Standardless multicomponent qNMR analysis of compounds with overlapped resonances based on the combination of ICA and PULCON

A fast and reliable nuclear magnetic resonance (NMR) method for quantitative analysis of targeted compounds with overlapped signals in complex mixtures has been established. The method is based on the combination of chemometric treatment for spectra deconvolution and the PULCON principle (pulse length based concentration determination) for quantification. Independent component analysis (ICA) (mutual information least dependent component analysis (MILCA) algorithm) was applied for spectra deconvolution in up to six component mixtures with known composition. The resolved matrices (independent components, ICs and ICA scores) were used for identification of analytes, calculating their relative concentrations and absolute integral intensity of selected resonances. The absolute analyte concentrations in multicomponent mixtures and authentic samples were then calculated using the PULCON principle. Instead of conventional application of absolute integral intensity in case of undisturbed signals, the multiplication of resolved IC absolute integral and its relative concentration in the mixture for each component was used. Correction factors that are required for quantification and are unique for each analyte were also estimated. The proposed method was applied for analysis of up to five components in lemon and orange juice samples with recoveries between 90% and 111%. The total duration of analysis is approximately 45 min including measurements, spectra decomposition and quantification. The results demonstrated that the proposed method is a promising tool for rapid simultaneous quantification of up to six components in case of spectral overlap and the absence of reference materials. Copyright © 2015 John Wiley & Sons, Ltd.     

Chemometrics-assisted spectrophotometric method for simultaneous determination of vitamins in complex mixtures

An advanced independent component analysis algorithm (MILCA) is applied for simultaneous chemometric determination of fat- and water-soluble vitamins in complex mixtures. The analysis is based on the decomposition of spectra of multicomponent mixtures in the UV region. The key features of the proposed method are simplicity, accuracy, and reliability. Comparisons between the new algorithm and other established methods (MCR-ALS, SIMPLISMA, other ICA techniques) were made. Our results indicate that in most cases, MILCA is comparable or even outperforms other chemometrics methods taken for comparisons. The influence of different factors (abundance of components, noise, step of spectral scan, and scan speed) on decomposition performance has been investigated. The optimal conditions for spectroscopic registration have been identified. The proposed method was used for analysis of model mixtures and real objects (multivitamin drugs, food additives, and energy drinks). The resolved concentrations match well with the declared amounts and the results of reference methods.     

Methods of the decomposition of spectra of various origin in the analysis of complex mixtures

Different algorithms of the decomposition of spectral curves are compared by the precision of identification and quantitative analysis of complex mixtures. The available conventional methods of self-modeling curve resolution (SIMPLISMA, MCR-ALS) and algorithms implementing the independent component analysis (MILCA, SNICA) are used. The results are illustrated by a series of examples of different spectral signals (UV, IR, Raman, fluorescence).     

Comments on a recently published paper ‘some surprising properties of multivariate curve resolution‐alternating least squares (MCR‐ALS) algorithms’

Some of the results given in a recently published paper in this journal concerning some surprising properties of the multivariate curve resolution‐alternating least squares (MCR‐ALS) method are discussed. My results showed that the surprising properties of MCR‐ALS refer only to the slow linear convergence properties of ALS algorithms and to rounding error computer calculations. Results obtained by MCR‐ALS for the first data example were correct and no significant differences were observed in the resolved profiles. In the second more complex data example, large rotation ambiguities were present for the spectrum profile of the very minor second component which was not correctly estimated by MCR‐ALS. However, even in this case, the subspaces spanned by the MCR‐ALS solutions were also very close to the correct ones apart from slow convergence properties of the MCR‐ALS algorithm in this case. Copyright © 2009 John Wiley & Sons, Ltd.     

