Application of chemometrics methods with kinetic constraints for estimation of rate constants of second order consecutive reactions.

To determine the rate constants for the second order consecutive reactions of the form U + V -(k1)--> W -(k2)--> P, a number of chemometrics and hard modeling-based methods are described. The absorption spectroscopic data from the reaction were utilized for performing the analysis. Concentrations and extinctions of components were comparable, and all of them were absorbing species. The number of steps in the reaction was less than the number of absorbing species, which resulted in a rank-deficient response matrix. This can cause difficulties for some of the methods described in the literature. The standard MATLAB functions were used for determining the solutions of the differential equations as well as for finding the optimal rate constants to describe the kinetic profiles. The available knowledge about the system determines the approaches described in this paper. The knowledge includes the spectra of reactants and products, the initial concentrations, and the exact kinetics. Some of this information is sometimes not available or is hard to estimate. Multiple linear regression for fitting the kinetic parameters to the obtained concentration profiles, rank augmentation using multiple batch runs, a mixed spectral approach which treats the reaction using a pseudo species concept, and principal components regression are the four groups of methods discussed in this study. In one of the simulated datasets the spectra are quite different, and in the other one the spectra of one reactant and of the product share a high degree of overlap. Instrumental noise, sampling error are the sources of error considered. Our aim was the investigation of the relative merits of each method.     

Combined on-line transmission FTIR measurements and BTEM analysis for the kinetic study of a consecutive reaction in aqueous-organic phase medium

Combined on-line transmission FTIR spectroscopy and band-target entropy minimization (BTEM) analysis were employed in order to monitor and analyze the kinetics of the alkaline hydrolysis reaction of diethyl phthalate (DEP) in aqueous-ethanol solvent mixture. This reaction is irreversible and involves two consecutive steps with the formation of the observable mono-ion intermediate species. The pure component mid-FTIR spectra of the reactive species involved in this reaction, namely DEP, mono-ion intermediate and di-ion product were successfully reconstructed using BTEM. Their corresponding concentrations were also calculated and subsequently employed to derive the kinetic rate parameters. The effect of temperature and the solvent mixture compositions on these two consecutive reaction steps were also discussed. The temperature variation study showed that both reaction rate coefficients increased with temperature. Both rate coefficients were also affected by the solvent mixture compositions and reached minimum values at certain water-ethanol solvent composition (circa 60% (v/v)). This study shows the utility of combined on-line transmission FTIR spectroscopy and chemometric techniques for the present, rather complex, consecutive organic reaction. Moreover, the present type of approach could facilitate better understanding of a wide variety of organic reactions that are performed in aqueous and mixed aqueous-organic solvents.     

Rank annihilation factor analysis method for spectrophotometric study of second-order reaction kinetics

In this study several methods are described to determine the rate constant of a second-order reaction in the form of A+B→C. These approaches allow circumventing a rank deficiency inherent of a second-order reaction when the spectroscopic data is influenced by additional source of variance. Classically, to determine the unknown rate constant in this kind of systems, one needs to have extra knowledge about the system, including the spectra of the reactants or product and the exact kinetics. In the case of the presence of an unknown phenomenon in the data set that cannot be explained by the model, such as baseline drift, the estimated rate constant might be erroneous. Present work is a modification of the rank annihilation factor analysis (RAFA) algorithm by inclusion of I) pure spectra of reactants, or IIA) mean centering step, or IIB) mean spectrum. The proposed methods can interestingly be applied on a single kinetic run. The performances of the new methods have been evaluated by applying them to analysis of simulated and experimental data.     

Estimation of first-order kinetic parameters by using the extended kalman filter

A model for first-order kinetics is derived for spectra obtained while a reaction is taking place. A technique for nonlinear-regression analysis known as the extended Kalman filter is used to estimate the initial concentrations of the reactants and the rate constant from the spectral data. The effects of the magnitude of the rate constant and the identity of the absorbing species are examined for synthetic spectra containing overlapped responses. The technique is used successfully to obtain the rate constant for the dissociation reaction of a praseodymium complex. The filter is also shown to be useful for the detection of erros in the kinetic model employed to fit the data. The extended Kalman filter can be used to fit kinetic models other than the one discussed here, and may prove to be a valuable technique for estimation of kinetic parameters.     

