Michaelis-Menten kinetics principles

The kinetic behavior of drugs in the body can generally be accounted for by first-order kinetics that are saturable, i.e., Michaelis-Menten kinetics. A brief review of the principles of Michaelis-Menten kinetics is given next (4). 

The quantity of any given solute being presented to the reabsorptive mechanisms is determined by the product of the GFR and the solute concentration in plasma. One of the features of any carrier-mediated process is its limited capacity. Binding of a substance to its transport protein follows the same principles as substrate binding to an enzyme or hormone binding to its receptor so we may appropriately liken the dynamics to Michaelis-Menten kinetics. 

Shaw and Bell (1991) examined this effect in the case of competition between radiocaesium and the K+ and NH4+ ions during root uptake by wheat (Triticum aestivum). These authors formalised the observed relationships in terms of classical Michaelis-Menten kinetics which necessitates the assumption that each of these ions is taken up by identical sites associated with the root plasmalemma. Lembrechts et al. (1990) found a similar negative and non-linear relationship between the concentration of Ca either in soil or in solution culture and the degree of radiostrontium uptake by lettuce Lactuca saliva). The principle of competitive exclusion of a radionuclide by an ion analogue may be exploited, with varying degrees of success, as a post-con-... 

According to the principles of Michaelis-Menten kinetics, the rate of drug metabolism changes as a function of drug concentration, as illustrated in Fig. 15.5. 

Supramolecular chemistry has been a very popular research topic for three decades now. Most applications are foreseen in sensors and opto-electronical devices. Supramolecular catalysis often refers to the combination of a catalyst with a synthetic receptor molecule that preorganizes the substrate-catalyst complex and has also been proposed as an important possible application. The concept, which has proven to be powerful in enzymes, has mainly been demonstrated by chemists that investigated hydrolysis reactions. Zinc and copper in combination with cyclodextrins as the receptor dramatically enhance the rate ofhydrolysis. So far, the ample research devoted to transition metal catalysis has not been extended to supramolecular transition metal catalysis. A rare example of such a supramolecular transition metal catalyst was the results of the joined efforts of the groups of Nolte and Van Leeuwen [SO], They reported a basket-shaped molecule functionalized with a catalytically active rhodium complex that catalyzed hydrogenation reactions according to the principles of enzymes. The system showed substrate selectivity, Michaelis Menten kinetics and rate enhancement by cooperative binding of substrate molecules. The hydroformylation of allyl catachol substrates resulted in a complex mixture of products. 

Satisfaction of kinetic order. Carriers follow Michaelis-Menten-type saturation kinetics or first-order kinetics. Ion channels follow the type of respective structure—unimolecular transmembrane channels and bimolecular half-channels follow first- and second-order kinetics, respectively. The kinetic order of supramolecular channels depends on the assembly number. However, this principle can be applied only when the association constants are small. If the association becomes strong, the kinetic order decreases down to zero. Then the validity becomes dubious in view of the absolute criterion of the mechanism. Decreased activation energy compared to the carrier transport mechanism and competitive inhibition by added other cations stand as criteria. 

Substrate-catalyst interaction is also essential for micellar catalysis, the principles of which have long been established and consistently described in detail [63-66]. The main feature of micellar catalysis is the ability of reacting species to concentrate inside micelles, which leads to a considerable acceleration of the reaction. The same principle may apply for polymer systems. An interesting way to concentrate the substrate inside polymer catalysts is the use of cross-linked amphiphilic polymer latexes [67-69]. Liu et al. [67] synthesized a histidine-containing resin which was active in hydrolysis of p-nitrophenyl acetate (NPA). The kinetics curve of NPA decomposition in the presence of the resin was of Michaelis-Menten type, indicating that the catalytic act was accompanied by sorption of the substrate. However, no discussion of the possible sorption mechanisms (i.e., sorption by the interfaces or by the core of the resin beads) was presented. 

