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BackgroundThe numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches.ResultsFor the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study.ConclusionsThe second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.
BackgroundThe numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches.ResultsFor the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study.ConclusionsThe second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.
Names for chemical substances have developed from terms based on their source, properties, or effects into an elaborate system in which names encode precise information about chemical structures. Nomenclature in inorganic chemistry developed first; it is primarily concerned with elemental composition and with ionic and oxidation states. Organic nomenclature at first followed the inorganic pattern, but diverged from it because of the importance of connectivity and isomerism in organic compounds. The present system of organic nomenclature is based on the principles of the Geneva Conference of 1892, developed and expanded by international conferences and commissions into the nomenclature recommended by the International Union of Pure and Applied Chemistry (IUPAC). The nomenclatures of inorganic, organic, and macromolecular chemistry and of biochemistry are in a continuing state of development; new recommendations from international bodies are published in appropriate journals, such as Pure and Applied Chemistry and Biochemistry. Rules and recommendations are collected in book form at intervals. Computer interactions with different aspects of nomenclature that began during the later years of the twentieth century have increased enormously during the last decade.
Benzbromarone (BBR) is metabolized to 1'-hydroxy BBR and 6-hydroxy BBR in the liver. 6-Hydroxy BBR is further metabolized to 5,6-dihydroxy BBR. The aim of this study was to identify the CYP isozymes involved in the metabolism of BBR to 1'-hydroxy BBR and 6-hydroxy BBR and in the metabolism of 6-hydroxy BBR to 5,6-dihydroxy BBR in human liver microsomes. Among 11 recombinant P450 isozymes examined, CYP3A4 showed the highest formation rate of 1'-hydroxy BBR. The formation rate of 1'-hydroxy BBR significantly correlated with testosterone 6β-hydroxylation activity in a panel of 12 human liver microsomes. The formation of 1'-hydroxy BBR was completely inhibited by ketoconazole in pooled human liver microsomes. On the other hand, the highest formation rate of 6-hydroxy BBR was found in recombinant CYP2C9. The highest correlation was observed between the formation rate of 6-hydroxy BBR and diclofenac 4'-hydroxylation activity in 12 human liver microsomes. The formation of 6-hydroxy BBR was inhibited by tienilic acid in pooled human liver microsomes. The formation of 5,6-dihydroxy BBR from 6-hydroxy BBR was catalysed by recombinant CYP2C9 and CYP1A2. The formation rate of 5,6-dihydroxy BBR was significantly correlated with diclofenac 4'-hydroxylation activity and phenacetin O-deethylation activity in 12 human liver microsomes. The formation of 5,6-dihydroxy BBR was inhibited with either tienilic acid or α-naphthoflavone in human liver microsomes. These results suggest that (i) the formation of 1'-hydroxy BBR and 6-hydroxy BBR is mainly catalysed by CYP3A4 and CYP2C9, respectively, and (ii) the formation of 5,6-dihydroxy BBR is catalysed by CYP2C9 and CYP1A2 in human liver microsomes.
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