Multivariate Curve Resolution Approach Research Articles

Multivariate curve resolution-soft independent modelling of class analogy (MCR-SIMCA)

BackgroundVarious classification, class modeling, and clustering techniques operate within abstract spaces, utilizing Principal Components (e.g., Linear Discriminant Analysis (LDA), Principal Component Analysis (PCA)) or latent variable spaces (e.g., Partial Least Squares Discriminant Analysis (PLS-DA)). It's important to note that PCA, despite being a mathematical tool, defines its Principal Components under certain mathematical constraints, it has a wide range of applications in the analysis of real-world systems. In this research, we assess the viability of employing the Multivariate Curve Resolution (MCR) subspace within class modeling techniques, as an alternative to the PC subspace. (92). ResultsThis study evaluates the use of the MCR subspace in class modeling methods, specifically in tandem with soft independent modeling of class analogy (SIMCA), to investigate the advantages of employing the meaningful physico-chemical subspace of MCR over the mathematical subspace of PCA. In the MCR-SIMCA strategy, the model is constructed by applying MCR to training samples from a target class. The MCR model effectively partitions the data into two smaller sub-matrices: the contribution matrix and the corresponding response matrix. In the next step, the contribution matrix resulting from the decomposition of the training set develops a distance plot (DP). First, the theory of the MCR-SIMCA model is discussed in detail. Next, two real experimental datasets were analyzed, and their performance was compared with the DD-SIMCA model. In most cases, the results were as good as or even more satisfactory than those obtained with the DD-SIMCA model. (146). SignificanceThe suggested class modeling method presents a promising avenue for the analysis of real-world natural systems. The study's results emphasize the practical utility of the MCR approach, underscoring the significance of the MCR subspace advantages over the PCA subspace. (39).

Linking MS1 and MS2 signals in positive and negative modes of LC-HRMS in untargeted metabolomics using the ROIMCR approach

Data-independent acquisition (DIA) mode in liquid chromatography (LC) high-resolution mass spectrometry (HRMS) has emerged as a powerful strategy in untargeted metabolomics for detecting a broad range of metabolites. However, the use of this approach also represents a challenge in the analysis of the large datasets generated. The regions of interest (ROI) multivariate curve resolution (MCR) approach can help in the identification and characterization of unknown metabolites in their mixtures by linking their MS1 and MS2 DIA spectral signals. In this study, it is proposed for the first time the analysis of MS1 and MS2 DIA signals in positive and negative electrospray ionization modes simultaneously to increase the coverage of possible metabolites present in biological systems. In this work, this approach has been tested for the detection and identification of the amino acids present in a standard mixture solution and in fish embryo samples. The ROIMCR analysis allowed for the identification of all amino acids present in the analyzed mixtures in both positive and negative modes. The methodology allowed for the direct linking and correspondence between the MS signals in their different acquisition modes. Overall, this approach confirmed the advantages and possibilities of performing the proposed ROIMCR simultaneous analysis of mass spectrometry signals in their differing acquisition modes in untargeted metabolomics studies.Graphical

Mutual information map as a new way for exploring the independence of chemically meaningful solutions in two-component analytical data

In the present contribution, a new approach based on mutual information (MI) is proposed for exploring the independence of feasible solutions in two component systems. Investigating how independent are different feasible solutions can be a way to bridge the gap between independent component analysis (ICA) and multivariate curve resolution (MCR) approaches and, to the best of our knowledge, has not been investigated before. For this purpose, different chromatographic and hyperspectral imaging (HSI) datasets were simulated, considering different noise levels and different degrees of overlap for two-component systems. Feasible solutions were then calculated by both grid search (GS) and Lawton-Sylvester (LS) plots. MI map which is the plot of MI vs. rotation matrix elements was used to estimate the degree of independence between different solutions. Inspection of the results showed that the different solutions in the feasible bands correspond to different MI values and that those values are lower for spectral profiles (more independent) than for concentration profiles (more dependent) as expected from the duality concept and the opposite is true. In addition, component profiles are found near more dependent solutions for concentration profiles and near less dependent solutions for spectral profiles which is due to the fact that “independence” constraint was applied to the spectral profiles in ICA algorithms. The performance of three well-known ICA algorithms (mean-field independent component analysis (MF-ICA), mutual information-based least dependent component analysis (MILCA) and joint approximate diagonalization of eigenmatrices (JADE)) as well as MCR-alternating least squares (MCR-ALS) were investigated. MI maps showed that the solutions of MF-ICA and MCR-ALS are in the feasible bands but the MILCA and JADE solutions which are just based on the independence maximization are outside the MI maps.

