Pure component spectral recovery and constrained matrix factorizations: concepts and applications

We present new ideas underlying a self‐modelling factor analytical method which allows to extract pure component spectra and the associated concentration profiles from a set of spectroscopic measurements. The usefulness of the method is demonstrated and compared with established tools for model problems and for a system from catalytic hydroformylation by Rhodium complexes both with overlapping component spectra. Self‐modelling methods tend to minimize the overlap of the recovered spectra, which can result in an unwanted distortion of the spectra and concentration profiles. For strongly overlapping spectra a penalty condition on a specific singular value of the absorptivity matrix factor and a global decomposition approach are appropriate tools to construct improved factorizations. Copyright © 2010 John Wiley & Sons, Ltd.     

Reduction of the rotational ambiguity of curve resolution techniques under partial knowledge of the factors. Complementarity and coupling theorems

Multivariate curve resolution techniques allow to uncover from a series of spectra (of a chemical reaction system) the underlying spectra of the pure components and the associated concentration profiles along the time axis. Usually, a range of feasible solutions exists because of the so‐called rotational ambiguity. Any additional information on the system should be utilized to reduce this ambiguity. Sometimes the pure component spectra of certain reactants or products are known, or the concentration profiles of the same or other species are available. This valuable information should be used in the computational procedure of a multivariate curve resolution technique. The aim of this paper is to show how such supplemental information on the components can be exploited. The knowledge of spectra leads to linear restrictions on the concentration profiles of the complementary species and vice versa. Further, affine–linear restrictions can be applied to pairs of a concentration profile and the associated spectrum of a species. These (affine) linear constraints can also be combined with the usual non‐negativity restrictions. These arguments can reduce the rotational ambiguity considerably. In special cases, it is possible to determine the unknown concentration profile or the spectrum of a species only from these constraints. Copyright © 2012 John Wiley & Sons, Ltd.     

A fast polygon inflation algorithm to compute the area of feasible solutions for three‐component systems. I: concepts and applications

The multicomponent factorization of multivariate data often results in nonunique solutions. The so‐called rotational ambiguity paraphrases the existence of multiple solutions that can be represented by the area of feasible solutions (AFS). The AFS is a bounded set that may consist of isolated subsets. The numerical computation of the AFS is well understood for two‐component systems and is an expensive numerical process for three‐component systems. In this paper, a new fast and accurate algorithm is suggested that is based on the inflation of polygons. Starting with an initial triangle located in a topologically connected subset of the AFS, an automatic extrusion algorithm is used to form a sequence of growing polygons that approximate the AFS from the interior. The polygon inflation algorithm can be generalized to systems with more than three components. The efficiency of this algorithm is demonstrated for a model problem including noise and a multicomponent chemical reaction system. Further, the method is compared with the recent triangle‐boundary‐enclosing scheme of Golshan, Abdollahi, and Maeder (Anal. Chem. 2011, 83, 836–841). Copyright © 2013 John Wiley & Sons, Ltd.     

On generalized Borgen plots. I: From convex to affine combinations and applications to spectral dataSpectra

In 1985, Borgen and Kowalski (Anal. Chim. Acta 1985; 174 : 1‐26) published their landmark paper on the geometric construction of feasible regions for nonnegative factorizations of spectral data matrices for three‐component systems. These geometric constructions are called Borgen plots. Borgen plots are principally restricted to nonnegative data and are sometimes considered as analytical tool. Major contributions to this theory have been given by Rajkó. In contrast to these geometric constructions, numerical methods to compute the so‐called area of feasible solutions (AFS) have been studied by Golshan et al. (Anal. Chem. 2011; 83 (3): 836‐841) and by Sawall et al. (J. Chemom. 2013; 27 : 106‐116). These numerical methods can even treat spectral data, which include slightly negative components. In this work, the concept of generalized Borgen plots is introduced for spectral data, which are polluted by small negative entries. The analysis is not restricted to three‐component systems but can be applied to general s‐component systems. Generalized Borgen plots are identical to the classical Borgen plots for nonnegative data. The analysis in this work also bridges the gap between the different scalings (Borgen norms) used for AFS computations. The algorithmic procedure of generalized Borgen plots for three‐component systems and its implementation in the FAC‐PACK software are described in the second part of this paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Central composite design with the help of multivariate curve resolution in loadability optimization of RP‐HPLC to scale‐up a binary mixture

