiers. In general, increasing the degree of kinetic cooperativity decreases the degree of binding cooperativity; selective pressure to maximize the sensitivity and response of allosteric enzymes may act to optimize cooperativity of binding modifiers and kinetic cooperativity of substrate turnover. The initial velocity equations including modifiers can be extended to bi-substrate, cooperative kinetics. The kinetics of methanol dehydrogenase are discussed.