Second-Order Advantage Achieved with Four-Way Fluorescence Excitation−Emission−Kinetic Data Processed by Parallel Factor Analysis and Trilinear Least-Squares. Determination of Methotrexate and Leucovorin in Human Urine

Fluorescent spectroscopy paired with parallel factor analysis for quantitative monitoring of phenanthrene biodegradation and metabolite formation

Polycyclic aromatic hydrocarbons (PAHs) are a class of environmental contaminants released into the environment from both natural and anthropogenic sources that are associated with carcinogenic, mutagenic, and teratogenic health effects. Many remediation strategies for the treatment of PAH contaminated material, including bioremediation, can lead to the formation of toxic transformation products. Analytical techniques for PAHs and PAH transformation products often require extensive sample preparation including solvent extraction and concentration, chromatographic separation, and mass spectrometry to identify and quantify compounds of interest. Excitation-emission matrix (EEM) fluorescent spectroscopy paired with parallel factor analysis (PARAFAC) is an approach for analyzing PAHs that eliminates the need for extensive sample preparation and separation techniques before analysis. However, this technique has rarely been applied to monitoring PAH biotransformation and formation of PAH metabolites. The objectives of this research were to compare an established targeted analytical method to two-dimensional fluorescent spectroscopy and combined EEM-PARAFAC methods to monitor phenanthrene degradation by a bacterial pure culture, Mycobacterium Strain ELW1, identify and quantify phenanthrene transformation products, and derive kinetic constants for phenanthrene degradation and metabolite formation. Both phenanthrene and its primary transformation product, trans-9,10-dihydroxy-9,10-dihydrophenanthrene, were identified and quantified with the EEM-PARAFAC method. The value of the EEM-PARAFAC method was demonstrated in the superiority of sensitivity and accuracy of quantification to two-dimensional fluorescent spectroscopy. Quantification of targets and derivation of kinetic constants using the EEM-PARAFAC method were validated with an established gas chromatography-mass spectrometry (GC-MS) method. To the authors' knowledge, this is the first study to use an EEM-PARAFAC method to monitor, identify, and quantify both PAH biodegradation and PAH metabolite formation by a bacterial pure culture.

Multilinear Mathematical Separation in Chromatography

Chromatography is a powerful and generally applicable method for the analytical separation and quantification of the chemical constituents in complex mixtures because chromatographic separation can provide high selectivity by isolating all analytes from interferences. Multiway analysis based on the multilinear model is an increasingly widely used method for interference-free and fast determination of the chemical constituents also in complex mixtures because multilinear mathematical separation can provide high selectivity by extracting the pure signal of the analyte from the mixed signal of a real sample. By combining chromatographic separation with mathematical separation, multiway calibration method, multiway standard additions method, and multiway internal standard method can be established. Chromatography assisted by multiway analysis can reduce the requirements for complete chromatographic separation, save elution time, and decrease the consumption of the mobile phase, particularly when the peak coelution problem is difficult to solve. This review presents the fundamentals and analytical applications of multilinear mathematical separation in chromatography.

Novel Approach to the Analysis of Chemical Third-Order Data

For the more complex samples, chemical higher-order data can be collected from various information sources, which become the necessary foundation of accurate analysis. In this article, the Tchebichef cubic moment (TCM) was developed for the analysis of chemical third-order data for the first time. Then, the proposed TCM approach was applied to the fluorescence excitation-emission time data for the analysis of adrenaline and noradrenaline in urinary samples (Data I) and the data fusion of the excitation-emission matrix (EEM), NMR, and liquid chromatography-mass spectrometry (LC-MS) spectra for the determination of the five target components (Data II). For Data I, all of the cross-validation correlation coefficients (R_cv²) of the obtained linear models on the calibration set were more than 0.9937 and the prediction root-mean-square errors (RMSE_p) of the external independent test samples were less than 0.0250 μM. For Data II, all of the R_cv² were higher than 0.9846 and RMSE_p were less than 0.2267 μM. Compared with several conventional methods, the proposed method was more convenient and accurate. This study provides another effective approach to the analysis of complex samples based on their chemical third-order data.

Coupling of digital image processing and three-way calibration to assist a paper-based sensor for determination of nitrite in food samples

In this work, a novel and very interesting analytical methodology based on coupling of digital image processing and three-way calibration has been developed for determination of nitrite in food samples.

