Kinetic evaluation of multiple initial rate data by simultaneous analysis with two equations

During the acetylcholinesterase catalytic process, the acetylcholine substrate attaches to the peripheral anionic site and then slides to the catalytic site situated in the center of the enzyme, at the bottom of a deep and narrow active gorge. Before the first catalytic cycle is complete, a second substrate molecule approaches and modulates the reaction. An inhibitor interferes with all steps and further complicates the situation. The reaction can be studied separately in the presence of two substrates, one good and one poor, and it can also be conducted simultaneously using a poor substrate as an inhibitor of the hydrolysis of a good substrate. Here, we have performed such an analysis, reducing the number of unknowns to those for the two substrates, while gaining additional information from the inhibition measurements without introducing new unknowns. To lower the number of realistic global minima in the analysis, we coupled the specific rate equation of the model to the rational polynomial of the corresponding degree. In contrast to the good substrate, the acetylation step by the poor substrate is found to be enhanced by the binding of the second substrate molecule to the peripheral anionic site. We attribute this to the different rate-limiting steps during the acetylation process: enhanced accommodation of the substrate paranitrophenylacetate is still slower than the hindered exit of the product paranitrophenol.