Grover L. Waldrop From the Division of Biochemistry and Molecular Biology, Louisiana State University, Baton Rouge, Louisiana 70803

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1 Q 2009 by The International Union of Biochemistry and Molecular Biology BIOCHEMISTRY AND MOLECULAR BIOLOGY EDUCATION Vol. 37, No. 1, pp , 2009 Articles A Qualitative Approach to Enzyme Inhibition Received for publication, July 7, 2008, and in revised form, September 16, 2008 Grover L. Waldrop From the Division of Biochemistry and Molecular Biology, Louisiana State University, Baton Rouge, Louisiana Most general biochemistry textbooks present enzyme inhibition by showing how the basic Michaelis Menten parameters K m and V max are affected mathematically by a particular type of inhibitor. This approach, while mathematically rigorous, does not lend itself to understanding how inhibition patterns are used to determine the kinetic aspects of an enzyme. The discussion here describes a qualitative approach to teaching enzyme inhibition that allows for a physical or mechanistic understanding. This qualitative approach to enzyme inhibition starts by recognizing that the two fundamental kinetic parameters of an enzyme catalyzed reaction are V max and V max /K m, which correspond to the apparent rates of reaction at very high and very low concentrations of substrate, respectively. It just so happens that the reciprocals of V max and V max /K m correspond to the y-intercept and slope of the Lineweaver Burk plot, respectively. Thus, an inhibitor that affects the y-intercept binds to the enzyme at very high substrate concentrations, and thus binds to the enzyme substrate complex, while an inhibitor that affects the slope binds to the enzyme at very low substrate concentrations, and thus binds only to free enzyme. These simple precepts can be used to interpret the basic inhibition patterns, competitive, uncompetitive and noncompetitive, and more importantly, derive mechanistic information, especially in multisubstrate reactions. The application of these principles is illustrated by using an example from cancer chemotherapy, the inhibition of thymidylate synthase by 5-fluorouracil and leucovorin. Keywords: Enzymes and catalysis, medical biochemistry, sources of difficulties and teaching strategies to correct difficulties. Of all the subjects covered in a general biochemistry textbook enzyme inhibition is perhaps the one topic that has the most tangible relevance to everyday life. Inhibitors of enzymes are used as pharmaceutical agents in human and veterinary medicine as well as herbicides and pesticides. Most of the public doesn t even realize they are bombarded with advertisements for enzyme inhibitors through both print and broadcast media. Yet, despite the wide ranging importance of enzyme inhibition most general biochemistry textbooks present the subject as an intricate and cumbersome set of facts to just be memorized for the test. In fact, a review of 20 general biochemistry textbooks commonly used in undergraduate and medical school courses revealed that the description of the three common types of enzyme inhibition (competitive, uncompetitive, and noncompetitive) varied from simply stating whether the inhibitor increased or decreased the Michaelis constant (K m ) and maximal velocity (V max ) all the way to showing mathematically how the K m and V max were affected by an inhibitor. When To whom correspondence should be addressed. Department of Biological Sciences, Room 206 Life Sciences Building, Louisiana State University, Baton Rouge, LA 70803, USA. Tel.: ; Fax: ; gwaldro@lsu.edu. This paper is available on line at 11 memorizing this bewildering set of facts the mechanistic utility of enzyme inhibition often gets overlooked. While a quantitative understanding of enzyme inhibition is certainly important the actual mechanistic utility of enzyme inhibition is qualitative. As W.W. Cleland has pointed out... most of the understanding derived from kinetic studies comes from the patterns rather than the actual numbers... [1]. Unfortunately, this is not how most general biochemistry textbooks present the subject. The purpose of this article is to describe a less tedious approach to enzyme inhibition that allows one to interpret the Lineweaver Burk patterns of the three basic types of inhibition from a mechanistic or physical perspective. This approach has been used for the last 10 years for teaching enzyme inhibition and has been received favorably by the students. The qualitative approach for interpreting the Lineweaver Burk patterns and mechanism of the three types of enzyme inhibitors stems from the fact that the two fundamental constants of Michaelis Menten kinetics are V max and V max /K m. The Michaelis constant K m is simply the ratio of these two parameters [2, 3]. Part of the reason that textbooks focus on the effect of inhibitors on K m and V max is because most textbooks state that K m and V max are the fundamental parameters of an enzyme catalyzed DOI /bmb.20243

