Substrate binding, enzyme kinetics

Reversibly fonned micelles have long been of interest as models for enzymes, since tliey provide an amphipatliic environment attractive to many substrates. Substrate binding (non-covalent), saturation kinetics and competitive inliibition are kinetic factors common to botli enzyme reaction mechanism analysis and micellar binding kinetics. 

Kinetics is the branch of science concerned with the rates of chemical reactions. The study of enzyme kinetics addresses the biological roles of enzymatic catalysts and how they accomplish their remarkable feats. In enzyme kinetics, we seek to determine the maximum reaction velocity that the enzyme can attain and its binding affinities for substrates and inhibitors. Coupled with studies on the structure and chemistry of the enzyme, analysis of the enzymatic rate under different reaction conditions yields insights regarding the enzyme s mechanism of catalytic action. Such information is essential to an overall understanding of metabolism. 

The above rate equation is in agreement with that reported by Madhav and Ching [3]. Tliis rapid equilibrium treatment is a simple approach that allows the transformations of all complexes in terms of [E, [5], Kls and Kjp, which only deal with equilibrium expressions for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme kinetics are reduced to the simplest Michaelis-Menten model, as shown in Figure 5.21. The rate equation for the Michaelis-Menten model is given in ordinary textbooks and is as follows 11... 

A linear form of the Hill equation is used to evaluate the cooperative substrate-binding kinetics exhibited by some multimeric enzymes. The slope n, the Hill coefficient, reflects the number, nature, and strength of the interactions of the substrate-binding sites. A... 

Fig. 6. Vectorial phosphorylation by a mechanism in which translocation and phosphorylation of the sugar are two distinct steps. The product binding site of the translocator T (domain C of II ") would be the substrate binding site of the kinase K (domains A and B). Since both the left-hand cycle and the right-hand cycle are catalyzed by the same enzyme they will very likely be kinetically dependent. Note that the kinetic cycle on the left-hand side of the figure is identical to Fig. 5.

In conclusion, the steady-state kinetics of mannitol phosphorylation catalyzed by II can be explained within the model shown in Fig. 8 which was based upon different types of experiments. Does this mean that the mechanisms of the R. sphaeroides II " and the E. coli II are different Probably not. First of all, kinetically the two models are only different in that the 11 " model is an extreme case of the II model. The reorientation of the binding site upon phosphorylation of the enzyme is infinitely fast and complete in the former model, whereas competition between the rate of reorientation of the site and the rate of substrate binding to the site gives rise to the two pathways in the latter model. The experimental set-up may not have been adequate to detect the second pathway in case of II " . The important differences between the two models are at the level of the molecular mechanisms. In the II " model, the orientation of the binding site is directly linked to the state of phosphorylation of the enzyme, whereas in the II" model, the state of phosphorylation of the enzyme modulates the activation energy of the isomerization of the binding site between the two sides of the membrane. Steady-state kinetics by itself can never exclusively discriminate between these different models at the molecular level since a condition may be proposed where these different models show similar kinetics. The II model is based upon many different types of data discussed in this chapter and the steady-state kinetics is shown to be merely consistent with the model. Therefore, the II model is more likely to be representative for the mechanisms of E-IIs. 

A steady-state kinetics study for Hod was pursued to establish the substrate binding pattern and product release, using lH-3-hydroxy-4-oxoquinoline as aromatic substrate. The reaction proceeds via a ternary complex, by an ordered-bi-bi-mechanism, in which the first to bind is the aromatic substrate then the 02 molecule, and the first to leave the enzyme-product complex is CO [359], Another related finding concerns that substrate anaerobically bound to the enzyme Qdo can easily be washed off by ultra-filtration [360] and so, the formation of a covalent acyl-enzyme intermediate seems unlikely in the... 

Two other general ways of treating micellar kinetic data should be noted. Piszkiewicz (1977) used equations similar to the Hill equation of enzyme kinetics to fit variations of rate constants and surfactant concentration. This treatment differs from that of Menger and Portnoy (1967) in that it emphasizes cooperative effects due to substrate-micelle interactions. These interactions are probably very important at surfactant concentrations close to the cmc because solutes may promote micellization or bind to submicellar aggregates. Thus, eqn (1) and others like it do not fit the data for dilute surfactant, especially when reactants are hydrophobic and can promote micellization. 

Substrates may affect enzyme kinetics either by activation or by inhibition. Substrate activation may be observed if the enzyme has two (or more) binding sites, and substrate binding at one site enhances the alfinity of the substrate for the other site(s). The result is a highly active ternary complex, consisting of the enzyme and two substrate molecules, which subsequently dissociates to generate the product. Substrate inhibition may occur in a similar way, except that the ternary complex is nonreactive. We consider first, by means of an example, inhibition by a single substrate, and second, inhibition by multiple substrates. 