Kinetic and product distribution analysis for competitive recombination reactions

Exact solution methods are developed for the complex kinetic and product distribution equations encountered in a particular type of competitive recombination or crossover reaction involving “cages.” Pertinent reaction systems are those where scavenging of the intermediates escaping the cages is restricted to species similar to these intermediates, thereby limiting potentially undesired side effects of the scavenger. The trustworthiness of the reaction constants which may be obtained, particularly the fraction of recombination occurring within the cage, are analyzed in terms of sources of possible error. Several extensions of the method are briefly discussed, such as in distinctions between inter- and intramolecular rearrangements. Full detailing of the solution methods should facilitate their use in the analysis of similar reaction schemes.     

On-Line Multicomponent Determination of the Flux of Mixtures of Phenols Through a Liquid Membrane in Real Time

 The analysis of mixtures of four phenolic compounds in an on-line system using UV-visible measurements with a fibre optic probe is discussed in this work. The aim of this system is to provide accurate real time concentration profiles in order to monitor the transport of phenols across a solid supported liquid membrane in both the feed and stripping phases. Different calibration models are taking into account the pH of the solution, using experimental designs and the first derivative in combination with different multivariate approaches like multiple linear regression (MLR), inverted least squares (ILS) and partial least squares regression (PLS). The comparison of all these combinations is carried out by means of the predictive residual error sum of squares (PRESS) evaluated from an independent set of spectra. From this comparison it is concluded that a PLS model using first derivative spectra offers the most accurate and robust prediction in the permeation experiments. Additionally, the stability of the model and the figures of merit obtained are also discussed. Received July 22, 1999. Revision October 23, 2000.     

Enzyme catalyzed reactions: From experiment to computational mechanism reconstruction

The traditional experimental practice in enzyme kinetics involves the measurement of substrate or product concentrations as a function of time. Advances in computing have produced novel approaches for modeling enzyme catalyzed reactions from time course data. One example of such an approach is the selection of appropriate chemical reactions that best fit the data. A common limitation of this approach resides in the number of chemical species considered. The number of possible chemical reactions grows exponentially with the number of chemical species, which makes difficult to select reactions that uniquely describe the data and diminishes the efficiency of the methods. In addition, a method’s performance is also dependent on several quantitative and qualitative properties of the time course data, of which we know very little. This information is important to experimentalists as it could allow them to setup their experiments in ways that optimize the network reconstruction. We have previously described a method for inferring reaction mechanisms and kinetic rate parameters from time course data. Here, we address the limitations in the number of chemical reactions by allowing the introduction of information about chemical interactions. We also address the unknown properties of the input data by determining experimental data properties that maximize our method’s performance. We investigate the following properties: initial substrate–enzyme concentration ratios; initial substrate–enzyme concentration variation ranges; number of data points; number of different experiments (time courses); and noise. We test the method using data generated in silico from the Michaelis–Menten and the Hartley–Kilby reaction mechanisms. Our results demonstrate the importance of experimental design for time course assays that has not been considered in experimental protocols. These considerations can have far reaching implications for the computational mechanism reconstruction process.     

Kinetics study of the OH + alkene --> H2O + alkenyl reaction class

In this paper we report on the kinetics of hydrogen abstraction for the OH + alkene reaction class, using the reaction class transition state theory (RC-TST) combined with the linear energy relationship (LER) and the barrier height grouping (BHG) approaches. Parameters for the RC-TST were derived from theoretical calculations using a set of 15 reactions representing the hydrogen abstractions from the terminal and nonterminal carbon sites of the double bond of alkene compounds. Both the RC-TST/LER, where only reaction energy is needed at either density functional theory BH&HLYP or semiempirical AM1 levels, and RC-TST/BHG, where no additional information is required, are found to be promising methods for predicting rate constants for a large number of reactions in this reaction class. Detailed error analyses show that, when compared to explicit theoretical calculations, the averaged systematic errors in the calculated rate constants using both the RC-TST/LER and RC-TST/BHG methods are less than 25% in the temperature range 300-3000 K. The estimated rate constants using these approaches are in good agreement with available data in the literature.     

