Kinetics of the two-sited enzyme. I. Activation and inhibition by substrate

Equations have been derived and plotted to describe apparent modifier effects of a single substrate which is randomly bound, in rapid binding equilibria, at two sites of an enzyme. Three special cases have been considered: independent, non-equivalent catalytic sites; equivalent, interacting catalytic sites; one catalytic site and one modifier site. In each case, the curvature of Lineweaver-Burk plots has been determined by evaluating the limits of the derivatives, d(1/υ₀)/d(1/S) and d(S/υ₀)/dS. The direction of curvature has been correlated with modifier effects by distinguishing between activating and inhibiting effects on maximal velocities (V), or on dissociation constants of enzyme-substrate complexes (K). Upward curvature, with a minimum in the plot, corresponds to V-inhibition. Upward curvature without a minimum corresponds to various combinations of activating effects. Downward curvature represents either K-inhibition, with or without simultaneous V-activation, or no interaction at all.