Ordered bisubstrate mechanism

Nearly all NAD+-dependent dehydrogenases studied follow an ordered bisubstrate mechanism. In this mechanism, the oxidation of a substrate proceeds in a sequential manner first, NAD+ binds in the active site of the dehydrogenase then the substrate binds next a hydride equivalent is transferred in a chemical step from the bound substrate to the bound NAD+, hence, oxidising the substrate and reducing the NAD+ to NADH the oxidised substrate is then released from the active site and is finally followed by the NADH. 

For example, for the Ordered bisubstrate mechanism, the apparent Michaelis constants for A and B are... 

The intersecting pattern for an Ordered bisubstrate mechanism in Fig. 1 (left) will also be obtained with a Rapid Equilibrium bisubstrate mechanism in each case, an intersecting point may be above, below, or on the axis. 

The theory of kinetic isotope effect outlined in Section 17.3.3 is essential because it provides an insight into how a change in one step of kinetic mechanism is expressed in kinetic parameters that can be measured. Consider an ordered bisubstrate mechanism depicted in Fig. 3 ... 

It is important to note that commitment factors may depend on the level of other reactants present, and this variation can be used to determine the kinetic mechanism. For an ordered bisubstrate mechanism, the commitment of B (the second substrate to add) is independent of A (the first substrate to add), and depends only on how fast B is released from the enzyme relative to the forward rate constant for the bond-breaking step. Conversely, the commitment for A varies from infinity at saturating B to the value for B at near zero B, and thus the actual rate constant for release of A from the EA complex does not affect the commitment of B, even if it is quite small. 

In an ordered bisubstrate mechanism one must vary the second substrate, B, and determine V/JSTb, regardless of whether the label is in A or B, since ly AwiU not show an isotope effect. For a random mechanism one must vary both A and B, since one may see different isotope effects on VfK and V/Aa, a distinction that may help to characterize the mechanism. The effects onV/K and V/Aa shouldbe different when one or both substrates are sticky, that is, dissociate more slowly from the enzyme than they react to give products. The substrate with the lower V7A is the sticky one. Larger effects on Vthan on either V7A show that both substrates are sticky smaller ones show that a slow step follows release of the first product. A rapid equilibrium random mechanism will show equal isotope effects on V, V/Ab, and F/Aa, aU larger than unity. 

An experimental protocol in Fig. 8 is shown for an ordered bisubstrate mechanism. A small volume of enzyme is incubated with sufficient labeled substrate. A, to convert most or all of the enzyme into a binary complex, EA. This solution is then diluted into a large volume containing the unlabeled substrate. A, plus variable amounts of cosubstrate, B. After several seconds, add is added to stop the enzymatic reaction, and labeled product, Q, is determined analytically. A blank is then run with the labeled reactant already diluted in the large solution, plus only the enzyme present in the small volume. The experiment is then repeated at different levels of the second substrate B, and a reciprocal plot is made of the amount of labeled product, Q, as a function of the reciprocal of the substrate B concentration thus, by extrapolation, the maximum amount of labeled product formed, Q a. is obtained. 

Then, let us fit the scrambled data from Table 2, shown in column 5 as Input ifo > to a rate equation for two suspected mechanisms an ordered bisubstrate mechanism (18.50) and a Ping Pong bisubstrate mechanism ... 

Let us now examine the behavior of enzymes operating by way of ordered and random kinetic bisubstrate mechanisms ... 

This rate equation is identical to that for a rapid equilibrium ordered addition bisubstrate mechanism (/.c., a scheme where substrate A rapidly binds prior to the addition of the second substrate B). Huang has presented the theoretical basis for mechanisms giving rise to... 

More recently, the Auclair group has reported a more extensive investigation of bisubstrate analog inhibitors toward aminoglycoside 6 -A-acetyltransferase (AAC(6 )-Ii) from Enterococcus faecium. AAC(6 )-Ii is chromoso-mally encoded in E. faecium and has been shown to use an ordered kinetic mechanism with acetyl-CoA binding... 

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... 

Figure 1, Comparison of double reciprocal plots for the Ordered bisubstrate (left) and the Ping Pong bisubstrate mechanism (right), with A as a variable, and B as a fixed substrate. The crossover point on the left panel can be above, on or below the axis.