Application of maximum likelihood multivariate curve resolution to noisy data sets

In this work, two different maximum likelihood approaches for multivariate curve resolution based on maximum likelihood principal component analysis (MLPCA) and on weighted alternating least squares (WALS) are compared with the standard multivariate curve resolution alternating least squares (MCR‐ALS) method. To illustrate this comparison, three different experimental data sets are used: the first one is an environmental aerosol source apportionment; the second is a time‐course DNA microarray, and the third one is an ultrafast absorption spectroscopy. Error structures of the first two data sets were heteroscedastic and uncorrelated, and the difference between them was in the existence of missing values in the second case. In the third data set about ultrafast spectroscopy, error correlation between the values at different wavelengths is present. The obtained results confirmed that the resolved component profiles obtained by MLPCA‐MCR‐ALS are practically identical to those obtained by MCR‐WALS and that they can differ from those resolved by ordinary MCR‐ALS, especially in the case of high noise. It is shown that methods that incorporate uncertainty estimations (such as MLPCA‐ALS and MCR‐WALS) can provide more reliable results and better estimated parameters than unweighted approaches (such as MCR‐ALS) in the case of the presence of high amounts of noise. The possible advantage of using MLPCA‐MCR‐ALS over MCR‐WALS is then that the former does not require changing the traditional MCR‐ALS algorithm because MLPCA is only used as a preliminary data pretreatment before MCR analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Quantitative iterative target transformation factor analysis

Traditionally, improvement of the constrained alternating least squares (ALS) solution has been executed by the addition of a priori information in the initial estimates and or constraints. However, there are cases where this information simply does not exist or is impossible to acquire under the process conditions. Therefore, new strategies are required to produce starting estimates close to the actual solution without the need of a priori information. Quantitative iterative target transformation factor analysis (QITTFA) is developed as a solution to this problem. The QITTFA approach combines the strengths of both iterative target transformation factor analysis (ITTFA) and simple‐to‐use interactive self‐modelling mixture analysis (SIMPLISMA) to (1) produce a solution space spanned by the independent factors such that the variance contribution due to noise is reduced, (2) to iteratively refine the solutions space prior to ALS and (3) to select the most pure variables from the refined solution space using the purity criterion. It has been observed that the QITTFA approach markedly improves the conventional SIMPLISMA and second derivative SIMPLISMA performance in the presence and absence of selectivity. In addition, components of differing spectral characteristics (narrow or broad spectral features) can be resolved, without a priori knowledge of the shapes of the pure components. This has been demonstrated with a simulated high performance liquid chromatography‐diode array detection (HPLC‐DAD) dataset, a laboratory‐based UV–Vis calibration dataset and a gaseous near infrared (NIR) dataset from an industrial process. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of modern chemometric methods to the study of equilibria in solutions

The possibility of the spectrometric-chemometric study of equilibria in solutions is demonstrated for substances with strongly overlapping spectra, in particular, using the independent component analysis (MILCA and SIMPLISMA algorithms) and the alternating least squares algorithm (MCR-ALS). Using the chemometric approach allows one to resolve spectral curves, identify species present in the solution, and calculate the characteristics of equilibria. The proposed approach is illustrated on a series of examples (study of a tautomeric equilibrium and complexation reactions).     

On the implementation of spatial constraints in multivariate curve resolution alternating least squares for hyperspectral image analysis

Hyperspectral imaging (HSI) is a method for exploring spatial and spectral information associated with the distribution of the different compounds in a chemical or biological sample. Amongst the multivariate image analysis tools utilized to decompose the raw data into a bilinear model, multivariate curve resolution alternating least squares (MCR‐ALS) can be applied to obtain the distribution maps and pure spectra of the components of the sample image. However, a requirement is to have the data in a two‐way matrix. Thus, a preliminary step consists of unfolding the raw HSI data into a single‐pixel direction. Consequently, through this data manipulation, the information regarding pixel neighboring is lost, and spatial information cannot directly be constrained on the component profiles in the current MCR‐ALS algorithm. In this short communication, we propose an adaptation of the MCR‐ALS framework, enabling the potential implementation of any variation of spatial constraint. This can be achieved by adding, at each least‐squares step, refolding/unfolding of the distribution maps for the components. The implementation of segmentation, shape smoothness, and image modeling as spatial constraints is proposed as a proof of concept. Copyright © 2015 John Wiley & Sons, Ltd.     

