Random ternary-complex mechanism

A critical feature of the random ternary complex mechanism is that for either substrate the dissociation constant from the binary enzyme complex may be different from that of the ternary enzyme complex. For example, the Ks value for AX dissociation from the E AX complex will have a value of K v<. The affinity of AX for the enzyme may, however, be modulated by the presence of the other substrate B, so that the dissociation constant for AX from the ternary E.AX.B complex may now be c/Xax, where a is a constant that defines the degree of positive or negative regulation of the affinity of AX for the enzyme by the other substrate. The overall steady state velocity equation for this type of mechanism is given by Equation (2.15) ... 

Fig. 6. A set of possible relations between volume changes in a two-substrate reaction with a random ternary-complex mechanism. Note that these volume changes as defined by Eq. (77) are dissociation volumes.

These qualitative conclusions can be justified in terms of rate equations derived for each exchange catalyzed by ordered and random ternary complex mechanisms . ... 

One mechanism which may apply to a two-substfate reaction is the so-called random ternary-complex mechanism. In this mechanism the enzyme E can form binary complexes EA and EB with the two substrates A and B. It can also form the ternary complex EAB, with no restriction on the order in which A and B are attached. In Figure 10.4 this mechanism is represented in two different ways. The lower one is a shorthand notation introduced by the American biophysical chemist... 

The random ternary-complex mechanism two alternative representations. 

This equation shows that the rate will be reduced with pressure, but according to Eq. (80) this reduction will be absorbed into kt, which is really constant. The rate constants kt and k-t have been removed in the initial approximation, and nothing can be said about the pressure dependences of the steps 1 and —1. The interpretation will be that the rate-determining step 2 becomes slower with pressure, while in fact the rate determination has been displaced to step 1. It is immediately clear that such an interpretation would be disastrous for the clarification of the high-pressure mechanism. The condition for a relatively simple rate equation of the random ternary-complex two-substrate mechanism was a small ka. This constant k3 may not be as small at high pressures, and the whole rate equation breaks down. 

Random Bi Bi Ternary Complex Mechanism The random or noncompulsory ordered mechanism is noticeably symmetrical, with two different paths for producing the EAB complex from free enzyme E and its substrates A and B, as well as two different pathways for producing the EPQ complex from free enzyme E and its products P and Q ... 

MULTISUBSTRATE MECHANISM Random Bi Bi ternary complex mechanism, ISOTOPE EXCHANGE AT EQUILIBRIUM RANDOM Bl UNI MECHANISM RANDOM Bl UNI UNI Bl PING PONG MECHANISM... 

The mechanism of enzyme catalysis drawn, using (a)random ternary complex theory, (b)ordered ternary complex mechanism and (c) ping-pong bi-bi mechanism ... 

In the case of enzymes working via a ternary complex mechanism, we have two extreme cases. The easiest to comprehend is the rapid equilibrium random mechanism (Scheme 5.4) this is the mechanism where the chemistry is most likely to be rate determining and kinetic isotope effects or structure-reactivity correlations are likely to be mechanistically informative. Enzymes acting on their physiological substrates at optimal pH are likely to show a degree of preference for one or the other substrate binding first, but they can often be induced to revert to a rapid equilibrium random mechanism by the use of non-optimal substrates or pH. 

This nomenclature has been introduced by Cleland (1963), but other descriptions of bisubstrate mechanisms are also found in the biochemical literature. For example, a sequential addition in bisubstrate reactions, an Ordered Bi Bi mechanism is also called a compulsory-order ternary-complex mechanism whereas a Random Bi Bi mechanism is called a random-order ternary-complex... 

The products of the ER reaction, butyryl-CoA and NAD, were utihzed as inhibitors in an attempt to determine whether the reaction proceeds via a random or compulsory order ternary-complex mechanism using the rules of Cleland[5]. Assays were carried out in triplicate. The data was analyzed by linear regression and statistical t-tests were employed to determine if lines intersected at the same or significantly different point on the vertical axis. 

When crotonyl-Co was varied in the presence of butyryl-CoA the lines appeared to intersect to the left of the vertical axis. However, statistical analysis of the y-axis intercepts showed that they in fact intercept the vertical axis at points which are not significantly different from each other. That is, they intercept at a common point and therefore show a competitive pattern of inhibition. This combination of inhibition patterns is indicative of a random order ternary complex mechanism. 

The reaction proceeds via a ternary complex mechanism (CAT Ac-CoA Cm CAT CoA Ac-Cm) with a random order of addition of substrates (18). The progression from the binary complex to the ternary complex involves subtle changes in the structure of the enzyme and/or the conformations of bound substrates and accompanies a threefold decrease in affinity the fCj of Cm and Ac-CoA in respective binary complexes are 4 and 30 fxM, whereas the corresponding values of the ternary complex are 12 and 90 (iM, respectively (20). The RDS is thought to involve both product release and ternary complex interconversion. No evidence exists for the formation of an acetyl-enzyme intermediate. 

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

This mechanism can be considered as a special case of the foregoing random mechanism, where the complex EB cannot be formed. If the ternary complex is very short-lived, i.e., k3 k-t, we can interpret the kinetic constants as W = fc3[E]o, KA = ks/kt, KB = kjh, and KA = k-i/k2. Accordingly, the volume changes will be... 

ATP + (d)CMP = ADP + (d)CDP (<4> formation of a ternary complex, addition of substrates is random [5] <1> reaction proceeds by a sequential mechanism, a ternary complex of the enzyme with both substrates is formed as the central intermediate in the reaction [12] <3> reaction mechanism is sequential and nonequilibrium in nature, substrates bind to the enzyme in a random order, substrate binding is cooperative [14] <7> the mechanism is analogous to the phosphoryl transfer mechanism in cAMP-dependent protein kinase that phosphorylates the hydroxyl groups of serine residues [16] <8> random bi-bi mechanism [17])... 

