Fast-Slow Analysis of a Model For the Stimulation of Enzymatic Activity by a Competitive Inhibitor

Abstract: Competitive inhibitors can, paradoxically, stimulate an enzymatic reaction at low to moderate doses. Competitive inhibition of an enzyme occurs when an inhibitor binds to the enzyme's binding site and blocks the enzyme's target molecule from binding. We recently proposed a detailed but straightforward mass action model for competitive inhibition of phosphoglycerate kinase 1 (PGK1) by Terazosin (TZ). The full PGK1 model has two substrates and two products which can be bound and released in either order, known as a random bi-bi mechanism. This model, with no further modification, predicts an increased reaction rate at low or moderate TZ doses, suggesting that stimulation is an intrinsic feature of competitive inhibition in enzymes with two products. This mechanism can aid in the development of novel therapies, particularly since enzyme activators are more rare and difficult to design than inhibitors. Here we propose a three-timescale reduction of that detailed model and show that the resulting rate equation retains three essential attributes of competitive inhibitor stimulation. These attributes are the biphasic dose response, the dependence on the relative rates of product dissociation from the binary and ternary complexes, and the parameter region where stimulation is possible. The resulting rate equation is a rational function which is a Monod function of each substrate, but quadratic in the denominator as a function of inhibitor dose.