Second‐Order Data Obtained from Differential Pulse Voltammetry: Determination of Lead in River Water Using Multivariate Curve Resolution‐Alternating Least‐Squares (MCR‐ALS)

Multivariate curve resolution by alternating least squares (MCR‐ALS) with the aim of achieving the electrochemical second order advantage has been applied to potential‐time second‐order data. In this work a simple way is reported as a first approach towards generation of the instrumental electrochemical second‐order data by differential pulse voltammetry (DPV). A linear dependency exists in the pulse duration profiles of the electroactive species in the mixture samples. Rank deficiency of the mixture data matrix is broken by matrix augmentation. Due to existence of potential shift in the obtained data, MCR‐ALS could not be achieved the convergence on the augmented data. So this shift was corrected with potential shift correction algorithm. Results of MCR‐ALS after shift correction show that the proposed method could be efficiently used for determination of Pb²⁺ in the presence of unexpected interferents in the river water sample.     

Multivariate curve resolution of mixed bacterial DNA sequence spectra: identification and quantification of bacteria in undefined mixture samples

A comprehensive understanding of factors that influence microbial competition and cooperation, their diversity and processes will be greatly beneficial in many research areas. Current tools for microflora determinations are far from suitable for high‐throughput monitoring of development in complex microbial communities. Here, we describe the application of a calibration free method, multivariate curve resolution with alternating least squares (MCR‐ALS), for identification and quantification of different microbes in mixture samples. The idea is to utilize MCR‐ALS to enable close monitoring of ecology in a variety of microbial communities. The data from two designed experiments consisting of DNA sequence spectra measured on mixtures were analysed with MCR‐ALS using no prior information on the data except for appropriate constraints, such as non‐negativity and closure. The results were compared both to the known true concentrations as well as to the results obtained from the well‐established multivariate calibration method partial least squares (PLS) regression. MCR‐ALS performed as well as PLS regression, successfully extracting all pure bacterial spectra and quantitative information on these, with 97.81% and 97.91% explained variance for the first and the second data set, respectively. Copyright © 2008 John Wiley & Sons, Ltd.     

A Multivariate Curve Resolution Approach to the Study of the Degradation Kinetics of Valsartan under Photolytic and Acid Conditions

The analysis of UV‐spectrophotometric data with second‐order chemometrics techniques, including multivariate curve resolution with alternating least‐squares (MCR‐ALS) and hybrid hard‐ and soft MCR (HS‐MCR), was examined as an alternative tool for studying the kinetics of drug degradation under stress conditions, employing valsartan (VAL) as a model drug. Despite small structural and spectroscopic differences between VAL and its degradation products, MCR‐ALS and HS‐MCR were able to detect the generation of two photoneutral degradation products (DP‐1 and DP‐2) and a single acid hydrolysis product (DP‐3), providing good approximations to their pure spectra and concentration profiles, from which estimations of the kinetic profiles and rate constants were obtained. Kinetic models based on first‐order reactions explained the degradation processes. MCR‐ALS and HS‐MCR analyses yielded similar rate constants; however, the latter was capable of more properly fitting the experimental data to a kinetic model in the case of drug photolysis. The results were confirmed by comparison with data obtained by HPLC analysis of the degraded samples.     

Application of multivariate curve resolution methods to on-flow LC-NMR

The application of evolving window factor analysis (EFA), subwindow factor analysis (SFA), iterative target transformation factor analysis (ITTFA), alternating least squares (ALS), Gentle, automatic window factor analysis (AUTOWFA) and constrained key variable regression (CKVR) to resolve on-flow LC-NMR data of eight compounds into individual concentration and spectral profiles is described. CKVR has been reviewed critically and modifications are suggested to obtain improved results. A comparison is made between three single variable selection methods namely, orthogonal projection approach (OPA), simple-to-use interactive self-modelling mixture analysis approach (SIMPLISMA) and simplified Borgen method (SBM). It is demonstrated that LC-NMR data can be resolved if NMR peak cluster information is utilised.     