Effect of pH and temperature on physicochemical properties, aggregation behaviour and degradation kinetics of quercetin and baicalein in nearly aqueous media

Recently, flavonoids like quercetin and baicalein have drawn the attention of many researchers worldwide owing to their potential therapeutic applications. But they are still not used for biomedical purposes due to their low solubility and bioavailability. Moreover, there are very few reports available on various factors that can modulate the physicochemical properties of these flavonoids in an aqueous medium. This work explores the physicochemical behaviour of quercetin and baicalein in an aqueous medium under different solution conditions (like pH and temperature). UV–vis and fluorescence studies revealed that quercetin and baicalein show quite different optical properties from each other under same aqueous conditions. Quercetin undergoes autooxidation at alkaline pH and the rate of this autooxidation was enhanced at higher temperature whereas no autooxidation of baicalein was observed at any pH or temperature. Different anionic forms of quercetin and baicalein formed at different pH were characterized with the aid of density functional theory (DFT) and multivariate curve resolution (MCR) approach. Dynamic light scattering (DLS) studies suggest that temperature affects the particle size of both the flavonoids significantly and this aggregation phenomenon was observed to be reversible.

Quantification strategies for two-dimensional liquid chromatography datasets using regions of interest and multivariate curve resolution approaches

In this work, three chemometrics-based approaches are compared for quantification purposes when using two-dimensional liquid chromatography (LC×LC-MS), taking as a study case the quantification of amino acids in commercial drug mixtures. Although the approaches have been already used for one-dimensional gas or liquid chromatography, the main novelty of this work is the demonstration of their applicability to LC×LC-MS datasets. Besides, steps such as peak alignment and modelling, commonly applied in this type of data analysis, are not required with the approaches proposed here. In a first step, regions of interest (ROI) strategy is used for the spectral compression of the LC×LC-MS datasets. Then the first strategy consists of building a calibration curve from the areas obtained in this ROI compression step. Alternatively, the ROI intensity matrices can be used as input for a second analysis step employing the multivariate curve resolution alternating least squares (MCR-ALS) method. The main benefit of MCR-ALS is the resolution of elution and spectral profiles for each of the analytes in the mixture, even in the case of strong coelutions and high signal overlapping. Classical MCR-ALS based calibration curve from the peak areas resolved only applying non-negativity constraints (second strategy) is compared to the results obtained when an area correlation constraint is imposed during the ALS optimization (third strategy). All in all, similar quantification results were achieved by the three approaches but, especially in prediction studies, the more accurate quantification is obtained when the calibration curve is built from the peak areas obtained with MCR-ALS when the area correlation constraint is imposed.

State of Charge and State of Health Assessment of Viologens in Aqueous-Organic Redox-Flow Electrolytes Using In Situ IR Spectroscopy and Multivariate Curve Resolution.

Aqueous‐organic redox flow batteries (RFBs) have gained considerable interest in recent years, given their potential for an economically viable energy storage at large scale. This, however, strongly depends on both the robustness of the underlying electrolyte chemistry against molecular decomposition reactions as well as the device's operation. With regard to this, the presented study focuses on the use of in situ IR spectroscopy in combination with a multivariate curve resolution approach to gain insight into both the molecular structures of the active materials present within the electrolyte as well as crucial electrolyte state parameters, represented by the electrolyte's state of charge (SOC) and state of health (SOH). To demonstrate the general applicability of the approach, methyl viologen (MV) and bis(3‐trimethylammonium)propyl viologen (BTMAPV) are chosen, as viologens are frequently used as negolytes in aqueous‐organic RFBs. The study's findings highlight the impact of in situ spectroscopy and spectral deconvolution tools on the precision of the obtainable SOC and SOH values. Furthermore, the study indicates the occurrence of multiple viologen dimers, which possibly influence the electrolyte lifetime and charging characteristics.

