A widely applicable rate equation for the determination of enzyme activity at advanced stages of reaction

Abstract

An empirical equation for representing the course of the reaction has been developed for amylase ofAspergillus oryzae by using the method of time value estimation as a measure of enzyme activity. A convenient form of the equation for calculating and plotting results is t/x=bt+a/(E), where t=reaction time, x=amount of reaction products formed, (E)=enzyme concentration, a/(E)=reciprocal of initial velocity. The parameter b makes the equation of a rather universal applicability over large portions of the reaction curves. If b=0, the reaction is of zero order; if b=1/(S)o, the reaction is of second order; a first order reaction can be represented over a range from 0 to 55% if b≏1/2(S)o. In the case of aMichaelis-Menten mechanism, b=Ks/2(S)o[(S)o+Ks] afterBrant andAlberty (1961, personal communication), and then the ratio of (S)o/Ks limits the range of validity of the empirical equation. As a tool for determining enzyme activity over a wide range of reaction, the equation is most useful in cases where the rate of reaction decreases rapidly,e.g. if (S)o/Ks is small, or if inactivation and/or inhibition of the enzyme during the reaction is involved. For the assay of enzymes the main advantages of the empirical equation over the integratedMichaelis-Menten equation, and other more complicated variations thereof, are ease of handling and applicability to a large number of enzymes.