Association of enzymes and substrates

A complete description of an enzyme-catalyzed reaction requires direct measurement of the rates of individual reaction steps—for example, measurement of the association of enzyme and substrate to form the ES complex. It is during the pre-steady state that the rates of many reaction steps can be measured independently. Experimenters adjust reaction conditions so that they can observe events during reaction of a single substrate molecule. Because the pre-steady state phase is gener-... 

In the Briggs-Maldane mechanism, when k2 is much greater than k-i, kcJKM is equal to kx, the rate constant for the association of enzyme and substrate. It is shown in Chapter 4 that association rate constants should be on the order of 108 s l M l. This leads to a diagnostic test for the Briggs-Haldane mechanism the value of kaJKu is about 107 to 108 s-1 M-1. Catalase, acetylcholinesterase, carbonic anhydrase, crotonase, fumarase, and triosephosphate isomerase all exhibit Briggs-Haldane kinetics by this criterion (see Chapter 4, Table 4.4). 

The value of kcJKM cannot be greater than that of any second-order rate constant on the forward reaction pathway.3 It thus sets a lower limit on the rate constant for the association of enzyme and substrate. 

Another parameter often referred to when discussing Michaelis-Menten kinetics is kcaJ Ky. This is an apparent second-order rate constant that relates the reaction rate to the free (not total) enzyme concentration. As described above, at very low substrate concentrations when the enzyme is predominantly unbound, the velocity (f) is equal to [El Ky. The value of Is JKy sets a lower limit on the rate constant for the association of enzyme and substrate. It is sometimes referred to as the specificity constant because it determines the specificity of the enzyme for competing substrates. 

At low substrate concentrations, the enzyme is largely unbound and E Eo therefore, fccat/ A is an apparent second-order rate constant, which is not a tme microscopic rate constant except in the extreme case in which the rate-limiting step in the reaction is the encounter of enzyme and substrate. Only in the Briggs-Haldane mechanism, when is much greater than fc, fccat/JSC is equal to ku the rate constant for the association of enzyme and substrate. Recently, Northrop (1999) raised a serious objection to this classical definition of the specificity constant, and pointed out that fcc t/ 0 actually provides a measure of the rate of capture of substrate by free enzyme into a productive complex or complexes destined to go on to form products and complete a turnover at some later time. 

It is stated that during an in vitro enzymatic reaction the concentration of the enzyme shall not change during the test, and that the substrate concentration exceeds the enzyme concentration in orders of magnitude in a first approximation the substrate concentration is practically constant, too. Both of these assumptions transform a reaction of 2" order into the much simpler reaction of 0 order. If the concentrations of enzyme and substrate are similar, we get a reaction of order. The reaction rate v for the association reaction... 

Many inhibitors with very low dissociation constants appear to have a slow onset of inhibition when they are added to a reaction mixture of enzyme and substrate. This was once interpreted as the inhibitors having to induce a slow conformational change in the enzyme from a weak binding to a tight binding state. But in most cases, the slow binding is an inevitable consequence of the low concentrations of inhibitor used to determine its Ki. For example, consider the inhibition of trypsin by the basic pancreatic trypsin inhibitor. Kx is 6 X 10-14 M and the association rate constant is 1.1 X 106 s-1 M-1 (Table 4.1). To determine the value of Ki, inhibitor concentrations should be in the range of K1, where the observed first-order rate constant for association is (6 X Q U M) X (1.1 X 106 s-1 M-1) that is, 6.6 X 10-8 s 1. The half-life is (0.6931/6.6) X 108 s, which is more than 17 weeks. 

The quantitation of enzymes and substrates has long been of critical importance in clinical chemistry, since metabolic levels of a variety of species are known to be associated with certain disease states. Enzymatic methods may be used in complex matrices, such as serum or urine, due to the high selectivity of enzymes for their natural substrates. Because of this selectivity, enzymatic assays are also used in chemical and biochemical research. This chapter considers quantitative experimental methods, the biochemical species that is being measured, how the measurement is made, and how experimental data relate to concentration. This chapter assumes familiarity with the principles of spectroscopic (absorbance, fluorescence, chemi-and bioluminescence, nephelometry, and turbidimetry), electrochemical (poten-tiometry and amperometry), calorimetry, and radiochemical methods. For an excellent coverage of these topics, the student is referred to Daniel C. Harris, Quantitative Chemical Analysis (6th ed.). In addition, statistical terms and methods, such as detection limit, signal-to-noise ratio (S/N), sensitivity, relative standard deviation (RSD), and linear regression are assumed familiar Chapter 16 in this volume discusses statistical parameters. 