Four- and five-way excitation-emission luminescence-based data acquisition and modeling for analytical applications. A review

The latest advances in both theory and experimental procedures on third-order/four-way and fourth-order/five-way calibration methods are discussed. This report is focused on excitation-emission (fluorescence and phosphorescence) matrices generation, employing different variables as the third data mode (time retention in chromatography, pH gradient, fluorescence/phosphorescence lifetime, kinetics, or other chemical treatments). Fully capitalizing on the second-order advantage, it has been possible to develop appealing analytical applications in spite of the complexity of the data. Extraction of the significant chemical information about the system under study as well as the individual abundance of the contributing constituents after proper higher-order data decomposition has allowed to analytical researchers performing quantitative analysis of complex samples. The experimental works reported up to the present are introduced and discussed in order to illustrate concepts. Throughout this work, the analytical benefits achieved by modeling third- and fourth-order data are exposed, attempting to contribute to the ongoing debate in the chemometric community regarding the existence and the true nature of the third-order advantage.

Simultaneously quantifying intracellular FAD and FMN using a novel strategy of intrinsic fluorescence four-way calibration

The simultaneous quantitative analysis of intracellular metabolic coenzymes flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN) is of interest because they participate in many electron-transfer reactions of metabolism. But, the simultaneous quantitative analysis of FAD and FMN is hard to be achieved by traditional analytical methods. This paper proposes a novel strategy of intrinsic fluorescence coupled with four-way calibration method for simultaneous quantitative analysis of intracellular metabolic coenzymes FAD and FMN. Through mathematical separation, this proposed analytical method efficiently achieved the simultaneous quantitative analysis of metabolic coenzymes FAD and FMN in the cell, despite the fact that uncalibrated spectral interferents coexist in the system. The predicted concentrations of FAD and FMN in the cell are 217.0 ± 6.9 and 155.0 ± 1.7 pmol/10⁶ cells respectively, which were validated by the approved liquid chromatography-tandem mass spectrometry (LC-MS/MS) method. This analytical method with second-order advantage simply requires the cell solution to be diluted by a buffer, it could introduce an interesting analytical strategy for multianalyte direct quantitative analysis in complex biological systems. In addition, we explore the third-order advantage of four-way calibration by a comparative study based on this real fluorescence data. The comparisons indicate that a four-way calibration method can provide higher sensitivity and more resolving power than a three-way calibration method.

Comparison of several third-order correction algorithms applied to fluorescence excitation-emission-sample data array: Interference-free determination of polycyclic aromatic hydrocarbons in water pollution

Interference-free determination of polycyclic aromatic hydrocarbons (PAHs) in water pollution is proposed based on third-order correction algorithms with quadrilinear component modeling applied to the constructed four way fluorescence excitation-emission-sample data array with higher accuracy and better predictive ability than second-order (three-dimension) correction. Alternating weighted residue constraint quadrilinear decomposition (AWRCQLD), quadrilinear parallel factor analysis (4-PARAFAC), alternate penalty quadrilinear decomposition (APQLD) and alternate penalty trilinear decomposition (APTLD) are applied to acenaphthene (ANA), naphthalene (NAP) and fluorene (FLU) respectively. Fulvic acid affects PAHs determination seriously in real-world situation, so it is simulated as an interfering agent. Excitation-emission fluorescence matrixes (EEMs) of PAHs are measured at different volumes of fulvic acid simulated different interference conditions, to construct a four-way data array. After the four-way spectra data is analyzed by AWRCQLD, 4-PARAFAC, and APQLD, three-way EEMs analyzed by APTLD, results show that, on the one hand, PAHs can be measured more accurately with four-way data combined with third-order calibration than lower-order. On the other hand, AWRCQLD algorithm can reflect the superiority of third-order advantage better with higher recovery rate and smaller root mean square error, than other third-order or second-order correction algorithms.

Angle Distribution of Loading Subspace (ADLS) for estimating chemical rank in multivariate analysis: Applications in spectroscopy and chromatography

Multivariate analyses are increasingly popular to explore the underlying structure of multivariate datasets, which are more and more prevalent in analytical chemistry. However, difficulties can be associated with estimating the number of components for the data with considerable coherence and noise. The method of Angle Distribution of Loading Subspace (ADLS) has been proposed to estimate the number of components for Principal Component Analysis (PCA) and PARAllel FACtor analysis (PARAFAC), which showed some advantages, in particular in the case of datasets with high coherence, over the commonly used methods (scree plot and cross-validation in PCA, and core consistency diagnostics (CORCONDIA) in PARAFAC). In this paper, we systematically improved and applied ADLS to estimate the number of components in different multivariate methods including, Multivariate Curve Resolution (MCR), PARAFAC and four-way PARAFAC. Firstly, we showed that ADLS performed better when estimating the chemical rank for MCR analysis, compared with scree plots. As well as this, we improved ADLS in multi-way analysis (three- and four-way PARAFAC) by calculating the loading subspace in advance using the Khatri-Rao product. The improved ADLS in multi-way analysis provided the correct result for the simulated three-way fluorescence datasets with unevenly distributed coherence at different dimensions, while the previous version of ADLS showed biased results and CORCONDIA / split-half analysis provided relatively unstable results. Moreover, ADLS was used to estimate the chemical rank for a four-way real-life fluorescence dataset analyzed by four-way PARAFAC. In this case the result of chemical rank results from ADLS was more precise and informative compared with CORCONDIA /split-half analysis in four-way analysis.

