Enzyme-catalyzed reactions description

An exponential function that describes the increase in product during a first-order reaction looks a lot like a hyperbola that is used to describe Michaelis-Menten enzyme kinetics. It s not. Don t get them confused. If you can t keep them separated in your mind, then just forget all that you ve read, jump ship now, and just figure out the Michaelis-Menten description of the velocity of enzyme-catalyzed reaction—it s more important to the beginning biochemistry student anyway. 

A detailed kinetic description of enzyme-catalyzed reactions is paramount to kinetic modeling of metabolic networks and one of the most challenging steps... 

A kinetic description of large reaction networks entirely in terms of elementary reactionsteps is often not suitable in practice. Rather, enzyme-catalyzed reactions are described by simplified overall reactions, invoking several reasonable approximations. Consider an enzyme-catalyzed reaction with a single substrate The substrate S binds reversibly to the enzyme E, thereby forming an enzyme substrate complex [/iS ]. Subsequently, the product P is irreversibly dissociated from the enzyme. The resulting scheme, named after L. Michaelis and M. L. Menten [152], can be depicted as... 

The detailed description of the models currently being used to describe tunneling in enzyme-catalyzed reactions will be undertaken in a later part of our treatment in which theoretical studies will be reviewed and ideas about the role of protein motions will be a focus. At this point, we will briefly sketch the most commonly used ideas. 

If a detailed theoretical knowledge of the system is available, it is often possible to construct a mechanistic model which will describe the general behavior of the system. For example, if a biochemist is dealing with an enzyme system and is interested in the rate of the enzyme catalyzed reaction as a function of substrate concentration (see Figure 1.15), the Michaelis-Menton equation might be expected to provide a general description of the system s behavior. 

A complete description of an enzyme-catalyzed reaction requires direct measurement of the rates of individual reaction steps—for example, measurement of the association of enzyme and substrate to form the ES complex. It is during the pre-steady state that the rates of many reaction steps can be measured independently. Experimenters adjust reaction conditions so that they can observe events during reaction of a single substrate molecule. Because the pre-steady state phase is gener-... 

Enzyme kinetics is studied for two reasons (1) it is a practical concern to determine the activity of the enzyme under different conditions (2) frequently the analysis of enzyme kinetics gives information about the mechanism of enzyme action. Chapter 7, Enzyme Kinetics, begins with an introductory section on the discovery of enzymes, basic enzyme terminology and a description of the six main classes of enzymes and the reactions they catalyze. The remainder of the chapter deals with basic aspects of chemical kinetics, enzyme-catalyzed reactions and various factors that affect the kinetics. 

The effects of macromolecules other than surfactants on the rates of organic reactions have been investigated extensively (Morawetz, 1965). In many cases, substrate specificity, bifunctional catalysis, competitive inhibition, and saturation (Michaelis-Menten) kinetics have been observed, and therefore these systems also serve as models for enzyme-catalyzed reactions and, in these and other respects, resemble micellar systems. Indeed, in some macromolecular systems micelle formation is very probable or is known to occur, and in others mixed micellar systems are likely. Recent books and reviews should be consulted for a more detailed description of macromolecular systems and for their applicability as models for enzymatic catalysis and other complex interactions (Morawetz, 1965 Bruice and Benkovic, 1966 Davydova et al., 1968 Winsor, 1968 Jencks, 1969 Overberger and Salamone, 1969). 

In enzyme-catalyzed reactions, parameters such as concentration of water, reaction temperature, pH, enzyme immobilizing agents, and the nature of any solvent may be of great importance. A brief description of each of these factors is given below. 

The study of the rates of chemical reactions is called kinetics, and the study of the rates of enzyme-catalyzed reactions is called enzyme kinetics. A kinetic description of enzyme activity will help us understand how enzymes function. We begin by briefly examining some of the basic principles of reaction kinetics. 

The kinetic description of enzyme-catalyzed reactions in vitro has allowed their rates to be expressed as a function of reactant and enzyme concentrations, and a set of empirically defined kinetic parameters. Enzymologists also have sought to modify this basic relationship in systematic ways so as to reveal something about the mechanism by which the enzyme acts. Traditionally, in such studies the enzymologist has been concerned primarily with the enzyme, its proper substrates and products, and closely related chemical analogs of these proper reactants (Jencks, 1969). 

