Bisubstrate Reaction Mechanisms

Let us consider an enzymatic reaction in which two substrates are utilized to from two products (in the nomenclature of enzyme reaction mechanisms this situation is referred to as a bi-bi mechanism). A reaction in which one substrate yields two products is referred to as a uni-bi mechanism, and one in which two substrates combine to form a single product is referred to as a bi-uni mechanism (see Copeland, 2000, for further details). For the purposes of illustration let us use the example of a group transfer reaction, in which a chemical species, X, is transferred from one substrate to the other in forming the products of the reaction  

Examples of such systems include the reactions of kinases, phosphatases, hydroxylases, acetylases, ubiquitin transferases, and many other enzyme classes that represent attractive targets for drug discovery. There are several mechanisms by which an enzyme can catalyze these types of reactions, and the details of the mechanism are important in determining the best approach to designing activity assays for the enzyme and for proper evaluation of inhibitors that are identified through those activity assays. 

A critical feature of the random ternary complex mechanism is that for either substrate the dissociation constant from the binary enzyme complex may be different from that of the ternary enzyme complex. For example, the Ks value for AX dissociation from the E AX complex will have a value of K v . The affinity of AX for the enzyme may, however, be modulated by the presence of the other substrate B, so that the dissociation constant for AX from the ternary E.AX.B complex may now be c/Xax, where a is a constant that defines the degree of positive or negative regulation of the affinity of AX for the enzyme by the other substrate. The overall steady state velocity equation for this type of mechanism is given by Equation (2.15)  

The three bi-bi mechanisms described here provide some sense of the diversity of mechanisms available to enzymes that act on multiple substrates. This is by no 

In this chapter we have seen that enzymatic catalysis is initiated by the reversible interactions of a substrate molecule with the active site of the enzyme to form a non-covalent binary complex. The chemical transformation of the substrate to the product molecule occurs within the context of the enzyme active site subsequent to initial complex formation. We saw that the enormous rate enhancements for enzyme-catalyzed reactions are the result of specific mechanisms that enzymes use to achieve large reductions in the energy of activation associated with attainment of the reaction transition state structure. Stabilization of the reaction transition state in the context of the enzymatic reaction is the key contributor to both enzymatic rate enhancement and substrate specificity. We described several chemical strategies by which enzymes achieve this transition state stabilization. We also saw in this chapter that enzyme reactions are most commonly studied by following the kinetics of these reactions under steady state conditions. We defined three kinetic constants—kai KM, and kcJKM—that can be used to define the efficiency of enzymatic catalysis, and each reports on different portions of the enzymatic reaction pathway. Perturbations 

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The determination of bisubstrate reaction mechanism is based on a combination of steady state and, possibly, pre-steady state kinetic studies. This can include determination of apparent substrate cooperativity, as described in Chapter 2, study of product and dead-end inhibiton patterns (Chapter 2), and attempts to identify... 

The modality of compounds that inhibit enzymes catalyzing bisubstrate reactions will differ with respect to the two substrates of the reaction, and the pattern of inhibition will depend on the reaction mechanism of the enzyme. Thus, when we use terms like competitive, noncompetitive, or uncompetitive inhibition, we must... 

The example of methotrexate points out that the inhibition modality of dead end inhibitors, with respect to a specific substrate, will depend on the reaction mechanism of the target enzyme. Thus a complete understanding of inhibition mechanism requires an understanding of the underlying reaction mechanism of the target enzyme. A comprehensive discussion of these issues has been provided by Segel (1975). Table 3.6 summarizes the pattern of dead-end inhibition observed for competitive inhibitors of one substrate in the common bisubstrate reaction mecha-... 

In this chapter we described the thermodynamics of enzyme-inhibitor interactions and defined three potential modes of reversible binding of inhibitors to enzyme molecules. Competitive inhibitors bind to the free enzyme form in direct competition with substrate molecules. Noncompetitive inhibitors bind to both the free enzyme and to the ES complex or subsequent enzyme forms that are populated during catalysis. Uncompetitive inhibitors bind exclusively to the ES complex or to subsequent enzyme forms. We saw that one can distinguish among these inhibition modes by their effects on the apparent values of the steady state kinetic parameters Umax, Km, and VmdX/KM. We further saw that for bisubstrate reactions, the inhibition modality depends on the reaction mechanism used by the enzyme. Finally, we described how one may use the dissociation constant for inhibition (Kh o.K or both) to best evaluate the relative affinity of different inhibitors for ones target enzyme, and thus drive compound optimization through medicinal chemistry efforts. 