Chromatographic method development for preparative targets is a time‐consuming and subjective process. This can be particularly problematic because of the use of valuable samples for isolation and the large consumption of solvents in preparative scale. These processes could be improved by using statistical computations to save time, solvent and experimental efforts. Thus, contributed by ESI‐MS, after applying DryLab software to gain an overview of the most effective parameters in separation of synthesized celecoxib and its co‐eluted compounds, design of experiment software that relies on multivariate modeling as a chemometric approach was used to predict the optimized touching‐band overloading conditions by objective functions according to the relationship between selectivity and stationary phase properties. The loadability of the method was investigated on the analytical and semi‐preparative scales, and the performance of this chemometric approach was approved by peak shapes beside recovery and purity of products.     

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     

Daubechies小波主成分回归法机理及算法研究

将小波变换与主成分回归相结合,提出一种新型多元校正算法---小波基主成分回归法。理论分析和仿真实验表明,该法可更有效地去除噪声,提取有用信息。将其用于氯霉素及甲硝唑实际药物体系分析,与主成分回归法(PCR)相比,得到的回收率总平均相对误差由1.70%下降到0.90%。此外,通过将统计判据和小波多尺度分析相结合,发展了一种新的因子数判定方法。理论和实验研究表明,该法比传统因子数判定法具有更高的可靠性。     

Geographical classification of Epimedium based on HPLC fingerprint analysis combined with multi‐ingredients quantitative analysis

A reliable and comprehensive method for identifying the origin and assessing the quality of Epimedium has been developed. The method is based on analysis of HPLC fingerprints, combined with similarity analysis, hierarchical cluster analysis (HCA), principal component analysis (PCA) and multi‐ingredient quantitative analysis. Nineteen batches of Epimedium , collected from different areas in the western regions of China, were used to establish the fingerprints and 18 peaks were selected for the analysis. Similarity analysis, HCA and PCA all classified the 19 areas into three groups. Simultaneous quantification of the five major bioactive ingredients in the Epimedium samples was also carried out to confirm the consistency of the quality tests. These methods were successfully used to identify the geographical origin of the Epimedium samples and to evaluate their quality.     

Correlation‐assisted nearest shrunken centroid classifier with applications for high dimensional spectral data

High throughput data are frequently observed in contemporary chemical studies. Classification through spectral information is an important issue in chemometrics. Linear discriminant analysis (LDA) fails in the large‐p‐small‐n situation for two main reasons: (1) the sample covariance matrix is singular when p > n and (2) there is an accumulation of noise in the estimation of the class centroid in high dimensional feature space. The Independence Rule is a class of methods used to overcome these drawbacks by ignoring the correlation information between spectral variables. However, a strong correlation is an essential characteristic of spectral data. We proposed a new correlation‐assisted nearest shrunken centroid classifier (CA‐NSC) to incorporate correlation information into the classification. CA‐NSC combines two sources of information [class centroid (mean) and correlation structure (variance)] to generate the classification. We used two real data analyses and a simulation study to verify our CA‐NSC method. In addition to NSC, we also performed a comparison with the soft independent modeling of class analogy (SIMCA) approach, which uses only correlation structure information for classification. The results show that CA‐NSC consistently improves on NSC and SIMCA. The misclassification rate of CA‐NSC is reduced by almost half compared with NSC in one of the real data analyses. Generally, correlation among variables will worsen the performance of NSC, even though the discriminatory information contained in the class centroid remains unchanged. If only correlation structure information is used (as in the case of SIMCA), the result will be satisfactory only when the correlation structure alone can provide sufficient information for classification. Copyright © 2015 John Wiley & Sons, Ltd.     

