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.     

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.     

Voltammetric,UV–Vis Spectrometric and Fluorescence Study of the Interaction of Ractopamine and DNA with the Aid of Multivariate Curve Resolution‐Alternating Least Squares

Interaction of a steroid drug, Ractopamine (RAC), and DNA was investigated by electroanalysis‐differential pulse and cyclic voltammetry (DPV and CV), and UV‐vis and fluorescence spectroscopy. DPV showed that RAC intercalated with DNA, and CV indicated that the reaction mechanism of RAC and dsDNA involved irreversible oxidation with the loss of two H⁺ and a transfer of two electrons. Reaction binding parameters were obtained. Pure spectra of RAC, DNA and the RAC‐DNA complex, and their concentrations were extracted by multivariate curve resolution‐alternating least squares method (MCR‐ALS). Concentration profiles indicated quantitatively the course of the reaction.     

Complexation of Hg2+ with α‐Lipoic and Dihydrolipoic Acids: Study by Differential Pulse Voltammetry on Rotating Au‐Disk Electrode and ESI‐MS

The complexation of the natural antioxidants α‐lipoic acid (ALA) and its reduced form dihydrolipoic acid (DHLA) with Hg²⁺ was investigated by a recently proposed differential pulse voltammetric (DPV) method using the rotating Au‐disk electrode. Complexation processes are proposed from the multivariate curve resolution by alternating least squares (MCR‐ALS) analysis of DPV titration data. Main complexes were both 1 : 1 Hg : ALA and Hg : DHLA, although the formation of 1 : 2 complexes can be also deduced. ALA and DHLA show different Hg²⁺‐binding patterns at different pH. Voltammetric findings are completed with the data obtained by electrospray ionization mass‐spectrometry (ESI‐MS), especially in negative mode.     

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.     

Principal component analysis with boundary constraints

Observed data often belong to some specific intervals of values (for instance in case of percentages or proportions) or are higher (lower) than pre‐specified values (for instance, chemical concentrations are higher than zero). The use of classical principal component analysis (PCA) may lead to extract components such that the reconstructed data take unfeasible values. In order to cope with this problem, a constrained generalization of PCA is proposed. The new technique, called bounded principal component analysis (B‐PCA), detects components such that the reconstructed data are constrained to belong to some pre‐specified bounds. This is done by implementing a row‐wise alternating least squares (ALS) algorithm, which exploits the potentialities of the least squares with inequality (LSI) algorithm. The results of a simulation study and two applications to bounded data are discussed for evaluating how the method and the algorithm for solving it work in practice. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Resolution and identification of co‐eluting alkylphenols in comprehensive two‐dimensional gas chromatography–mass spectrometry by multivariate curve resolution‐alternating least squares

The interest in the analysis of alkylphenols (APs) has widely increased in the last decades because of the endocrine disrupting features of these phenol derivatives. However, the isolation and identification of many of the multiple chemical structures of all APs is a very challenging task because of their similar physicochemical properties. In this work, the co‐elution of the isomers present in technical mixtures and using comprehensive two‐dimensional gas chromatography coupled to quadrupole mass spectrometry was resolved using multivariate curve resolution‐alternating least squares algorithm. The mass spectrum of each resolved compound was compared with the theoretical mass spectrum obtained from the literature, in order to assign the appropriate identification of each isomer. Two commercial mixtures were studied; in one of them, 34 compounds were resolved, and in the second mixture, 40 compounds were resolved. The relative abundances of the compounds were also calculated in both mixtures. Copyright © 2015 John Wiley & Sons, Ltd.     

