Multi-substrate kinetics

It is emphasized that in the case of kinetic resolution, the MS measurements must be performed in the appropriate time window (near 50% conversion). If this is difficult to achieve due to different amounts or activities of the mutants being screened in the wells of microtiter plates, the system needs to be adapted in terms of time resolution. This means that samples for MS evaluation need to be taken as a function of time. Finally, it is useful to delineate the possibility of multi-substrate ee screening using the MS-based assay, which allows for enzyme fingerprinting with respect to the enantioselectivity of several substrates simultaneously. 

While the majority of these concepts are introduced and illustrated based on single-substrate single-product Michaelis-Menten-like reaction mechanisms, the final section details examples of mechanisms for multi-substrate multi-product reactions. Such mechanisms are the backbone for the simulation and analysis of biochemical systems, from small-scale systems of Chapter 5 to the large-scale simulations considered in Chapter 6. Hence we are about to embark on an entire chapter devoted to the theory of enzyme kinetics. Yet before delving into the subject, it is worthwhile to point out that the entire theory of enzymes is based on the simplification that proteins acting as enzymes may be effectively represented as existing in a finite number of discrete states (substrate-bound states and/or distinct conformational states). These states are assumed to inter-convert based on the law of mass action. The set of states for an enzyme and associated biochemical reaction is known as an enzyme mechanism. In this chapter we will explore how the kinetics of a given enzyme mechanism depend on the concentrations of reactants and enzyme states and the values of the mass action rate constants associated with the mechanism. 

Seker, S., Beyenal, H., Salih, B., Tanyolac, A. (1997). Multi-substrate growth kinetics of Pseudomonas putida for phenol removal. Applied Microbiology and Biotechnology 47 610-614. 

This analysis can be applied to enzymatic as well as to simple chemical transformations [9-11], for uni- and multi-substrate [12] reactions according to Eqs. (1) and (2). nNKM denotes the product of Michealis-Menten constants for all substrates. In this analysis one assumes that kinetics follow the Michaelis-Menten model, which is the case for most antibody-catalyzed processes discussed below. The kcat denotes the rate constant for reaction of the antibody-substrate complex, Km its dissociation constant, and kuncat the rate constant for reaction in the medium without catalytic antibody or when the antibody is quantitatively inhibited by addition of its hapten. In several examples given below there is virtually no uncatalyzed reaction. This of course represents the best case. 

The National Science Foundation is sponsoring a study led by Dr. Richard Bartha of Rutgers University on the multisubstrate biodegradation kinetics of PAHs from creosote, coal tar, and diesel fuel. The relative biodegradabilities and substrate interactions of PAHs in sole and multi-substrate systems will be determined and related to dissolution kinetics processes governing bioavailability. An integrated mathematical model of the behavior of PAHs in NAPL-contaminated soils will be developed and validated. 

In the almost 20 years since this volume s predecessor appeared enzyme kinetics has come of age. Extended theory and the availability of much more sensitive measuring equipment have made possible incisive kinetic analysis of multi-substrate enzymes. One must also add, however, that the full potential of the method has been achieved in rather few cases. Much of the published information has been collected by investigators primarily interested in function rather than mechanism, and is therefore of descriptive value only. Even when a more thorough-going analysis is attempted, it is often difficult and tedious to obtain enough data to remove all ambiguity. Hence doubt and controversy regarding the mechanisms of many important enzymes remain. In the space available here it is not possible to go into much detail about individual cases. The intention, therefore, is to sketch out current approaches and problems. 

The previous sections may give the impression that it is an easy matter to establish the mechanism of a multi-substrate enzyme. In fact, more often than not uncertainty and controversy surround such mechanisms for many years despite an abundance of experimental work. We have assumed an ideal situation whereas there are a number of possible obstacles in practice. For example the reaction may be effectively irreversible so that it is only possible to measure the kinetic parameters for one direction of reaction the substrate specificity may be so stringent that it is impossible to apply tests which rely on using a range of alternative substrates the available methods of rate measurement may not be sufficiently sensitive to allow all the kinetic parameters to be determined rehably. The last problem at least is one that allows some hope the kinetic study of NAD-dependent dehydrogenases became much more incisive once fluorescence measurement took over from absorbance measurement as the method of choice [52,57]. Nevertheless there is clearly a need for as many criteria of mechanism as may be mustered and the study of inhibition patterns is a valuable adjunct to the methods already discussed. 