2 12 BAMBED, Vol. 37, No. 1, pp , 2009 FIG. 1.(a) The vertical asymptote of rectangular hyperbola corresponds to V max /K m, while the horizontal asymptote corresponds to V max.(b) Lineweaver Burk plot of the rectangular hyperbola in A. reaction. However, K m and V max are not independent parameters. A variation in V max will lead to a concomitant change in K m [4, 5]. In contrast, V max and V max /K m are independent parameters and represent the apparent rate constants of an enzymatic reaction at very high and very low substrate concentration, respectively [2]. The rate at infinitely high substrate concentrations (V max ) is the horizontal asymptote of a rectangular hyperbola, while the rate at infinitely low substrate concentrations (V max /K m ) corresponds to the vertical tangent of the hyperbola [5] (Fig. 1a). Conveniently, the two fundamental kinetic parameters of an enzymatic reaction (V max and V max /K m ) just so happen to also correspond to the two fundamental parameters of the linear Lineweaver Burk plot. The y- intercept corresponds to the reciprocal of V max while the slope corresponds to the reciprocal of V max /K m (Fig. 1b). Thus, the y-intercept of a Lineweaver Burk plot represents the rate of an enzymatic reaction at infinitely high concentrations of substrate, whereas the slope represents the rate at very low concentrations of substrate. If an inhibitor changes the slope of a Lineweaver Burk plot the effect was achieved at a very low concentration of substrate. Whereas an inhibitor that changes the intercept of a Lineweaver-Burk plot means the effect was achieved at a very high concentration of substrate. The correspondence between the two parameters of a Lineweaver Burk plot and the two kinetic parameters allows for a qualitative and mechanistic interpretation of the Lineweaver Burk plots for the three types of inhibition. COMPETITIVE INHIBITION Competitive inhibitors affect the slope of a Lineweaver Burk plot but do not alter the y-intercept (Fig. 2a). Therefore, a competitive inhibitor only binds to the enzyme at very low concentrations of substrate (i.e., an effect on V max /K m, which is the reciprocal of the slope). However, at infinitely high levels of substrate the inhibitor does not bind (i.e., no effect on V max, which is the reciprocal of the y-intercept). This is in accord with the common mechanistic interpretation of a competitive inhibitor which binds in the same place as the varied substrate and thus, only binds to free enzyme (Fig. 2a). 1 UNCOMPETITIVE INHIBITION In contrast to competitive inhibitors, uncompetitive inhibitors only affect the y-intercept of a Lineweaver Burk plot and do not alter the slope (Fig. 2b). Therefore, an uncompetitive inhibitor only binds to the enzyme at infinitely high substrate concentration (i.e., an effect on V max, the reciprocal of the y-intercept) but at very low concentrations of substrate the inhibitor does not bind (i.e., no effect on the slope). This agrees exactly with the mechanistic scheme for uncompetitive inhibition in Fig. 2b where the inhibitor only binds to the ES complex. NONCOMPETITIVE INHIBITION A noncompetitive inhibitor binds to both the free enzyme (E) and the ES complex, in which case it will affect both the slope and the y-intercept of a Lineweaver Burk plot (Fig. 2c) 2. In other words, a noncompetitive inhibitor binds to an enzyme when the varied substrate is either at very low or very high concentrations. In essence it is a combination of competitive and uncompetitive inhibition. 1 In most cases competitive inhibition results from the inhibitor and substrate competing for binding to the same site on the enzyme. However, it is theoretically possible that saturation with substrate can cause a conformational change in the enzyme preventing the inhibitor from binding to an allosteric site. 2 Some textbooks have reserved the designation noncompetitive inhibition for when the lines intersect only on the abscissa. When the intersection point lies above or below the abscissa (which is most of the time) this is called mixed inhibition. The interpretation of noncompetitive inhibition described here only requires that there is both an intercept and slope effect, and therefore is independent of the intersection point. To avoid yet another layer of confusing terms this discussion will treat any inhibitor that exhibits both a slope and intercept effect as noncompetitive irrespective of the intersection point.

