Theory of enzyme kinetics

The general theory of enzyme kinetics is based on the work of L. Michaelis and M. L. Menten, later extended by G. E. Briggs and J. B. S. Haldane.la The basic reactions (E = enzyme, S = substrate, P = product) are shown in equation 2.1 ... 

If enzymes are described under tbe aspect of reaction mechanisms, the maximal rate of turnover Vmax. the Michaelis and Menten constant Km, the half maximal inhibitory concentration ICso, and tbe specific enzyme activity are keys of characterization of the biocatalyst. Even though enzymes are not catalysts in a strong chemical sense, because they often undergo an alteration of structure or chemical composition during a reaction cycle, theory of enzyme kinetics follows the theory of chemical catalysis. 

Coulson, R.A. (1993). The flow theory of enzyme kinetics role of solid geometry in the control of reaction velocity in live animals. Inti. J. Biochem. 25 1445-1474. 

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. 

The earliest quantitative theory of enzyme kinetics dates back to 1913, when Michaelis and Menten [27] succeeded in explaining a key feature of enzyme reactions with a very simple model. As an introduction and to establish the relationship between trace-level and bulk-species catalysis, this classical work and its subsequent refinements will now be reviewed. 

A study of enzyme kinetics is extremely important, as it often gives information about the mechanism of action of the enzyme concerned. We shall therefore outline some of the theories of enzyme kinetics that have been applied to starch-metabolizing enzymes. 

Lenore Michaelis and Maud L. Menten proposed a general theory of enzyme action in 1913 consistent with observed enzyme kinetics. Their theory was based on the assumption that the enzyme, E, and its substrate, S, associate reversibly to form an enzyme-substrate complex, ES ... 

For the time being, our basic understanding of pressure effects is far from complete. However, some new developments concerning theory and application have occurred over the years. A short theoretical treatment of pressure effects was presented almost 30 years ago (Laidler, 1951). In this article we will present an extensive treatment of the present theoretical basis for pressure effects, incorporating contemporary knowledge of enzyme kinetics, physical biochemistry, and high-pressure theory. The theoretical level in this field is still not very sophisticated, but it is important enough so that theoretical considerations should be applied when future experiments are planned. 

In applying this theory to enzyme kinetics, one should be careful with explanations of the activation quantities found. Generally, these will be averaged quantities which in most cases have lost their character as single-step quantities. These aspects will be treated more fully in later sections. 

The ES complex is the key to understanding this kinetic behavior, just as it was a starting point for our discussion of catalysis. The kinetic pattern in Figure 6-11 led Victor Henri, following the lead of Wurtz, to propose in 1903 that the combination of an enzyme with its substrate molecule to form an ES complex is a necessary step in enzymatic catalysis. This idea was expanded into a general theory of enzyme action, particularly by Leonor Michaelis and Maud Menten in 1913. They postulated that the enzyme first combines reversibly with... 

Michaelis and Menten developed a kinetic theory of enzyme action. 

TWO FORMALISMS. FORMALISM OF ENZYME KINETICS AND OF STEADY-STATE-REACTION THEORY... 

Bottom-up systems biology does not rely that heavily on Omics. It predates top-down systems biology and it developed out of the endeavors associated with the construction of the first mathematical models of metabolism in the 1960s [10, 11], the development of enzyme kinetics [12-15], metabolic control analysis [16, 17], biochemical systems theory [18], nonequilibrium thermodynamics [6, 19, 20], and the pioneering work on emergent aspects of networks by researchers such as Jacob, Monod, and Koshland [21-23]. 

In 1913, Michaelis and Men ten presented a general theory for enzyme kinetics, extended later by Briggs and Haldane, which accounts for the velocity curve shown in Figure 5.5. This theory for reactions catalyzed by enzymes having a single substrate assumes that the substrate S binds to the active site of the enzyme E to form the enzyme-substrate complex ES, which yields the product P and the free enzyme E ... 

O. Tapia, Beyond standard quantum chemical semi-classic approaches Towards a quantum theory of enzyme catalysis, in P. Paneth, A. Dybala-Defratyka (Eds.), Kinetics and Dynamics, From nano- to bio-scale, Challenges and advances in computational chemistry and physics 12, Springer Science, Dordrecht, 2010, p. 267-298. 

Kinetics involving rapid pre-equilibrium steps finds numerous applications both within and beyond the study of enzyme kinetics. Other important examples are the theory of proton-deuterium exchange kinetics of a protein [169] and gene activation involving DNA looping [186], Because of its central importance in biological kinetics, let us provide a more complete mathematical treatment of the problem in a short digression. 

Sellers, P. H., Combinatorial aspects of enzyme kinetics. In Applications of Combinatorics and Graph Theory in the Biological and Social Sciences (F. Roberts, ed.). Springer-Verlag, Berlin, 1989. 

In this section the basic kinetic model for enzyme-catalyzed bioconversions is presented. Understanding this model is the foundation for deriving more complex models. In their theory of enzyme catalysis, Michaelis and Menten 113 postulated the existence of an enzyme substrate complex (ES), which is built up in a reversible... 

Bardsley [28] and Childs and Bardsley [29] have provided a substantial body of mathematical theory to facilitate the categorisation of detailed curve shapes in cases where the data do not fit the linear transformations of Eqn. 4. This approach may be seen as essentially inductive. It is an attempt to set up rigorous procedures for empirical mathematical description of enzymes kinetic behaviour. Such description should in theory define minimum levels of complexity for physical models. Application of this approach will severely test the precision of rate measurements in real cases, and there is a risk that vaUd mechanisms may be ruled out on the basis of apparent subtleties of curve shape that are no more than experimental error. This, however, is certainly no excuse for ignoring genuine non-linearity. 

Several theories of sigmoid kinetics are based on the idea that certain enzyme molecules are composed of a number of subunits which interact with each other. 

The most widely accepted theory of enzyme action is based on the formation of an intermediate compound or adsorption complex between enzyme and substrate (Brown, 1902 Henri, 1903). Since both conceptions of the nature of the enzyme-substrate complex can lead to the same kinetic equations, the distinction seems unimportant at present. In the following development of the kinetic equations, the original scheme of Michaelis and Menten (1913) will be followed and compound formation will be considered to take place. However, in later discussions, the process will be considered as a type of adsorption. 

The first notion on the deviation of elementary catalytic acts of enzyme reaction, from that prescribed by classical thermodynamic and kinetic approaches, was, probably, formulated in 1971 [19]. It had been shown that the application of basic postulates of activated state theory to the majority of enzyme processes can lead to physically meaningless values of the activation parameters (energy and entropy of activation). It was emphasized that enzyme functioning is more similar to the work of a mechanical construction than to the catalytic homogeneous chemical reaction. The selfconsistent phenomenological relaxation theory of enzyme catalysis was proposed in 1972 [20, 21]. 

Transition state theory has been useful in providing a rationale for the so-called kinetic isotope effect. The kinetic isotope effect is used by enzy-mologists to probe various aspects of mechanism. Importantly, measured kinetic isotope effects have also been used to monitor if non-classical behaviour is a feature of enzyme-catalysed hydrogen transfer reactions. The kinetic isotope effect arises because of the differential reactivity of, for example, a C-H (protium), a C-D (deuterium) and a C-T (tritium) bond. 

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