Rejoinder to ‘Comments on a recently published paper “Some surprising properties of multivariate curve resolution‐alternating least squares (MCR‐ALS) algorithms”’

This rejoinder addresses comments recently published in this journal on the paper titled ‘Some surprising properties of multivariate curve resolution‐alternating least squares (MCR‐ALS) algorithms’. It is explained again that the revealed discrepancy of MCR‐ALS algorithms, i.e. the sub‐ and even the final solutions can be outside the range of the data matrix, does exist and this theoretical fact could not be refuted by Tauler. Copyright © 2009 John Wiley & Sons, Ltd.     

Independent component analysis and its applications in signal processing for analytical chemistry

Independent component analysis (ICA) is a statistical method the goal of which is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible. In an ICA procedure, the estimated independent components (ICs) are identical to or highly correlated to the spectral profiles of the chemical components in mixtures under certain circumstances, so the latent variables obtained are chemically interpretable and useful for qualitative analysis of mixtures without prior information about the sources or reference materials, and the calculated demixing matrix is useful for simultaneous determination of polycomponents in mixtures. We review commonly used ICA algorithms and recent ICA applications in signal processing for qualitative and quantitative analysis. Furthermore, we also review the preprocessing method for ICA applications and the robustness of different ICA algorithms, and we give the empirical criterion for selection of ICA algorithms in signal processing for analytical chemistry.     

Simultaneous Anodic Stripping Voltammetric Determination of Pb and Cd,Using a Vibrating Gold Microwire Electrode,Assisted by Chemometric Techniques

Simultaneous anodic stripping voltammetric determination of Pb and Cd is restricted on gold electrodes as a result of the overlapping of these two peaks. This work describes the quantitative determination of a binary mixture system of Pb and Cd, at low concentration levels (up to 15.0 and 10.0 µg L^?1 for Pb and Cd, respectively) by differential pulse anodic stripping voltammetry (DPASV; deposition time of 30 s), using a green electrode (vibrating gold microwire electrode) without purging in a chloride medium (0.5 M NaCl) under moderate acidic conditions (HCl 1.0 mM), assisted by chemometric tools. The application of multivariate curve resolution alternating least squares (MCR‐ALS) for the resolution and quantification of both metals is shown. The optimized MCR‐ALS models showed good prediction ability with concentration prediction errors of 12.4 and 11.4 % for Pb and Cd, respectively. The quantitative results obtained by MCR‐ALS were compared to those obtained with partial least squares (PLS) and classical least squares (CLS) regression methods. For both metals, PLS and MCR‐ALS results are comparable and superior to CLS. For Cd, as a result of the peak shift problem, the application of CLS was unsuitable. MCR‐ALS provides additional advantage compared to PLS since it estimates the pure response of the analytes signal. Finally, the built up multivariate calibration models, based either in MCR‐ALS or PLS regression, allowed to quantify concentrations of Pb and Cd in surface river water samples, with satisfactory results.     

Real-time two-dimensional wavelet compression and its application to real-time modeling of ion mobility data

Real-time data analysis is important in many applications. However, many chemometric algorithms have difficulty processing data in real-time. A novel real-time two-dimensional wavelet compression (WC²) has been developed to compress data as it is acquired from analytical instrumentation. The WC algorithm was enhanced so that data with an arbitrary number of points were compressed, and truncation or padding to a dyadic number was avoided. After compression, the noise level is reduced while useful chemical information is retained. A modified simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) algorithm was applied to the wavelet-compressed data and the model was transformed back to the original representation while leaving the data compressed. The reduced size of the wavelet-compressed data furnished a faster implementation of SIMPLISMA that facilitates real-time acquisition.

