Substrates bisubstrate kinetics

With the exception of a recent bisubstrate kinetic analysis of bilirubin UDP-glucuronyltransferase (P5), saturation with either one of the substrates was investigated at some rather arbitrarily fixed concentration of the other substrate. The results, therefore, have to be interpreted with caution. 

In determining enzyme activities, it is usually assumed that at a fixed set of so-called saturating substrate concentrations a sufficiently accurate value of F, ax is obtained. Bisubstrate kinetic analyses of UDP-glucu-ronyltransferase [assayed with bilirubin (P5) and p-nitrophenol (V6), respectively] indicate that a true measure of the amount of enzyme can be obtained only by suitable extrapolation procedures. This restriction applies in particular to bilirubin (A2, HIO, T8) and other aglycons (M15, V6) because of substrate inhibition. UDP-glucuronic acid was inhibitory at concentrations only about 10-fold higher than the apparent Km value (HIO) this was most pronounced at relatively short incubation times. Mg was noninhibitory at concentrations equal to 20 times the apparent Km values (F3, HIO). 

From bisubstrate, kinetic analysis with a transferase from hen oviduct that, under the conditions of the assay, formed only GlcNAc-PP-Dol, it followed that both dolichol phosphate and UDP-GlcNAe have to he bound to the enzyme before release of the product occurs.52 However, the fact that only partially purified preparations have thus far been obtained (the preparations may also still be contaminated with substrates and product), together with experimental difficulties in handling both the substrate dolichol phosphate (which, furthermore, is not one compound, see the earlier discussion) and the unstable enzyme (enveloped in micelles of detergent), make difficult a sensible interpretation and comparison of the kinetic parameters detenuined for the different enzvme-preparations. The solubilized enzymes catalyzing reactions 1,2, and 3 have in common their alkaline pH optima and dependence on Mg2+ or Mn2+ ions. The latter fact makes (ethylenedinitrilo)tetraacetic acid (EDTA) a reversible inhibitor of enzyme activity and an important experimental tool. 

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. 

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... 

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. 

The general rule for writing the rate equation according to the quasi-equilibrium treatment of enzyme kinetics can be exemplified for the random bisubstrate reaction with substrates A and B forming products P and Q (Figure 7.1), where KaKab = KbKba and KpKpq = KqKqp. 

Nazari K, Mahmoudi A, Khosraneh M et al (2009) Kinetic analysis for suicide-substrate inactivation of microperoxidase-11 a modified model for bisubstrate enzymes in the presence of reversible inhibitors. J Mol Catal B Enzym 56 61-69... 

Typically, the kinetics of bisubstrate reactions are studied by measuring the initial reaction rates over a range of concentrations of one substrate. A, while holding the concentration of the second substrate, B, constant and doing this for several fixed values of [B]. If specific concentrations of A are used for all of the reaction series, these same rates can also be used to examine changes in reaction rate when [B] is varied at fixed concentrations of A for several values of [A]. 

When one of the substrates is water (i.e., when the process is one of hydrolysis), with the reaction taking place in aqueous solution, only a fraction of the total number of water molecules present participates in the reaction. The small change in the concentration of water has no effect on the rate of reaction and these pseudo-one substrate reactions are described by one-substi ate kinetics. More generally the concentrations of both substrates may be variable, and both may affect the rate of reaction. Among the bisubstrate reactions important in clinical enzymology are the reactions catalyzed by dehydrogenases, in which the second substrate is a specific coenzyme, such as the oxidized or reduced forms of nicotinamide adenine dinucleotide, (NADH), or nicotinamide adenine dinucleotide phosphate, (NADPH), and the amino-group transfers catalyzed by the aminotransferases. 

Most enzymatic reactions involving two-substrate reactions show more complex kinetics than do one-substrate reactions. Examples are catalyzed by dehydrogenases and aminotransferases. Hydrolytic reactions are bisubstrate reactions in which water is one of the substrates. The change in water concentration is negligible and has no effect on the rate of reaction. A two-suhstrate reaction can be written as... 

For a sequential bisubstrate enzyme, the rate of dissociation of the hrst substrate can be estimated by substrate trapping methods. The rationale for this experimental approach is shown in Scheme XXII. The enzyme is first preincubated with radiolabeled substrate A and is then mixed with an excess of unlabeled substrate A and substrate B to initiate the reaction. The recovery of radio-labeled product is a function of the kinetic partitioning of the enzyme-bound substrate between dissociation to yield free S and forward reaction with substrate B to yield product P. 