Four-dimensional data coupled to alternating weighted residue constraint quadrilinear decomposition model applied to environmental analysis: Determination of polycyclic aromatic hydrocarbons

Qualitative and quantitative analysis of polycyclic aromatic hydrocarbons (PAHs) was carried out by three-dimensional fluorescence spectroscopy combining with Alternating Weighted Residue Constraint Quadrilinear Decomposition (AWRCQLD). The experimental subjects were acenaphthene (ANA) and naphthalene (NAP). Firstly, in order to solve the redundant information of the three-dimensional fluorescence spectral data, the wavelet transform was used to compress data in preprocessing. Then, the four-dimensional data was constructed by using the excitation-emission fluorescence spectra of different concentration PAHs. The sample data was obtained from three solvents that are methanol, ethanol and Ultra-pure water. The four-dimensional spectral data was analyzed by AWRCQLD, then the recovery rate of PAHs was obtained from the three solvents and compared respectively. On one hand, the results showed that PAHs can be measured more accurately by the high-order data, and the recovery rate was higher. On the other hand, the results presented that AWRCQLD can better reflect the superiority of four-dimensional algorithm than the second-order calibration and other third-order calibration algorithms. The recovery rate of ANA was 96.5%~103.3% and the root mean square error of prediction was 0.04μgL^-1. The recovery rate of NAP was 96.7%~115.7% and the root mean square error of prediction was 0.06μgL^-1.

Multivariate Analysis of Mixed Lipid Aggregate Phase Transitions Monitored Using Raman Spectroscopy

The phase behavior of aqueous 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC)/1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) mixtures between 8.0 ℃ and 41.0 ℃ were monitored using Raman spectroscopy. Temperature-dependent Raman matrices were assembled from series of spectra and subjected to multivariate analysis. The consensus of pseudo-rank estimation results is that seven to eight components account for the temperature-dependent changes observed in the spectra. The spectra and temperature response profiles of the mixture components were resolved by applying a variant of the non-negative matrix factorization (NMF) algorithm described by Lee and Seung (1999). The rotational ambiguity of the data matrix was reduced by augmenting the original temperature-dependent spectral matrix with its cumulative counterpart, i.e., the matrix formed by successive integration of the spectra across the temperature index (columns). Successive rounds of constrained NMF were used to isolate component spectra from a significant fluorescence background. Five major components exhibiting varying degrees of gel and liquid crystalline lipid character were resolved. Hydrogen-bonded water networks exhibiting varying degrees of organization are associated with the lipid components. Spectral parameters were computed to compare the chain conformation, packing, and hydration indicated by the resolved spectra. Based on spectral features and relative amounts of the components observed, four components reflect long chain lipid response. The fifth component could reflect the response of the short chain lipid, DHPC, but there were no definitive spectral features confirming this assignment. A minor component of uncertain assignment that exhibits a striking response to the DMPC pre-transition and chain melting transition also was recovered. While none of the spectra resolved exhibit features unequivocally attributable to a specific aggregate morphology or step in the gelation process, the results are consistent with the evolution of mixed phase bicelles (nanodisks) and small amounts of worm-like DMPC/DHPC aggregates, and perhaps DHPC micelles, at low temperature to suspensions of branched and entangled worm-like aggregates above the DMPC gel phase transition and perforated multi-lamellar aggregates at high temperature.

Quantitative fluorescence kinetic analysis of NADH and FAD in human plasma using three- and four-way calibration methods capable of providing the second-order advantage

The metabolic coenzymes reduced nicotinamide adenine dinucleotide (NADH) and flavin adenine dinucleotide (FAD) are the primary electron donor and acceptor respectively, participate in almost all biological metabolic pathways. This study develops a novel method for the quantitative kinetic analysis of the degradation reaction of NADH and the formation reaction of FAD in human plasma containing an uncalibrated interferent, by using three-way calibration based on multi-way fluorescence technique. In the three-way analysis, by using the calibration set in a static manner, we directly predicted the concentrations of both analytes in the mixture at any time after the start of their reactions, even in the presence of an uncalibrated spectral interferent and a varying background interferent. The satisfactory quantitative results indicate that the proposed method allows one to directly monitor the concentration of each analyte in the mixture as the function of time in real-time and nondestructively, instead of determining the concentration after the analytical separation. Thereafter, we fitted the first-order rate law to their concentration data throughout their reactions. Additionally, a four-way calibration procedure is developed as an alternative for highly collinear systems. The results of the four-way analysis confirmed the results of the three-way analysis and revealed that both the degradation reaction of NADH and the formation reaction of FAD in human plasma fit the first-order rate law. The proposed methods could be expected to provide promising tools for simultaneous kinetic analysis of multiple reactions in complex systems in real-time and nondestructively.