Determining balanced conditions for a single substrate enzyme reaction is usually straightforward one simply performs a substrate titration of reaction velocity, as described in Chapter 2, and sets the substrate concentration at the thus determined Ku value. For bisubstrate and more complex reaction mechanism, however, the determination of balanced conditions can be more complicated. 

We saw in Chapter 3 that bisubstrate reactions can conform to a number of different reaction mechanisms. We saw further that the apparent value of a substrate Km (KT) can vary with the degree of saturation of the other substrate of the reaction, in different ways depending on the mechanistic details. Hence the determination of balanced conditions for screening of an enzyme that catalyzes a bisubstrate reaction will require a prior knowledge of reaction mechanism. This places a necessary, but often overlooked, burden on the scientist to determine the reaction mechanism of the enzyme before finalizing assay conditions for HTS purposes. The importance of this mechanistic information cannot be overstated. We have already seen, in the examples of methotrexate inhibition of dihydrofolate, mycophenolic acid inhibiton of IMP dehydrogenase, and epristeride inhibition of steroid 5a-reductase (Chapter 3), how the [5]/A p ratio can influence one s ability to identify uncompetitive inhibitors of bisubstrate reactions. We have also seen that our ability to discover uncompetitive inhibitors of such reactions must be balanced with our ability to discover competitive inhibitors as well. 

Because mechanism-based inactivators behave as alternative substrates for the enzyme, they must bind in the enzyme active site. Binding of a mechanism-based inactivator is therefore mutually exclusive with binding of the cognate substrate of the normal enzymatic reaction (we say cognate substrate here because for bisubstrate reactions, the mechanism-based inactivator could be competitive with one substrate and noncompetitive or uncompetitive with the other substrate of the reaction, depending on the details of the reaction mechanism). Thus, as the substrate concentration is increased, the observed rate of inactivation should decrease (Figure 8.10) as... 

For bisubstrate reactions that conform to a ternary complex mechanism (see Chapter 3), inactivation should require the presence of the noncognate substrate. 

Almost all enzymes—in contrast to the simplified description given on p. 92—have more than one substrate or product. On the other hand, it is rare for more than two substrates to be bound simultaneously. In bisubstrate reactions of the type A + B C+D, a number of reaction sequences are possible. In addition to the sequential mechanisms (see p.90), in which all substrates are bound in a specific sequence before the product is released, there are also mechanisms in which the first substrate A is bound and immediately cleaved. A part of this substrate remains bound to the enzyme, and is then transferred to the second substrate B after the first product C has been released. This is known as the ping-pong mechanism, and it is used by transaminases, for example (see p.l78). In the Lineweaver— Burk plot (right see p.92), it can be recognized in the parallel shifting of the lines when [B] is varied. 

We have introduced kinetics as the primary method for studying the steps in an enzymatic reaction, and we have also outlined the limitations of the most common kinetic parameters in providing such information. The two most important experimental parameters obtained from steady-state kinetics are kcat and kcat/Km. Variation in kcat and kcat/Km with changes in pH or temperature can provide additional information about steps in a reaction pathway. In the case of bisubstrate reactions, steady-state kinetics can help determine whether a ternary complex is formed during the reaction (Fig. 6-14). A more complete picture generally requires more sophisticated kinetic methods that go beyond the scope of an introductory text. Here, we briefly introduce one of the most important kinetic approaches for studying reaction mechanisms, pre-steady state kinetics. 

FIGURE 6-13 Common mechanisms for enzyme-catalyzed bisubstrate reactions, (a) The enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must bind before substrate 2 can bind productively. In random binding, the substrates can bind in either order. 

In practice, uncompetitive and mixed inhibition are observed only for enzymes with two or more substrates—say, Sj and S2—and are very important in the experimental analysis of such enzymes. If an inhibitor binds to the site normally occupied by it may act as a competitive inhibitor in experiments in which [SJ is varied. If an inhibitor binds to the site normally occupied by S2, it may act as a mixed or uncompetitive inhibitor of Si. The actual inhibition patterns observed depend on whether the and S2-binding events are ordered or random, and thus the order in which substrates bind and products leave the active site can be determined. Use of one of the reaction products as an inhibitor is often particularly informative. If only one of two reaction products is present, no reverse reaction can take place. However, a product generally binds to some part of the active site, thus serving as an inhibitor. Enzymologists can use elaborate kinetic studies involving different combinations and amounts of products and inhibitors to develop a detailed picture of the mechanism of a bisubstrate reaction. 