3 13 FIG. 2. Lineweaver Burk plots of (a) competitive inhibition; (b) uncompetitive inhibition; (c) noncompetitive inhibition. Thus, to interpret any inhibition pattern plotted as a Lineweaver Burk plot all one has to learn is that the slope corresponds to V max /K m, which is the rate at a very low concentration of substrate; and the y-intercept corresponds to V max, which is the rate at a very high concentration of substrate. With this in hand it is an easy step to remember that if an inhibitor affects the slope then it binds to free enzyme, and if the inhibitor affects the y- intercept it binds to the ES complex. That is all that is needed to interpret most enzyme inhibition patterns. The utility of this qualitative approach to enzyme inhibition becomes particularly apparent when interpreting inhibition patterns of multisubstrate reactions, which are frequently overlooked in many biochemistry textbooks despite the fact that they constitute the majority of biochemical reactions. To illustrate how this qualitative analysis can be applied an example from clinical medicine, specifically cancer chemotherapy, will be used. INHIBITION OF THYMIDYLATE SYNTHASE BY 5-FLUOROURACIL AND LEUCOVORIN Thymidylate synthase is the target for the anti-cancer drugs 5-fluorouracil (5-FU) and leucovorin. Thymidylate synthase catalyzes the transfer of a methyl group from N 5, N 10 -methylene-tetrahydrofolate to dump to form

4 14 BAMBED, Vol. 37, No. 1, pp , 2009 FIG. 3. Reaction catalyzed by thymidylate synthase. dump, deoxyuridine monophosphate; dtmp, deoxythymidine monophosphate; THF, tetrahydrofolate. FIG. 4. Inhibition of thymidylate synthase by 10-methyl THF. (a) Competitive inhibition versus 5,10-methylene THF. (b) Uncompetitive inhibition versus 5,10-methylene THF. 3 Patients are administered 5-fluorouracil (5-FU) which is metabolized to fluorodeoxyuridylate monophosphate (FdUMP). dtmp and 7,8-dihydrofolate (Fig. 3). Because thymidylate synthase catalyzes an essential step in DNA replication, inhibiting the reaction slows down the growth of rapidly dividing cells such as some types of cancers. The dump analog 5-FU 3 is a mechanism based inhibitor where the enzyme initially reacts with 5-FU to form a covalent intermediate and then tries to abstract the fluorine atom as F þ. Because fluorine is the most electronegative element the reaction sequence is halted and the inhibitor remains covalently attached and in turn thymidylate synthase is inhibited. Leucovorin is an analog of N 5,N 10 -methylenetetrahydrofolate that is often given along with 5-FU to enhance its cytotoxicity [6]. The mechanism by which leucovorin increases the cytotoxicity of 5-FU is best understood by inhibition studies. A structural analog of N 5,N 10 -methylene-tetrahydrofolate, 10-methyl-tetrahydrofolate, that is unreactive exhibited competitive inhibition versus N 5,N 10 -methylene-tetrahydrofolate 4 (Fig. 4a) [7]. Because the slope, which corresponds to V max /K m, is affected by the inhibitor this means 10-methyl-tetrahydrofolate only binds to the enzyme at very low levels of substrate. In contrast, the intercept is not affected by 10-methyl-tetrahydrofolate which means at very high levels of substrate (i.e., V max ) the inhibitor does not bind to the enzyme. Thus, 10- methyl-tetrahydrofolate competes with the substrate N 5, N 10 -methylene-tetrahydrofolate for binding to the same place on the enzyme which explains why the inhibitor binds only at low levels of substrate but not at very high levels of substrate. In contrast, when dump is the varied substrate, 10- methyl-tetrahydrofolate exhibits uncompetitive inhibition 4 To generate inhibition patterns using multisubstrate enzymes, one substrate is varied while the other(s) is (are) held constant at a subsaturating concentration, usually near the K m value for the enzyme. This series of assays is repeated at increasing concentrations of inhibitor.

