Complicated enzyme reactions

In the remaining part of our presentation of the formal kinetics of enzyme isotope effects a few more complicated examples will be discussed. The methods developed here should be also useful for unraveling other complicated enzyme reactions, and in reading and understanding the modern literature on isotope effects on enzymatic processes. 

The reactants in enzyme reactions are known as substrates. Enzyme reactions may involve uni-, bi-, or trimolecule reactants and products. An analysis of the reaction kinetics of such complicated enzyme reactions, however, is beyond the scope of this chapter, and the reader is referred elsewhere [1] or to other reference books. Here, we shall treat only the simplest enzyme-catalyzed reaction - that is, an irreversible, unimolecular reaction. 

Determining balanced conditions for a single substrate enzyme reaction is usually straightforward one simply performs a substrate titration of reaction velocity, as described in Chapter 2, and sets the substrate concentration at the thus determined Ku value. For bisubstrate and more complex reaction mechanism, however, the determination of balanced conditions can be more complicated. 

For heterogeneous catalytic reactions, the first step is the adsorption of reactants on the surface of a catalyst and the second step is the chemical reaction between the reactants to produce products. Since the first step involves only weak physical or chemical interaction, its speed is much quicker than that of the second step, which requires complicated chemical interaction. This phenomena is fairly analogous to enzyme reactions. 

It should be noted that this solution procedure requires the knowledge of elementary rate constants, klt k2, and k3. The elementary rate constants can be measured by the experimental techniques such as pre-steady-state kinetics and relaxation methods (Bailey and Ollis, pp. 111 -113, 1986), which are much more complicated compared to the methods to determine KM and rmax. Furthermore, the initial molar concentration of an enzyme should be known, which is also difficult to measure as explained earlier. However, a numerical solution with the elementary rate constants can provide a more precise picture of what is occurring during the enzyme reaction, as illustrated in the following example problem. 

Over the last 20 years, many reservations with respect to biocatalysis have been voiced, contending that (i) enzymes only feature limited substrate specificity (ii) there is only limited availability of enzymes (iii) only a limited number of enzymes exist (iv) protein catalyst stability is limited (v) enzyme reactions are saddled with limited space-time yield and (vi) enzymes require complicated cosubstrates such as cofactors. 

The concepts involved in this approach are simple, but the equations become rather complicated. Biochemical reactions are written in terms of reactants like ATP that are made up of sums of species, and they are referred to as biochemical reactions to differentiate them from the underlying chemical reactions that are written in terms of species. The thermodynamics of biochemical reactions is independent of the properties of the enzymes that catalyze them. However, the fact that enzymes may couple reactions that might otherwise occur separately increases the number of constraints that have to be considered in thermodynamics. 

The most common enzymatic reactions are those with two or more substrates and as many products. But many of the simpler single-substrate schemes are valuable for the development of kinetic ideas concerning effects of pH, temperature, etc., on enzyme reaction rates. Although the mechanisms of multisubstrate reactions are complicated, their kinetics can often be described by an equation of the form ... 

Kinetic behavior becomes complicated when there are two chemical species that can both complex with the enzyme molecules. One of the species might behave as an inhibitor of the enzyme reaction with... 

The industrial scale-up of enzymatic technology is both highly complicated and expensive. Moreover, a primary regulatory hurdle will involve demonstrating that the end products of the cholesterol-enzyme reaction and the novel compounds formed through genetic engineering are harmless. 

Besides steady state measurements, there is probably good reason to use flow micro calorimetry for the study of non-steady-state behavior in systems with immobilized bio catalysts. Here, the mathematical description is more complicated, requiring the solution of partial differential equations. Moreover, the heat response can evolve non-specific heats, like heat of adsorption/desorption or mixing phenomena. In spite of these complications, the possibility of the on-line monitoring of the enzyme reaction rate can provide a powerful tool for studying the dynamics of immobilized biocatalyst systems. 

Unfortunately, most enzymes do not obey simple Michaelis-Menten kinetics. Substrate and product inhibition, presence of more than one substrate and product, or coupled enzyme reactions in multi-enzyme systems require much more complicated rate equations. Gaseous or solid substrates or enzymes bound in immobilized cells need additional transport barriers to be taken into consideration. Instead of porous spherical particles, other geometries of catalyst particles can be apphed in stirred tanks, plug-flow reactors and others which need some modified treatment of diffusional restrictions and reaction technology. 

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