Theoretical analysis of the relationship between positive/negative cooperativity and enzyme activation/inhibition

Cooperativity is one of the "paradigms" in enzyme kinetics and molecular biology. But the classical textbook treatment of enzyme kinetics always indeed separates the concepts of positive/negative cooperativity from enzyme activation/inhibition, at least partially. Few theoretical analysis of their relationship has been discussed, although its experimental investigations might date back at least to 1970s. In the present paper, we try to apply the change of free energy as a connective parameter for investigating the relationship between positive/negative cooperativity and enzyme activation/inhibition through several classic equilibrium binding models. It is explicitly shown that the terms of positive/negative cooperativity could be equivalently regarded as enzyme activation/inhibition of the saturation function induced by the substrate molecule itself rather than any other additional effectors. Moreover, both the degree of cooperativity phenomenon and the degree of enzyme activation/inhibition monotonically increase with the change of free energy. Note that this result is quite different from the idea of relating cooperativity to the concepts of "substrate activation/inhibition", which is identified when at high substrate concentrations the reaction rate decreases instead of tending towards the maximum velocity, since it always needs a second substrate molecule.