Quantification Strategies for Two-Dimensional Liquid Chromatography Datasets Using Regions of Interest and Multivariate Curve Resolution Approaches

Quantification Strategies for Two-Dimensional Liquid Chromatography Datasets Using Regions of Interest and Multivariate Curve Resolution Approaches

Multivariate Curve Resolution Slicing of Multiexponential Time-Resolved Spectroscopy Fluorescence Data.

Time-resolved fluorescence spectroscopy (TRFS), i.e., measurement of fluorescence decay curves for different excitation and/or emission wavelengths, provides specific and sensitive local information on molecules and on their environment. However, TRFS relies on multiexponential data fitting to derive fluorescence lifetimes from the measured decay curves and the time resolution of the technique is limited by the instrumental response function (IRF). We propose here a multivariate curve resolution (MCR) approach based on data slicing to perform tailored and fit-free analysis of multiexponential fluorescence decay curves. MCR slicing, taking as a basic framework the multivariate curve resolution-alternating least-squares (MCR-ALS) soft-modeling algorithm, relies on a hybrid bilinear/trilinear data decomposition. A key feature of the method is that it enables the recovery of individual components characterized by decay profiles that are only partially describable by monoexponential functions. For TRFS data, not only pure multiexponential tail information but also shorter time delay information can be decomposed, where the signal deviates from the ideal exponential behavior due to the limited time resolution. The accuracy of the proposed approach is validated by analyzing mixtures of three commercial dyes and characterizing the mixture composition, lifetimes, and associated contributions, even in situations where only ternary mixture samples are available. MCR slicing is also applied to the analysis of TRFS data obtained on a photoswitchable fluorescent protein (rsEGFP2). Three fluorescence lifetimes are extracted, along with the profile of the IRF, highlighting that decomposition of complex systems, for which individual isomers are characterized by different exponential decays, can also be achieved.

Untargeted analysis of TD-NMR signals using a multivariate curve resolution approach: Application to the water-imbibition kinetics of Arabidopsis seeds

The aim of this study is to investigate the ability of Time-Domain Nuclear Magnetic Resonance (TD-NMR) combined with Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) analysis to detect changes in hydration properties of nineteen genotypes of Arabidopsis (Arabidopsis thaliana) seeds during the imbibition process.The Hybrid hard and Soft modelling version of MCR-ALS (HS-MCR) applied to raw TD-NMR data allowed the introduction of kinetic models to elucidate underlying biological mechanisms. The imbibition process of all investigated hydrated Arabidopsis seeds could be described with a kinetic model based on two consecutive first-order reactions related to an initial absorption of water from the bulk around the seed and a posteriori hydration of the internal seed tissues, respectively. Good data fit was achieved (LOF % = 0.98 and r2% = 99.9), indicating that the hypothesis of the selected kinetic model was correct. An interpretation of the mucilage characteristics of the studied Arabidopsis seeds was also provided.The presented methodology offers a novel and general strategy to describe in a comprehensive way the kinetic process of plant tissue hydration in a screening objective. This work also proves the potential of the MCR methods to analyse raw TD-NMR signals as alternative to the controversial and time-consuming pre-processing techniques of this kind of data, known to be an ill-conditioned and ill-posed problem.

NMF-Based Spectral Deconvolution with a Web Platform GC Mixture Touch.

Complete separation of chemicals in a complex mixture is far from being achieved even with the current high-performance separation technology, such as gas chromatography–mass spectrometry (GC–MS). Several deconvolution techniques based on multivariate curve resolution (MCR), or model peak methods, which are represented by AMDIS, have been developed to address the above-mentioned issue. The model peak methods have been developed to provide easy-to-use tools, including AMDIS, but are limited for MCR with approximation methods. The objective of this study was to provide an easy-to-use deconvolution tool based on the MCR approach for GC–MS data. The spectral deconvolution tool based on non-negative matrix factorization (NMF), which calculates outputs using an approximation method, was implemented as a free web platform, namely, GC Mixture Touch, clarifying the effects of the parameters required for the deconvolution. The GC Mixture Touch was applied to the actual mixture sample of road dust spiked with chemical standards. The recommended parameter settings for smoothing of the chromatogram, the number of ranks, and the NMF algorithm for the deconvolution were clarified through the study. The performance with the suggested parameters was evaluated with respect to compound identification for the actual sample. All of the test compounds in the sample were correctly identified with the GC Mixture Touch, outperforming AMDIS with respect to the identification. The GC Mixture Touch is easy to use on the web even for users without programming skills. This is expected to enhance the application of the NMF-based deconvolution, and it should prove helpful in finding the compounds hidden in complex mixtures that are difficult to find using conventional approaches.