5 15 FIG. 5. Ordered addition of substrates and inhibitors to thymidylate synthase. (Fig. 4b) [7]. In this case, the intercept is affected which means at very high levels of dump (i.e., V max ) 10-methyltetrahydrofolate binds to the enzyme. On the other hand, at very low levels of dump (i.e., V max /K m ) there is very little of the enzyme dump complex, and therefore, the inhibitor does not bind to the enzyme which is manifested as no effect on the slope. This is a classic example of using inhibition studies to show that thymidylate synthase has an ordered addition of substrate where dump binds first (Fig. 5). The inhibitor 10-methyl-tetrahydrofolate, which binds in place of N 5,N 10 -methylene-tetrahydrofolate will only bind when dump is already bound (the intercept effect). If dump is at very low concentrations then 10-methyl-tetrahydrofolate will not bind and there is no effect on the slopes. Therefore, dump binds before N 5,N 10 -methylene-tetrahydrofolate. Given that dump binds to thymidylate synthase before N 5,N 10 -methylene-tetrahydrofolate it is now possible to understand how leucovorin increases the cytotoxicity of 5-FU. Leucovorin (aka folinic acid) is a derivative of folic acid that is metabolized to N 5,N 10 -methylene-tetrahydrofolate. Just like the two substrates, dump and N 5,N 10 - methylene-tetrahydrofolate, 5-FU (which is metabolized to fluorodeoxyuridylate monophosphate (FdUMP)) binds to thymidylate synthase before N 5,N 10 -methylene-tetrahydrofolate. When a patient is given a high dose of leucovorin in conjunction with 5-FU it effectively results in a large increase in the level of N 5,N 10 -methylene-tetrahydrofolate which blocks 5-FU or FdUMP from dissociating from the enzyme (Fig. 5). This results in an increase in the extent of inhibition and in turn cytotoxicity (Fig. 5) [6]. Essentially, leucovorin double parks FdUMP in the active site of the enzyme. This is an excellent example to show students how enzyme kinetics, and enzyme inhibition in particular, can be used to help solve a very practical and in this case very serious medical problem. It also illustrates how a qualitative approach to enzyme inhibition can be used to infer mechanism. REFERENCES [1] W.W. Cleland (1977) Determining the chemical mechanisms of enzyme-catalyzed reactions by kinetic studies, Adv. Enzymol. 45, [2] W.W. Cleland (1970) Steady-State Kinetics, The Enzymes, 3rd ed., Vol. 2, Academic Press, pp [3] D.B. Northrop (1998) On the meaning of Km and V/K in enzyme kinetics, J. Chem. Ed. 75, [4] W.W. Cleland (1967) The statistical analysis of enzyme kinetic data, Advan Enzymol 29, [5] D.B. Northrop (1983) Fitting enzyme-kinetic data to V/K, Anal. Biochem. 132, [6] K. Keyomarsi, R.G. Moran (1988) Mechanism of the cytotoxic synergism of fluoropyrimidines and folinic acid in mouse leukemic cells. J. Biol. Chem. 263, [7] P.V. Danenberg, K.D. Danenberg (1978) Effect of 5,10-methylenetetrahydrofolate on the dissociation of 5-fluoro-2 0 -deoxyuridylate from thymidylate synthetase: Evidence for an ordered mechanism. Biochemistry 17,