ES complex

Enzyme and substrate first reversibly combine to give an enzyme-substrate (ES) complex. Chemical processes then occur in a second step with a rate constant called kcat, or the turnover number, which is the maximum number of substrate molecules converted to product per active site of the enzyme per unit time. The kcat is, therefore, a rate constant that refers to the properties and reactions of the ES complex. For simple reactions kcat is the rate constant for the chemical conversion of the ES complex to free enzyme and products. 

The substrate concentration when the half maximal rate, (Vmax/2), is achieved is called the Km. For many simple reactions it can easily be shown that the Km is equal to the dissociation constant, Kd, of the ES complex. The Km, therefore, describes the affinity of the enzyme for the substrate. For more complex reactions, Km may be regarded as the overall dissociation constant of all enzyme-bound species. 

The quantity kcat/Km is a rate constant that refers to the overall conversion of substrate into product. The ultimate limit to the value of k at/Km is therefore set by the rate constant for the initial formation of the ES complex. This rate cannot be faster than the diffusion-controlled encounter of an enzyme and its substrate, which is between 10 to 10 per mole per second. The quantity kcat/Km is sometimes called the specificity constant because it describes the specificity of an enzyme for competing substrates. As we shall see, it is a useful quantity for kinetic comparison of mutant proteins. 

That is, the change in concentration of ES with time, t, is 0. Eigure 14.8 illustrates the time course for formation of the ES complex and establishment of the steady-state condition. 

The overall direction of the reaction will be determined by the relative concentrations of ATP, ADP, Cr, and CrP and the equilibrium constant for the reaction. The enzyme can be considered to have two sites for substrate (or product) binding an adenine nucleotide site, where ATP or ADP binds, and a creatine site, where Cr or CrP is bound. In such a mechanism, ATP and ADP compete for binding at their unique site, while Cr and CrP compete at the specific Cr-, CrP-binding site. Note that no modified enzyme form (E ), such as an E-PO4 intermediate, appears here. The reaction is characterized by rapid and reversible binary ES complex formation, followed by addition of the remaining substrate, and the rate-determining reaction taking place within the ternary complex. 

Any or all of these mechanisms may contribute to the net rate acceleration of an enzyme-catalyzed reaction relative to the uncatalyzed reaction. A thorough understanding of any enzyme would require that the net acceleration be accounted for in terms of contributions from one or (usually) more of these mechanisms. Each of these will be discussed in detail in this chapter, but first it is important to appreciate how the formation of the enzyme-substrate (ES) complex makes all these mechanisms possible. 

FIGURE 16.2 The intrinsic binding energy of the enzyme-snbstrate (ES) complex (AGi ) is compensated to some extent by entropy loss dne to the binding of E and S (TAS) and by destabilization of ES (AGt) by strain, distortion, desolvation, and similar effects. If AGi, were not compensated by TAS and AG, the formation of ES would follow the dashed line. 

FIGURE 16.3 (a) Catalysis does not occur if the ES complex and the transition state for the reaction are stabilized to equal extents, (b) Catalysis will occur if the transition state is stabilized to a greater extent than the ES complex right). Entropy loss and destabilization of the ES complex ensure that this will be the case. 

Destabilization of the ES complex can involve structural strain, desolvation, or electrostatic effects. Destabilization by strain or distortion is usually just a consequence of the fact (noted previously) that the enzyme is designed to bind the transition state more strongly than the substrate. When the substrate binds, the imperfect nature of the fit results in distortion or strain in the substrate, the enzyme, or both. This means that the amino acid residues that make up the active site are oriented to coordinate the transition-state structure precisely, but will interact with the substrate or product less effectively. 

FIGURE 16.4 Formation of the ES complex results in a loss of entropy. Prior to binding, E and S are free to undergo translational and rotational motion. By comparison, the ES complex is a more highly ordered, low-entropy complex. 

FIGURE 16.5 Substrates typically lose waters of hydration in the formation of the ES complex. Desolvation raises the energy of the ES complex, making it more reactive. 

In the chymotrypsiii mechanism, the nitrophenylacetate combines with the enzyme to form an ES complex. This is followed by a rapid second step in which an acyl-enzyme intermediate is formed, with the acetyl group covalently bound to the very reactive Ser . The nitrophenyl moiety is released as nitrophenolate (Figure 16.22), accounting for the burst of nitrophenolate product. Attack of a water molecule on the acyl-enzyme intermediate yields acetate as the second product in a subsequent, slower step. The enzyme is now free to bind another molecule of nitrophenylacetate, and the nitrophenolate product produced at this point corresponds to the slower, steady-state formation of product in the upper right portion of Figure 16.21. In this mechanism, the release of acetate is the rate-llmitmg step, and accounts for the observation of burst kinetics—the pattern shown in Figure 16.21. 

Hence, l/K only approximates l/K under conditions where the association and dissociation of the ES complex is rapid relative to the rate-limiting step in catalysis. For the many enzyme-catalyzed reactions for which + kj is not approximately equal to k j, IIK will underestimate IIK,. 

