Michaelis-Menten kinetics and

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

Kemp and Waters also found the oxidations of cyclohexanone and of mandelic, malonic and a-hydroxyisobutyric acids by Cr(VI) to be Mn(II)-catalysed. In these cases, as with oxalic acid, the [Cr(VI)] versus time plots are almost linear and the reaction becomes first order in substrate (or involves Michaelis-Menten kinetics), and, except at lowest catalyst concentrations, approximately first order in [Mn(II)]. Detailed examination of the initial rate of oxidation of a-hydroxyrobutyric acid as a function of oxidant concentration revealed, however, that the dependence is... 

The effect of non-participating ligands on the copper catalyzed autoxidation of cysteine was studied in the presence of glycylglycine-phosphate and catecholamines, (2-R-)H2C, (epinephrine, R = CH(OH)-CH2-NHCH3 norepinephrine, R = CH(OH)-CH2-NH2 dopamine, R = CH2-CH2-NH2 dopa, R = CH2-CH(COOH)-NH2) by Hanaki and co-workers (68,69). Typically, these reactions followed Michaelis-Menten kinetics and the autoxidation rate displayed a bell-shaped curve as a function of pH. The catecholamines had no kinetic effects under anaerobic conditions, but catalyzed the autoxidation of cysteine in the following order of efficiency epinephrine = norepinephrine > dopamine > dopa. The concentration and pH dependencies of the reaction rate were interpreted by assuming that the redox active species is the [L Cun(RS-)] ternary complex which is formed in a very fast reaction between CunL and cysteine. Thus, the autoxidation occurs at maximum rate when the conditions are optimal for the formation of this species. At relatively low pH, the ternary complex does not form in sufficient concentration. 

Results have generally been disappointing. It can be difficult to remove the TSA from the polymer, but a more fundamental problem concerns the efficiency of the catalysis observed. The most efficient systems catalyze the hydrolysis of carboxylate and reactive phosphate esters with Michaelis-Menten kinetics and accelerations (koAJKM)/kunoJ approaching 103,1661 but the prospects for useful catalysis of more complex reactions look unpromising. Apart from the usual difficulties the active sites produced are relatively inflexible, and the balance between substrate binding and product inhibition is particularly acute. 

Characteristically, within certain concentration limits, if a chemical is absorbed by passive diffusion, then the concentration of toxicant in the gut and the rate of absorption are linearly related. However, if absorption is mediated by active transport, the relationship between concentration and rate of absorption conforms to Michaelis-Menten kinetics and a Lineweaver-Burk plot (i.e., reciprocal of rate of absorption plotted against reciprocal of concentration), which graphs as a straight line. 

Equation (4) corresponds to saturation-type (Michaelis-Menten) kinetics and rate constants obtained over a suitable range of [CD], sufficient to reflect the hyperbolic curvature, can be analysed to provide the limiting rate constant, kc, and the dissociation constant, Ks (VanEtten et al., 1967a Bender and Komiyama, 1978 Szejtli, 1982 Sirlin, 1984 Tee and Takasaki, 1985). The rate constant ku is normally determined directly (at zero [CD]), and sometimes Ks can be corroborated by other means (Connors, 1987). 

Antibody 15C5 was able to catalyse the hydrolysis of the triester [105] with cat 2.65 x 10 3 min 1 whilst a second antibody from the same immunization programme was later found to hydrolyse the acetylcholinesterase inhibitor Paraoxon [106] with kcat = 1.95 x 10 3min-1 at 25°C (Appendix entry 6.2) (Lavey and Janda, 1996b). Antibody 3H5 showed Michaelis-Menten kinetics and was strongly inhibited by the hapten [104]. It exhibited a linear dependence of the rate of hydrolysis on hydroxide ion concentration, suggesting that 3H5 effects catalysis by transition state stabilization rather than by general acid/base catalysis. 

Transport of O2 away from a root and its consumption in microbial processes—in addition to nitrification—and oxidation of mobile reductants such as Fe +. Microbial O2 consumption is described with Michaelis-Menten kinetics and Fe + oxidation with first-order kinetics with respect to both... 

The order of reaction is not always integral and sometimes the rate cannot be expressed in a simple form. For example, some enzyme-catalysed reactions obey Michaelis—Menten kinetics and the rate is given by... 

MW 27,500) with no cofactors or metal ions reqnirement for its function, it displays Michaelis-Menten kinetics and it is secreted in large amounts by a wide variety of Bacillus species. Subtilisin is also among the most important industrial enzymes due to its use in laundry detergents. Protein engineering strategies for subtilisin have focused on a number of aspects, namely catalysis, substrate specificity, thermal and oxidative stability and pH profile. We will describe briefly each of these aspects. 

Enzymatic transesterifications in organic solvents follow Michaelis-Menten kinetics, and in quite a few cases, the values of v/Ku roughly correlate with the solvent s hydrophobicity (Zaks, 1988a). The dependence of the catalytic activity of the enzyme in organic media on the pH of the aqueous solution from which it was recovered is bell-shaped, with the maximum coinciding with the pH optimum of the enzymatic activity in water. 

Criteria for calling a compound a synthetic enzyme are (i) completion of at least one catalytic cycle (ii) its presence after the catalytic cycle in unchanged form and (iii) a saturation kinetics behavior such as is manifested by Michaelis-Menten kinetics. There is a tetrameric helical peptide that catalyzes the decarboxylation of oxaloacetate with Michaelis-Menten kinetics and accelerates the reaction 103-104-fold faster than n-butylamine as control, a record for a chemically derived artificial enzyme. 