The power-law formalism was used by Savageau [27] to examine the implications of fractal kinetics in a simple pathway of reversible reactions. Starting with elementary chemical kinetics, that author proceeded to characterize the equilibrium behavior of a simple bimolecular reaction, then derived a generalized set of conditions for microscopic reversibility, and finally developed the fractal kinetic rate law for a reversible Michaelis-Menten mechanism. By means of this fractal kinetic framework, the results showed that the equilibrium ratio is a function of the amount of material in a closed system, and that the principle of microscopic reversibility has a more general manifestation that imposes new constraints on the set of fractal kinetic orders. So, Savageau concluded that fractal kinetics provide a novel means to achieve important features of pathway design. 

In situ methods involve the external perfusion of an isolated segment of intestinal tissne." The rat has been shown to be an excellent model for human intestinal permeability." One of the principle advantages of the in situ method is that the intact rat intestinal tissne maintains a normal complement of influx and efQux transporters. Cephalosporins and beta-lactam antibiotics are known to be absorbed by oligopeptide transporters in the GI tract. The rat in situ permeability method was used to determine the saturable Michaelis-Menten-type kinetics for this class of drug molecules. In like fashion, the permeabilities of thymidine anti-viral drugs, like AZT, involving the nncleoside transporter were determined in situ. ... 

The fact that cellulase enzymes act on an insoluble substrate, cellulose, moves the kinetics outside Michaelis-Menten on several counts. First of all, the enzyme can be adsorbed to the substrate or imadsorbed, but only the adsorbed enzyme acts on the cellulose. Even more puzzHng is the substrate concentration. Do we count the entire substrate, or just that in close contact with the enzyme Clearly, we have to start from first principles in characterizing the cellulase/cel-lulose system. 

The use of kinetics to characterize the behavior of integrated biochemical systems is a more recent and less developed practice. One of the more important issues in this integrative context is the selection of an appropriate formal representation. The most common approach is simply to adopt the Michaelis-Menten Formalism that has served so well for the elucidation of isolated reaction mechanisms. However, as the discussion above showed, there are difficulties in estimating the parameters of this formalism in general, and there is a combinatorial explosion in the amount of data required to characterize the rate law by kinetic means. Thus, even if the Michaelis-Menten Formalism were appropriate in principle, there... 

This textbook for advanced courses in enzyme chemistry and enzyme kinetics covers the field of steady-state enz5mie kinetics from the basic principles inherent in the Michaelis-Menten equation to the expressions that describe the multi-substrate enzyme reactions. The purpose of this book is to provide a simple but comprehensive framework for the study of enzymes with the aid of kinetic studies of enzyme-catalyzed reactions. The aim of enzyme kinetics is twofold to study the kinetic mechanism of enz5mie reactions, and to study the chemical mechanism of action of enzymes. 

A to the first line, Rossler (1976) was the first to provide a chemical model of chaos. It was not a mass-action-type model, but a three-variable system with Michaelis-Menten-type kinetics. Next Schulmeister (1978) presented a three-variable Lotka-type mechanism with depot. This is a mass-action-type model. In the same year Rossler (1978) presented a combination of a Lotka-Volterra oscillator and a switch he calls the Cause switch showing chaos. This model was constructed upon the principles outlines by Rossler (1976a) and is a three-variable nonconservative model. Next Gilpin (1979) gave a complicated Lotka-Volterra-type example. Arneodo and his coworkers (1980, 1982) were able to construct simple Lotka-Volterra models in three as well as in four variables having a strange attractor. 

With these principles, the most elementary biochemical model can be understood in Ihe world of the almost mystic field of enz5miatic reactions -notoriously complex in mechanism and kinetics. It is well known that the rate of an enzyme-catalyzed reaction in which a substrate S is converted into product P is foimd to depend on the concentration of enzyme E even though the enzyme imdeigoes no net change (Schnell Maini, 2003). As a mechanism, it is assiuned that the substrate enz5mie forms an intermediate ES, with the rates and A , which then irreversibly breaks down into the product and the enzyme (Brown, 1892, 1902 Henri, 1901 Michaelis Menten, 1913) ... 

Principle 1 a defined endpoint biological activity, then generalized to the final product rate in the ligand-receptor interaction, as based on the Michaelis-Menten enz34ne-substrate kinetics ... 

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