Four Convenient Methods for the Determination of Enzyme Inhibitor Constants Virtually all biochemistry texts devote one or more chapters to enzymes, and in these chapters there is usually a discussion of enzyme kinetics centered around both the Michaelis-Menton equation and enzyme inhibltian. Bioehemistry laboratory texts, however, frequently ignore enzyme kinetic experiments, especially enzyme inhibitor kinetic experiments. Since enzyme inhibition studies are so important to the biologist, biochemist, and medicinal chemist we decided to develop and summarize convenient methods for the determination of enzyme inhibitor binding constants. was a modification d Method I from a The enzyme, cu-chymotrypsin (CT), was used, and the assay previous paper.' This method is a spectrophotometric assay which follows the liberation of p-nitroaniline at 410 nm from the CT catalyzed cleavage of N-glutaryl-L-phenylalanine-p-nitroanilid(S). The inhihitor, indole = I, was used since it is soluble in the assay solution. is inexpensive, and is a competitive inhibitor of CT with a small binding eanstant, Ki Four methods were developed, and all four involve eqn. (1) or (2) where
K J I K,r[Sl + K.,
V"1V. =
+
)
(2)
Vj and VOare the rates with and without I, respectively, and where Km is the Michaelis-Menton constant. Method A utilizes a double reciprocal plot of 1/V, versus 1/[S] a t various concentrations of I. The 1/[S] intercept is equal to -11 K,, and KI can he obtained from K , if K, is known. See eqn. (3).
K,
=
[I1
(Kn/Km)-7
(3)
Method B utilizes a Diaon plot of 1/V, versus [I] a t two different concentrations of S . The intercept of the two lines is equal to -K,. Method C has not been reported in the literature and consists of the determination of the concentration of inhibitornecessary for 50% inhibition, 150, where VO/VI= 2, and the conversion of this 150value to K,. See eqn. (4).
K, =
K,,[IMI
[Sl
141
+ K,,
Method D is essentially a Hofstee plot of V, versus V,/[S] a t various concentrations of I.Z The value for Kj can he obtained from the slope. See eqn. (5).
K,
=
511
+
(5)
ISlopzlK,) 1 All f o u ~methods can he completed in one or two 3-hr laboratory periods, and all yield similar values for Kj (3 X M),and Methods A and D readily indicate whether the 10-3 M). Methods A, C and D require a value for K,, ( 2 X inhibitor is competitive or noncompetitive. The assay and methods can be used with other inhibitors, and the values for K,, V,,,, and kc,, can also he obtained, All four methods demonstrate both valuable biochemistry and analytical chemistry principles, and a detailed copy of the procedures, results. and enzyme kinetics involved is available upon renllP - Ft.~ Acknowlrdcmcnl is g i \ m to the l,~.tporlr Small (;r:tnt w a r d Fnneram i u r rhrir fbnunrlsl supporr 01 l h ~ pi n w r t , and lhsnks are nlau cwen r u rhe sludenti i n o w adwnrr
