Problem of mixtures with known compositions and IRONFLEA method for multivariate curve resolution

A special case of gray spectral data systems [(a) F.-T. Chau, Y.-Z. Liang, J. Gao, X.-G. Shao (Eds.), Chemometrics: From Basics to Wavelet Transform, Chemical Analysis Series, vol. 164, John Wiley & Sons, Inc., 2004; (b) Y.Z. Liang, O.M. Kvalheim, R. Manne, Chemom. Intell. Lab. Syst. 18 (1993) 235-250] is discussed here and the least-squares method for the multivariate curve resolution (MCR) named IRONFLEA is proposed. The system under consideration is the bilinear spectral data of the samples with known chemical compositions and unknown concentration matrix. If the spectra of samples (A_i) and (Q + A_i) (i = 1, …, n, n ≥ 2) are available, then the spectrum and the concentrations of Q could be found and the solution is unique. A practical chemical model for this problem could be mixtures, polymers, peptides, oligosaccharides, or supramolecular formations made of a limited number of monomeric components. In the cases of polymeric or oligomeric samples the spectral contributions and the concentrations of the particular monomeric units are extracted. The method is capable of extracting chemically meaningful spectra of components. The method is implemented in SAS IML code and tested for the deconvolution of spectra of polymers made of styrene derivatives with known monomeric compositions [(a) H. Fenniri, L. Ding, A.E. Ribbe, Y. Zyrianov, J. Am. Chem. Soc. 123 (2001) 8151-8152; (b) H. Fenniri, S. Chun, L. Ding, Y. Zyrianov, K. Hallenga, J. Am. Chem. Soc. 125 (2003) 10546-10560]. The method performs calculations fast enough to allow the incorporation of leave-one-out outlier removal procedure.     

Curing reaction of glycidylthioether resins: Kinetic model study by near infrared spectroscopy and multivariate curve resolution

The reactivity of sulfur‐based epoxy monomers was studied by monitoring of a model system involving phenylglycidylthioether and aniline. The reaction was carried out under isothermal conditions and monitored in situ by near infrared spectroscopy. Using multivariate curve resolution‐alternating least squares made it possible to obtain the concentration and spectral profiles of each species throughout the reaction. To obtain the kinetic rate constants, the values of the recovered concentration profiles were fitted to a kinetic model proposed for the reaction. Reactivity was evaluated by comparing the concentration profiles and kinetic rate constants obtained with the same parameters obtained for phenylglycidylether/aniline as a reference system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4846–4856, 2006     

Parametric signal fitting by gaussian peak adjustment: A new multivariate curve resolution method for non-bilinear voltammetric measurements

A new methodology based on the fitting of signals to parametric functions is proposed for the multivariate curve resolution (MCR) analysis of overlapping and peak-shaped voltammetric signals which progressively get broader or narrower and move along the potential axis, thus causing a dramatic loss of linearity. The method is based on the least squares fitting of gaussian functions at both sides of the peaks by using adjustable parameters for the peak height, position and symmetry. It consists of several home-made programs written in Matlab environment, which are freely available as supplementary material of the present work. The application to the systems Zn(II)–oxalate, and to the phytochelatin PC₅ in a wide pH range provides excellent results as compared to these of more conventional linear methods, which raises good expectations about future application to electrochemical and even non-electrochemical data.     

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.     

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.     

An approach for simultaneous estimation of reaction kinetics and curve resolution from process and spectral data

Parameter estimation of reaction kinetics from spectroscopic data remains an important and challenging problem. This study describes a unified framework to address this challenge. The presented framework is based on maximum likelihood principles, nonlinear optimization techniques, and the use of collocation methods to solve the differential equations involved. To solve the overall parameter estimation problem, we first develop an iterative optimization‐based procedure to estimate the variances of the noise in system variables (eg, concentrations) and spectral measurements. Once these variances are estimated, we then determine the concentration profiles and kinetic parameters simultaneously. From the properties of the nonlinear programming solver and solution sensitivity, we also obtain the covariance matrix and standard deviations for the estimated kinetic parameters. Our proposed approach is demonstrated on 7 case studies that include simulated data as well as actual experimental data. Moreover, our numerical results compare well with the multivariate curve resolution alternating least squares approach.     