Anisotropy resolved multidimensional emission spectroscopy (ARMES): A new tool for protein analysis

Structural analysis of proteins using the emission of intrinsic fluorophores is complicated by spectral overlap. Anisotropy resolved multidimensional emission spectroscopy (ARMES) overcame the overlap problem by the use of anisotropy, with chemometric analysis, to better resolve emission from different fluorophores. Total synchronous fluorescence scan (TSFS) provided information about all the fluorophores that contributed to emission while anisotropy provided information about the environment of each fluorophore. Here the utility of ARMES was demonstrated via study of the chemical and thermal denaturation of human serum albumin (HSA). Multivariate curve resolution (MCR) analysis of the constituent polarized emission ARMES data resolved contributions from four emitters: fluorescence from tryptophan (Trp), solvent exposed tyrosine (Tyr), Tyr in a hydrophobic environment, and room temperature phosphorescence (RTP) from Trp. The MCR scores, anisotropy, and literature validated these assignments and showed all the expected transitions during HSA unfolding. This new methodology for comprehensive intrinsic fluorescence analysis of proteins is applicable to any protein containing multiple fluorophores.

Analysis of variation matrix array by bilinear least squares-residual bilinearization (BLLS-RBL) for resolving and quantifying of foodstuff dyes in a candy sample

Bilinear least square (BLLS) method is one of the most suitable algorithms for second-order calibration. Original BLLS method is not applicable to the second order pH-spectral data when an analyte has more than one spectroscopically active species. Bilinear least square-residual bilinearization (BLLS-RBL) was developed to achieve the second order advantage for analysis of complex mixtures. Although the modified method is useful, the pure profiles cannot be obtained and only the linear combination will be obtained. Moreover, for prediction of analyte in an unknown sample, the original algorithm of RBL may diverge; instead of converging to the desired analyte concentrations. Therefore, Gauss Newton-RLB algorithm should be used, which is not as simple as original protocol. Also, the analyte concentration can be predicted on the basis of each of the equilibrating species of the component of interest that are not exactly the same. The aim of the present work is to tackle the non-uniqueness problem in the second order calibration of monoprotic acid mixtures and divergence of RBL. Each pH-absorbance matrix was pretreated by subtraction of the first spectrum from other spectra in the data set to produce full rank array that is called variation matrix. Then variation matrices were analyzed uniquely by original BLLS-RBL that is more parsimonious than its modified counterpart. The proposed method was performed on the simulated as well as the analysis of real data. Sunset yellow and Carmosine as monoprotic acids were determined in candy sample in the presence of unknown interference by this method.

Progress Towards Simple and Direct Detection of Adenylosuccinate Lyase Deficiency in Human Urine

A rhodamine based boronic acid linearly responds to increasing 5-aminoimidazole-4-carboxamide riboside (AICAr) concentrations in human urine. This method is thus an advance in detecting adenylosuccinate lyase (ADSL) deficiency as AICAr is a model riboside for the ADSL substrates succinyladenosine (S-Ado) and succinylaminoimidazolecarboxamide riboside (SAICAr). ADSL deficiency is a rare but devastating disease of de novo purine synthesis in infants. Its diagnosis is also significant as it is one of the autism spectrum disorders.

Nonlinear four-way kinetic-excitation-emission fluorescence data processed by a variant of parallel factor analysis and by a neural network model achieving the second-order advantage: malonaldehyde determination in olive oil samples

Four-way data were obtained by recording the kinetic evolution of excitation-emission fluorescence matrices for the product of the Hantzsch reaction between the analyte malonaldehyde and methylamine. The reaction product, 1,4-disubstituted-1,4-dihydropyridine-3,5-dicarbaldehyde, is a highly fluorescent compound. The nonlinear nature of the kinetic fluorescence data has been demonstrated, and therefore the four-way data were processed with parallel factor analysis combined with a nonlinear pseudounivariate regression, based on a quadratic polynomial fit, and also with a recently introduced neural network methodology, based on the combination of unfolded principal component analysis, residual trilinearization, and radial basis functions. The applied chemometric strategies are not only able to adequately model the nonlinear data but also to successfully determine malonaldehyde in olive oil samples. This is possible since the experimentally recorded four-way data, modeled with the above-mentioned advanced chemometric approaches, permit the achievement of the second-order advantage. This allows us to predict the analyte concentration in a complex background, in spite of the nonlinear behavior and in the presence of uncalibrated interferences. The present work is a new example of the use of higher-order data for the resolution of a complex nonlinear system, successfully employed in the context of food chemical analysis.