Kemp elimination was used as a probe of catalytic efficiency in antibodies, in non-specific catalysis by other proteins, and in catalysis by enzymes. Several simple reactions were found to be catalyzed by the serum albumins with Michaelis-Menten kinetics and could be shown to involve substrate binding and catalysis by local functional groups (Kirby, 2000). Known binding sites on the protein surface were found to be involved. In fact, formal general base catalysis seems to contribute only modestly to the efficiency of both the antibody and the non-specific albumin system, whereas antibody catalysis seems to be boosted by a non-specific medium effect. 

In perchloric acid, hexoses and pentoses are oxidized by Ce(IV) via formation of two complex intermediates. The first is partly oxidized following Michaelis-Menten kinetics and partly dissociated to the second, which is oxidized more slowly than the former.180 The first step in the oxidation of aldoses by Tl(III) in the same medium involves the C-l-C-2 cleavage of the aldehydo form of the sugar. Thus, D-glucose gives D-arabinose and formic acid. With an excess of oxidant the final product is carbon dioxide.181 In the presence of a catalytic amount of sulfuric acid in acetic acid, Tl(III) oxidizes maltose and lactose to the corresponding disaccharide aldonic acids. The reaction showed activation enthalpies and enthropies characteristic of second-order reactions.182... 

Cyclodextrin ketones have been used as powerful catalysts of amine oxidation in the presence of hydrogen peroxide as the stoichiometric oxidant. This oxidation follows Michaelis-Menten kinetics and depending on the substrate the oxidation rate is increased up to 1100-fold. It has been proposed that hydrogen peroxide reacts with the ketone to form a hydroperoxide adduct and this adduct is responsible for oxidizing the amine, bound in the cavity, to the hydroxylamine.189... 

Most P450 oxidations and drug interactions can be predicted from inhibition studies, since most P450 inhibitors show competitive Michaelis-Menten kinetics. However, there are examples of unusual kinetics, and most of these are associated with CYP3A oxidations. In this chapter, both Michaelis-Menten kinetics and more complex kinetics will be discussed. General experimental protocols that can be used to obtain and analyze kinetic data will be presented, and the implications of the results when predicting drug interactions will be discussed. 

More complex enzymatic reactions usually display Michaelis-Menten kinetics and can be described by Eq. (2). However, the forms of constants Km and Vm can be very complicated, consisting of many individual rate constants. King and Altman (7) have provided a method to readily derive the steady-state equations for enzymatic reactions, including the forms that describe Km and Vm. The advent of symbolic mathematics programs makes the implementation of these methods routine, even for very complex reaction schemes. The P450 catalytic cycle (Fig. 2) is an example of a very complicated reaction scheme. However, most P450-mediated reactions display standard hyperbolic saturation kinetics. Therefore, although the rate constants that determine Km and Vm are... 

The MIP-mediated hydrolysis of ester 70 in HEPES buffer (0.15 M, pH 7.3) and MeCN at 20 °C showed Michaelis-Menten kinetics and a 325-fold rate enhancement compared to the reaction performed in solution. By comparison, the hydrolysis of ent-70 showed a 234-fold enhancement under the same conditions, resulting in a pronounced enantioselectivity. Interestingly, the apparently slight difference between 70 and 71 resulted in a significant decrease in catalyst activity, as the rate enhancement compared to the reaction performed in solution was only 103-fold. 

The adrenal cortex releases Cortisol (CORT) depending on ACTH (also following Michaelis-Menten kinetics) and degrades with a time constant kcoRT ... 

It was noted earlier that Michaelis-Menten kinetics and its linear transformations are not valid for allosteric enzymes. Instead, the Hill equation, an equation originally empirically developed to describe the cooperative binding of Oz to hemoglobin (Chapter 7), is used. The expression describing such a straight-line plot is... 

The one-plus rate equation 8.22 is of the same algebraic form as the Michaelis-Menten equation 8.18, only the physical significance of the coefficients is different [instead of the constant K, the expression kAX /(k + kXP) now appears]. Accordingly, the behavior is the same as for Michaelis-Menten kinetics, and that name is often used for Briggs-Haldane kinetics as well. 

Michaelis-Menten kinetics and empirical kinetic parameters can be joined to give pieces of information on optimum (diffusion-controlled) catalytic kinetics, just assuming that optimum turnover means use of the best catalytic center species and half substrate saturation. This holds for small substrate concentrations, probably subject to intracellular control or limited take-up. Then ... 

The assumption of uniformity is in fact justified for some realistic kinetic schemes, such as Langmuir isotherm catalyzed reactions, Michaelis-Menten kinetics, and others (Aris, 1989 Cicarelli et al, 1992). The assumption bears a more than superficial analogy with those systems termed pseudo-monomolecular by Wei and Prater (1962). Mathematically, it is a very powerful assumption By crossing out the dependence of F[ ] on x, its value has been reduced from an infinite-dimensional vector (a function of x) to a scalar. This simplification makes Eq. (102) a quasilinear one, and it can be integrated explicitly by introducing a warped time scale t(0. (0) = 0. The solution, as can be verified by inspection, is... 

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