FIGURE 6-13 Common mechanisms for enzyme-catalyzed bisubstrate reactions, (a) The enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must bind before substrate 2 can bind productively. In random binding, the substrates can bind in either order. 

Enzymes often require multiple substrates to complete their catalytic cycle. This may involve combining two compounds into one molecule or transferring atoms or electrons from one substrate to another. The substrates may both bind to an enzyme and react collectively, or each substrate might bind, react, and release sequentially. With two substrates, if both bind to the enzyme, a ternary complex (ES S2) will form (Scheme 4.8). The order of substrate addition may be important (ordered) or not (random order). Cases in which the two substrates react sequentially follow a double-displacement, or ping-pong, mechanism (Scheme 4.9). Enzymes requiring more than two substrates have more complicated complexation pathways. 

Figure 7.1. Diagram for random bi bi kinetic mechanism. The random addition of substrates, A and B to form binary (EA and EB) and ternary (EAB) complexes. The two ternary complexes EAB and EPQ interconvert with the rate constant of k and k. The release of products P and Q also proceeds in a random manner. Ks are dissociation constants where KaKab = KbKba and KpKpq = KqKqp.

If a ternary complex is formed, the mechanism may be considered ordered or random. The ordered mechanism requires that the first substrate (Si) must bind to the enzyme before the second substrate (S2) will bind, and is represented by Eq. 2.26 ... 

Sequential Reactions. In sequential reactions, all substrates must bind to the enzyme before any product is released. Consequently, in a bisubstrate reaction, a ternary complex of the enzyme and both substrates forms. Sequential mechanisms are of two types ordered, in which the substrates bind the enzyme in a defined sequence, and random. 

Steady-state kinetics have been used to determine the kinetic mechanisms of many of these enzymes. The questions that have been primarily addressed are the sequence of steps that occur in substrate binding prior and subsequent to the catalytic reaction and the potential formation of covalent enzyme intermediates. Classical interpretation of kinetic analyses has been the determination of the relevant reactions occurring via a random or an ordered sequential reaction, or if the reaction is a double-displacement or Ping-Pong reaction. In the former case, phosphoryl transfer occurs in the ternary complex that contains enzyme, phosphoryl donor, and phosphoryl acceptor. In the latter case, enzyme reacts with... 

The donor and acceptor can be bound in compulsory order or random order, the main point being that both must be bound at adjacent sites before group transfer can occur. This mechanism is kinetically indistinguishable from one in which an additional covalent phosphoryl-enzyme or nucleotidyl-enzyme exists and connects the two ternary complexes, as in Eq. (3). In this mechanism the enzyme mediates group transfer by nucleophilic catalysis, utilizing an enzymic nucleophile as the catalytic functional group. 

The catalytic pathway is best described as a random binding kinetic mechanism involving the formation of the ternary complex E-acetyl-P-ADP, with direct phosphoryl group transfer between enzyme-bound substrates to form the product ternary complex E-acetate-ATP. The formation and decomposition of these ternary complexes involve only noncovalent binding interactions of the enzyme with the substrates and products. The stereochemistry is inconsistent with a mechanism in which the phosphoryl group is transferred to an enzymic nucleophile as a step in the interconversion of the ternary complexes. The case of acetate kinase is one in which the stereochemical course of phosphoryl group transfer essentially discredited a double-displacement mechanism that had been reasonably well supported by other evidence. 

A recent detailed study of the kinetic mechanism of the E. coli enzyme using steady-state kinetics and ITC shows that the enzyme has a random bi-bi mechanism in which a ternary complex of enzyme, ATP, and phosphopantetheine are formed. The following apparent kinetic parameters for the forward reaction were determined 220 10 pmoll and cat 1.59 0.01 s (for ATP), and 4.7 0.5 pmolP and ifcat... 

The initial rate equation derived by steady-state analysis is of the second degree in A and B (SO). It simplifies to the form of Eq. (1) if the rates of dissociation of substrates and products from the complexes are assumed to be fast compared with the rates of interconversion of the ternary complexes k, k )] thus, the steady-state concentrations of the complexes approximate to their equilibrium concentrations, as was first shown by Haldane (14)- The kinetic coefficients for this rapid equilibrium random mechanism (Table I), together with the thermodynamic relations KeaKeab — KebKeba and KepKepq — KeqKeqp, suffice for the calculation of k, k and all the dissociation constants Kea = k-i/ki, Keab = k-i/ki, etc. 

The steady-state rate equation for the random mechanism will also simplify to the form of Eq. (1) if the relative values of the velocity constants are such that net reaction is largely confined to one of the alternative pathways from reactants to products, of course. It is important, however, that dissociation of the coenzymes from the reactant ternary complexes need not be excluded. Thus, considering the reaction from left to right in Eq. (13), if k-2 k-i, then product dissociation will be effectively confined to the upper pathway this condition can be demonstrated by isotope exchange experiments (Section II,C). Further, if kakiB kik-3 -f- kikiA, then the rate of net reaction through EB will be small compared with that through EA 39). The rate equation is then the same as that for the simple ordered mechanism, except that a is now a function of the dissociation constant for A from the ternary complex, k-i/ki, as well as fci (Table I). Thus, Eqs. (5), (6), and (7) do not hold instead, l/4> < fci and ab/ a b < fc-i, and this mechanism can account for anomalous maximum rate relations. In contrast to the ordered mechanism with isomeric complexes, however, the same values for these two functions of kinetic coefficients would not be expected if an alterna-... 

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