Kinetic sparse data

In the field of pharmacokinetics, there has been much recent work on developing methods for estimating interindividual variation in kinetic model parameters, particularly in sparse data situations where there are... 

The population estimation methods developed by pharmacokineticists to handle sparse data have potential use in the relatively data-rich studies encountered in metabolism and experimental nutrition. They provide a consistent and logical method to combine information from several experiments, accounting for interindividual variation in a theoretically sound manner. Anyone working in kinetic analysis should be aware of these tools, their advantages, and their limitations. 

There are a number of commercial operations where the objecl is to make useful produces with solid reactions. Design and practice, however, do not appear to rely generally on sophisticated kinetics, and they are rarely divulged completely. The desirable information is about temperatures, configuration, quahty of mixing, and residence times or space velocities. Most of the information about current practice of reaclions of solids is proprietary. Some of the sparse published data can... 

Equilibria between tetrahedral and octahedral cobalt(II) complexes in nonaqueous solution are well characterized. Kinetic data are sparse but those available from T-jump experiments in pyridine solution are interpreted in terms of (X = Cl and Br) ... 

The ion Rh(H20) + is well characterized in aqueous solution from H2 0 exchange studies. The hydroxy species is more labile. There is an absence of pressure dependency measurements, but an mechanism is favored. 2-22 The formation and cleavage of some hydroxo-bridged rhodium(lll) and iridium(lll) eomplexes have been studied. Kinetic studies of oxidation by Rh(lll) indieate that RhOH2+ is the sole oxidant. 22 Kinetic data for substitution in Rh(N)5H20 + are sparse. An mechanism is favored for water exchange... 

Although scheme (138) is the standard mechanism for the radical-catalyzed isomerization of isomeric alkenes, kinetic data for both substitution and isomerization are sparse. Using cis- or frcms-diiodo-ethene and labeled iodine atoms, Noyes et al. (1945) demonstrated that iodine atoms exchanged with predominant retention isomerization was the slower process, the barrier being <4 kcal/mole. Corresponding studies with dibromoethene and bromine atoms indicate a barrier of ca. 3 kcal/mole (Steinmetz and Noyes, 1952) in which bromine-atom departure from and isomerization of the intermediate were competitive. Qualitative selective or stereospecific radical-initiated additions to alkenes have since indicated that radical intermediates probably have stereostability, but the studies cited are definitive. The kinetic analysis provided the essential model for SS in mechanistic schemes such as (138), whether for SE, SH or SN processes. 

The reason why chemical reactions take place and the mechanism by which they operate are matters of increasing interest and call for some knowledge of thermodynamics and kinetics. The brief excursions into these subjects are synoptic and intended to provide the reader with no more than he will need in pursuing the main part of the book. Information about the kinetics of inorganic reactions is still sparse, but there is a wealth of thermodynamical data, standard electrode potentials and dissociation constants and the student must acquire facility in using these figures. 

This ability is available in many software programs. NONMEM (Iconus, EUicott City, MD) has been widely used to estimate population models arising from both sparse and intensely sampled data. Other programs include WinNonMix (Pharsight Corp., Palo Alto, CA), Kinetica 2000 (Innaphase Corp, Philadelphia, PA), and Pop-Kinetics (SAAM Institute, Seattle, WA). ADAPT II and WinNonlin have focused on PK/PD models and have been combined with Bayesian approaches to estimate population models. 

Two examples are given to demonstrate that direct effect models can still be used in complex PD behavior. As technological advances in biochemistry and molecular pharmacology techniques continue to provide greater and greater detail of biosensor and transduction systems, these mechanisms need not necessarily be included in an appropriate PK/PD model. When the kinetics of those systems are rapid compared to pharmacokinetics and biophase kinetics, a direct effect PD model may be a better choice—especially when facing the identifiable pitfalls of sparse or incomplete data. 

Redox reactions A large array of data exists for the electrode kinetics of various redox couples on mercury and to a lesser extent solid electrodes in aqueous and organic solvents. Data are rather sparse, however, for the temperature dependence, particularly at low temperatures. At sufficiently low temperatures, the Levich-Dogonadze-Kuznetsov treatment predicts quite abnormal behavior as a result of tunneling of the nuclei in reaction coordinate space (31,35). 

Kinetic data on complexing of other +2 transition metal ions is sparse and scattered. However, sufficient information is available to allow a comparison to be made of the rates of formation of complexes of Mn Fe Co " " and Cu with the common ligands bipyridine, terpyridine and phenanthroline (Table 13). There follows an account of some of the more recent studies. 

Detailed experimental data on the rate constants associated adsorption/desorption kinetics or conformational interconversion of different forms of a protein chromatographed on -alkylsilicas are currently very sparse. The kinetics of de-naturation of several proteins on n-butyl-bonded silica surfaces have been reported. Fig. 18 for example, shows the dependence of peak area on the incubation time of lysozyme on the bonded phase surface, from which rate constants for interconversion on the stationary phase, i.e. were derived [63]. The graphical representations derived from quantitative numerical solutions of the probabihty distributions... 

Although X2 could play a role in some systems, supporting data are sparse. Accordingly, we begin with a model that considers micelhzation-demicellization kinetics to be very fast, so that micelles are preserved as a whole. Solubilization takes place when a singly dispersed oil molecule colhdes with a micelle or when a micelle collides with the oil-water interface. 

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