Inactivation equation

In order to clear up the mechanism of inactivation of excited states, we examined the processes of quenching of fluorescence and phosphorescence in PCSs by the additives of the donor and acceptor type253,2S5,2S6 Within the concentration range of 1 x 1CT4 — 1 x 10"3 mol/1, a linear relationship between the efficiency of fluorescence quenching [(/0//) — 1] and the quencher concentration was found. For the determination of quenching constants, the Stem-Volmer equation was used, viz. 

When the concentration of inactivator is far below saturation, such that [/] Kh the term [/] in the denominator of the right side of Equation (8.3) can be ignored. Under these conditions we obtain... 

Only when k5 is rate-limiting can we equate kma with k5. Likewise K, has a complex form for mechanism-based inactivation ... 

Figure 8.10 Substrate protection of an enzyme against irreversible inactivation by a mechanism-based inactivator. The data points in this plot are fitted to Equation (8.7).

Note that in some cases one may follow the time course of covalent E-A formation by equilibrium binding methods (e.g., LC/MS, HPLC, NMR, radioligand incorporation, or spectroscopic methods) rather than by activity measurements. In these cases substrate should also be able to protect the enzyme from inactivation according to Equation (8.7). Likewise a reversible competitive inhibitor should protect the enzyme from covalent modification by a mechanism-based inactivator. In this case the terms. S and Ku in Equation (8.7) would be replaced by [7r] and K respectively, where these terms refer to the concentration and dissociation constant for the reversible inhibitor. 

Numerous studies have shown that oxidation of a wide range of AH2 by HRP in the presence of H202 is characterized by a loss of enzyme activity. It is now well established that HRP is inactivated by H202.32 Because the final step (Equation 17.4), during which the oxidized ferryl intermediate is... 

Equation 17.13 has been derived without taking account of HRP inactivation by H202, which is described in Equation 17.5. One simple way to remedy this situation is to introduce an inactivation constant into Equation 17.13 ... 

The most fundamental reaction is the alkylation of benzene with ethene.38,38a-38c Arylation of inactivated alkenes with inactivated arenes proceeds with the aid of a binuclear Ir(m) catalyst, [Ir(/x-acac-0,0,C3)(acac-0,0)(acac-C3)]2, to afford anti-Markovnikov hydroarylation products (Equation (33)). The iridium-catalyzed reaction of benzene with ethene at 180 °G for 3 h gives ethylbenzene (TN = 455, TOF = 0.0421 s 1). The reaction of benzene with propene leads to the formation of /z-propylbenzene and isopropylbenzene in 61% and 39% selectivities (TN = 13, TOF = 0.0110s-1). The catalytic reaction of the dinuclear Ir complex is shown to proceed via the formation of a mononuclear bis-acac-0,0 phenyl-Ir(m) species.388 The interesting aspect is the lack of /3-hydride elimination from the aryliridium intermediates giving the olefinic products. The reaction of substituted arenes with olefins provides a mixture of regioisomers. For example, the reaction of toluene with ethene affords m- and />-isomers in 63% and 37% selectivity, respectively. 

The palladium-catalyzed reaction of benzol]quinoline in the presence of PhI(OAc)2 as an oxidant in MeCN gives an 11 1 mixture of 10-acetoxy- and 10-hydroxybenzo[ ]quinolines in 86% yield (Equation (98)).135 This chelation-directed oxidation can be extended to the benzylic C-H bond of 8-methylquinoline. The inactivated sp3 C-H bonds of oximes and pyridines undergo the same palladium-catalyzed oxidation with PhI(OAc)2 (Equation (99)).1... 

The condition (4) is never exactly valid, because every chemical system contains some impurities which inactivate the initiator. Some of the impurities come from the walls of the vessel, some from the solvent, and some from the monomer. We have shown how these can be determined (4) and it will suffice here to correct the equation (4) to the more realistic form (8) ... 

