Monosubstrate enzyme reactions

In this section, we shall examine the kinetics of monosubstrate enzymes that are capable of binding two different inhibitors. Although the monosubstrate enzyme reactions are not very realistic because they are relatively rare in nature, we shah, for the sake of simplicity, open this section with monosubstrate reactions. 

Inhibition of monosubstrate enzyme reactions with an inhibitor may be expressed in a more general way ... 

The steady-state kinetics of monosubstrate enzyme reactions has been described in Chapter 3. However, tme monosubstrate reactions are quite rare in nature and are restricted only to some isomerases and epimerases. The majority of enzyme reactions are multisubstrate reactions, with two or three substrates and one, two, or three products of reaction (lUBMB, 1992). 

Monosubstrate enzyme reactions are rare in nature and, therefore, a substrate inhibition in monosubstrate reactions must be considered an extremely rare occurrence in the nature, although a Uni Bi mechanism does occur. 

Let us start the derivation of rate equations for kinetic isotope effects with analysis of a simple monosubstrate enzyme reaction ... 

London and Steck (1969) have developed a general model, based on rapid equilibrium assumptions, for a monosubstrate enzyme that combines with substrate, activator, and a substrate-activator complex. The kinetic model for this type of activation is rather complex (Reaction (7.7)). 

Consider again a monosubstrate enzyme-catalyzed reaction with two central complexes in more detail. Such a reaction will proceed via three transition states if it proceeds from A to P, or similarly in the reverse direction ... 

Bisubstrate enzyme reactions are among the most common in nature, and we must leave the monosubstrate and turn to bisubstrate reactions if we are to understand real enzymes (Northrop, 1975,1981,1982,1995 Cleland etal, 1977 Blanchard Wong, 1991). 

It has been demonstrated that lin-log equations capture hyperbolic kinetics slightly better than either a linear approximation or the power-law approach [318, 320 322]. One reason for the improved performance is that for lin-log kinetics the elasticities (and kinetic orders) are not constant, but change with changing metabolite concentrations. For a monosubstrate reaction v(Sj, and omitting the dependence on the enzyme concentration, we obtain... 

Phosphofructokinase possesses two substrates, ATP and F6P, which it transforms into ADP and FBP. A complete model for this reaction should therefore take into account the evolution of these four metabolites. However, studies carried out in yeast indicate that the couple ATP-ADP plays a more important role than the couple F6P-FBP in the control of oscillations. Indeed, the addition of ADP ehcits an immediate phase shift of the oscillations (fig. 2.8) while the effect of FBP is much weaker (Hess Boiteux, 1968b Pye, 1969). The predominant regulation is thus exerted by ADP. In order to keep the model as simple as possible and to limit the number of variables to only two, which allows us to resort to the powerful tools of phase plane analysis, the situation in which an allosteric enzyme is activated by its unique reaction product is considered (fig. 2.10). This monosubstrate, product-activated. 

The binding of substrate to an enzyme is a necessary feature of all enzymatic reactions. However, most enzymes other than hydrolytic ones catalyze bisubstrate reactions, with two substrates and one or more products of reaction. Tme monosubstrate reactions are rare and trisubstrate reactions are less numerous than the bisubstrate reactions (lUBMB, 1992). One substrate is always a molecule of a metabolite, while the other reactant may be another metabolite, a molecule of water, a metal ion, etc. in many cases, however, the other reactant is a coenzyme (Zubay, 1988 Walsh, 1998). In addition to substrates, an enzyme may bind specifically the molecules of inhibitors, activators, allosteric activators or inhibitors, etc., at or near the active site, as well as at regions distant from the same. 

In this model, we must recognize that the total enzyme Eo is divided between three forms free enzyme E, enzyme-substrate complex EA, and the enzyme-inhibitor complex El. Keeping this in mind, a velocity equation in the presence of a competitive inhibitor can be easily derived from either rapid equilibrium or steady-state assumptions by an algebraic procedure described for monosubstrate reactions (Sections 3.1 and 3.2) ... 

In monosubstrate and bisubstrate reactions with a mixture of two inhibitors, the two inhibitors may bind nonexclusively to the enzyme or may be mutually... 

Consider the first case, a parabolic competitive inhibition. This case occurs in a monosubstrate reaction in which an enzyme can bind two molecules of the same competitive inhibitor, in a random manner at different sites (Yonetani, 1982). The binding of I at either site is sufficient to exclude the substrate. 

Let us consider the influence of pH on a monosubstrate reaction of the Michaelis-Menten type, a case when both forms of enzyme are protonated (Mahler Cordes, 19. ... 

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