Some hyperbolic bisubstrate mechanisms can be easily distinguished by their primary double reciprocal plots in the absence of products, such as ordered from the Ping Pong mechanism. However, in many cases, the bisubstrate mechanisms cannot be distinguished in this way. Fortunately, in most cases, they can be clearly separated on the basis of their product inhibition patterns (Plowman, 1972) (Table 3). 

The Rapid Equilibrium Ordered Bi Bi system (Section 8.2) is a limiting case of the more realistic Steady-State Ordered Bi Bi system (Section 9.2). In bisubstrate mechanisms, the two approaches yield different velocity equations. As described... 

As already pointed out in Chapter 9, the steady-state expressions for the catalytic constant, Vu and for the specificity constant, Vi/Ksi for bisubstrate mechanisms are rather complex. For the ordered mechanism in reaction (17.18), as we have already pointed out in Section 9.2.2, even if we leave out the isomerizations, that is, the complexes EAB and EPQ, expressions for VJK and V, are rather complex. If we include the isomerization complexes, IiAB and EPQ, the rate equations for the catalytic constant, V, and for the specificity constant, VJKji, appear quite formidable compared to equations for the monosubstrate reaction (Eqs. (17.13) and (17.14)). Further, if we remember that the kinetic expression for isotope efects is the ratio of both entire rate equations describing the disappearance of hydrogen and deuterium substrates (or other isotopes), than the rate equations for isotope effects may appear awesome. 

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. 

In practice, uncompetitive and mixed inhibition are observed only for enzymes with two or more substrates—say, Sj and S2—and are very important in the experimental analysis of such enzymes. If an inhibitor binds to the site normally occupied by it may act as a competitive inhibitor in experiments in which [SJ is varied. If an inhibitor binds to the site normally occupied by S2, it may act as a mixed or uncompetitive inhibitor of Si. The actual inhibition patterns observed depend on whether the and S2-binding events are ordered or random, and thus the order in which substrates bind and products leave the active site can be determined. Use of one of the reaction products as an inhibitor is often particularly informative. If only one of two reaction products is present, no reverse reaction can take place. However, a product generally binds to some part of the active site, thus serving as an inhibitor. Enzymologists can use elaborate kinetic studies involving different combinations and amounts of products and inhibitors to develop a detailed picture of the mechanism of a bisubstrate reaction. 

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. 

Figure. 6.8. Sequential ordered mechanism for bisubstrate reactions.

Previously, while discussing the general theory of complex reactions, we have considered some other mechanisms with linear steps, such as one given by eq. (4.107) corresponding to three-step sequence or eq. (4.116). In a similar way kinetic expressions could be derived for more complicated reaction networks, as presented for instance in Chapter 5 (see equations 5.76 for 4 step sequence, eq. 5.84 for 6 steps eq. 5.88 and 5.89 for a mechanism with 8 linear steps and the general form for n-step mechanism eq. 5.94). Ordered sequential bisubstrate reactions can be expressed by eq. 5.76 for the 4 step sequence (Figure 6.11)... 

TABLE 11.5 Cleland nomenclature for bisubstrate reactions exemplified. Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi hi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1A versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (KiaKb) in the denominator. These three kinetic mechanisms can be further differentiated by their product inhibition patterns (Cleland, 1963b)... 

Let us consider a more complicated mechanism, an Ordered Bi Bi mechanism which is very common with bisubstrate enzymes. In this mechanism, an enzyme reacts with two substrates in an ordered fashion affording two products, which are also released in an ordered fashion. 

This example clearly shows that completely randomized steady-state bisubstrate reactions wiU produce extremely complex rate equations which are, in most cases, unmanageable and almost useless for practical purposes. Thus, for example, the rate equation for an Ordered Bi Bi mechanism has 12 terms in the denominator (compare Eq. (9.8)). A completely Random Bi Bi mechanism yields an even more comphcated rate equation with 37 new terms in the denominator. Eor this reason, and in such cases, we shah usuahy revert to simplifying assumptions, usually introducing the rapid equilibrium segments in the mechanism in order to reduce the rate equations to manageable forms. 

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