Application of the "kobs" method for the study of tight-binding reversible inhibitors

The mathematics and geometry of the "kobs" method under the tight-binding experimental conditions, when inhibitor depletion is significant, has not been fully explored in the existing biochemical kinetic literature. It is shown here that under tight-binding conditions a plot of the pseudo-first order rate constant against the inhibitor concentration is always nonlinear and concave upward, as opposed to either linear or hyperbolic (concave downward) in the absence of inhibitor depletion. If and when the apparent inhibition constant is lower than the active enzyme concentration, the plot has a distinct local minimum occurring at an inhibitor concentration that is equal to the enzyme concentration minus the inhibition constant. The slope of the plot at inhibitor concentrations significantly higher than the enzyme concentration is equal to the second order bimolecular association rate constant. The intercept on the vertical axis is equal to the sum of the dissociation rate constant of the enzyme–inhibitor complex, plus the product of the enzyme concentration multiplied by the association rate constant. Most importantly, we show here that specifically under tight-binding experimental conditions the “kobs” method only applies to the one-step binding model, without a possible involvement of a transient enzyme–inhibitor complex. Thus, as a matter of principle, under tight binding this method cannot be used to discriminate between the one-step and two-step inhibition mechanisms, nor can it be used to determine the dissociation equilibrium of a transient complex even if such a complex is in fact present.