Estimating reaction rate constants: comparison between traditional curve fitting and curve resolution

Applying constraints on model-based methods: estimation of rate constants in a second order consecutive reaction

This paper describes estimation of reaction rate constants and pure ultraviolet/visible (UV-vis) spectra of the component involved in a second order consecutive reaction between Ortho-Amino benzoeic acid (o-ABA) and Diazoniom ions (DIAZO), with one intermediate. In the described system, o-ABA was not absorbing in the visible region of interest and thus, closure rank deficiency problem did not exist. Concentration profiles were determined by solving differential equations of the corresponding kinetic model. In that sense, three types of model-based procedures were applied to estimate the rate constants of the kinetic system, according to Levenberg/Marquardt (NGL/M) algorithm. Original data-based, Score-based and concentration-based objective functions were included in these nonlinear fitting procedures. Results showed that when there is error in initial concentrations, accuracy of estimated rate constants strongly depends on the type of applied objective function in fitting procedure. Moreover, flexibility in application of different constraints and optimization of the initial concentrations estimation during the fitting procedure were investigated. Results showed a considerable decrease in ambiguity of obtained parameters by applying appropriate constraints and adjustable initial concentrations of reagents.

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.

Systematic method for the kinetic modeling of temporally resolved hyperspectral microscope images of fluorescently labeled cells

In this paper we report the application of a novel method for fitting kinetic models to temporally resolved hyperspectral images of fluorescently labeled cells to mathematically resolve pure-component spatial images, pure-component spectra, and pure-component reaction profiles. The method is demonstrated on one simulated image and two experimental cell images, including human embryonic kidney cells (HEK 293) and human A549 pulmonary type II epithelial cells. In both cell images, inhibitor kappa B kinase alpha (IKK(alpha)) and mitochondrial antiviral signaling protein (MAVS) were labeled with green and yellow fluorescent protein, respectively. Kinetic modeling was performed on the compressed images by using a separable least squares method. A combination of several first-order decays were needed to adequately model the photobleaching processes for each fluorophore observed in these images, consistent with the hypothesis that each fluorophore was found in several different environments within the cells. Numerous plausible mechanisms for kinetic modeling of the photobleaching processes in these images were tested and a method for selecting the most parsimonious and statistically sufficient model was used to prepare spatial maps of each fluorophore.

Application of soft- and hard-modelling approaches to resolution of kinetics of electron donor-acceptor complex formation of 2,3-dichloro-5,6-dicyano-1,4-benzoquinone with imipramine in different solutions

Kinetics of electron donor-acceptor (EDA) complex formation of imipramine and 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) was investigated spectrophotometrically in acetonitrile, 1,2-dichloroethane, and chloroform solutions using soft- and hard-modelling approaches. From the results of exploratory analysis of kinetic data and the spectral changes by soft-modelling approaches, evolving factor analysis (EFA) and orthogonal projection approach (OPA), a consecutive two-steps reaction with two intermediates was proposed for the process in acetonitrile and 1,2-dichloroethane media and one with a single intermediate in chloroform solution. Secondly, by applying, multivariate nonlinear least squares hard-modelling approach on the collected experimental kinetic data matrix, the nonlinear parameters (rate constants) as well as the linear parameters (spectral profiles) were obtained by fitting the collected experimental kinetic data matrix to the proposed model. Small values of standard deviation in the resulting parameters and sum of squares of the residuals (ssq) obtained showed the proper selection of the model. Furthermore, the values of lack of fit and percent of explained variance confirmed the correct identified models. Identification of the model with the aid of soft-modelling approaches followed by application of the hard-modelling approaches decreases significantly the rotational ambiguity associated with the obtained concentration and spectral profiles. Variations in the kinetic constants were in complete agreement with the model proposed and the solvent polarities.