Estimation of rotation ambiguity in multivariate curve resolution with charged particle swarm optimization (cPSO‐MCR)

Rotation ambiguity (RA) in multivariate curve resolution (MCR) is an undesirable case, when the physicochemical constraints are not sufficiently strong to provide a unique resolution of the data matrix of the mixtures into spectra and concentration profiles of individual chemical components. RA is often met in MCR of overlapped chromatographic peaks, kinetic and equilibrium data, and fluorescence two‐dimensional spectra. In case of RA, a single candidate solution has little practical value. So, the whole set of feasible solutions should be characterized somehow. It is a quite intricate task in a general case. In the present paper, a method was proposed to estimate RA with charged particle swarm optimization (cPSO), a population‐based algorithm. The criteria for updating the particles were modified, so that the swarm converged to the steady state, which spanned the set of feasible solutions. The performance of cPSO‐MCR was demonstrated on test functions, simulated datasets, and real‐world data. Good accordance of the cPSO‐MCR results with the analytical solutions (Borgen plots) was observed. cPSO‐MCR was also shown to be capable of estimating the strength of the constraints and of revealing RA in noisy data. As compared with analytical methods, cPSO‐MCR is simpler to implement, expands to more than three chemical compounds, is immune to noise, and can be easily adapted to virtually all types of constraints and objective functions (constraint based or residue based). cPSO‐MCR also provides natural visual information about the level of RA in spectra and concentration profiles, similar to the methods of two extreme solutions (e.g., MCR‐BANDS). Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Assessment of maximum likelihood PCA missing data imputation

Maximum likelihood principal component analysis (MLPCA) was originally proposed to incorporate measurement error variance information in principal component analysis (PCA) models. MLPCA can be used to fit PCA models in the presence of missing data, simply by assigning very large variances to the non‐measured values. An assessment of maximum likelihood missing data imputation is performed in this paper, analysing the algorithm of MLPCA and adapting several methods for PCA model building with missing data to its maximum likelihood version. In this way, known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR) methods are implemented within the MLPCA method to work as different imputation steps. Six data sets are analysed using several percentages of missing data, comparing the performance of the original algorithm, and its adapted regression‐based methods, with other state‐of‐the‐art methods. Copyright © 2016 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.     

Efficient recovery of electrophoretic profiles of nucleoside metabolites from urine samples by multivariate curve resolution

Chemometric techniques usually employed in purity assessment and resolution of multicomponent peaks have been applied to analytical data from complex biological samples obtained with CE‐DAD. In the assessment of the purity of the electrophoretic peaks, the orthogonal projection approach, the orthogonal projection approach with Durbin–Watson criterion, and the simple‐to‐use interactive self‐modeling mixture analysis method have been employed. Multivariate curve resolution with alternating least squares has been successfully implemented to resolve co‐migrating peaks of metabolites in CE‐DAD and to recover qualitative and quantitative information about co‐migrating components of urine extract. The main challenge consisted of developing high‐quality multivariate curve resolution with alternating least squares models of multicomponent peaks acquired during the CE analysis of nucleoside patterns in 18 urine samples. The recovered ultraviolet visible (UV–Vis) spectra have been employed to identify additional nucleosides, such as 1‐methylinosine, 2‐methylguanosine, and 1‐methylguanosine, whose presence in the metabolic profile produced by the applied CE‐DAD method has not yet been recognized. Concentration profiles of these compounds can be used in metabonomic studies.     

Resolution of overlapping capillary electrophoresis peaks by using chemometric analysis: quantification of the components in compound reserpine tablets

The application of multivariate curve resolution with alternating least squares (MCR-ALS) methods to second-order data from capillary electrophoresis with diode array detector (CE-DAD) is reported. Initial qualitative solutions obtained by evolving factor analysis (EFA) and pure-variable detection method can be further optimized by a simultaneous analysis of multiple electrophoresis run data with ALS regression. While unknown samples are analyzed simultaneously against the corresponding standards in different composition ratios, the exact amounts of common components in different CE runs can be determined by the traditional calibration curve method, and quantification can thus be achieved. The above methods are applied to the determination of the components in compound reserpine tablets in overlapping peaks from CE. The quantification results are compared with those of the first derivative of the electropherogram method and artificial neural network (ANN) method.     