Kalman filtering of data from first- and second-order kinetics

The Kalman filter algorithm was used to process data obtained in the simultaneous determination of species following first- and second-order kinetics. The performance of the algorithm in the quantification of chemical components from simulated data was assessed, and the influence of various parameters involved was estimated. The algorithm was applied to the resolution of cysteine-ascorbic acid and glutathione-ascorbic acid mixtures where the ascorbic acid followed pseudo first-order kinetics and the amino acids second-order kinetics in the reaction with the copper(II)-neocuproine system. Some features of the determinations (namely, afforded concentration ratios, accuracy and precision) are discussed.     

Strategies for generating peptide radical cations via ion/ion reactions

Several approaches for the generation of peptide radical cations using ion/ion reactions coupled with either collision induced dissociation (CID) or ultraviolet photo dissociation (UVPD) are described here. Ion/ion reactions are used to generate electrostatic or covalent complexes comprised of a peptide and a radical reagent. The radical site of the reagent can be generated multiple ways. Reagents containing a carbon–iodine (C―I) bond are subjected to UVPD with 266‐nm photons, which selectively cleaves the C―I bond homolytically. Alternatively, reagents containing azo functionalities are collisionally activated to yield radical sites on either side of the azo group. Both of these methods generate an initial radical site on the reagent, which then abstracts a hydrogen from the peptide while the peptide and reagent are held together by either electrostatic interactions or a covalent linkage. These methods are demonstrated via ion/ion reactions between the model peptide RARARAA (doubly protonated) and various distonic anionic radical reagents. The radical site abstracts a hydrogen atom from the peptide, while the charge site abstracts a proton. The net result is the conversion of a doubly protonated peptide to a peptide radical cation. The peptide radical cations have been fragmented via CID and the resulting product ion mass spectra are compared to the control CID spectrum of the singly protonated, even‐electron species. This work is then extended to bradykinin, a more broadly studied peptide, for comparison with other radical peptide generation methods. The work presented here provides novel methods for generating peptide radical cations in the gas phase through ion/ion reaction complexes that do not require modification of the peptide in solution or generation of non‐covalent complexes in the electrospray process. Copyright © 2015 John Wiley & Sons, Ltd.     

General statement of the problem of substance analysis by the products of photochemical reactions

The aim of this study was to formulate the problem and develop a formal procedure for structure determination and substance quantification by the products of its photochemical reaction. This problem appears in studies of rapid photochemical processes, when the lifetime of the initial substance is shorter than the time to the moment of its registration (ecology, toxic substances, etc.). Algorithms of solving corresponding inverse problems are considered, and procedure including several steps is proposed. It includes the determination of the composition and concentrations of mixture components by the spectra of a test substance using the theory of molecular spectra; the recovery of the quantitative composition of the initial substance by the structural formulae of the products of a chemical reaction; and the determination of the initial concentrations of substances and the kinetics of the process on the basis of the developed theory of chemical transformations using information on the reactants and their concentrations. The application of the proposed approach is demonstrated on examples.     

Quantification of analytes in overlapping peaks from capillary electrophoresis using multivariate curve resolution-alternating least squares methods

Application of multivariate curve resolution with alternating least squares (ALS) methods to second-order data from capillary electrophoresis diode array detector (CE-DAD) is shown. Second-order data are easily obtained by setting individual data matrix of CE run one in top of the other. Initial qualitative solutions obtained by evolving factor analysis can be further optimized by simultaneous analysis of multiple electrophoresis run data with ALS regression. Quantification is achieved by the comparison of the analyte peak areas with that of pure standards. During the ALS regression procedure, the following constraints were applied: (i) both concentrations and unit pure spectra of the resolved components must be positive; (ii) elution profiles have an unimodal shape; (iii) correspondence exists between common species in the different data matrices; (iv) the pure spectrum of each species is the same in all runs where it is present. The above methods were applied for the determination of dinitrotoluene (DNT) isomeric compounds in overlapping peaks from CE.     

