Steady-State Ordered bisubstrate mechanism

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... 

Bisubstrate reactions (Chapters 8 and 9). In bisubstrate reactions, a frequent case is a need to distinguish between the Steady-State Ordered, Ping Pong, and Equihbrium Ordered mechanism the rate equations involved are... 

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)... 

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. 

In some steady-state mechanisms, such as an Ordered Bi Bi mechanism, all or some of the rate constants can be calculated directly from the kinetic constants. Quantities like and /Cm wiU not necessarily show the normal temperature behavior, since they are usually combinations of several rate constants, but if certain rate constants predominate, normal temperature behavior maybe obeyed. This is often the case with bimolecular rate constants /Ccat/ A and fccat/AB in bisubstrate reactions. 

Distribution equations for bisubstrate reactions in the steady state are often very complex expressions (Chapter 9). However, in the chemical equilibrium, the distribution equations for all enzyme forms are usually less complex. Consider an Ordered Bi Bi mechanism in reaction (16.12) with a single central complex ... 

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. 

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