Methods for kinetic modeling of temporally resolved hyperspectral confocal fluorescence images

Elucidating kinetic information (rate constants) from temporally resolved hyperspectral confocal fluorescence images offers some very important opportunities for the interpretation of spatially resolved hyperspectral confocal fluorescence images but also presents significant challenges, these being (1) the massive amount of data contained in a series of time-resolved spectral images (one time course of spectral data for each pixel) and (2) unknown concentrations of the reactants and products at time = 0, a necessary precondition normally required by traditional kinetic fitting approaches. This paper describes two methods for solving these problems: direct nonlinear (DNL) estimation of all parameters and separable least squares (SLS). The DNL method can be applied to reactions of any rate law, while the SLS method is restricted to first-order reactions. In SLS, the inherently linear and nonlinear parameters of first-order reactions are solved in separate linear and nonlinear steps, respectively. The new methods are demonstrated using simulated data sets and an experimental data set involving photobleaching of several fluorophores. This work demonstrates that both DNL and SLS hard-modeling methods applied to the kinetic modeling of temporally resolved hyperspectral images can outperform traditional soft-modeling and hard/soft-modeling methods which use multivariate curve resolution-alternating least squares (MCRALS) methods. In addition, the SLS method is much faster and is able to analyze much larger data sets than the DNL method.

Tautomerization equilibria in aqueous micellar solutions: a spectrophotometric and factor-analytical study

The keto-enol equilibria of benzoylacetone (BZA) as a model for 1,3-dicarbonyl compounds are studied in aqueous acid and cationic micellar solution. Evolving factor analysis (EFA), multivariate curve resolution-alternating least-squares (MCR-ALS), and rank annihilation factor analysis (RAFA) are used for complete resolving of measured spectrophotometric data. The acidity constants of the enolic, KaE, and ketonic, KaK, forms of BZA and also the tautomerization constant, Kt, and its related thermodynamic parameters have been determined by using EFA and MCR-ALS methods and spectral variation of BZA solutions in various pHs and temperatures. The concentration and spectral profiles of all species were calculated without any assumption about chemical models. The spectral variation of BZA solutions as a function of cationic micelle concentration sufficiently beyond its critical micelle concentration is analyzed according to the partition model for distribution between water and micellar pseudo-phase and RAFA. The outputs of using RAFA on measured rank deficient data are the spectrum of enolic form in the micellar pseudo-phase, free from contribution of the enolic form in the aqueous phase, the partition coefficient of enolic form, KdE, between the micelle and water phases, and the tautomerization constant in the micellar pseudo-phase, Ktm.

Tackling calibration problems of spectroscopic analysis in high-throughput experimentation

High-throughput experimentation and screening methods are changing work flows and creating new possibilities in biochemistry, organometallic chemistry, and catalysis. However, many high-throughput systems rely on off-line chromatography methods that shift the bottleneck to the analysis stage. On-line or at-line spectroscopic analysis is an attractive alternative. It is fast, noninvasive, and nondestructive and requires no sample handling. The disadvantage is that spectroscopic calibration is time-consuming and complex. Ideally, the calibration model should give reliable predictions while keeping the number of calibration samples to a minimum. In this paper, we employ the net analyte signal approach to build a calibration model for Fourier transform near-infrared measurements, using a minimum number of calibration samples based on blank samples. This approach fits very well to high-throughput setups. With this approach, we can reduce the number of calibration samples to the number of chemical components in the system. Thus, the question is no longer how many but which type of calibration samples should one include in the model to obtain reliable predictions. Various calibration models are tested using Monte Carlo simulations, and the results are compared with experimental data for palladium-catalyzed Heck cross-coupling.

Q-mode curve resolution of UV–vis spectra for structural transformation studies of anthocyanins in acidic solutions

Chemometric analysis of ultraviolet-visible (UV-vis) spectra for pH values 1.0, 3.3, 5.3, and 6.9 was used to investigate the kinetics and the structural transformations of anthocyanins in extracts of calyces of hibiscus flowers of the Hibiscus acetosella Welw. ex Finicius for the first time. Six different species were detected: the quinoidal base (A), the flavylium cation (AH+), the pseudobase or carbinol pseudobase (B), cis-chalcone (C(C)), trans-chalcone (C(t)), and ionized cis-chalcone (C(C)-). Four equilibrium constant values were calculated using relative concentrations, hydration, pK(h) = 2.60 +/- 0.01, tautomeric, K(T) = 0.14 +/- 0.01, acid-base, pK(a) = 4.24 +/- 0.04, and ionization of the cis-chalcone, pK(C(C)) = 8.74 +/- 1.5 x 10(-2). The calculated protonation rate of the tautomers is K(H+) = 0.08 +/- 7.6 x 10(-3). These constants are in excellent agreement with those measured previously in salt form. From a kinetic viewpoint, the situation encountered is interesting since the reported investigation is limited to visible light absorption in acid medium. These models have not been reported in the literature.

