Kinetics of enzymatic reactions

Quasi-equilibrium, also known as rapid equilibrium, assumes that an enzyme (E) reacts with substrate (S) rapidly to form an enzyme-substrate complex (ES) (with a rate constant, kj) that breaks down to release the enzyme and product (P). The enzyme, substrate, and the enzyme-substrate complex are at equilibrium that is the rate at which ES dissociates to E + S (rate constant of k2) is much faster than 

This is known as the Michaelis-Menten equation, where there are two kinetic parameters, the maximum velocity V = k3[E] and the Michaelis constant KS(K J = fca/ki- 

Write the initial velocity expression v = k[EAB] — fc [EPQ], where the interconversion between the ternary complexes is associated with the rate constants k and k in the forward and reverse directions, respectively. 

The term for any enzyme-containing complex is composed of a numerator, which is the product of the concentrations of all ligands in the complex, and a denominator, which is the product of all dissociation constants between 

The steady-state treatment of enzyme kinetics assumes that concentrations of the enzyme-containing intermediates remain constant during the period over which an initial velocity of the reaction is measured. Thus, the rates of changes in the concentrations of the enzyme-containing species equal zero. Under the same experimental conditions (i.e., [S]0 [E]0 and the velocity is measured during the very early stage of the reaction), the rate equation for one substrate reaction (uni uni reaction), if expressed in kinetic parameters (V and Ks), has the form identical to the Michaelis-Menten equation. However, it is important to note the differences in the Michaelis constant that is, Ks = k2/k1 for the quasi-equilibrium treatment whereas Ks = (k2 + k3)/k i for the steady-state treatment. 

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As the above discussion indicates, assigning mechanisms to simple anation reactions of transition metal complexes is not simple. The situation becomes even more difficult for a complex enzyme system containing a metal cofactor at an active site. Methods developed to study the kinetics of enzymatic reactions according to the Michaelis-Menten model will be discussed in Section 2.2.4. 

The book is organized in nine chapters and eleven appendices. Chapters 1 and 2 introduce the fundamental concepts and definitions. Chapters 3 to 7 treat binding systems of increasing complexity. The central chapter is Chapter 4, where all possible sources of cooperativity in binding systems are discussed. Chapter 8 deals with regulatory enzymes. Although the phenomenon of cooperativity here is manifested in the kinetics of enzymatic reactions, one can translate the description of the phenomenon into equilibrium terms. Chapter 9 deals with some aspects of solvation effects on cooperativity. Here, we only outline the methods one should use to study solvation effects for any specific system. 

It was early discovered that enzyme activity in organic solvents depends very much on the nature of the solvent. It was realized that the polarity or hydrophobicity of the solvent had a large influence, with non-polar hydrophobic solvents often providing higher reaction rates than more polar, hydrophilic solvents. When the kinetics of enzymatic reactions is studied, it is often found that Km values in organic solvents are much higher than those in water for the corresponding... 

The Henri-Michaelis-Menten Treatment Assumes That the Enzyme-Substrate Complex Is in Equilibrium with Free Enzyme and Substrate Steady-State Kinetic Analysis Assumes That the Concentration of the Enzyme-Substrate Complex Remains Nearly Constant Kinetics of Enzymatic Reactions Involving Two Substrates... 

In this chapter, some principles of the kinetics of enzymatic reactions are discussed. A more detailed description of enzyme kinetics is covered in a number of textbooks and articles[45, 101-1041, First of all, a few general definitions will be given. 

Because resolution is a kinetic phenomenon, an expression for the relative rates of conversion of the two enantiomers is desirable for a quantitative analysis of resolution. As the development and use of such an expression requires an understanding of the kinetics of enzymatic reactions, we defer considering this to Chapter 20 which deals with biochemical methods of enhancing reaction rates and selectivities. 

An alternative to the purchase of sophisticated apparatuses for the study of pre-steady-state kinetics of enzymatic reactions is the use of poor substrates, or carrying out the reaction at low temperatures. By using a poor substrate, the pre-steady-state region of the reaction is effectively shifted from a range of milliseconds to one of seconds. Carrying out the enzymatic reaction at low temperatures (e.g., —50 °C) will also slow down the reaction considerably. 

The kinetics of enzymatic reactions in microemulsions obey, as a rule, the classic Michaelis-Menten equation [6,26,35], but difhculties arise in interpreting the results because of the distribution of reactants, products, and enzyme molecules among the microphases of the microemulsion [8,36-38], In addition, there are some enzymes in reverse micelles that exhibit enhanced activity as compared to that expressed in water this has given rise to the concept of superactivity [6,26,39], The superactivity has been explained in terms of the state of water in reverse micelles, the increased rigidity of the enzymes caused by the surfactant layer, and the enhanced substrate concentration at the enzyme microenvironment [36,40],... 

Fig. 9.15 Prof. Dr. chem. Victor Andreyevich Yakovlev (1915-1977). Graduated from the Academy of Chemical Protection (1940) and worked in lahoratories of chemical plant protection. Fields of research kinetics of enzymatic reactions, electronic mechanism of enzymatic nitrogen fixation, etc. (monographs [160, 161]). Organizer and head of the Laboratory of Kinetics of Enzymatic Catalysis, Institute of Chemical Physics, USSR AS (1962-1967), director of VNfVI, and head of the biochemical laboratory (1967-1977). He ensured the organization of scientific and technological research, including electrosynthesis, in VNIVI and established creative climate. Photo in his office in VNlVl, January 1970...

Figure 4.6 shows the electrochemical activity of deposited poly(MG) onto RVC, and in each case, a nonlinear dependence that resembles Michaelis-Menten-type kinetics is observed. This observation agrees with the model proposed in 1985 by Gorton et al. [51] for mediator-modified electrodes for NADH oxidation, and it agrees with similar studies in 1990 and 2001 [53,105]. This model postulates the formation of a charge transfer (CT) complex in the reaction sequence between NADH and the mediator, because the observed reaction rate starts to decrease with the increase in NADH concentration, analogous to the Michaelis-Menten kinetics of enzymatic reactions. Catalytic activity of poly(MG) is inversely proportional to the thickness of the polymer, and the number of deposition cycles is consistent with observations in the literature for other NADH mediators [26,44,47,49]. This is attributed to the low partition coefficient of NADH and the diffusion coefficient of NADH within the... 

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