A comparative study of MCR-based kinetic analyses for chemical reaction systems with rate constant ambiguities

The results of multivariate curve resolution (MCR) methods, specially solution’s ambiguity, can be influenced by the chosen MCR approach. We compare three MCR tools that support kinetic modeling in order to investigate this influence. These methods are Hard-Soft-Multivariate Curve Resolution, Multivariate Curve Resolution-Net Analyte Signal and a FACPACK implementation of a hard-modeling approach. As a common roof the more general approach of computing the set of feasible rate constants is used as implemented in the FACPACK kinetic hard-modeling software. The focus is on the comparison of the determined reaction rate constants and the occurrence of the corresponding solution ambiguities.Three spectroscopic data sets are considered in this study: First, an alkaline hydrolysis (UV–Vis) with a two-step consecutive first-order mechanism is used as a reference system. No rate constant ambiguity is present and all MCR methods give comparable, consistent results. The second data set concerns a formation of an iridium acyl complex (FTIR) based on a two-component reversible mechanism. Herein, k1 and k−1 (in h−1) range between 2.0 ​× ​10−3 ​− ​3.0 ​× ​10−3 and 3.0 ​× ​10−4 ​− ​9.0 ​× ​10−4, respectively. Due to similar data and model fit errors below 1%, it is not possible to distinguish the solutions. The reaction of 3-chlorophenylhydrazonopropane dinitrile with 2-mercaptoethanol (UV–Vis) based on a three-component partially reversible mechanism is the third studied data set. The resolved rate constants k1, k−1 and k2 (in min−1) range between 1.89 ​× ​10−1 ​− ​2.30 ​× ​10−1, 6.12 ​× ​10−2 ​− ​9.71 ​× ​10−2 and 3.83 ​× ​10−2 ​− ​4.48 ​× ​10−2, respectively. Analogous to the second data set an intrinsic rate constant ambiguity is observed. With this paper we would like to point out the existence of possible ambiguities when using kinetic models in combination with MCR methods for non-simulated, spectroscopic data. Furthermore we would like to suggest to include the calculation of these ambiguities as a postprocessing step in corresponding analyses, as this can increase the significance and reliability of the results.

Characterisation of complex perfume and essential oil blends using multivariate curve resolution-alternating least squares algorithms on average mass spectrum from GC-MS

Quality control of essential oil blends and the discovery of potential adulterations and product fraud is a significant challenge within the natural oil and perfume industry. In this research, total chromatogram average mass spectra (TCAMS), created from the GC-MS three-way raw data, were employed for the characterisation of complex samples of perfumes and essential oil blends. A multivariate approach for curve resolution was used to resolve the TCAMS of pure essential oils within such perfume and essential oil blends. Resolved TCAMS, in combination with unsupervised pattern recognition approaches revealed the distillation grade and origin of used ylang-ylang oils in perfume mixtures. TCAMS resolved from the essential oil blends were used with a supervised machine learning classification model to identify oils, used in creating the blends. Quantification was performed using a multivariate curve resolution approach, resulting in relative errors of prediction lower than 17.84% with root mean square errors of prediction smaller than 3.43.

Mass spectral reconstruction of LC/MS data with entropy minimization

Liquid chromatography-mass spectrometry (LC/MS) is a major technique for the analysis of complex samples. Data processing for LC/MS untargeted analysis is very challenging due to the presence of asymmetric, co-eluted at trace-level peaks. We report a multivariate curve resolution approach based on entropy minimization to resolve LC/MS data. Our liquid chromatography band-target entropy minimization (lc-BTEM) approach enables automated resolution of complex LC/MS peaks without the requirement of any parameter inputs. We demonstrated the performance of our approach on a co-eluted and trace-level peaks in an American ginseng extract. Consequently, we were able to putatively annotate the presence of more than 50 ginsenosides. The extracted pure mass spectra and in-source fragments information further enabled the annotation of [M+H]+, [M+H-Neu]+ and [M-H]- ions. This approach is expected to benefit LC/MS untargeted analysis and data independent analysis of complex samples.