Comprehensive characterization and quantification of multiple components in Dan‐Huang‐Qu‐Yu capsule using a multivariate data processing approach based on microwave‐assisted extraction with UHPLC and Q Exactive quadrupole‐orbitrap high‐resolution mass spectrometry

Dan‐Huang‐Qu‐Yu capsule, a Chinese herbal medicine compound preparation, is widely used for chronic pelvic inflammatory disease. In this study, a rapid, selective, and sensitive microwave‐assisted extraction ultra‐high‐performance liquid chromatography‐Q Exactive quadrupole‐orbitrap high‐resolution mass spectrometry method was developed for analyzing its chemical compositions. A total of 85 compounds, including 22 flavonoids, 8 terpenoids, 5 quinones, 5 phthaleolactone, 23 organic acids, and 22 other compounds were identified from Dan‐Huang‐Qu‐Yu capsule. Among them, 35 major compounds were unambiguously detected by comparing them with reference standards and selected as quality control markers, which were simultaneously determined in Dan‐Huang‐Qu‐Yu capsule. The established method was successfully validated and applied for simultaneous determination of 35 bioactive compounds in Dan‐Huang‐Qu‐Yu capsule from ten sample batches. The quantitative data of the analytes were analyzed by principal component analysis for quality assessment of Dan‐Huang‐Qu‐Yu capsule. Six compounds (e.g., astragaloside IV, salvianolic acid B, ellagic acid, chlorogenic acid, N‐butylidenephthalide, and luteolin) were screened out and regarded as chemical markers for quality control of Dan‐Huang‐Qu‐Yu capsule. The established method has been proved to be a novel and useful tool for rapid research of Dan‐Huang‐Qu‐Yu capsule. This research will provide reference for the scientific research of traditional Chinese medicines.     

Multivariate curve resolution based chromatographic peak alignment combined with parallel factor analysis to exploit second-order advantage in complex chromatographic measurements

In the present contribution, a new combination of multivariate curve resolution-correlation optimized warping (MCR-COW) with trilinear parallel factor analysis (PARAFAC) is developed to exploit second-order advantage in complex chromatographic measurements. In MCR-COW, the complexity of the chromatographic data is reduced by arranging the data in a column-wise augmented matrix, analyzing using MCR bilinear model and aligning the resolved elution profiles using COW in a component-wise manner. The aligned chromatographic data is then decomposed using trilinear model of PARAFAC in order to exploit pure chromatographic and spectroscopic information. The performance of this strategy is evaluated using simulated and real high-performance liquid chromatography-diode array detection (HPLC-DAD) datasets. The obtained results showed that the MCR-COW can efficiently correct elution time shifts of target compounds that are completely overlapped by coeluted interferences in complex chromatographic data. In addition, the PARAFAC analysis of aligned chromatographic data has the advantage of unique decomposition of overlapped chromatographic peaks to identify and quantify the target compounds in the presence of interferences. Finally, to confirm the reliability of the proposed strategy, the performance of the MCR-COW-PARAFAC is compared with the frequently used methods of PARAFAC, COW-PARAFAC, multivariate curve resolution-alternating least squares (MCR-ALS), and MCR-COW-MCR. In general, in most of the cases the MCR-COW-PARAFAC showed an improvement in terms of lack of fit (LOF), relative error (RE) and spectral correlation coefficients in comparison to the PARAFAC, COW-PARAFAC, MCR-ALS and MCR-COW-MCR results.     

