Enzymes equations

A number of 1- and 2-aminophosphonates were resolved by a straight CAL-B-promoted acetylation of the amino group in the substrates rac-SS. Surprisingly, ethyl acetate had to be used as an acetylating agent, since the commonly applied vinyl acetate reacted with aminoalkanephosphonates even in the absence of an enzyme (Equation 30, Table 6). ... 

In such a case, a Michaelis pH function becomes useful in describing the pH profile for inactivation. Starting with the conservation of enzyme equation ... 

Net Rate Constant Method for Deriving Enzyme Equations... 

NET RATE CONSTANT METHOD FOR DERIVING ENZYME EQUATIONS... 

Kinetic resolution of racemic secondary hydroperoxides rac-16 can be effected by selective reduction of one enantiomer with employing either chiral metal complexes or enzymes (equation 10). In this way hydroperoxides 16 and the opposite enantiomer of the corresponding alcohols 19 can be produced in enantiomerically enriched form. As side products sometimes the corresponding ketones 20 are produced. 

Equation 9-15 provides a relationship between the velocity observed at a particular substrate concentration and the maximum velocity that would be achieved at infinite substrate concentration. The quantities Vmax and Km are often referred to as the kinetic parameters of an enzyme and their determination is an important part of the characterization of an enzyme. Equation 9-15 can be derived by setting the rate of formation of the ES complex (/cl[E][S]) in the steady state equal to its rate of breakdown, ([/c2 + /c3][ES]). Rearranging and substituting Km, as defined in Eq. 9-15, we obtain Eq. 9-17. 

The treatment of peroxidases in the FeUI resting form with hydrogen peroxide gives a green species (for HRP) known as compound I, which is oxidized to a level of two equivalents above Fein. On slow decomposition, compound I is converted into a red product, compound II, which has one oxidizing equivalent above Fe111. In the presence of a substrate, compound I is reduced to compound II, and then compound II is reduced to the native enzyme (equations 71-73, where AH is a reducing substrate, and A the radical product which will react further). In some cases oxidation of substrate is a direct two electron process. 

The Hill equation is used to estimate Km for allosteric enzymes. Equations based on classic Michaelis-Menten kinetics are not applicable. 

Stereoselectivity will be dictated in most cases by the binding of the substrate to the hydroxylating enzyme. One exception to this occurs in the 6p-hydroxylation of 3-keto A -steroids. In this case the stereochemistry of substitution at C-6 of the product is determined largely by conventional stereoelec-tronic processes, as the mechanism is believed to involve axial addition of oxidant to a conjugate of the substrate and the hydroxylating enzyme (equation 24). ... 

When the first electron transfer is rate limiting, it has been suggested that the thermodynamic argument for gating by substrate binding overlooked the effect of O2 binding. The reduction potential of the P450 enzymes (equation 7) are measured under anaerobic conditions. Under turnover conditions, O2 is present and rapidly binds to the heme Fe(II) center (equation 8). 

This equation is formally similar to the Michaelis-Menten equation of enzyme kinetics, although the analogy is limited because most enzymic reactions are studied with substrate in large excess over enzyme. Equation (1) could be rearranged to give (2) which is formally similar to the Lineweaver-Burk equation, and which permits calculation of and K provided that... 

The limiting stoichiometry of the Mo-based enzyme Equation (11) is identical to that of Equation (12), implicating the obligatory evolution of one molecule of dihydrogen arising from generation of a vacant site on the enzyme at which dinitrogen can bind [61]. This has been elaborated upon in (i) the mechanism of action of the enzyme and (ii) model systems. 

Note that the reaction used to generate the Michaelis-Menten equation was the simplest enzyme equation possible, that with a single substrate going to a single product. Most enzymes catalyze reactions containing two or more substrates. This does not invalidate our equations, however. For enzymes with multiple substrates, the same equations can be used, but only one substrate can be studied at a time. If, for example, we had the enzyme-catalyzed reaction... 

The rate of the reaction can then be derived in terms of and 4,ax (or = /max/[E]). From the knowledge of the dissociation constant and the rate constant for catalysis it is then possible to compare inhibitors and the dissociation constant for the inhibitors, K, in relation to the natural substrates and the effect on the catalytic rates. These kinetic parameters, k and (or K) can then give an indication as to the affinity (K versus and specificity (/general scheme of reversible inhibition, and Figure... 

The next step was the most distinguishing point in our scheme the condensation of the saturated acyl-CoA with the malonyl-enzyme to form the -ketoacyl enzyme [equation (9)]. The accompanying decarboxylation merely adheres to the principle discussed earlier. 

The proposed reactions of pyruvate and sodium O-methyl acetylphosphonate 1-1 with TPP are shown in Scheme 1.6. As described in Scheme 1.6, the normal catalytic process involves addition of TPP to pyruvate and the subsequent loss of carbon dioxide (equation a in Scheme 1.6). Sodium O-methyl acetylphosphonate 1-1 was thought to be strucmrally and functionally similar to pymvate, it could also bind with TPP to form a phosphonic adduct 5, which resembled the reactive intermediate a-lactyl-TPP 4, and was assumed to form during the normal catalytic cycle of the enzyme (equation b in Scheme 1.6). However, phosphonic adduct 5 would not undergo a reaction analogous to the decarboxylation in equation a. 

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