Reactivity of silicon‐based epoxy monomers as studied by near‐infrared spectroscopy and multivariate curve resolution methods

The reaction of glycidyloxydimethylphenyl silane with aniline was used as a model system to study the reactivity of silicon‐based epoxy monomers. The reaction was monitored online by near‐infrared spectroscopy, and the evolution of the concentration of each species throughout the reaction was determined by the application of multivariate curve resolution/alternating least squares to the set of recorded spectra. The reactivity was evaluated by a comparison of the concentration profiles obtained for the glycidyloxydimethylphenyl silane/aniline system with those of phenylglycidyl ether/aniline as a reference system. The results confirmed that the reactivity of the silicon‐based epoxy monomer was higher and that its ring opening reaction was faster because of electronic effects. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1447–1456, 2006     

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.     

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.     

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.     

Two-dimensional correlation spectroscopy and multivariate curve resolution for the study of lipid oxidation in edible oils monitored by FTIR and FT-Raman spectroscopy

Accelerate oxidative degradation of six vegetable oils was monitored using FTIR and FT-Raman spectroscopy. Two-dimensional correlation spectroscopy and multivariate curve resolution alternating least squares (MCR-ALS) were applied to the analysis of the data. The use of hetero-spectral two-dimensional correlation of FTIR and FT-Raman data allowed the use of well established band assignments to interpret less clearly assigned spectral features. With a moving window approach it was possible to obtain simplified two-dimensional correlation maps and to detect compounds evolving with different kinetic. Simultaneous analysis of the oxidation experiments of the six different oils monitored by both spectroscopic techniques was performed using MCR-ALS. Although a complete resolution of the data was not possible, the spectral changes occurring during the oxidative degradation of the oils were described with a five-component model. The two fundamentally different chemometric approaches lead to coincident results.     

Chemistry at level of individual aerosol particle using multivariate curve resolution of confocal Raman image

Airborne particles with aerodynamic diameter in the 10-1 microm range have been collected in an industrial/urban zone by impaction and have been investigated by automated confocal Raman microspectrometry. The computer-microcontrolled XY scanning and Z focusing of Raman images provided many pixel Raman spectra which are characteristics of complex mixture at level of individual particle. The large heterogeneity was not resolved by the spatial resolution of the instrument which is limited by the optical diffraction. The severe spectral overlaps generated by heterogeneity were resolved by multivariate curve resolution (MCR) methods. The purity based method (SIMPLISMAX) was used to resolve both luminescence spectra and pure Raman spectra without prior information. The MCR-alternating least square (ALS) was used as a refined method of both spectra and spectral concentrations. The reconstructing Raman images of the respective spectral contribution supply a versatile potential to characterize the chemistry of atmospheric aerosols at the level of the individual particles.     

Response surface methodology based on central composite design accompanied by multivariate curve resolution to model gradient hydrophilic interaction liquid chromatography: Prediction of separation for five major opium alkaloids

Hydrophilic interaction liquid chromatography on bare silica presents some benefits for analysis and purification of ionizable basic alkaloids. This mode was used to separate five major opium alkaloids: morphine, codeine, thebaine, papaverine, and noscapine. Central composite design based on response surface methodology was applied for experimental design, modeling, and optimization in a single‐step gradient method. The main effects and their interactions (initial percentage of modifier, changing range of modifier in run time, pH of buffer, and its concentration) were investigated in 30 experiments. Multivariate curve resolution‐alternating least squares, by resolving overlapped curves, helped in the accurate calculation of baseline resolution factors to be modeled and optimized more accurately. Then three crucial resolution factors besides elution time were modeled in quadratic and cubic equations and optimized. In addition to the four factors, five extra logarithmic, and nonlogarithmic factors extracted from the four factors to give nine factors overall were inspected on mechanism of retention. It was shown that a linear combination consist of four independence variables successfully describes morphinans retentivity in a single‐step gradient method.     

Recent trends in application of multivariate curve resolution approaches for improving gas chromatography-mass spectrometry analysis of essential oils

Essential oils (EOs) are valuable natural products that are popular nowadays in the world due to their effects on the health conditions of human beings and their role in preventing and curing diseases. In addition, EOs have a broad range of applications in foods, perfumes, cosmetics and human nutrition. Among different techniques for analysis of EOs, gas chromatography-mass spectrometry (GC-MS) is the most important one in recent years. However, there are some fundamental problems in GC-MS analysis including baseline drift, spectral background, noise, low S/N (signal to noise) ratio, changes in the peak shapes and co-elution. Multivariate curve resolution (MCR) approaches cope with ongoing challenges and are able to handle these problems. This review focuses on the application of MCR techniques for improving GC-MS analysis of EOs published between January 2000 and December 2010. In the first part, the importance of EOs in human life and their relevance in analytical chemistry is discussed. In the second part, an insight into some basics needed to understand prospects and limitations of the MCR techniques are given. In the third part, the significance of the combination of the MCR approaches with GC-MS analysis of EOs is highlighted. Furthermore, the commonly used algorithms for preprocessing, chemical rank determination, local rank analysis and multivariate resolution in the field of EOs analysis are reviewed.     

