Enzyme-bound substrates, equilibrium constant

In the absence of an enzyme, the reaction rate v is proportional to the concentration of substance A (top). The constant k is the rate constant of the uncatalyzed reaction. Like all catalysts, the enzyme E (total concentration [E]t) creates a new reaction pathway, initially, A is bound to E (partial reaction 1, left), if this reaction is in chemical equilibrium, then with the help of the law of mass action—and taking into account the fact that [E]t = [E] + [EA]—one can express the concentration [EA] of the enzyme-substrate complex as a function of [A] (left). The Michaelis constant lknow that kcat > k—in other words, enzyme-bound substrate reacts to B much faster than A alone (partial reaction 2, right), kcat. the enzyme s turnover number, corresponds to the number of substrate molecules converted by one enzyme molecule per second. Like the conversion A B, the formation of B from EA is a first-order reaction—i. e., V = k [EA] applies. When this equation is combined with the expression already derived for EA, the result is the Michaelis-Menten equation. 

Pettersson, G. (1991). Why do many Michaelian enzymes exhibit an equilibrium constant close to imity for the interconversion of enzyme-bound substrate and product Eur.J. Biochem. 195, 663—670. 

The ability to isolate and monitor exclusively the step of interconversion of the reactants and products on the surface of the enzyme is one of the attractive features of the P NMR of enzyme-bound substrates of these reactions. It must be noted, however, that the accuracy in the determination of the different parameters, equilibrium constants, and exchange rates is primarily governed by the feasibility of having the substrates present only in the active complexes, (e.g., in the case of Fig. 9B, all enzyme-bound complexes should be in either of the two forms E-MgATP-ai nine or E - MgADP- P-aiginine). Departure from this condition leads to the presence of a substantial fraction of enzyme-bound complexes that do not undergo the reaction. In such cases the interconveision rates determined from the spectra may only be taken as lower limits of the rates. 

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. 

For a binding reaction we can pick whether we show the reaction as favorable or unfavorable by picking the substrate concentration we use. Association constants have concentration units (M-1)- The equilibrium position of the reaction (how much ES is present) depends on what concentration we pick for the substrate. At a concentration of the substrate that is much less than the dissociation constant for the interaction, most of the enzyme will not have substrate bound, the ratio[ES]/[E] will be small, and the apparent equilibrium constant will also be small. This all means that at a substrate concentration much less than the dissociation constant, the binding of substrate is unfavorable. At substrate concentrations higher than the dissociation constant, most of the enzyme will have substrate bound and the reaction will be shown as favorable (downhill). (See also the discussion of saturation behavior in Chap. 8.)... 

Equihbria involving the productively bound substrates and the products formed during an enzyme-catalyzed reaction. These equihbria can be treated in terms of internal equilibrium constants (i mt) between these enzyme-bound species. 

Table III also shows the values of the equilibrium constants, KVAp for the conversion of iron nitrosyl complexes into the corresponding nitro derivatives. Keq decreases downwards, meaning that the conversions are obtained at a lower pH for the complexes at the top of the table. Thus, NP can be fully converted into the nitro complex only at pHs greater than 10. The NO+ N02 conversion, together with the release of N02 from the coordination sphere, are key features in some enzymatic reactions leading to oxidation of nitrogen hydrides to nitrite (14). The above conversion and release must occur under physiological conditions with the hydroxylaminoreductase enzyme (HAO), in which the substrate is seemingly oxidized through two electron paths involving HNO and NO+ as intermediates. Evidently, the mechanistic requirements are closely related to the structure of the heme sites in HAO (69). No direct evidence of bound nitrite intermediates has been reported, however, and this was also the case for the reductive nitrosylation processes associated with ferri-heme chemistry (Fig. 4) (25).

In the active site of the enzyme PLP forms an internal aldimine (Schiff base) with Lys-270 (Fig. 9.13,1). When the substrate is bound at the active site, its a-amino group attacks the C-4 atom of the coenzyme and replaces the -amino group of Lys-270 from its bond with PLP. This transaldimination reaction probably proceeds via a tetrahedral intermediate (a gem-diamine). Spectral evidence for formation of a gem-diamine in this step has recently been obtained in studies of the reaction of tryptophanase with L-homophenylalanine.41 The gem-diamine is subsequently converted to an external, PLP-substrate aldimine, and the -amino group of Lys-270 is released (Fig. 9.13, II). The equilibrium constant of this step with L-tryptophan is determined to be 11.6 mM.78 ... 

Significant differences in the equilibrium constants for carbon monoxide binding to cytochromes P450 from bacterial, liver microsomal, and adrenal cortex microsomal sources, different isozymes of the liver microsomal proteins, and for substrate-free and substrate-bound enzymes, have been observed and have been related to similar factors that affect O2 and CO binding in oxygen transport and storage heme proteins. The importance of the cis and tmns effects, that is electronic effects associated with the porphyrin... 

