Kinetics of Enzyme Reaction

This chapter solely reviews tlie kinetics of enzyme reactions, modeling, and simulation of biochemical reactions and scale-up of bioreactors. More comprehensive treatments of biochemical reactions, modeling, and simulation are provided by Bailey and Ollis [2], Bungay [3], Sinclair and Kristiansen [4], Volesky and Votruba [5], and Ingham et al. [6]. 

Each of the processes shown in Figure 2.8 can be described by a Michaelis-Menten type of biochemical reaction, a standard generalized mathematical equation describing the interaction of a substrate with an enzyme. Michaelis and Men ten realized in 1913 that the kinetics of enzyme reactions differed from the kinetics of conventional... 

The kinetics of enzyme reactions were first studied by the German chemists Leonor Michaelis and Maud Menten in the early part of the twentieth century. They found that, when the concentration of substrate is low, the rate of an enzyme-catalyzed reaction increases with the concentration of the substrate, as shown in the plot in Fig. 13.41. However, when the concentration of substrate is high, the reaction rate depends only on the concentration of the enzyme. In the Michaelis-Menten mechanism of enzyme reaction, the enzyme, E, and substrate, S, reach a rapid preequilibrium with the bound enzyme-substrate complex, ES ... 

Nannipieri P, Gianfreda L (1999) Kinetics of enzyme reactions in soil environments. In Huang PM, Senesi N, Buffle J (eds) Structure and surface reactions of soil particles, vol 4, IUPAC series on analytical and physical chemistry of environmental systems. Wiley Chichester UK, pp 449-479... 

The subject of biochemical reactions is very broad, covering both cellular and enzymatic processes. While there are some similarities between enzyme kinetics and the kinetics of cell growth, cell-growth kinetics tend to be much more complex, and are subject to regulation by a wide variety of external agents. The enzymatic production of a species via enzymes in cells is inherently a complex, coupled process, affected by the activity of the enzyme, the quantity of the enzyme, and the quantity and viability of the available cells. In this chapter, we focus solely on the kinetics of enzyme reactions, without considering the source of the enzyme or other cellular processes. For our purpose, we consider the enzyme to be readily available in a relatively pure form, off the shelf, as many enzymes are. 

The kinetics of enzyme reactions were first studied by the German chemists Leonor Michaelis and Maud Menten in the early part of the twentieth century. They found that when the concentration of substrate is... 

An understanding of the influence of environmental conditions on the kinetics of enzyme reactions is essential for the design of processes based upon the use of these materials as catalysts. Their growth kinetics are also governed by similar kinetic equations (c.f. Monod growth equations, Section S.9). 

An enzyme is immobilized on solid surface. Assume that the external mass-transfer resistance for substrate is not negligible and that the Michaelis-Menten equation describes the intrinsic kinetics of enzyme reaction. 

The kinetics of enzyme reactions was first established by Michaelis and Menten, following the earlier work of Henri [23]. The famous Michaelis-Menten equation for the kinetics of an enzyme reaction with a single substrate is often written [23]... 

The determination of flow control coefficients is difficult, and requires the independent variation of the activity of all the enzymes within the pathway. Based on linear nonequilibrium thermodynamics, the kinetics of enzyme reactions can be described by the linear functions of the change in Gibbs free energy. This yields a direct relation between the elasticity coefficients and the change in Gibbs free energy for the reactions in a simple two-step pathway. 

In developing some of the elementary principles of the kinetics of enzyme reactions, we shall discuss an enzymatic reaction that has been suggested by Levine and LaCourse as part of a system that would reduce the size of an artificial kidney. The desired result is the production of an artificial kidney that could be worn by the patient and would incorporate a replaceable unit for the elimination of tte nitrogenous waste products such as uric acid and creatinine, In the microencapsulation scheme proposed by Levine and LaCourse, the enzyme urease would be used in tire removal of urea from ti)e bloodstream. Here, the catalytic action of urease would cause urea to decompose into ammonia and carbon dioxide. The mechanism of the reaction is believed to proceed by the following sequence of elementary reactions ... 

The basis of the operational model is the experimental finding that the experimentally obtained relationship between agonist-induced response and agonist concentration resembles a model of enzyme function presented in 1913 by Louis Michaelis and Maude L. Menten. This model accounts for the fact that the kinetics of enzyme reactions differ significantly from the kinetics of conventional chemical reactions. It describes the reaction of a substrate with an enzyme as an equation of the form reaction velocity = (maximal velocity of the reaction x substrate concentration)/(concentration of substrate A a... 

Describe the effects of competitive and noncompetitive inhibitors on the kinetics of enzyme reactions. Apply kinetic measurements and analysis to determine the nature of an inhibitor. 

A different approach is the direct determination of a and the intrinsic kinetic parameters from experimental rate data. This method was proposed by Chen (in Buchholz 1982) and is based on the determination of initial rates within a broad range of bulk substrate concentration. The kinetics of enzyme reaction, represented by the right-hand side of Eq. 4.14 is a very complex function of... 

More recently, M.J.S. Dewar developed a different rationale [99] in attempting to explain the high conversimi rates of enzymatic reactions, which are generally substantially faster than the chemically catalyzed equivalent processes. This so-called desolvation theory assumes that the kinetics of enzyme reactions have much in common with those of gas-phase reactions. If a substrate enters the active site of the enzyme, it replaces all of the water molecules at the active site of the enzyme. Then, a formal gas-phase reaction can take place which mimics two reaction partners interacting without a disturbing solvent. In solution, the water molecules impede the approach of the partners, hence the reaction rate is reduced. This theory would, inter alia, explain why small substrate molecules are often more slowly converted than larger analogues, since the former are unable to replace all the water molecules at the active site. 

Briggs Haldane (1925) removed the restrictive assumption that the enzyme-substrate complex is in equilibrium with free enzyme and substrate and introduced the steady state model, which gives the Michaelis parameters, ATm and a more complex meaning. The principles of steady state kinetics of enzyme reactions can be demonstrated with the more realistic, though still oversimplified, model of Haldane (1930). This contains the minimum number of intermediates, namely enzyme-substrate and enzyme-product complexes ... 

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