Analysis of Complex Molecular Systems: The Impact of Multivariate Analysis for Resolving the Interactions of Small Molecules with Biopolymers – a Review

This review is focused on the impact of chemometrics for resolving data sets collected from investigations of the interactions of small molecules with biopolymers. These samples have been analyzed with various instrumental techniques, such as fluorescence, ultraviolet–visible spectroscopy, and voltammetry. The impact of two powerful and demonstrably useful multivariate methods for resolution of complex data—multivariate curve resolution–alternating least squares (MCR–ALS) and parallel factor analysis (PARAFAC)—is highlighted through analysis of applications involving the interactions of small molecules with the biopolymers, serum albumin, and deoxyribonucleic acid. The outcomes illustrated that significant information extracted by the chemometric methods was unattainable by simple, univariate data analysis. In addition, although the techniques used to collect data were confined to ultraviolet–visible spectroscopy, fluorescence spectroscopy, circular dichroism, and voltammetry, data profiles produced by other techniques may also be processed. Topics considered including binding sites and modes, cooperative and competitive small molecule binding, kinetics, and thermodynamics of ligand binding, and the folding and unfolding of biopolymers. Applications of the MCR–ALS and PARAFAC methods reviewed were primarily published between 2008 and 2013.     

Applications of maximum likelihood principal component analysis: incomplete data sets and calibration transfer

The application of a new method to the multivariate analysis of incomplete data sets is described. The new method, called maximum likelihood principal component analysis (MLPCA), is analogous to conventional principal component analysis (PCA), but incorporates measurement error variance information in the decomposition of multivariate data. Missing measurements can be handled in a reliable and simple manner by assigning large measurement uncertainties to them. The problem of missing data is pervasive in chemistry, and MLPCA is applied to three sets of experimental data to illustrate its utility. For exploratory data analysis, a data set from the analysis of archeological artifacts is used to show that the principal components extracted by MLPCA retain much of the original information even when a significant number of measurements are missing. Maximum likelihood projections of censored data can often preserve original clusters among the samples and can, through the propagation of error, indicate which samples are likely to be projected erroneously. To demonstrate its utility in modeling applications, MLPCA is also applied in the development of a model for chromatographic retention based on a data set which is only 80% complete. MLPCA can predict missing values and assign error estimates to these points. Finally, the problem of calibration transfer between instruments can be regarded as a missing data problem in which entire spectra are missing on the ‘slave’ instrument. Using NIR spectra obtained from two instruments, it is shown that spectra on the slave instrument can be predicted from a small subset of calibration transfer samples even if a different wavelength range is employed. Concentration prediction errors obtained by this approach were comparable to cross-validation errors obtained for the slave instrument when all spectra were available.     

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.     

Multivariate curve resolution modeling of liquid chromatography-mass spectrometry data in a comparative study of the different endogenous metabolites behavior in two tomato cultivars treated with carbofuran pesticide

A metabonomic study based on the application of multivariate curve resolution and alternating least squares (MCR-ALS) to three-way data sets obtained by liquid chromatography coupled to mass spectrometry detection (LC-MS) was carried out for Rambo and Raf tomato cultivars treated with carbofuran pesticide. Samples were picked up during a 21 days period after treatment and analyzed by LC-MS in scan mode, along with the corresponding blank samples. Then, MCR-ALS was applied to the three-way data sets using column wise augmented matrices, and the evolutionary profiles as a function of the time after treatment were estimated for the metabolites present in both cultivars, as well as their corresponding pure spectra estimations. A comparative study using those estimations showed that some of these metabolites followed different behavior for the different cultivars after treatment. Since all treated and untreated Rambo and Raf samples were picked up according to the same sampling protocol and in a similar state of maturation, any difference in the behavior between profiles can be interpreted as an effect due to the presence of pesticide and to the kind of cultivar. Based on this hypothesis, several PLS-DA approaches were tested to check if it would be possible to classify samples by using the metabolites MCR estimations. Results showed that PLS-DA models for classification of treated or non-treated (blank) samples were the best ones obtained (98.44% of correct classifications for the validation set), which supports the stress effects related to carbofuran treatment. In addition, excellent discrimination among the four groups could be attained (89.06% of correct classifications for the validation set).