Aleshin and coworkers (49) have reported the X-ray crystal structure at 2.2-A resolution of a G2-type variant produced by Aspergillus awamori. Meanwhile, an attempt was made to determine the amino acid residues that participate in the substrate binding and catalysis provided by G2 of A. niger (52). The results of the chemical approach indicated that the Asp-176, Glu-179, and Glu-180 form an acidic cluster crucial to the functioning of the enzyme. This conclusion was then tested by site-specific mutagenesis of these amino acid residues, which were replaced, one at a time, with Asn, Gin, and Gin, respectively (53). The substitution at Glu-179 provided an inactive protein. The other two substitutions affected the kinetic parameters but were not of crucial importance to the maintenance of activity. The crystal structure (49) supports the conclusion that Glu-179 functions as the catalytic acid but Asp-17 6 does not appear to be a good candidate for provision of catalytic base. Thus, there still exists considerable uncertainty as to how the disaccharide is accepted into the combining site for hydrolysis. Nevertheless, the kind of scheme presented by Svensson and coworkers (52) almost surely prevails. 

Enzyme-catalyzed reactions can be described at least at two distinct levels. At the basic level, the interconversion of substrates by enzymes is governed by a set of elementary steps, including enzyme substrate binding, isomerization and dissociation steps, see Fig. 6 for a schematic depiction. Assuming the intracellular medium is an ideal solution, each elementary step is governed by mass-action kinetics, that is, the reaction rates are proportional to the probability of collision of the reactants. For a reaction of the type... 

When binding of a substrate molecule at an enzyme active site promotes substrate binding at other sites, this is called positive homotropic behavior (one of the allosteric interactions). When this co-operative phenomenon is caused by a compound other than the substrate, the behavior is designated as a positive heterotropic response. Equation (6) explains some of the profile of rate constant vs. detergent concentration. Thus, Piszkiewicz claims that micelle-catalyzed reactions can be conceived as models of allosteric enzymes. A major factor which causes the different kinetic behavior [i.e. (4) vs. (5)] will be the hydrophobic nature of substrate. If a substrate molecule does not perturb the micellar structure extensively, the classical formulation of (4) is derived. On the other hand, the allosteric kinetics of (5) will be found if a hydrophobic substrate molecule can induce micellization. 

Another type of inhibitor combines with the enzyme at a site which is often different from the substrate-binding site and as a result will inhibit the formation of the product by the breakdown of the normal enzyme-substrate complex. Such non-competitive inhibition is not reversed by the addition of excess substrate and generally the inhibitor shows no structural similarity to the substrate. Kinetic studies reveal a reduced value for the maximum activity of the enzyme but an unaltered value for the Michaelis constant (Figure 8.7). There are many examples of non-competitive inhibitors, many of which are regarded as poisons because of the crucial role of the inhibited enzyme. Cyanide ions, for instance, inhibit any enzyme in which either an iron or copper ion is part of the active site or prosthetic group, e.g. cytochrome c oxidase (EC 1.9.3.1). 

The quantity of any given solute being presented to the reabsorptive mechanisms is determined by the product of the GFR and the solute concentration in plasma. One of the features of any carrier-mediated process is its limited capacity. Binding of a substance to its transport protein follows the same principles as substrate binding to an enzyme or hormone binding to its receptor so we may appropriately liken the dynamics to Michaelis-Menten kinetics. 

One of the important consequences of studying catalysis by mutant enzymes in comparison with wild-type enzymes is the possibility of identifying residues involved in catalysis that are not apparent from crystal structure determinations. This has been usefully applied (Fersht et al., 1988) to the tyrosine activation step in tyrosine tRNA synthetase (47) and (49). The residues Lys-82, Arg-86, Lys-230 and Lys-233 were replaced by alanine. Each mutation was studied in turn, and comparison with the wild-type enzyme revealed that each mutant was substantially less effective in catalysing formation of tyrosyl adenylate. Kinetic studies showed that these residues interact with the transition state for formation of tyrosyl adenylate and pyrophosphate from tyrosine and ATP and have relatively minor effects on the binding of tyrosine and tyrosyl adenylate. However, the crystal structures of the tyrosine-enzyme complex (Brick and Blow, 1987) and tyrosyl adenylate complex (Rubin and Blow, 1981) show that the residues Lys-82 and Arg-86 are on one side of the substrate-binding site and Lys-230 and Lys-233 are on the opposite side. It would be concluded from the crystal structures that not all four residues could be simultaneously involved in the catalytic process. Movement of one pair of residues close to the substrate moves the other pair of residues away. It is therefore concluded from the kinetic effects observed for the mutants that, in the wild-type enzyme, formation of the transition state for the reaction involves a conformational change to a structure which differs from the enzyme structure in the complex with tyrosine or tyrosine adenylate. The induced fit to the transition-state structure must allow interaction with all four residues simultaneously. 

The relationship between substrate concentration ([S]) and reaction velocity (v, equivalent to the degree of binding of substrate to the active site) is, in the absence of cooperativity, usually hyperbolic in nature, with binding behavior complying with the law of mass action. However, the equation describing the hyperbolic relationship between v and [S] can be simple or complex, depending on the enzyme, the identity of the substrate, and the reaction conditions. Quantitative analyses of these v versus [S] relationships are referred to as enzyme kinetics. 

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