Kinetic of enzyme systems

Varon, R., Garrido-del Solo, C., Garcia-Moreno, M., Garcoa-Canovas, F., Moya-Garcia, G., Vidal de Labra, J., Havsteen BH. (1998). Kinetics of enzyme systems with unstable suicide substrates. Biosystems, vol. 47, no.3, (August 1998), pp.177-192, ISSN 0303-2647... 

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 kinetics of this relationship are straightforward the effector system (enzyme activity) is a zero order process (i.e. the substrate S saturates the enzyme Ej whereas the inactivation reaction E2 is a first order process. The consequences of the kinetics of this system is that the magnitude of the change in Ei results in precisely the same quantitative change in the concentration of X. For example a fivefold increase in Ei produces a fivefold increase in the concentration of X. This relationship is shown in Box 12.2. Three examples are given. 

A typical chemical system is the oxidative decarboxylation of malonic acid catalyzed by cerium ions and bromine, the so-called Zhabotinsky reaction this reaction in a given domain leads to the evolution of sustained oscillations and chemical waves. Furthermore, these states have been observed in a number of enzyme systems. The simplest case is the reaction catalyzed by the enzyme peroxidase. The reaction kinetics display either steady states, bistability, or oscillations. A more complex system is the ubiquitous process of glycolysis catalyzed by a sequence of coordinated enzyme reactions. In a given domain the process readily exhibits continuous oscillations of chemical concentrations and fluxes, which can be recorded by spectroscopic and electrometric techniques. The source of the periodicity is the enzyme phosphofructokinase, which catalyzes the phosphorylation of fructose-6-phosphate by ATP, resulting in the formation of fructose-1,6 biphosphate and ADP. The overall activity of the octameric enzyme is described by an allosteric model with fructose-6-phosphate, ATP, and AMP as controlling ligands. 

The homogeneous hydrogenation systems discussed in this paper may be treated as analogues of enzyme systems with the rhodium catalyst as the enzyme (E), hydrogen (Si) and cyclohexene (S2) as the substrates, and excess ligand or other donor site as the inhibitor (I). The well-established mathematical operations of enzyme kinetics (12) can then be used to derive rate equations for various possible mechanisms. 

We have dealt so far with enzymes that react with a single substrate only. The majority of enzymes, however, involve two substrates. The dehydrogenases, for example, bind both NAD+ and the substrate that is to be oxidized. Many of the principles developed for the single-substrate systems may be extended to multisubstrate systems. However, the general solution of the equations for such systems is complicated and well beyond the scope of this book. Many books devoted almost solely to the detailed analysis of the steady state kinetics of multisubstrate systems have been published, and the reader is referred to these for advanced study.11-14 The excellent short accounts by W. W. Cleland15 and K. Dalziel16 are highly recommended. 

Fluorescence microspectrophotometry typically provides chemical information in three modes spectral characterization, constituent mapping in specimens, and kinetic measurements of enzyme systems or photobleaching. All three approaches assist in defining chemical composition and properties in situ and one or all may be incorporated into modem instruments. Software control of monochrometers allows precise analysis of absoiption and/or fluorescence emission characteristics in foods, and routine detailed spectral analysis of large numbers of food elements (e.g., cells, fibers, fat droplets, protein bodies, crystals, etc.) is accomplished easily. The limit to the number of applications is really only that which is imposed by the imagination - there are quite incredible numbers of reagents which are capable of selective fluorescence tagging of food components, and their application is as diverse as the variety of problems in the research laboratory. 

Iatsimirskaia E, Tulebaev S, Storozhuk E, et al. Metabolism of rifabutin in human enterocyte and liver microsomes kinetic paramters, identification of enzyme systems, and drug interactions with macrolides and antifungal agents. Clin Pharmacol Ther 1997 61 554-562. 

Part II of this book represents the bulk of the material on the analysis and modeling of biochemical systems. Concepts covered include biochemical reaction kinetics and kinetics of enzyme-mediated reactions simulation and analysis of biochemical systems including non-equilibrium open systems, metabolic networks, and phosphorylation cascades transport processes including membrane transport and electrophysiological systems. Part III covers the specialized topics of spatially distributed transport modeling and blood-tissue solute exchange, constraint-based analysis of large-scale biochemical networks, protein-protein interactions, and stochastic systems. 