Kinetic studies of cascade reactions in high-throughput systems

The application of robotic systems to the study of complex reaction kinetics is considered, using the cascade reaction A --> B --> C as a working example. Practical problems in calculating the rate constants k1 and k2 for the reactions A --> B and B --> C from concentration measurements of CA, CB, or CC are discussed in the light of the symmetry and invertability of the rate equations. A D-optimal analysis is used to determine the points in time and the species that will give the best (i.e., most accurate) results. When exact data are used, the most robust solution results from measuring the pair of concentrations (CA, CC). The system's information function is computed using numeric methods. This function is then used to estimate the amount of information obtainable from a given cascade reaction at any given time. The theoretical findings are compared with experimental results from a set of two-stage cascade experiments monitored using UV-visible spectroscopy. Finally, the pros and cons of using a single reaction sample to estimate both k1 and k2 are discussed.

Multivariate curve resolution: a method of evaluating the kinetics of biotechnological reactions

In biotechnology, strong emphasis is placed on the development of wet chemical analysis and chromatography to separate target components from a complex matrix. In bioprocessing, the development of single compound biosensors is an important activity. The advantages of these techniques are their high sensitivity and specificity. Inline or online monitoring by means of spectroscopy has the potential to be used as an "all-in-one" analysis technique for biotechnological studies, but it lacks specificity. Multivariate curve resolution (MCR) can be used to overcome this limitation. MCR is able to extract the number of components involved in a complex spectral feature, to attribute the resulting spectra to chemical compounds, to quantify the individual spectral contributions, and to use this quantification to develop kinetic models for the process with or without a priori knowledge. After a short introduction to MCR, two applications are presented. In the first example, the spectral features of hemp are monitored and analysed during growth. MCR provides unperturbed spectra on the activity of, for example, lignin and cellulose during plant development. In a second example, the kinetics of a laccase enzyme-catalysed degradation of aromatic hydrocarbons are calculated from UV/VIS spectra.

Multivariate curve resolution methods in imaging spectroscopy: influence of extraction methods and instrumental perturbations

Imaging spectroscopy is becoming a key field of analytical chemistry. In the face of more and more complex samples, we actually need accurate microscopic insight. Nowadays, the methods used to produce concentration maps of the pure compounds from spectral data sets are based on the classical univariate approach although multivariate approaches are sometimes investigated. But in any case, the analytical quality of the chemical images thus provided cannot be discussed since no reference methods are at our disposal. Thus the proposed research focuses on the application of multivariate methods such as Orthogonal Projection Approach (OPA), SIMPLE-to-use Self-modeling Mixture Analysis (SIMPLISMA), Multivariate Curve Resolution - Alterning Least Squares (MCR-ALS), and Positive Matrix Factorization (PMF) for imaging spectroscopy. A systematic and quantitative characterization of the accuracy of spectra and images extraction is investigated on mid-infrared spectral data sets. Of special interest is the influence of instrumental perturbations such as noise and spectral shift on the extraction ability to access the algorithm's robustness.

Model Selection and Optimal Sampling in High-Throughput Experimentation

The practical difficulties encountered in analyzing the kinetics of new reactions are considered from the viewpoint of the capabilities of state-of-the-art high-throughput systems. There are three problems. The first problem is that of model selection, i.e., choosing the correct reaction rate law. The second problem is how to obtain good estimates of the reaction parameters using only a small number of samples once a kinetic model is selected. The third problem is how to perform both functions using just one small set of measurements. To solve the first problem, we present an optimal sampling protocol to choose the correct kinetic model for a given reaction, based on T-optimal design. This protocol is then tested for the case of second-order and pseudo-first-order reactions using both experiments and computer simulations. To solve the second problem, we derive the information function for second-order reactions and use this function to find the optimal sampling points for estimating the kinetic constants. The third problem is further complicated by the fact that the optimal measurement times for determining the correct kinetic model differ from those needed to obtain good estimates of the kinetic constants. To solve this problem, we propose a Pareto optimal approach that can be tuned to give the set of best possible solutions for the two criteria. One important advantage of this approach is that it enables the integration of a priori knowledge into the workflow.