Synthesis of Co(II), Cu(II), Hg(II), UO2(II) and Pb(II) binuclear nanometric complexes from multi‐donor ligand: Spectral,modeling, quantitative structure–activity relationship,docking and antitumor studies

New synthesis of Co(II), Cu(II), Hg(II), UO₂(II) and Pb(II) binuclear nanometric complexes derived from multi‐donor ligand is reported. Structural and molecular formulae of all isolated complexes were established. Bi‐negative hexa‐dentate mode of ligand was proposed for the two central atoms in all complexes. Infrared, UV–visible, magnetic moments, electron paramagnetic resonance, thermogravimetric analysis and elemental analysis were used to build all structural formulae. X‐ray diffraction and scanning electron microscopy were used to determine the morphological features of the compounds and to compute particle sizes. Theoretical computations were implemented to support the proposed formulae. Kinetic study was executed over suitable stages to clarify the comparative stabilities. The DFT/B3LYP method, using the Gaussian 09 program, was utilized for optimizing the distribution of atoms over all compounds except the UO₂²⁺ complex. This exclusion refers to an inability to find a suitable method. Significant parameters were estimated using frontier energies (highest occupied and lowest unoccupied molecular orbitals) and data log file. A quantitative structure–activity relationship study applying HyperChem was executed for the organic compound tautomer forms to give a significant view about their biological character. AutoDock tools 4.2 were used to investigate the biological trend of organic compounds (keto and enol) against three types of proteins. The types were chosen related to in vitro investigation: breast, prostate and liver carcinoma proteins. IC₅₀ values indicated insignificant inhibition activity towards all carcinoma cell lines under investigation, except for the Hg(II) complex which displayed distinct activity against breast carcinoma compared with reference drug (doxorubicin).     

Impact of fat and muscle in energy dispersive X‐ray diffraction‐based identification of heroin using multivariate data analysis

As for the detection of drug body packing, skin is a typical interference factor. In this paper, multivariate data analysis was proposed to analyze the impact of fat and muscle on heroin identification based on the profile of spectra of energy dispersive X‐ray diffraction. In the space of principal components, the results showed that different pure samples (heroin, muscle, fat) clustered in different areas, whereas the location of mixture samples moved between locations of pure samples. The impact of fat and muscle lies in moving the feature points between pure materials in the space of principal components. Furthermore, the model of heroin covered by fat and muscle of different thicknesses was set up, and a linear relationship was proven to be suitable. Our findings indicate that multivariate data analysis would be a promising method in the detection of drug body packing. Copyright © 2011 John Wiley & Sons, Ltd.     

Disentangling Complex Mixtures of Compounds with Near‐Identical 1H and 13C NMR Spectra using Pure Shift NMR Spectroscopy

The thorough analysis of highly complex NMR spectra using pure shift NMR experiments is described. The enhanced spectral resolution obtained from modern 2D HOBS experiments incorporating spectral aliasing in the ¹³C indirect dimension enables the distinction of similar compounds exhibiting near‐identical ¹H and ¹³C NMR spectra. It is shown that a complete set of extremely small Δδ(¹H) and Δδ(¹³C) values, even below the natural line width (1 and 5 ppb, respectively), can be simultaneously determined and assigned.     

Chemical differentiation of volatile compounds in crude and processed Atractylodis Macrocephalae Rhizoma by using comprehensive two‐dimensional gas chromatography with time‐of‐flight mass spectrometry combined with multivariate data analysis

In the present study, comprehensive 2D GC—TOF‐MS combined with multivariate data analysis was applied to analyze the differences of the volatile components in crude and processed Atractylodis Macrocephalae Rhizoma (AMR) samples. As a result, 26 compounds that were found in crude AMR samples disappeared in processed AMR samples, and 19 compounds were newly generated and identified in AMR after processing with wheat bran. Meanwhile, principal component analysis demonstrated that there were significant chemical differences between crude and processed AMR samples, and processing procedure caused obvious quantitative and qualitative changes of volatile components in AMR. The established method could be used to explain the chemical differentiation between crude and processed AMR, and to further understand the processing mechanism of herbal medicines.     

