Parallel Factor Analysis 2 Research Articles

Plant metabolomics: Resolution and quantification of elusive peaks in liquid chromatography–mass spectrometry profiles of complex plant extracts using multi-way decomposition methods

Previous studies on LC–MS metabolomic profiling of 127 F2 Barbarea vulgaris plants derived from a cross of parental glabrous (G) and pubescent (P) type, revealed four triterpenoid saponins (hederagenin cellobioside, oleanolic acid cellobioside, epihederagenin cellobioside, and gypsogenin cellobioside) that correlated with resistance of plants against the insect herbivore, Phyllotreta nemorum. In this study, for the first time, we demonstrate the efficiency of the multi-way decomposition method PARAllel FACtor analysis 2 (PARAFAC2) for exploring complex LC–MS data. PARAFAC2 enabled automated resolution and quantification of several elusive chromatographic peaks (e.g. overlapped, elution time shifted and low s/n ratio), which could not be detected and quantified by conventional chromatographic data analysis. Raw LC–MS data of 127 F2 B. vulgaris plants were arranged in a three-way array (elution time point×mass spectra×samples), divided into 17 different chromatographic intervals and each interval were individually modeled by PARAFAC2. Three main outputs of the PARAFAC2 models described: (1) elution time profile, (2) relative abundance, and (3) pure mass spectra of the resolved peaks modeled from each interval of the chromatographic data. PARAFAC2 scores corresponding to relative abundances of the resolved peaks were extracted and further used for correlation and partial least squares (PLS) analysis. A total of 71 PARAFAC2 components (which correspond to actual peaks, baselines and tails of neighboring peaks) were modeled from 17 different chromatographic retention time intervals of the LC–MS data. In addition to four previously known saponins, correlation- and PLS-analysis resolved five unknown saponin-like compounds that were significantly correlated with insect resistance. The method also enabled a good separation between resistant and susceptible F2 plants. PARAFAC2 spectral loadings corresponding to the pure mass spectra of chromatographic peaks matched well with experimentally recorded mass spectra (correlation based similarity >95%). This enabled to extract pure mass spectra of highly overlapped and low s/n ratio peaks.

Rapid quantification of tryptophan and tyrosine in chemically defined cell culture media using fluorescence spectroscopy

The rapid and inexpensive analysis of the complex cell culture media used in industrial mammalian cell culture is required for quality and variance monitoring. Excitation-emission matrix (EEM) spectroscopy combined with multi-way chemometrics is a robust methodology applicable for the analysis of raw materials, media, and bioprocess broths. We have shown that the methodology can identify compositional changes and predict the efficacy of media in terms of downstream titer [1]. Here we describe how to extend the measurement methodology for the quantification of tryptophan (Trp), tyrosine (Tyr) in complex chemically defined media. The sample type is an enriched basal RDF medium in which five significant fluorophores were identified: Trp, Tyr, pyridoxine, folic acid, and riboflavin. The relatively high chromophore concentrations and compositional complexity lead to very significant matrix effects which were assessed using PARAllel FACtor analysis2 (PARAFAC2). Taking these effects into account, N-way partial least squares (NPLS) combined with a modified standard addition method was used to build calibration models capable of quantifying Trp and Tyr with errors of ∼4.5 and 5.5% respectively. This demonstrates the feasibility of using the EEM method for the rapid, quantitative analysis of Trp and Tyr in complex cell culture media with minimal sample handling as an alternative to chromatographic based methods.

Exploiting second-order advantage using PARAFAC2 for fast HPLC-DAD quantification of mixture of aflatoxins in pistachio nuts

A new methodology using second-order calibration based on PARAllel FACtor analysis 2 (PARAFAC2) is developed for fast quantification of aflatoxins B1, B2, G1 and G2 in pistachio samples by liquid chromatography with diode array detection (LC-DAD). Solvent and solid phase extractions were used for sample preparation steps. In this work, a gradient elution programme was optimised to make co-elutions between analytes and also to shorten the analysis time. Prediction was made on synthetic and real validation samples with a mixture calibration design. Special circumstances such as overlapping of analytes, the lack of spectral selectivity and also the lack of trilinearity, have been compensated with “mathematic separation” through PARAFAC2 modelling. The results showed an acceptable performance of PARAFAC2 for resolution and quantification of all analytes in a single array exploiting the second-order advantage. With the proposed method, the chromatographic run time and also the time for data analysis were reduced significantly.

Metabolic profiling of meat: assessment of pork hygiene and contamination with Salmonella typhimurium

Spoilage in meat is the result of the action of microorganisms and results in changes of meat and microbial metabolism. This process may include pathogenic food poisoning bacteria such as Salmonella typhimurium, and it is important that these are differentiated from the natural spoilage process caused by non-pathogenic microorganisms. In this study we investigated the application of metabolic profiling using gas chromatography-mass spectrometry, to assess the microbial contamination of pork. Metabolite profiles were generated from microorganisms, originating from the natural spoilage process and from the artificial contamination with S. typhimurium. In an initial experiment, we investigated changes in the metabolic profiles over a 72 hour time course at 25 °C and established time points indicative of the spoilage process. A further experiment was performed to provide in-depth analysis of the metabolites characteristic of contamination by S. typhimurium. We applied a three-way PARAllel FACtor analysis 2 (PARAFAC2) multivariate algorithm to model the metabolic profiles. In addition, two univariate statistical tests, two-sample Wilcoxon signed rank test and Friedman test, were employed to identify metabolites which showed significant difference between natural spoiled and S. typhimurium contaminated samples. Consistent results from the two independent experiments were obtained showing the discrimination of the metabolic profiles of the natural spoiled pork chops and those contaminated with S. typhimurium. The analysis identified 17 metabolites of significant interest (including various types of amino acid and fatty acid) in the discrimination of pork contaminated with the pathogenic microorganism.