Multivariate Curve Resolution for 2D Solid-State NMR spectra.

We present a processing method, based on the multivariate curve resolution approach (MCR), to denoise 2D solid-state NMR spectra, yielding a substantial S/N ratio increase while preserving the lineshapes and relative signal intensities. These spectral features are particularly important in the quantification of silicon species, where sensitivity is limited by the low natural abundance of the 29Si nuclei and by the dilution of the intrinsic protons of silica, but can be of interest also when dealing with other intermediate-to-low receptivity nuclei. This method also offers the possibility of coprocessing multiple 2D spectra that have the signals at the same frequencies but with different intensities (e.g.: as a result of a variation in the mixing time). The processing can be carried out on the time-domain data, thus preserving the possibility of applying further processing to the data. As a demonstration, we have applied Cadzow denoising on the MCR-processed FIDs, achieving a further increase in the S/N ratio and more effective denoising also on the transients at longer indirect evolution times. We have applied the combined denoising on a set of experimental data from a lysozyme–silica composite.

MARS 2: A computational tool to resolve and extract features from large-scale GC-MS datasets

MARS (MS-Assisted Resolution of Signal) is a computational tool for feature extraction using multivariate curve resolution approaches. However, it is time-consuming for large-scale GC-MS datasets and sensitive to the component number estimation. Here we introduce MARS 2 with substantial improvements to overcome these limitations. Reverse matching (RM) and principal component optimization-iterative transformation target factor analysis (PCO-ITTFA) are developed to reduce the time for locating peak regions and determine the correct component number for resolving optimal features. The greatest strength of MARS 2 is “resolve once, extract anywhere”. It means that mass spectra of each component were needed to resolve from only one profile. Then, chromatographic features can be extracted automatically from hundreds of other profiles with the assistance from the resolved mass spectra. To evaluate its performance, plasma datasets and fatty acid standard mixtures were processed by MARS 2, AMDIS, ADAP-GC 3.0, eRah and MS-DIAL. Amino acid standard mixtures were analyzed by MARS 2 for calibration. Results show that MARS 2 can achieve better performance in both qualitative and quantitative analysis. It is implemented in Python programming language and open-sourced at https://github.com/mapancsu/MARS2.

Photochemical multivariate curve resolution models for the investigation of photochromic systems under continuous irradiation

We propose a multivariate curve resolution approach for the investigation of photochromic systems using UV-Visible spectroscopy. The incorporation of photochemical hard-models as constraints in multivariate curve resolution alternating least squares (MCR-ALS) allows extracting reaction quantum yields in situations where a complete knowledge of the system is not available. We apply this approach to the study of the photochromism of CMTE (cis-1,2-dicyano-1,2-bis(2,4,5-trimethyl-3-thienyl)ethene) under continuous monochromatic irradiation. The mechanism, involving 3 species and 2 reversible reactions, is written and translated into a kinetic constraint that can be applied to the concentration profiles within ALS. First, ambiguity of the solution obtained for photochemical model(s) is calculated and discussed for single set analysis. Multiset analysis is then proposed combining data obtained under different irradiation wavelengths to provide more reliable results. Finally, the photochemical reactivity of CMTE is widely unraveled, and some description of the mechanism observed under irradiation at 365 nm is given.

Increasing chromatographic resolution of analytical signals using derivative enhancement approach

A few decades ago, Giddings made a bleak statistical prediction stating that when using a chromatographic column with a peak capacity of n, one “has no real hope” of separating n compounds because of peak overlap. This statement holds true for today's far more complex separations including chiral, achiral or isotopic separations. Co-eluting chiral and isotopically labeled positional isomers pose a mass spectrometric challenge as isobaric analytes. Several advanced mathematical approaches exist to resolve and extract areas from overlapping data, such as Fourier self-deconvolution, wavelets, multivariate curve resolution, and iterative curve fitting. In this work, we develop a very straightforward approach to mathematically enhance signal resolution using the properties of derivatives while conserving peak area and its position. This technique is based on the fact that the area under a derivative of a distribution is equal to zero. Consequently, by alternately subtracting and adding multiples of even-derivatives (second, fourth, sixth, and so on) from the original peak, the area under a peak is conserved, and the bandwidth is reduced. Unlike multivariate curve resolution and iterative curve fitting approaches, this protocol does not require prior knowledge of the number of peaks. The concept is theoretically discussed for Gaussian and Lorentzian peaks. Several challenging chromatographic applications using deuterated benzenes, chiral separations, and biological applications are shown using twin-column recycling and conventional chromatography. The proposed protocol for a pair of overlapping peaks is currently limited to a Rs of 0.7 or greater with error < 1% under ideal conditions. Furthermore, tuning of peak shape by the first derivative is also described which can remove the exponential convolution of tailing peaks.