Use of Raman spectroscopy to determine the kinetics of chemical transformation in yogurt production

The kinetics of chemical transformation during the yogurt production was obtained using micro-Raman spectroscopy: Raman spectra were obtained as a function of the incubation time in the fermentation process from milk to yogurt. The milk fermentation by the lactic acid bacteria produces morphological, chemical and textural changes. The chemical transformations were followed using micro-Raman spectroscopy, while the aggregation process and some textural properties through the use of dynamic light scattering, viscosity and pH. Samples with three different starter culture concentrations and different incubation temperatures were prepared. The results indicate the presence of two regimes: the first one (primary metabolism) is characterized by an increment in the initial number of bacteria to reach a high concentration according to the conditions of food, temperature and space, together with some initial chemical transformations. The second regime corresponds properly to the fermentation process accelerated by the continuous reduction in pH due to the lactic acid production; this is accompanied by physical and chemical changes where new structures are created. Knowledge of the kinetics of chemical and physical transformations allows having a better control of the final product with an increase in the quality and shelf life of the final product; problems like phase separation, homogeneity, particle size, acidity, etc., can be controlled.     

Two-dimensional and three-dimensional fitting of enzyme kinetic data with the kalman filter

The availability of instrumentation which is capable of collecting multidimensional data has put increased demands on the data-processing methods utilized to obtain information about reaction kinetics. An enzyme-catalyzed reaction, the hydrolysis of p-nitrophenyl phosphate to p-nitrophenol, is examined so that various data-processing methods and data-collection formats can be examined and compared. The extended Kalman filter is used to obtain rate constants and values for the initial substrate concentration for three-dimensional data, and for two-dimensional kinetically perturbed data. In addition, non-linear least-squares regression with the simplex algorithm, and linear least-squares regression methods are used to analyze absorbance/time curves for this reaction. These results are compared to the results from a two-point kinetic method, and the accuracy and precision of each of the methods is evaluated. It is found that the methods based on the Kalman filter yielded results which were equivalent to or better than the results obtained from the other approaches.     

Reaction kinetics of dye decomposition processes monitored inside a photocatalytic microreactor

The photocatalytic decomposition processes of several kinds of dyes were monitored in real-time, in a TiO(2)-immobilized microcapillary. Their fluorescence spectra were measured directly from the UV-irradiated area. The photocatalytic reactions proceeded two orders of magnitude faster in the microcapillary than in a bulk reaction, and intermediate species were easily observed, due to their high concentrations compared with those of the reactants. Even for molecules that were not originally fluorescent, fluorescence was detected for the reactants or intermediate species of all the molecules studied. Photocatalytic reactions are typically analyzed in terms of pseudo-first-order or Langmuir-Hinshelwood reaction mechanisms, but it was ascertained that all of the dyes investigated in this study decomposed via a multi-step reaction such as a simple multi-step reaction, a self-catalytic reaction, and further, a more complicated reaction, depending on the molecular structure. These reactions were simulated using models based on the reaction kinetics, and reaction mechanisms were assigned to each type of dye. The fact that intermediate species (which are difficult to observe using conventional analytical methods) were successfully detected meant that mechanisms for different dyes could be further clarified.     