This textbook for advanced courses in enzyme chemistry and enzyme kinetics covers the field of steady-state enz5mie kinetics from the basic principles inherent in the Michaelis-Menten equation to the expressions that describe the multi-substrate enzyme reactions. The purpose of this book is to provide a simple but comprehensive framework for the study of enzymes with the aid of kinetic studies of enzyme-catalyzed reactions. The aim of enzyme kinetics is twofold to study the kinetic mechanism of enz5mie reactions, and to study the chemical mechanism of action of enzymes. 

Multi-substrate enzymes (see) catalyse reactions of two or more substrates. Such enzymes can form a number of different complexes (known as enzyme species) with one or both substrates and/or products. The order in which these species are formed may be random or ordered. Cleland s short notation (see) is a convenient way of representing the possibilities. The kinetics of such reactions become extremely complicated enzyme networks (see Enzyme graphs) provide a means of sununarizing them. To evaluate the kinetic data for such systems, one must resort to a computer. Furthermore, the information gained from steady-state experiments may not be sufficient. A number of methods of very rapid measiu ement have been used to investigate the pre-steady-state condition of reactions, including stopped flow, temperature jump and flash methods. 

A further requirement for the development of a multi-enzyme oxidizing process would be the determination of the kinetic parameters of the enzymes and hence development of a model of the intended reaction system in terms of the relative productivities of the enzymes with respect to substrate conversion rates as well as electron transfer stoichiometry. 

At the start of optimization of the reaction system, suitable values for pH and temperature have to be chosen as a function of the properties of the reactants and enzymes. Fortunately, most enzyme reactions operate in a narrow band with respect to pH value (7-10) and temperature (30-50 °C). The initial substrate concentration and, in the case of two-substrate reactions, the stoichiometric ratio of the two reactants, have to be selected. The selected enzyme concentration influences both the achievable space-time-yield as well as the selectivity in the case of undesired parallel or consecutive side reactions. In the case of multi-enzyme systems, the optimal activity ratio has to be found. The activity and stability of all the enzymes involved have to be known as a function of the reaction conditions, before the kinetic measurements are made. Enzyme stability is an important aspect of biocatalytic processes and should be expressed preferably as an enzyme unit consumption number, with the dimension unit of activity per mass of product (such as mole, lb, or kg). In multi-enzyme systems the stability of all the enzymes has to be optimized so that an optimal reaction rate and space-time-yield result. 

Detailed kinetics of ATP hydrolysis in single-site (uni-site) and steady-state (multi-site) conditions by beef heart Fi were studied extensively (Fig. 11.5).45 46) At an ATP/ Fi ratio of less than 1, ATP binds to a catalytic site and is hydrolyzed slowly (uni-site catalysis). The equilibrium constant between bound substrate (ATP) and products (ADP and Pi) bound at the catalytic site of Fi was close to 1, indicating that the equilibrium can occur without change in free energy. In the presence of excess ATP (multi-site catalysis), ATP binds to all three catalytic sites, and the ATP at the first site is hydrolyzed at a rate that is at least 106 times higher than is the case in uni-site catalysis. 

In addition to the reaction sequence shown, the substrate may have to mutarotate non-enzymically to the form favored for affording the first enzyme-substrate complex. In such multi-stage reactions, the observed isotope-effects for the overall reaction are usually low. The situation is further complicated by possible differences in Km between a deuterated substrate and the unlabeled substrate, so that, unless a full kinetic analysis of the reaction is performed, the values determined for the apparent isotope-effect may vary. 

The regulation of enzymes by metabolites leads to the concept of allostenc regulation. Allosteric means other structure. Allosteric modulators can bind at a site other than the active site in question and cause activation or inhibition. These modulators can include the substrate itself, which binds at another active site in a multi-subunit enzyme. In fact, allosterically modulated enzymes almost always have a complex quaternary structure (multiple subunits) and exhibit non-Michaelis-Menten kinetics. 

---