Resolution of overlapped NMR spectra by two-way multivariate curve resolution alternating least squares with imbedded kinetic fitting

This paper describes the investigation of the hydrolysis of Ally, which is a sulfonylurea (SU) herbicide. The hydrolysis of this compound was observed in situ by nuclear magnetic resonance (NMR) spectroscopy. The data were analyzed using a two-way, multivariate curve resolution (MCR) technique. The resolution of the overlapping aromatic region of the product and the reactant was of special interest. The reactant, product and intermediate spectra were successfully resolved and the rate constants for the degradation of the herbicide under these conditions were simultaneously determined. The results of the chemometric resolution of the overlapped NMR data were compared to the rates found by using a liquid chromatographic method with diode array detection.     

Study of the degradation of 5-azacytidine as a model of unstable drugs using a stopped-flow method and further data analysis with multivariate curve resolution

A general strategy for the study of degradation processes of drugs based on stopped-flow monitoring in a flow system is proposed. The flow system consists of a two-channel manifold for pumping sample and buffer solutions, which join and mix in a PTFE coil (57 cm × 0.7 mm i.d). The flow is stopped when the sample reaches the detection cell and, then, the corresponding kinetic processes are monitored in the spectral range 200-300 nm using a UV-vis diode array spectrophotometer. 5-Azacytidine has been chosen as a model of unstable drugs to illustrate the possibilities of the procedure. Kinetic runs have been developed at temperatures in the range 25-80 °C and pH values from 2 to 11 in order to investigate the influence of these factors on the degradation of the pharmaceutical agent. Multivariate curve resolution based on alternating least squares has been used for the data treatment in order to obtain the kinetic and spectral profiles of species involved in the degradation as well as to calculate the kinetic constants. Results indicate that 5-azacytidine is moderately stable in acid solutions while quickly decomposes in alkaline media. In addition, the degradation is dramatically accelerated with increasing temperature.     

Study of acid-base properties of fulvic acids using fluorescence spectrometry and multivariate curve resolution methods

Samples of fulvic acids obtained from cultivated calcareous soils are analyzed using acid-base titrations with spectrofluorimetric detection. Observed changes in both synchronous and emission spectra of fulvic acids when pH is changed are explained in terms of a limited number of fluorescent contributions each defined by its specific fluorescent spectrum and a concentration profile (species distribution) recovered from the multivariate curve resolution analysis of experimental data. Information on equilibrium is estimated from concentrations of the acid-base species.     

Matrix merging arrangements for the study protein dynamics by time-resolved step-scan Fourier transform infrared spectroscopy and multivariate curve resolution

In this paper, we propose the construction of merging arrangements for combining the information from various runs as a powerful approach to improve the resolution. The bacteriorhodopsin (bR) photocycle has been chosen in this study as an example dealing with the protein dynamics monitored by means of time-resolved step-scan FT-IR spectroscopy. The possibilities of matrix merging are evaluated and results are compared with those from the analysis of individual and augmented matrices. As a conclusion, this strategy provides excellent results for the analysis of this type of time-resolved FT-IR data.     

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.     

Detection of malathion in food peels by surface-enhanced Raman imaging spectroscopy and multivariate curve resolution

An analytical methodology was developed for detection of malathion in the peels of tomatoes and Damson plums by surface-enhanced Raman imaging spectroscopy and multivariate curve resolution. To recover the pure spectra and the distribution mapping of the analyzed surfaces, non-negative matrix factorization (NMF), multivariate curve calibration methods with alternating least squares (MCR-ALS) and MCR with weighted alternating least square (MCR-WALS) were utilized. Error covariance matrices were estimated to evaluate the structure of the error over all the data. For the tomato data, NMF-ALS and MCR-ALS presented excellent spectral recovery even in the absence of initial knowledge of the pesticide spectrum. For the Damson plum data, owing to heteroscedastic noise, MCR-WALS produced better results. This methodology enabled detection below to the maximum residue limit permitted for this pesticide. This approach can be implemented for in situ monitoring because it is fast and does not require extensive manipulation of samples, making its use feasible for other fruits and pesticides as well.