In the sequential mechanism, all substrates must bind to the enzyme before any product is released. Consequently, in a bisubstrate reaction, a ternary complex of the enzyme and both substrates forms. Sequential mechanisms are of two... 

Figure. 6.8. Sequential ordered mechanism for bisubstrate reactions.

Previously, while discussing the general theory of complex reactions, we have considered some other mechanisms with linear steps, such as one given by eq. (4.107) corresponding to three-step sequence or eq. (4.116). In a similar way kinetic expressions could be derived for more complicated reaction networks, as presented for instance in Chapter 5 (see equations 5.76 for 4 step sequence, eq. 5.84 for 6 steps eq. 5.88 and 5.89 for a mechanism with 8 linear steps and the general form for n-step mechanism eq. 5.94). Ordered sequential bisubstrate reactions can be expressed by eq. 5.76 for the 4 step sequence (Figure 6.11)... 

TABLE 11.5 Cleland nomenclature for bisubstrate reactions exemplified. Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi hi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1A versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (KiaKb) in the denominator. These three kinetic mechanisms can be further differentiated by their product inhibition patterns (Cleland, 1963b)... 

In the literature, literally dozens of kinetic mechanisms have been proposed for bisubstrate enzymes (Alberty, 1958 Alberty Hammes, 1958 Teller Alberty, 1959 Wong Hanes, 1962 Fromm, 1967 Dalziel, 1969 Hurst, 1969 Rudolph Fromm, 1969, 1971, 1973). However, only those pathways that are either weU documented, or seem to be a logical extension of established mechanisms, will be presented in this and the following chapters. Thus, we shall divide the rapid equilibrium bisubstrate reactions into the following major types, according to the type and number of enzyme-substrate or enzyme-product complexes that can form (Alberty, 1953 Cleland, 1970, 1977 Fromm, 1979 Engel, 1996 Purich Allison, 2000) ... 

In this chapter, we shall deal only with the hyperbolic bisubstrate mechanisms that produce the linear primary double reciprocd plots of i/uo versus 1/ [substrate]. In doing so, we shall describe the following major types of steady-state bisubstrate reactions (Fromm, 1979) ... 

This nomenclature has been introduced by Cleland (1963), but other descriptions of bisubstrate mechanisms are also found in the biochemical literature. For example, a sequential addition in bisubstrate reactions, an Ordered Bi Bi mechanism is also called a compulsory-order ternary-complex mechanism whereas a Random Bi Bi mechanism is called a random-order ternary-complex... 

This example clearly shows that completely randomized steady-state bisubstrate reactions wiU produce extremely complex rate equations which are, in most cases, unmanageable and almost useless for practical purposes. Thus, for example, the rate equation for an Ordered Bi Bi mechanism has 12 terms in the denominator (compare Eq. (9.8)). A completely Random Bi Bi mechanism yields an even more comphcated rate equation with 37 new terms in the denominator. Eor this reason, and in such cases, we shah usuahy revert to simplifying assumptions, usually introducing the rapid equilibrium segments in the mechanism in order to reduce the rate equations to manageable forms. 

Intersection points in the double reciprocal plots of i/vo versus A or fvo versus l/B, in bisubstrate reactions, provide a criterion for an initial estimate of the reaction mechanism (Rudolph Fromm, 1979). The choice of a mechanism listed in Table 4 could be made on the basis of the evaluation of the points of intersection in the double reciprocal plots in the forward and reverse directions. 

In some steady-state mechanisms, such as an Ordered Bi Bi mechanism, all or some of the rate constants can be calculated directly from the kinetic constants. Quantities like and /Cm wiU not necessarily show the normal temperature behavior, since they are usually combinations of several rate constants, but if certain rate constants predominate, normal temperature behavior maybe obeyed. This is often the case with bimolecular rate constants /Ccat/ A and fccat/AB in bisubstrate reactions. 

Distribution equations for bisubstrate reactions in the steady state are often very complex expressions (Chapter 9). However, in the chemical equilibrium, the distribution equations for all enzyme forms are usually less complex. Consider an Ordered Bi Bi mechanism in reaction (16.12) with a single central complex ... 

Kinetic isotope effects are sensitive to changing concentrations of substrates, products of reactions, and allosteric effectors (Cook, 1991). This sensitivity of isotope effects may be profitably applied to analyze luetic mechanisms. Consider the following reaction scheme for a bisubstrate reaction ... 

Bisubstrate reactions (Chapters 8 and 9). In bisubstrate reactions, a frequent case is a need to distinguish between the Steady-State Ordered, Ping Pong, and Equihbrium Ordered mechanism the rate equations involved are... 

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