Rapid equilibrium mechanism

The Rapid Equilibrium Mechanism The following scheme depicts this mechanism ... 

In this rapid equilibrium mechanism, with all binding steps expressed with dissociation constants, then under initial rate conditions (i.e., [P] = 0) the initial rate expres-... 

Rapid Equilibrium Mechanism. If the rate-determining step is the catalytic step and all binding steps can be described by dissociation constants (e.g., K = [E][A]/ [EA]), then, in the absense of products i.e., [P] and [Q] 0), the initial rate equation for the rapid equihbrium Uni Bi mechanism is identical to that of the Uni Uni... 

QUASI-EQUILIBRIUM ASSUMPTION RAPID EQUILIBRIUM MECHANISMS Rapid gel filtration of biomacromolecules, RAPID BUFFER EXCHANGE RAPID MIXING... 

Figure 8.1 Model energy diagrams for non-enzymic reactions (A), enzymic reaction following the rapid equilibrium mechanism (see Table 8.1) (B) and enzymic reaction following Briggs-Haldane kinetics (C). E represents the activation energy of transition and the positive and...

Raman scattering 192 Random mechanism 120 Rapid equilibrium mechanism 120 Rapid mixing techniques 133-136 Rapid quenching techniques 135-136... 

The primary graphs alone, the double reciprocal plots in the absence of products, can be quite valuable in the diagnostics of rapid equilibrium mechanisms. Thus, one can easily distinguish the ordered from the random rapid equilibrium system, even from the primary graphs in the absence of the products of reaction (Table 1). 

Rapid equilibrium mechanisms Steady-state ordered mechanisms ... 

The upper-part of Table 3 shows the rapid equilibrium mechanisms and the lower-part the steady-state mechanisms. At the end of the table is the Steady-State Random Bi Bi mechanism that is included for comparison. The steady-state random case in practice gives the same patterns as rapid equilibrium ones one can usually teU the difference only by differential rates of isotopic exchange or the measurement of stickiness. 

In this section, we shall reviewthe rate equations forthe majortypes of trisubstrate mechanisms, written in the absence of products (Cleland, 1963 Plowman, 1972 Fromm, 1975,1979). All trisubstrate mechanisms in the rapid equilibrium category are relatively rare and the steady-state mechanisms are more common. However, the derivation of rate equations for rapid equilibrium mechanisms, in the absence of products, is less demanding, as it requires only the rapid equilibrium assumptions and, therefore, the resulting rate equations are relatively simple. 

Because proton-transfer reactions between oxygen atoms are usually very fast, step 3 can be assumed to be a rapid equilibrium. With the above mechanism assume4 let us examine the rate expression which would result, depending upon which of the steps is rate-determining. 

The details of proton-transfer processes can also be probed by examination of solvent isotope effects, for example, by comparing the rates of a reaction in H2O versus D2O. The solvent isotope effect can be either normal or inverse, depending on the nature of the proton-transfer process in the reaction mechanism. D3O+ is a stronger acid than H3O+. As a result, reactants in D2O solution are somewhat more extensively protonated than in H2O at identical acid concentration. A reaction that involves a rapid equilibrium protonation will proceed faster in D2O than in H2O because of the higher concentration of the protonated reactant. On the other hand, if proton transfer is part of the rate-determining step, the reaction will be faster in H2O than in D2O because of the normal primary kinetic isotope effect of the type considered in Section 4.5. 

Mechanism III cannot be distinguished from the first two on the basis of kinetics alone, because the reactive species shown is in rapid equilibrium with the anion and therefore equivalent to it in terms of reaction kinetics. 

Enzyme reaction kinetics were modelled on the basis of rapid equilibrium assumption. Rapid equilibrium condition (also known as quasi-equilibrium) assumes that only the early components of the reaction are at equilibrium.8-10 In rapid equilibrium conditions, the enzyme (E), substrate (S) and enzyme-substrate (ES), the central complex equilibrate rapidly compared with the dissociation rate of ES into E and product (P ). The combined inhibition effects by 2-ethoxyethanol as a non-competitive inhibitor and (S)-ibuprofen ester as an uncompetitive inhibition resulted in an overall mechanism, shown in Figure 5.20. 

The rate law that we have derived is not the same as the experimental one. We have stressed that a reaction mechanism is plausible only if its predictions are in line with experimental results so should we discard our proposal Before doing so, it is always wise to explore whether under certain conditions the predictions do in fact agree with experimental data. In this case, if the rate of step 2 is very slow relative to the rapid equilibrium in step 1—so that N202] 2[N202][02],... 

