Non‐negativity constraints for elimination of multiple solutions in fitting of multivariate kinetic models to spectroscopic data

Abstract

Multiple solutions arise when fitting complicated multi-step kinetic models to spectroscopic data. For consecutive reactions of the type A ! B ! C this well-known ambiguity is due to the presence of multiple equivalent global minima in the response surfaces associated with the non-linear least squares fitting of rate constants to spectroscopic data. Several methods have been described to overcome the ambiguity when fitting consecutive reactions with univariate data but few attempts to solve the problem have been described for multivariate data. Additionally, for complicated multistep reaction schemes there may be several local minima that make selection of the initial parameter guesses difficult. This paper reports a general approach to overcome these types of ambiguities in multivariate kinetic fitting methods using non-negativity constraints for the determination of the pure component spectra estimated during the model-fitting process. Under many conditions these constraints reduce or eliminate entirely the incorrect local minima. The effectiveness and reliability of the new constraints were tested with several simulated and real data sets.

Characterization and prediction of solute properties in methanol–water association by chemometrics analysis of solvation data

“…The ambiguities existed in the results obtained by MCR-ALS can be overcame by using extra experimental data matrix and simultaneous analysis of all data, or constraining the algorithm by a predefined hard model [25][26][27][28][29][30]. In the present work, the data are bilinear and no extra salvation or other thermodynamic data are existed to get trilinear data.…”

“…Nowadays, combined hard-soft chemometrics methods have found extensive application for determining equilibrium or rate constants of different chemical reactions [25][26][27][28][29][30]. Here, a combined hard modeling MCR-ALS and iterative IRAFA that is also a combined hard-soft modeling method are utilized to give an estimate of the dissociation constant of methanol-water based on the solvation data.…”

Signal Decomposition and Pseudo-baseline Optimization in Spectrum Reconstruction

“…The numerical power of this stratagem has been demonstrated for many methods of spectrum reconstruction -by numerous researchers, including the authors of this paper [26][27][28][29][30] -and is still subject to further investigation, e.g. [31]. It may be shown, however, that the effectiveness of this approach depends on the structure of a reconstructed spectrum: it is diminishing if its component, called background or baseline, contains a considerable portion of its energy -cf.…”

Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

“…Generally, the intermediate species of a reaction cannot be separately investigated, thus their corresponding parameters (e.g., molar attenuation coefficients, if processing concentration–absorbance data) should be included in the estimation process. Joint estimation of molar absorbance coefficients and rate constants may lead to the slow–fast ambiguity representing an internal factor . The “slow–fast” term means the altered values of the rate constants when a greater value refers to the “fast stage” of a reaction, and a lower value refers to the “slow stage.” Altering the values implies altering the stages that gives rise to the “slow–fast ambiguity” meaning a set of counterpart equivalent solutions.…”