Enzyme kinetics is an area of science that seeks a general quantitative (mathematical) description of the rate of an enzyme-catalyzed reaction. The experimental aspects of enzyme kinetics are concerned with understanding those factors that affect the rate, with a view to determining the chemical mechanism of the... 

In this case, v is the velocity of the reaction, [S] is the substrate concentration, Vmax (also known as V or Vj ) is the maximum velocity of the reaction, and is the Michaelis constant. From this equation quantitative descriptions of enzyme-catalyzed reactions, in terms of rate and concentration, can be made. As can be surmised by the form of the equation, data that is described by the Michaelis-Menten equation takes the shape of a hyperbola when plotted in two-dimensional fashion with velocity as the y-axis and substrate concentration as the x-axis (Fig. 4.1). Use of the Michaelis-Menten equation is based on the assumption that the enzyme reaction is operating under both steady state and rapid equilibrium conditions (i.e., that the concentration of all of the enzyme-substrate intermediates (see Scheme 4.1) become constant soon after initiation of the reaction). The assumption is also made that the active site of the enzyme contains only one binding site at which catalysis occurs and that only one substrate molecule at a time is interacting with the binding site. As will be discussed below, this latter assumption is not always valid when considering the kinetics of drug metabolizing enzymes. 

The above power law is widely used in industrial chemistry since it is mathematically easy to handle. However, most reactions in which a catalyst is involved have a complex reaction mechanism which can make the mathematical description of the kinetics complicated. An example of this are enzyme-catalyzed reactions according to the Mi-... 

Given recent developments in computer modeling of chemical reactions, there is considerable interest in attempting to develop a mathematical understanding of enzyme catalysis. The sheer complexity of enzymes means that at present, it is possible to apply a strict quantum mechanical approach to only a limited region, such as the active site, and classical molecular mechanics are used to describe the remainder of the molecule. This combined approach had some success in modeling some aspects of enzyme-catalyzed reactions, such as the importance of particular side chains in the catalytic process.However, a complete mathematical description of enzyme catalysis remains a considerable way off. 

The diagram shown in this figure illustrates that one may link an observed kinetic isotope effect to a certain segment of an enzyme-catalyzed reaction. This description should be regarded as an idealized situation, because the magnitude of the isotope effect can be greatly influenced by the relative magnitude of the rate constants in certain steps. 

As can be concluded from this short description of the factors influencing the overall reaction rate in liquid-solid or gas-solid reactions, the structure of the stationary phase is of significant importance. In order to minimize the transport limitations, different types of supports were developed, which will be discussed in the next section. In addition, the amount of enzyme (operative ligand on the surface of solid phase) as well as its activity determine the reaction rate of an enzyme-catalyzed process. Thus, in the following sections we shall briefly describe different types of chromatographic supports, suited to provide both the high surface area required for high enzyme capacity and the lowest possible internal and external mass transfer resistances. 

Protein function can be described on three levels. Phenotypic function describes the effects of a protein on the entire organism. For example, the loss of the protein may lead to slower growth of the organism, an altered development pattern, or even death. Cellular function is a description of the network of interactions engaged in by a protein at the cellular level. Interactions with other proteins in the cell can help define the lands of metabolic processes in which the protein participates. Finally, molecular function refers to the precise biochemical activity of a protein, including details such as the reactions an enzyme catalyzes or the ligands a receptor binds. 

Frequently enzymes act in concert with small molecules, coenzymes or cofactors, which are essential to the function of the amino acid side chains of the enzyme. Coenzymes or cofactors are distinguished from substrates by the fact that they function as catalysts. They are also distinguishable from inhibitors or activators in that they participate directly in the catalyzed reaction. Chapter 10, Vitamins and Coenzymes, starts with a description of the relationship of water-soluble vitamins to their coenzymes. Next, the functions and mechanisms of action of coenzymes are explained. In the concluding sections of this chapter, the roles of metal cofactors and lipid-soluble vitamins in enzymatic catalysis are briefly discussed. 

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