In an attempt to avoid problems with the phosphate groups from the CoA moiety, the penultimate intermediate in the synthesis of the bisubstrate inhibitor, A-bromoacetyltryptamine, was tested as a possible affinity label inhibitor or as a substrate for the in situ enzymatic synthesis of the bisubstrate inhibitor through an acylation mechanism. N-Bromoacetyltryptamine did act as an inhibitor of the enzyme, but inhibition could be reversed by dialysis suggesting that the inhibition was not due to a covalent adduct. It was shown that the enzyme catalyzed the acylation of A-bromoacetyltryptamine by CoASH to form compound 6a with a rate enhancement of 3.3 x 10 relative to the uncatalyzed reaction. Ultimately, it was shown that the acylation reaction occurs at the same active site as the acetylation activity. A closer inspection of the kinetics of inhibition by tbe bisubstrate analog 6a resulted in the observation of slow-onset inhibition over the first few minutes of the reaction with a A) value of 84nmol 1 . Owing to its neutrality, A-bromoacetyltryptamine was tested as an inhibitor in vivo. The analog precursor was shown to inhibit melatonin production in norepinephrine-stimulated pinealocytes in a concentration-dependent manner and with low cytotoxicity. 

Kinetic measurements with bisubstrate reactions are performed by measuring the initial reaction rates in the presence of increasing concentrations of substrate A, keeping the substrate B constant and repeating the experiment at several fixed concentrations of substrate B thus, A represents a variable substrate and B a constant substrate. In the double reciprocal plot, the experimental data present a family of straight hnes, with a common intersection point which is found on ordinate, on abscissa, in the HI or in the IV quadrant. One can use the same set... 

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) ... 

Why product inhibition occurs. The products of reaction are formed at the active site of enzyme and are the substrates for the reverse reaction. Consequently, a product may act as an inhibitor by occupying the same site as the substrate from which it is derived. In the Rapid Equilibrium Random bisubstrate mechanism, most ligand dissociations are very rapid compared to the interconversion of EAB and EPQ. Thus, the levels of EP and EQ are essmtiaUy zero in the absence of added P and Q. In the presence of only one of the products, the reverse reaction can be neglected, as the concentration of the other product is essentially zero during the early part of the reaction. Nevertheless, the forward reaction will be inhibited because finite P (or Q) ties up some of the enzyme. The type of this product inhibition depends on the number and type of enzyme-product complexes that can form. Consequently, product inhibition studies can be very valuable in the diagnostics of kinetic mechanisms (Rudolph, 1979). 

The order of addition of substrates in the Bi Bi mechanisms, with a central ternary complex, can be strictly ordered, completely random or partially random. We can employ reaction (10.7) in order to analyze most kinetic mechanisms that occur in bisubstrate systems ... 

The general property of all above mechanisms is their adherence to the Michaelis-Menten kinetics. In the absence of products, the double reciprocal plots for aU bisubstrate mechanisms represent a family of straight lines with a common intersection point, if one substrate is varied while the other substrate is held at different fixed concentrations. Similarly, the double reciprocal plots for all trisubstrate mechanisms represent a family of straight lines with a common intersection point, if one substrate is varied while the second substrate is held at different fixed concentrations, and the third substrate is held at a fixed concentration. This, however, is tme only if each substrate adds just once if one of them adds twice in sequential fashion, the reciprocal plots will be parabolic. 

The foregoing examples show the complexity of the pH dependence of full rate equations for bisubstrate reactions. Therefore, when dealing with the pH effect on the kinetics of reaction of two substrates, a high concentration of one of the substrates is often used, so that the reaction may be treated by equations that describe the single-substrate case (Tipton Dixon, 1979). 

Very few complete thermod5mamic analyses have been performed with enzymic reactions involving more than one substrate. This is understandable, considering the usual complexities of kinetic constants in bisubstrate and trisubstrate reactions. Kinetic constants in such reactions are usually composed of several individual rate constants, each of which may have its own dependence on temperature. In such cases, the separation of rate constants is usually a very difficult task. However, there are cases that allow a meaningful separation of rate constants. 

As already pointed out in Chapter 9, the steady-state expressions for the catalytic constant, Vu and for the specificity constant, Vi/Ksi for bisubstrate mechanisms are rather complex. For the ordered mechanism in reaction (17.18), as we have already pointed out in Section 9.2.2, even if we leave out the isomerizations, that is, the complexes EAB and EPQ, expressions for VJK and V, are rather complex. If we include the isomerization complexes, IiAB and EPQ, the rate equations for the catalytic constant, V, and for the specificity constant, VJKji, appear quite formidable compared to equations for the monosubstrate reaction (Eqs. (17.13) and (17.14)). Further, if we remember that the kinetic expression for isotope efects is the ratio of both entire rate equations describing the disappearance of hydrogen and deuterium substrates (or other isotopes), than the rate equations for isotope effects may appear awesome. 

The kinetic expression for observed isotope effects is the ratio of both entire rate equations describing the disappearance of hydrogen and deuterium substrates. The isotopically sensitive step appears in multiple terms and cannot be factored out. In order to achieve factoring and subsequent simplification to useful kinetic equations, it is necessary to examine the Umits of rate equations at low and high substrate concentrations, where enzyme reactions approach first-order and zero-oider kinetics, respectively. To understand this, we must consider how isotope effects in bisubstrate reactions are measured. 

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