For the simple system that contains a single active layer at a distance L from the electrode surface and separated from it by a series of inactivated monolayers, the current is given by the following equation adapted from equation (5.13), in which [Q],=0 is replaced by [Q] and [S]l=0 by [S]x=L = c ... 

The diffusion-reaction problem in the more general case occurs in a system containing n — 1 inactivated enzyme layers adjacent to the electrode surface on top of which N — n active layers have been deposited. Table 6.9 lists the equations that govern the fluxes of the two forms of the cosubstrate in such systems. 

Mathematical Treatment of the Results. In almost all experiments inactivation followed first order kinetics with a high correlation. The half-lives of lignin peroxidase were calculated from the following equation, where k is a rate constant of inactivation ... 

This equation will describe the loss of enzyme activity, if the affinity label is binding at the active site. Moreover, reversibly bound ligands capable of occupying the same site as the affinity label will competitively inhibit the rate of enzyme inactivation. 

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

By integrating the second equation first, we get [R] = [R]initiaie 2 thus, we may substitute this expression for [R] into the first differential equation to obtain the rate law that allows for enzyme inactivation by a reagent which itself is undergoing deactivation. After separating variables and integrating the combined expression, we obtain... 

Inactivated alkenes are oxidatively cleaved by the hydrotrioxide to give ketones. For example, methyl oleate 73 reacts with the hydrotrioxide to produce two aldehydes, followed by LiAlFLj reduction to give 1-nonanol and nonane-1,9- diol in 64 and 74% yields (equation 81). 

A mechanism was proposed to account for the reaction of triethylsilyl hydrotrioxide with electron-rich alkenes as a dioxetane-forming process (route a equation 82) and with inactivated alkenes as a nondioxetane carbonyl-forming process (route b equation 83). 

Dekker et al. [170] studied the extraction process of a-amylase in a TOMAC/isooctane reverse micellar system in terms of the distribution coefficients, mass transfer coefficient, inactivation rate constants, phase ratio, and residence time during the forward and backward extractions. They derived different equations for the concentration of active enzyme in all phases as a function of time. It was also shown that the inactivation took place predominantly in the first aqueous phase due to complex formation between enzyme and surfactant. In order to minimize the extent of enzyme inactivation, the steady state enzyme concentration should be kept as low as possible in the first aqueous phase. This can be achieved by a high mass transfer rate and a high distribution coefficient of the enzyme between reverse micellar and aqueous phases. The effect of mass transfer coefficient during forward extraction on the recovery of a-amylase was simulated for two values of the distribution coefficient. These model predictions were verified experimentally by changing the distribution coefficient (by adding... 

In order to describe and optimize the reverse micellar extraction process, Dekker et al. [ 170] have proposed a mathematical model, which satisfactorily describes the time dependency of the concentration of active enzyme in all the phases, based on the flow, mass transfer, and first-order inactivation kinetics. For each phase, a differential equation is derived. For forward extraction ... 

Some bipyridinium salts are remarkable herbicides. They rapidly desiccate all green plant tissue with which they come into contact, and they are inactivated by adsorption on to clay minerals in the soil. This potent herbicidal activity is found only in quaternary salts, e.g. diquat (254) and paraquat (255), with redox potentials for the first reduction step between -300 and -500 mV (equations 158 and 159) (B-80MI20504). The first reduction step, which is involved in herbicidal activity, involves a completely reversible, pH independent, one-electron transfer to yield the resonance stabilized radicals (256) and (257). The second reduction step, (256 -> 258) and (257 -> 259), is pH dependent and the p-quinoid species formed are good reducing agents that may readily be oxidized to diquatemary salts. 

Inactivated aryl bromides do not react with /-PrMgCl in a sufficient rate even at temperatures as high as room temperamre. However, the presence of 1 equivalent of LiCl in the reaction mixmre enhances the rate of the exchange reaction tremendously, thus even allowing the use of electron-rich aryl bromides (equation 21). ... 

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