Progress curves of reactions catalyzed by unstable enzymes. A theoretical approach

When an enzyme is incubated with its substrate, the rate of catalysis will decline with time due to the combined effects of substrate utilization and product accumulation. These effects will be superimposed upon a progressive loss of catalytic activity if the enzyme is unstable, either spontaneously or as a result of an added reagent. In this report, the effect of enzyme inactivation on the progress curve for an enzyme-catalyzed reaction is considered. It is shown that under most circumstances catalysis will stop before the substrate is totally exhausted and that the amount of substrate remaining is related to the inactivation rate constants for various intermediates on the catalytic pathway. A graphical method for estimating these inactivation rate constants is suggested for several situations, including one which encompasses the effect of a suicide substrate. Expressions for the half time of the reaction are also given for some special cases.