L-Amino acid transaminases are ubiquitous in nature and are involved, be it directly or indirectly, in the biosynthesis of most natural amino acids. All three common types of the enzyme, aspartate, aromatic, and branched chain transaminases require pyridoxal 5 -phosphate as cofactor, covalently bound to the enzyme through the formation of a Schiff base with the e-amino group of a lysine side chain. The reaction mechanism is well understood, with the enzyme shuttling between pyridoxal and pyridoxamine forms [39]. With broad substrate specificity and no requirement for external cofactor regeneration, transaminases have appropriate characteristics to function as commercial biocatalysts. The overall transformation is comprised of the transfer of an amino group from a donor, usually aspartic or glutamic acids, to an a-keto acid (Scheme 15). In most cases, the equilibrium constant is approximately 1. 

In the Appendix to Chapter 7, we developed a quantitative description of the concerted model. Although developed to describe a binding process, the model also applies to enzyme activity because the fraction of enzyme active sites with substrate bound is proportional to enzyme activity. A key aspect of this model is the equilibrium between the T and the R states (p. 200), We defined L as the equilibrium constant between the R and the T forms. 

The internal equilibrium constant can be measured after finding conditions under which all of the substrate and product will be bound to the enzyme. This is done by working at concentrations of enzyme in 5- or 10-fold excess of the dissociation constants for each substrate. Accordingly, the ratio of [P]/[S] measured will reflect the ratio of [E-P]/[E-S] = Kim- The time required for the reaction to come to equilibrium can be approximated from the relationship /tobs itcai + kai to provide a minimum estimate of the rate of reaction at the active site. Usually the time calculated will be in the millisecond domain, but incubation for S sec is more convenient for manual mixing and usually no side products are formed on this time scale. Although in some cases it may be difficult to obtain concentrations of enzyme in excess of the dissociation constants for the substrates and products, the quantitation of the product/substrate ratio can be done quite accurately thanks to the fundamental property of enzyme catalysis that leads to an internal equilibrium constant close to unity for most enzymes (78-20). 

Quantitative analysis of the reaction is based on examining the effect of increasing concentrations of B on the recovery of radiolabeled product. In the limit, extrapolating to infinite concentration of B, one expects 100% conversion of the enzyme-bound radiolabeled substrate to product. Recoveries less than 100% have been attributed to dissociation of A from the ternary E-A -B complex, nonproductive binding of A in the E-A complex, or an appreciable fraction of dead enzyme. In addition, the analysis is dependent on an accurate knowledge of the equilibrium constant for the binding of the substrate A to the enzyme and of the concentration of active enzyme sites. Independent of these concerns, one can estimate the rate of dissociation of A from the enzyme by measurement of the concentration of B required to trap half of the maximal amount of radio-labeled A. At this concentration, the rate dissociation of A from the E-A complex is equal to the rate of binding of B. Such analysis was used to estimate the rates of dissociation of S3P and EPSP from the enzyme EPSP synthase (J). 

There have been extensive discussions in the literature regarding maximization of the catalytic efficiency of enzymes and the value of their internal equilibrium constants is the equilibrium constant between substrates and products of the enzyme when all are bound productively) (98-102). For example, the value of A int is near unity for both liver alcohol dehydrogenase (78) and lactate dehydrogenase (103) when measured with their natural substrates. The ability of these same enzymes to function with alternative substrates with widely differing external equilibrium constants raises important questions regarding the relationships of the internal thermodynamics of such reactions. 

The proton involved stoichiometrically in the reaction has been neglected in these formulations, and Keq/H+ is the true, pH-independent equilibrium constant. Consideration of the physical significance of < b and q (Table I) shows that the equilibrium constant for the reaction of enzyme-bound coenzymes and the substrates, EA - - B EP -p Q, is... 

It should also be considered that the formation of the complex between activator and lipid is an equilibrium reaction with a finite dissociation constant. Under the conditions used for the quantification of activators— that is, with pure glycolipid substrates at concentrations well above the Kq of the respective activator-lipid complex—the activator can be assumed to be saturated with the lipid, so that the activator concentration practically equals the concentration of the substrate of the reaction (the activator-lipid complex). However, the presence of other lipids such as phospholipids in the assay mixture may increase the experimental Kd by orders of magnitude since the mixed aggregates formed may be much more stable than the pure glycolipid micelles. (At a large excess of phospholipids as in the case of liposome-bound substrate, the may depend linearly on the phospholipid concentration.) As a consequence the concentration of the activator-lipid complex may be far below the total activator concentration, and the enzymic reaction will accordingly be much slower than with pure glycolipid substrates. 

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