Title: A model for stimulation of alcohol dehydrogenase by imidazole

Abstract: Alcohol dehydrogenase (ADH) is an enzyme that breaks down alcohol in the liver. Imidazole is a competitive inhibitor that binds to the enzyme in the place of alcohol. Despite the competition between imidazole and alcohol, at certain concentrations the inhibitor can speed up the reaction. Here we construct a model for the activity of the enzyme. We use techniques from singular perturbation theory to reduce the model and extract an equation for the rate of the reaction in terms of key parameters. This equation demonstrates that imidazole can stimulate or inhibit the reaction depending on its concentration relative to the substrates.