This real-time WC²-SIMPLISMA algorithm was applied to the rapid identification of explosives by ion mobility spectrometry (IMS). SIMPLISMA resolved concentration profiles and component spectra were displayed simultaneously while the data was acquired from an ion mobility spectrometer with a LabVIEW virtual instrument (VI).     

Comparative Study of Hard‐ and Soft‐Modeling Algorithms for Kinetic Data Processing

This article critically compares the efficacy of three algorithms, namely Alternating Least‐squares Multi Curve Resolution (ALS‐MCR), Hard Modeling Alternating Least‐squares (HM‐ALS), and classical Hard Modeling Multi Curve Resolution (HM‐MCR) in finding the true values of rate constants associated with a kinetic model. Simulated experiments on the simple system () indicate that soft‐modeling ALS‐MRC methodology, which is subject only to linear constraints, does not ensure that experimental responses are correctly deconvolved, thus preventing further calculations to determine the true rate constants. Inclusion of the kinetic model in the ALS scheme, which gives rise to the HM‐ALS methodology, was found to yield a correct assessment of the rate coefficients but had a large computational cost. Numerical experiments employing a more complex model () were also carried out, mainly to evaluate strategies for performing efficient searches on multidimensional multimodal least‐squares surfaces using HM‐ALS and HM‐MCR. This study again revealed the efficiency and reliability of classical HM‐MCR methods. Results from simulations were corroborated by analysis of data from an experimental study of chromate reduction by hydrogen peroxide; the mechanism of which is similar in complexity to those considered in simulations. The present work suggests that HM‐MCR algorithms implementing a multiminimum search strategy are the method of choice for analyzing two‐dimensional kinetic data.     

Processing of NMR,UV, and IR spectrometric data prior to chemometric simulation by independent component and principal component analysis

We consider methods for the mathematical preprocessing of signals in the spectrometric analysis of multicomponent mixtures using chemometric algorithms aimed at adjusting the baseline, experimental noise, and random shift of spectral bands. Practical examples of using simple mathematical operations (scaling, centering, derivatization) are given. The effectiveness of algorithms is illustrated by a wide range of spectroscopic signals (electronic absorption, IR, and NMR spectra) combined with chemometric methods of principal component analysis and independent component analysis.     

Deprotonative Metalation of Substituted Benzenes and Heteroaromatics Using Amino/Alkyl Mixed Lithium–Zinc Combinations

Different homoleptic and heteroleptic lithium–zinc combinations were prepared, and structural elements obtained on the basis of NMR spectroscopic experiments and DFT calculations. In light of their ability to metalate anisole, pathways were proposed to justify the synergy observed for some mixtures. The best basic mixtures were obtained either by combining ZnCl₂ ? TMEDA (TMEDA=N,N,N′,N′‐tetramethylethylenediamine) with [Li(tmp)] (tmp=2,2,6,6‐tetramethylpiperidino; 3 equiv) or by replacing one of the tmp in the precedent mixture with an alkyl group. The reactivity of the aromatic lithium zincates supposedly formed was next studied, and proved to be substrate‐, base‐, and electrophile‐dependent. The aromatic lithium zincates were finally involved in palladium‐catalyzed cross‐coupling reactions with aromatic chlorides and bromides.     

Chemometric resolution of ATR-IR spectra data for polycondensation reaction of bis(hydroxyethylterephthalate) with a combination of self-modeling curve resolution (SMCR) and local rank analysis

Self-modeling curve resolution (SMCR) methods, simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) and alternating least squares (ALS) were used to calculate pure concentration profiles and pure spectra for the two-way spectral data collected during the on-line polycondensation reaction of bis(hydroxyethylterephthalate) with an ATR-FT-IR spectrometer. In order to improve the resolution results, SIMPLISMA was combined with local rank analysis method, fixed size moving window evolving factor analysis (FSMWEFA) to search for selective regions of various components and then look for the purest wavenumber variables in the selective regions. Such combination allows more accurate determination of the number of chemical components in the reaction system and the calculations of more accurate concentration profiles and spectra.