Enzyme equilibrium binding

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... 

Note that in some cases one may follow the time course of covalent E-A formation by equilibrium binding methods (e.g., LC/MS, HPLC, NMR, radioligand incorporation, or spectroscopic methods) rather than by activity measurements. In these cases substrate should also be able to protect the enzyme from inactivation according to Equation (8.7). Likewise a reversible competitive inhibitor should protect the enzyme from covalent modification by a mechanism-based inactivator. In this case the terms. S and Ku in Equation (8.7) would be replaced by [7r] and K respectively, where these terms refer to the concentration and dissociation constant for the reversible inhibitor. 

Brain hexokinase is inhibited by its product glucose-6-phosphate and to a lesser extent by adenosine diphosphate. The isoenzyme of hexokinase found in brain may be soluble in the cytosol or be attached firmly to mitochondria [2 and references therein]. An equilibrium exists between the soluble and the bound enzyme. The binding changes the kinetic properties of hexokinase and its inhibition by Glc-6-P resulting in a more active enzyme. The extent of binding is inversely related to the ATP ADP ratio, i.e. conditions in which energy utilization... 

A second use of this type of analysis has been presented by Stewart and Benkovic (1995). They showed that the observed rate accelerations for some 60 antibody-catalysed processes can be predicted from the ratio of equilibrium binding constants to the catalytic antibodies for the reaction substrate, Km, and for the TSA used to raise the antibody, Kt. In particular, this approach supports a rationalization of product selectivity shown by many antibody catalysts for disfavoured reactions (Section 6) and predictions of the extent of rate accelerations that may be ultimately achieved by abzymes. They also used the analysis to highlight some differences between mechanism of catalysis by enzymes and abzymes (Stewart and Benkovic, 1995). It is interesting to note that the data plotted (Fig. 17) show a high degree of scatter with a correlation coefficient for the linear fit of only 0.6 and with a slope of 0.46, very different from the theoretical slope of unity. Perhaps of greatest significance are the... 

Binding of a reversible inhibitor to an enzyme is rapidly reversible and thus bound and unbound enzymes are in equilibrium. Binding of the inhibitor can be to the active site, or to a cofactor, or to some other site on the protein leading to allosteric inhibition of enzyme activity. The degree of inhibition caused by a reversible inhibitor is not time-dependent the final level of inhibition is reached almost instantaneously, on addition of inhibitor to an enzyme or enzyme-substrate mixture. 

To modify the activity of an enzyme, or any protein, the regulator must bind to the protein and, in almost all cases, the binding is reversible. Such binding is described as equilibrium-binding. 

Many of the 60 known reactions catalyzed by monoclonal antibodies involve kinetically favored reactions e.g., ester hydrolysis), but abzymes can also speed up kinetically disfavored reactions. Stewart and Benkovic apphed transition-state theory to analyze the scope and limitations of antibody catalysis quantitatively. They found the observed rate accelerations can be predicted from the ratio of equilibrium binding constants of the reaction substrate and the transition-state analogue used to raise the antibody. This approach permitted them to rationalize product selectivity displayed in antibody catalysis of disfavored reactions, to predict the degree of rate acceleration that catalytic antibodies may ultimately afford, and to highlight some differences between the way that they and enzymes catalyze reactions. 

The inhibitors are generally monoanions or neutral molecules capable of deprotonation to yield anionic species. These neutral inhibitors (mostly sulfonamides) (189) bind to the active site Zn-H O. Monovalent anions like I-, CN-, SCN-, N3, NCO-, SH- etc. (190,191), inhibit the catalyzed reaction of CA enzyme by binding directly to the metal ion either by displacing H2O to yield a tetra-coordinate metal ion or by adding to the coordination sphere to yield a penta-coordinate metal ion with H2O as the fifth ligand (see Table V). In some cases an equilibrium between these two coordination geometries is also reported. 

Nonproductive binding. If the enzyme has binding modes for S other than the catalytically productive mode, these will favor [ES] in the equilibrium. 

The process of reversible inhibition is described by an equilibrium interaction between enzyme and inhibitor. Most inhibition processes can be classified as competitive or noncompetitive, depending on how the inhibitor impairs enzyme action. A competitive inhibitor is usually similar in structure to the substrate and is capable of reversible binding to the enzyme active site. In contrast to the substrate molecule, the inhibitor molecule cannot undergo chemical transformation to a product however, it does interfere with substrate binding. A noncompetitive inhibitor does not bind in the active site of an enzyme but binds at some other region of the enzyme molecule. Upon binding of the noncompetitive inhibitor, the enzyme is reversibly converted to a nonfunctional conformational state, and the substrate, which is fully capable of binding to the active site, is not converted to product. 

The pH dependence of Ks/Km is similar for step 1 and step 2 reactions as shown in Fig. 26b, but this similarity in the pH curves indicate only that the same titratable groups on the free enzyme and/or free substrate are involved in the two steps. As discussed explicitly by Usher et al. (522) the roles of the two histidines could be reversed and this would make no difference since the ratio of HE EH where these are the two singly protonated species is independent of pH. Similar ks and Ka curves for the two steps would also fail to prove identical roles for the two histidines. Since a pentacovalent species—whether it is a transient activated complex or a more stable intermediate—is common to the various alternatives, pK shifts deduced from ka curves could be the same. Both substrates are monovalent anions with low pK values so that 1 /Km, whether interpreted as an equilibrium binding value or as a function of the kinetic parameters mirroring the total occupancy of all the stable intermediates, could also be the same for both steps. The values for the reverse of step 2 would behave differently since the pj of 3 -CMP, for example, is 5.9. It should also be noted that ks/Km curves should be and are ionic strength dependent (508) in the same way that the His 12 and His 119 pK values are as observed by NMR (280). 

In contrast to [E]free, [E]total is observable. Eq. (2.3) is written with fCM, the Michaelis constant, instead of the equilibrium binding constant Ks unless the enzyme reaction is very fast (Section 2.3.3.) i.e., in almost all cases, fCM = Ks. In Eq. (2.3), the reaction rate is traditionally denoted by v [concentration/time] and fccat is the reaction rate constant [time4]. The equation describes a two-parameter kinetics, with a monotonically rising reaction rate with respect to substrate concentration and saturation at high substrate concentration. The maximum reaction rate at saturation is denoted by vmax, with vmax = fccat[E], The fCM value corresponds to the substrate... 

The effect of an uncompetitive inhibitor on the Km of a substrate deserves some commentary. A lower Km implies that an enzyme has been inhibited by increasing the enzyme s affinity for its substrate. This seemingly counterintuitive statement can be made clearer by examining the equilibria in Scheme 4.14. By binding the enzyme-substrate complex, the inhibitor forces some free enzyme to bind substrate in order to maintain equilibrium concentrations of all species in solution. The inhibitor does indeed increase the affinity of the enzyme for its substrate (i.e., decrease Km). 

Fig. 1 Equilibrium between reactants (E + I) and noncovalent complex (E- I ) in a typical enzyme-inhibitor binding process...

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