Figure 4.4 illustrates how the fast time kinetics of this system are represented by the approximation of Equation (4.29). In the figure the enzyme complex concentration as a function of time is plotted based on a numerical simulation of the reactions of Equation (4.22). The parameter values are identical to those used in the simulation of the irreversible system in Section 3.1.3.3 of Chapter 3. (See Figure 3.5 for the corresponding plot of substrate and product concentrations.) The ES concentration predicted by Equation (4.29) approaches the value E0S0/(S0 + Km) 0.048 mM with the exponential time constant of l/(k+i(Km + S0)), which is approximately equal to 0.48 seconds for the parameter values listed in the figure legend. 

Appropriate expressions for the fluxes of each of the reactions in the system must be determined. Typically, biochemical reactions proceed through multiple-step catalytic mechanisms, as described in Chapter 4, and simulations are based on the quasi-steady state approximations for the fluxes through enzyme-catalyzed reactions. (See Section 3.1.3.2 and Chapter 4 for treatments on the kinetics of enzyme catalyzed reactions.)... 

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 ... 

A good example of the range of parameters available from flow calorimetric data can be found from the study of enzyme/substrate systems. The kinetic nature of enzyme systems has been previously described by Michaelis and Menten. In the treatment discussed here, the parameters sought are the enthalpy, rate constant, Michaelis constant and the enzyme activity. The following example describes a study on the well-known enzyme substrate system, urea/urease. 

The focus of this chapter is on enzyme mechanisms that employ multiple hydrogen transfers, where both transfers are mechanistically central steps. The exchange of hydrons with solvent often presents both challenges and opportunities to the kinetic analysis of enzyme systems that undergo multiple hydrogen transfers. The... 

Even though it is tempting to consider inhibition of allosteric enzymes in the same fashion as nonallosteric enzymes, much of the terminology is not appropriate. Competitive inhibition and noncompetitive inhibition are terms reserved for the enzymes that behave in line with Michaelis-Menten kinetics. With allosteric enzymes, the situation is more complex. In general, two types of enzyme systems exist, called K systems and V systems. A K system is an enzyme for which the substrate concentration that yields one-half is altered by the presence... 

The kinetics of enzyme-catalyzed reactions will be discussed followed by a listing of the different systems of importance in the metabolism of exogenous organic compounds. The objective will be to develop a background sufficient to project the metabolites one might expect to form from an organic compound. Some unique aspects of plant systems will be discussed followed by an analysis of degradation processes in soil. 

Bousquet-Dubouch MP, Graber M, Sousa N et al. (2(X)1) Alcoholysis catalyzed by Candida antarc-tica lipase B in a gas/soUd system obeys a ping pong bi bi mechanism with competitive inhibition by the alcohol substrate and water. Biochim Biophys Acta 1550 90-99 Briggs GE, Haldane IBS (1925) A note on the kinetics of enzyme action. Biochem J 19 338-339 Buchholz K, Kasche V, Bomscheuer UT (2005) Biocatalysts and enzyme technology. Whey VCH, Weinhein, 448 pp... 

Moruno-Davila, M.A., Solo, C.G., Garcla-Moreno, M, GarcIa-CAnovas, F. Varon, R (2001). Kinetic analysis of enzyme systems with suicide substrate in the ptresence of a reversible, imcompetitive inhibitor. Biosystems, vol. 61, no.l, Qime 2001), pp.5-14,... 

In addition, the concept of linear responses to graded levels of nutrient input is not consistent with the kinetics of enzymes or enzyme systems. A curved response for individual animals would be expected just as a Michaelis-Menton relationship is expected with increasing substrate concentration for an enzyme. Curved responses have been observed when lysine a-ketoglutarate reductase activity (a simple enzyme system) and lysine oxidation to CO2 (a more complicated pathway) were measured (Blemings et al, 1994). Lysine metabolism in liver homogenates may not be directly related to whole animal responses (an animal is not a big enzyme). An animal is a system of pools and fluxes, however, and there does not appear to be a set of discrete on/off switches. 

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