Oxygen concentration and modeling thermal decomposition of a high‐performance material: A case study of polyimide (Cirlex)

Kinetic decomposition models for the thermal decomposition of a high‐performance polymeric material (Polyimide, PI) were determined from specific techniques. Experimental data from thermogravimetric analysis (TGA) and previously elucidated decomposition mechanism were combined with numerical simulating tool to establish a comprehensive kinetic model for the decomposition of PI under three atmospheres: nitrogen, 2% oxygen, and synthetic air. Multistaged kinetic models with subsequent and competitive reactions were established by taking into consideration the different types of reactions that may be occurring during the thermal decomposition of the material (chain scission, thermo‐oxidation, char formation). The decomposition products and decomposition mechanism of PI which was established in our previous report allowed for the elucidation of the kinetic decomposition models. A three‐staged kinetic thermal decomposition pathway was a good fit to model the thermal decomposition of PI under nitrogen. The kinetic model involved an autocatalytic type of reaction followed by successive nth order reactions. Such types of models were set up for the evaluation of the kinetics of the thermal decomposition of PI under 2% oxygen and in air, leading to models with satisfactory fidelity.     

Cross‐validation in PCA models with the element‐wise k‐fold (ekf) algorithm: theoretical aspects

Cross‐validation has become one of the principal methods to adjust the meta‐parameters in predictive models. Extensions of the cross‐validation idea have been proposed to select the number of components in principal components analysis (PCA). The element‐wise k‐fold (ekf) cross‐validation is among the most used algorithms for principal components analysis cross‐validation. This is the method programmed in the PLS_Toolbox, and it has been stated to outperform other methods under most circumstances in a numerical experiment. The ekf algorithm is based on missing data imputation, and it can be programmed using any method for this purpose. In this paper, the ekf algorithm with the simplest missing data imputation method, trimmed score imputation, is analyzed. A theoretical study is driven to identify in which situations the application of ekf is adequate and, more importantly, in which situations it is not. The results presented show that the ekf method may be unable to assess the extent to which a model represents a test set and may lead to discard principal components with important information. On a second paper of this series, other imputation methods are studied within the ekf algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Insulator‐based dielectrophoresis combined with the isomotive AC electric field and applied to single cell analysis

We developed an insulator‐based dielectrophoretic (iDEP) creek‐gap device that enables the isomotive movement of cells and that is suitable for determining their DEP properties. In the iDEP creek‐gap device, a pair of planar insulators forming a single fan‐shaped channel allows the induction of the isomotive iDEP force on cells. Hence, the cells’ behavior is characterized by straight motion at constant velocity in the longitudinal direction of the channel. Operation of the device was demonstrated using human breast epithelial cells (MCF10A) by applying an AC voltage of V_pp = 34 V peak‐to‐peak and frequencies of 200 kHz and 50 MHz to the device. Subsequently, the magnitude of DEP forces and the real part of the ClausiusMossotti (CM) factor, Re(β), were deduced from the measured cell velocity. The values of Re(β) were 0.14 ± 0.01 for the frequency of 200 kHz and ?0.12 ± 0.01 for 50 MHz. These results demonstrated that the DEP properties of the cells could be extracted over a wide field frequency range. Therefore, the proposed iDEP creek‐gap device was found to be applicable to cell analysis.     

Rapidly differentiating grape seeds from different sources based on characteristic fingerprints using direct analysis in real time coupled with time‐of‐flight mass spectrometry combined with chemometrics

The seeds of grapevine (Vitis vinifera) are a byproduct of wine production. To examine the potential value of grape seeds, grape seeds from seven sources were subjected to fingerprinting using direct analysis in real time coupled with time‐of‐flight mass spectrometry combined with chemometrics. Firstly, we listed all reported components (56 components) from grape seeds and calculated the precise m/z values of the deprotonated ions [M–H]^–. Secondly, the experimental conditions were systematically optimized based on the peak areas of total ion chromatograms of the samples. Thirdly, the seven grape seed samples were examined using the optimized method. Information about 20 grape seed components was utilized to represent characteristic fingerprints. Finally, hierarchical clustering analysis and principal component analysis were performed to analyze the data. Grape seeds from seven different sources were classified into two clusters; hierarchical clustering analysis and principal component analysis yielded similar results. The results of this study lay the foundation for appropriate utilization and exploitation of grape seed samples. Due to the absence of complicated sample preparation methods and chromatographic separation, the method developed in this study represents one of the simplest and least time‐consuming methods for grape seed fingerprinting.