In summary, therefore, solution and fiber biochemistry have provided some idea about how ATP is used by actomyosin to generate force. Currently, it seems most likely that phosphate release, and also an isomerization between two AM.ADP.Pj states, are closely linked to force generation in muscle. ATP binds rapidly to actomyosin (A.M.) and is subsequently rapidly hydrolyzed by myosin/actomyosin. There is also a rapid equilibrium between M. ADP.Pj and A.M.ADP.Pj (this can also be seen in fibers from mechanical measurements at low ionic strength). The rate limiting step in the ATPase cycle is therefore likely to be release of Pj from A.M.ADP.Pj, in fibers as well as in solution, and this supports the idea that phosphate release is associated with force generation in muscle. 

Only three steps of the proposed mechanism (Fig. 18.20) could not be carried out individually under stoichiometric conditions. At pH 7 and the potential-dependent part of the catalytic wave (>150 mV vs. NHE), the —30 mV/pH dependence of the turnover frequency was observed for both Ee/Cu and Cu-free (Fe-only) forms of catalysts 2, and therefore it requires two reversible electron transfer steps prior to the turnover-determining step (TDS) and one proton transfer step either prior to the TDS or as the TDS. Under these conditions, the resting state of the catalyst was determined to be ferric-aqua/Cu which was in a rapid equilibrium with the fully reduced ferrous-aqua/Cu form (the Fe - and potentials were measured to be within < 20 mV of each other, as they are in cytochrome c oxidase, resulting in a two-electron redox equilibrium). This first redox equilibrium is biased toward the catalytically inactive fully oxidized state at potentials >0.1 V, and therefore it controls the molar fraction of the catalytically active metalloporphyrin. The fully reduced ferrous-aqua/Cu form is also in a rapid equilibrium with the catalytically active 5-coordinate ferrous porphyrin. As a result of these two equilibria, at 150 mV (vs. NHE), only <0.1%... 

Figure 2.12 Reaction pathway for a bi-bi rapid equilibrium, random sequential ternary complex reaction mechanism.

For the enzyme isomerization mechanism illustrated in scheme C of Figure 6.3, there are two steps involved in formation of the final enzyme-inhibitor complex an initial encounter complex that forms under rapid equilibrium conditions and the slower subsequent isomerization of the enzyme leading to the high-affinity complex. The value of kohs for this mechanism is a saturable function of [/], conforming to the following equation ... 

The mechanism that has been established for this reaction involves the reaction of OH" with the complex to produce its conjugate base by removing a proton from a coordinated NH3 molecule in a rapid equilibrium. 

Restricting ourselves to the rapid equilibrium approximation (as opposed to the steady-state approximation) and adopting the notation of Cleland [158 160], the most common enzyme-kinetic mechanisms are shown in Fig. 8. In multisubstrate reactions, the number of participating reactants in either direction is designated by the prefixes Uni, Bi, or Ter. As an example, consider the Random Bi Bi Mechanism, depicted in Fig. 8a. Following the derivation in Ref. [161], we assume that the overall reaction is described by vrbb = k+ [EAB — k EPQ. Using the conservation of total enzyme... 

Along these fines, Liebermeister and Klipp [161] suggested the use of a rapid-equilibrium random-order binding scheme as a generic mechanism for all enzymes, independent of the actual reaction stoichiometry. While there will be deviations from the (unknown) actual kinetics, such a choice, still outperforms power-law or lin-log approximations [161]. 

The results of a temperature jump relaxation study of the complexation of metal cations by dibenzo-30-crown-10 [14] in methanol led Chock (1972) to propose a two-step mechanism. The first step (9) comprises a rapid equilibrium... 

Diphosphine-based ligands form the basis of current research in hydroformylation. As Figure 9 shows, free energy profiles have been recently proposed [22] to discuss the kinetics and the reaction mechanism. We first see the rapid equilibrium between ee and ea... 

The SB-GA mechanism consists of a rapid equilibrium deprotonation of the ZH intermediate, followed by rate-limiting, general acid-catalysed leaving-group departure from the anionic cr-complex Z via the concerted transition state, 2. The derived expression for this mechanism is equation 4, where fctBH is the rate coefficient for acid-catalyzed expulsion of L from Z and K3 is the equilibrium constant for the reaction ZH Z- + BH. 

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