To date, the latex of Carica papaya L. is known to contain at least four different proteolytic enzymes, namely, papain (E.C. 3.4.22.2), chymopapain (E.C. 3.4.22.6), caricain or papaya proteinase III or 2 (E.C. 3.4.22.30), and glycyl endopeptidase or papaya proteinase IV (E.C. 3.4.22.25). The importance of the latex of the unripe fruit of the tropical tree Carica papaya L. was first noted by G. C. Roy, who in 1873 published in the Calcutta Medical Journal (see Ref. 1) an article entitled The solvent action of papaya juice on the nitrogenous articles of food. The name papain was used for the first time by Wurtz and Bouchet [2] to describe partially purified cysteine proteinases from the papaya latex. They wrote, nous designerons ce ferment sous le nom de papa ine." In 1880, Wurtz postulated that papain acts in fibrin digestion by becoming bound to the fibrin [3]. This is remarkable in that Emil Fisher first described the specific association of enzyme with substrate in 1898. Since that time, many names have been used for commercial latex products, e.g., papayotin, papaoid, etc. 

The interaction of dinucleosides, pyrimidine 2 3 -cyclic phosphates, or pyrimidine 3 -phosphates with the enzyme is characterized by two relaxation processes, in addition to the process associated with the unliganded enzyme. In all cases the results can be described by a two-step mechanism a bimolec-ular combination of enzyme and substrate followed by an isomerization or conformational change of the enzyme-substrate complex ... 

The introduction of deuterium in place of proton in water, and its consequent exchange into some positions of enzymes and substrates, produces solvent isotope effect on the kinetic and equilihrium constants associated with the enzymatic reactions. These effects, usually expressed as ratios of the appropriate constants in two isotopic solvents HOH and DOD, are useful in the study of reaction mechanisms (Candour Schowen, 1978 Cook, 1991 Quinn Sutton, 1991). 

The light hydrogen isotope protium (H) can be replaced by deuterium (D) in the hydrogenic sites of the water species (i.e. HOD, D2O, H+3O, H+2OD, I>20H, D+sO, etc), under certain circumstances, and as a consequence deuterium may replace protium into some sensitive positions of enzymes and substrates these replacements have been designated as solvent isotope effects (SIE) and usually they affect the kinetic and equilibrium constants associated with the enzymatic reactions. Obviously, these SIE are related to the isotopac solvents and thus... 

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... 

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,... 

Table 12.1 Host-released elicitors, pathogen-associated molecular patterns, and substrates of ROS-generating enzymes involved in algal defenses... 

When the inhibitor and substrate are structurally similar, the inhibitor forms a complex or associate with enzyme and decrease the rate of enzyme catalyzed reaction by reducing the proportion of enzyme-substrate complex as follows ... 

Related to these enzyme -catalysed reactions are electroreductions of acetophenone in the presence of chiral crown ethers. The low optical yields (<3%) are attributed to association of the prochiral substrate and the chiral crown ether salt complex in the electrochemical double layer (Horner and Brich, 1978). 

The binding sites of most enzymes and receptors are highly stereoselective in recognition and reaction with optical isomers (J, 2 ), which applies to natural substrates and synthetic drugs as well. The principle of enantiomer selectivity of enzymes and binding sites in general exists by virtue of the difference of free enthalpy in the interaction of two optical antipodes with the active site of an enzyme. As a consequence the active site by itself must be chiral because only formation of a diasteromeric association complex between substrate and active site can result in such an enthalpy difference. The building blocks of enzymes and receptors, the L-amino acid residues, therefore ultimately represent the basis of nature s enantiomer selectivity. 

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