A competitive inhibitor and substrate exert reciprocal effects on the concentration of the EI and ES complexes. Since binding substrate removes free enzyme available to combine with inhibitor, increasing the [S] decreases the concentration of the EI complex and raises the reaction velocity. The extent to which [S] must be increased to completely overcome the inhibition depends upon the concentration of inhibitor present, its affinity for the enzyme K-, and the of the enzyme for its substrate. 

The binary complex ES is commonly referred to as the ES complex, the initial encounter complex, or the Michaelis complex. As described above, formation of the ES complex represents a thermodynamic equilibrium, and is hence quantifiable in terms of an equilibrium dissociation constant, Kd, or in the specific case of an enzyme-substrate complex, Ks, which is defined as the ratio of reactant and product concentrations, and also by the ratio of the rate constants kM and km (see Appendix 2) ... 

Thus, as described by Equation (2.1), the equilibrium dissociation constant depends on the rate of encounter between the enzyme and substrate and on the rate of dissociation of the binary ES complex. Table 2.1 illustrates how the combination of these two rate constants can influence the overall value of Kd (in general) for any equilibrium binding process. One may think that association between the enzyme and substrate (or other ligands) is exclusively rate-limited by diffusion. However, as described further in Chapter 6, this is not always the case. Sometimes conformational adjustments of the enzyme s active site must occur prior to productive ligand binding, and these conformational adjustments may occur on a time scale slower that diffusion. Likewise the rate of dissociation of the ES complex back to the free... 

In practice, measurement of the individual rate constants or equilibrium constants for these various chemical steps requires specialized methodologies, such as transient state kinetics (see Johnson, 1992, Copeland, 2000, and Fersht, 1999, for discussion of such methods) and/or a variety of biophysical methods for measuring equilibrium binding (Copeland, 2000). These specialized methods are beyond the scope of the present text. More commonly, the overall rate of reaction progress after ES complex formation is quantified experimentally in terms of a composite rate constant given the symbol km. 

Consider the enzyme-catalyzed and noncatalyzed transformation of the ground state substrate to its transition state structure. We can view this in terms of a thermodynamic cycle, as depicted in Figure 2.4. In the absence of enzyme, the substrate is transformed to its transition state with rate constant /cM..M and equilibrium dissociation constant Ks. Alternatively, the substrate can combine with enzyme to form the ES complex with dissociation constant Ks. The ES complex is then transformed into ESt with rate constant kt , and dissociation constant The thermodynamic cycle is completed by the branch in which the free transition state molecule, 5 binds to the enzyme to form ESX, with dissociation constant KTX. Because the overall free energy associated with transition from S to ES" is independent of the path used to reach the final state, it can be shown that KTX/KS is equal to k, Jkail (Wolfenden,... 

The discussion above of enzyme reactions treated the formation of the initial ES complex as an isolated equilibrium that is followed by slower chemical steps of catalysis. This rapid equilibrium model was first proposed by Henri (1903) and independently by Michaelis and Menten (1913). However, in most laboratory studies of enzyme reactions the rapid equilibrium model does not hold instead, enzyme... 

As we have seen before, the enzymatic reaction begins with the reversible binding of substrate (S) to the free enzyme ( ) to form the ES complex, as quantified by the dissociation constant Ks. The ES complex thus formed goes on to generate the reaction product(s) through a series of chemical steps that are collectively defined by the first-order rate constant kCM. The first mode of inhibitor interaction that can be con-... 

An inhibitor that binds exclusively to the free enzyme (i.e., for which a = °°) is said to be competitive because the binding of the inhibitor and the substrate to the enzyme are mutually exclusive hence these inhibitors compete with the substrate for the pool of free enzyme molecules. Referring back to the relationships between the steady state kinetic constants and the steps in catalysis (Figure 2.8), one would expect inhibitors that conform to this mechanism to affect the apparent value of KM (which relates to formation of the enzyme-substrate complex) and VmJKM, but not the value of Vmax (which relates to the chemical steps subsequent to ES complex formation). The presence of a competitive inhibitor thus influences the steady state velocity equation as described by Equation (3.1) ... 

Because noncompetitive inhibitors bind to both the free enzyme and the ES complex, or subsequent species in the reaction pathway, we would expect these molecules to exert a kinetic effect on the E + S —> ES" process, thus effecting the apparent values of both VmdX/KM (influenced by both the K and al, terms) and Vmax (influenced by the aK term). This is reflected in the velocity equation for noncompetitive inhibition ... 

An inhibitor that binds exclusively to the ES complex, or a subsequent species, with little or no affinity for the free enzyme is referred to as uncompetitive. Inhibitors of this modality require the prior formation of the ES complex for binding and inhibition. Hence these inhibitors affect the steps in catalysis subsequent to initial substrate binding that is, they affect the ES —> ES1 step. One might then expect that these inhibitors would exclusively affect the apparent value of Vm and not influence the value of KM. This, however, is incorrect. Recall, as illustrated in Figure 3.1, that the formation of the ESI ternary complex represents a thermodynamic cycle between the ES, El, and ESI states. Hence the augmentation of the affinity of an uncompetitive inhibitor that accompanies ES complex formation must be balanced by an equal augmentation of substrate affinity for the El complex. The result of this is that the apparent values of both Vmax and Ku decrease with increasing concentrations of an uncompetitive inhibitor (Table 3.3). The velocity equation for uncompetitive inhibition is as follows ... 

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. 

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