Towards enhanced metabolomic data analysis of mass spectrometry image: Multivariate Curve Resolution and Machine Learning

Large amounts of data are generally produced from mass spectrometry imaging (MSI) experiments in obtaining the molecular and spatial information of biological samples. Traditionally, MS images are constructed using manually selected ions, and it is very challenging to comprehensively analyze MSI results due to their large data sizes and highly complex data structures. To overcome these barriers, it is obligatory to develop advanced data analysis approaches to handle the increasingly large MSI data. In the current study, we focused on the method development of using Multivariate Curve Resolution (MCR) and Machine Learning (ML) approaches. We aimed to effectively extract the essential information present in the large and complex MSI data and enhance the metabolomic data analysis of biological tissues. Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) algorithm was used to obtain major patterns of spatial distribution and grouped metabolites with the same spatial distribution patterns. In addition, both supervised and unsupervised ML methods were established to analyze the MSI data. In the supervised ML approach, Random Forest method was selected, and the model was trained using the selected datasets based on the distribution pattern obtained from MCR-ALS analyses. In the unsupervised ML approach, both DBSCAN (Density-based Spatial Clustering of Applications with Noise) and CLARA (Clustering Large Applications) were applied to cluster the MSI datasets. It is worth noting that similar patterns of spatial distribution were discovered through MSI data analysis using MCR-ALS, supervised ML, and unsupervised ML. Our protocols of data analysis can be applied to process the data acquired using many other types of MSI techniques, and to extract the overall features present in MSI results that are intractable using traditional data analysis approaches.

Comparison of two methods for extraction of dill essential oil by gas chromatography-mass spectrometry coupled with chemometric resolution techniques

ABSTRACTThe essential oil components of Iranian Anethumgraveolens L.(dill) were extracted using a Clevenger-type apparatus and microwave-assisted hydro distillation and analysed by gas chromatography-mass spectrometry. A multivariate curve resolution approach was used to overcome the problem of background, baseline offset, and overlapping/embedded peaks. Based on the results related to the GC-MS, 33 and 18 components for dill oil were extracted by hydro distillation and microwave-assisted hydro distillation, respectively. The numbers were extended to 64 and 55 components with concentrations higher than 0.01 g/100 g dry-solids using chemometric techniques. The results of this study showed that hydro distillation was suitable for extraction of β-phellandrene, O-cymen, 3, 6-Dimethyl-2, 3, 3a, 4, 5, 7a-hexahydrobenzofuran, Thymol, Germacrene D, Dill Apiole, 3-Octadecyne, and Phytol; and microwave distillation was suitable for the extraction of α-pinene and α-Phellandrene.

Untargeted assignment and automatic integration of 1H NMR metabolomic datasets using a multivariate curve resolution approach

In this article, we propose the use of the Multivariate Curve Resolution – Alternating Least Squares (MCR-ALS) chemometrics method to resolve the 1H NMR spectra and concentration of the individual metabolites in their mixtures in untargeted metabolomics studies. A decision tree-based strategy is presented to optimally select and implement spectra estimates and equality constraints during MCR-ALS optimization.The proposed method has been satisfactorily evaluated using different 1H NMR metabolomics datasets. In a first study, 1H NMR spectra of the metabolites in a simulated mixture were successfully recovered and assigned. In a second study, more than 30 metabolites were characterized and quantified from an experimental unknown mixture analyzed by 1H NMR. In this work, MCR-ALS is shown to be a convenient tool for metabolite investigation and sample screening using 1H NMR, and it opens a new path for performing metabolomics studies with this chemometric technique.