Quantitative determination of a nonpeptide antithrombotic in dog plasma by microbore high-performance liquid chromatography-tandem mass spectrometry utilizing pneumatically assisted electrospray ionization

A method has been developed and is described for the quantitative determination of a nonpeptide antithrombotic in dog plasma. The assay employs reversed phase microbore high-performance liquid chromatography in conjunction with tandem mass spectrometry utilizing pneumatically assisted electrospray ionization. The analyte and internal standard are isolated from the plasma matrix by solid-phase extraction. The mass spectrometer is operated in the positive ion multiple reaction monitoring mode and is set to detect the presence of a precursor-product ion pair for both the analyte and internal standard to generate product ion chromatograms for both species. The analyte is quantified by using weighted least-squares regression of the peak height ratio of drug:internal standard. The method provides linear response for plasma concentrations ranging from 5 ng/mL (25 pg on-column) to 2500 ng/mL. Statistical evaluation and examples of authentic sample assays are also presented.     

Near-infrared mass median particle size determination of lactose monohydrate, evaluating several chemometric approaches

The influence of particle size on near-infra red (NIR) spectra is typically considered a 'nuisance factor' which many scatter correction methods attempt to eliminate, e.g., multiplicative scatter correction. However, particle size is a key issue in the formulation of many pharmaceutical products and has a profound effect on the behaviour of both raw materials and drug substances during formulation. NIR has already been demonstrated as a potential alternative particle sizing technique to current accepted methodology. This investigation assessed several chemometric approaches that model this information, using lactose monohydrate as the raw material. A variety of modelling techniques were applied to both zero order and second derivative spectra namely multiple linear regression, partial least squares, principal component regression and artificial neural networks. One further data transformation evaluated was polar coordinates, although no statistical data were generated. Typically, cross-validation root mean square errors of calibration and cross-validation root mean square errors of prediction of approximately 5 microns were calculated for all of the modelling techniques. These values are comparable to those associated with the reference technique (laser diffractometry). Correlation coefficients of approximately 0.98 for all techniques were also calculated. The predictive abilities for models generated using second derivative spectra were found to be comparable to those obtained using zero order spectra.     

Polymer-supported palladium and platinum species as hydrogenation catalysts

The synthesis of new hydrogel copolymers and their use for anchoring Pd and Pt species is described. The supported catalysts are effective for the reduction of alkenes, dienes, alkynes, and nitroaromatics under mild conditions. The catalysts have been characterized by chemical analysis, particle size measurement, IR, TGA, and x-ray photoelectron spectra. Relative reactivities and the effects of substrate structure, solvents, catalyst loading, particle size of the catalysts, and partial pressure of hydrogen have been determined. The kinetics of hydrogenation have been analyzed using concepts useful under slurry reaction conditions. The recycling efficiencies of the catalysts and product analysis to establish selectivities have been assessed. © 1992 John Wiley & Sons, Inc.     

Stability of supramolecular compounds under heating

The decomposition of series of supramolecular compounds, namely inclusion compounds, was studied by means of different thermoanalytical methods, i.e., traditional thermogravimetry, quasi-equilibrium thermogravimetry, and thermomechanical analysis. The series of compounds included the intercalates on the base of fluorinated graphite C₂F, the clathrates on the base of carbamide and on the base of coordination compounds and microporous inclusion compounds on the base of coordination compounds. Kinetic parameters of decomposition processes were estimated within the approaches of the non-isothermal kinetics (“model-free” kinetics, linear and non-linear regression methods for the topochemical equation detection). The kinetic stability of the inclusion compounds under heating, the flexibility of the matrix structure, and the thermodynamic stability of the intermediate phases are discussed.     

Application of simplified complementary tristimulus colorimetry to chemical kinetics in solution-I: analysis of reaction mixtures and determination of first- or pseudo first-order rate constants

A graphical method is described which allows estimation of the number of reacting light-absorbing species from the plots of complementary colour points which are obtained with the use of simplified complementary tristimulus colorimetry (SCTS method) from absorption spectra of a series of kinetics solutions. It is shown that the mole function of the reactant or the product at any time can be calculated from the complementary colour points, so that the rate constant can also be determined. The present method has some advantages over the common approach to the determination or reaction rates in presence of a colour impurity.