Non-Trilinear Chromatographic Time Retention−Fluorescence Emission Data Coupled to Chemometric Algorithms for the Simultaneous Determination of 10 Polycyclic Aromatic Hydrocarbons in the Presence of Interferences

Multivariate calibration coupled to high-performance liquid chromatography-fast scanning fluorescence spectroscopy (HPLC-FSFS) was employed for the analysis of 10 selected polycyclic aromatic hydrocarbons (PAHs), six of which correspond to heavy PAHs. The goal of the present study was the successful resolution of a system even in the presence of real interferences. Second-order HPLC-FSFS data matrices were obtained in a short time with a chromatographic system operating in isocratic mode. The difficulties in aligning chromatographic bands in complex systems, such as the ones presented here, are discussed. Two second-order calibration algorithms which do not require chromatographic alignment were selected for data processing, namely, multivariate curve resolution-alternating least-squares (MCR-ALS) and parallel factor analysis 2 (PARAFAC2). These algorithms did also achieve the second-order advantage, and therefore they were able to overcome the problem of the presence of unexpected interferences. The study was employed for the discussion of the scopes of the applied second-order chemometric tools, demonstrating the superiority of MCR-ALS to successfully resolve this complex system. The quality of the proposed techniques was assessed on the basis of the analytical recoveries from different types of water and olive oil samples after solid-phase extraction. The studied concentration ranges in water samples were 5.6 x 10(-3)-0.20 ng mL(-1) for heavy PAHs and 0.036-0.80 ng mL(-1) for light PAHs, while in oil samples the PAHs concentrations were 0.13-9.6 and 2.3-49.5 ng mL(-1) for heavy and light PAHS, respectively. All real samples were analyzed in the presence of the studied interferences.

Solving GC-MS problems with PARAFAC2

Gas chromatography combined with mass spectrometry (GC-MS) is an important technique for identification and quantification of analytes in multifactor systems. Nevertheless, the experimental sources of variability related to GC-MS (e.g., column and flow-meter ageing, changes in certain characteristics or properties of the stationary phase, and changes in temperature, experimental conditions or preparation of standards or chemicals) may cause variations (e.g., elution time, baseline drifts, unexpected overlapping of peaks, or non-Gaussian peaks). Several approaches have been proposed to handle these problems, with the standardization of peak areas using internal standards being one of the most efficient techniques. However, such a solution is not sufficiently versatile when deviations from the ideal are more pronounced. Since a mass spectrum can be obtained at each elution time during chromatographic separation, GC-MS data of several samples can be considered a three-way structure. PARAllel FACtor analysis 2 (PARAFAC2) is a model capable of handling three-way data and, unlike the PARAFAC model, does not assume that the elution profiles of each factor are invariant across samples. This, coupled with its uniqueness property, allows PARAFAC2 to solve several problems derived from experimental conditions in GC-MS datasets. In this article, we aim to show the potential of PARAFAC2 for solving common GC-MS problems, using GC-MS data from wine samples to illustrate the solutions.

Optimization of Verapamil Drug Analysis by Excitation-Emission Fluorescence in Combination with Second-order Multivariate Calibration

Excitation emission fluorescence matrices (EEMs) of Verapamil drug were obtained by direct and by derivatization fluorescence spectroscopy. The fluorescence excitation and emission wavelengths were displaced to longer wavelengths and the fluorescence intensity was enhanced upon derivation with respect to the native fluorescence of the drug. The complete EEM of the native fluorescence of the drug and of the derivatization product were rapidly acquired by using a charged-coupled device detector (CCD), which is advantageous in terms of speed in the analysis, with respect to the use of a conventional photomultiplier detector. The EEMs were analyzed by several second-order multivariate calibration methods exploiting the second order advantage. The three-dimensional decomposition methods used, based in different assumptions about the trilinearity of the three way data structure under analysis, were parallel factor analysis (PARAFAC), bilinear least squares (BLLS), parallel factor analysis 2 (PARAFAC2) and multivariate curve resolution-alternating least squares (MCR-ALS). The determination was performed by using the standard addition approach. The figures of merit of the PARAFAC and BLLS methods were calculated, obtaining a lower limit of detection with the derivatization procedure, when compared with the direct measurement of the fluorescence of the drug. In Verapamil drug the best estimations were found with the BLLS and the MCR-ALS models. In the quantification of Verapamil in a pharmaceutical formulation the best estimation, when compared with the result obtained by the US Pharmacopeia high performance liquid chromatography approach, was obtained by direct fluorescence spectroscopy with MCR-ALS and by derivatization fluorescence spectroscopy with the PARAFAC2 model.

Univariate and multivariate modelling of flavour release in chewing gum using time-intensity: a comparison of data analytical methods

Sensory properties of chewing gum were measured using time-intensity (TI) methodology to record responses from assessors. Studying the information retrieved from a total of 800 TI curves, old and new data analysis methods were compared. These included the normalization method developed by Liu and MacFie, and ad hoc curve parameter retrieval, Principal Components Analysis (PCA) and ANOVA Partial Least Squares Regression (APLSR) methods. Two alternative methods have been developed for handling the multiple sources of variation in the data, including a dual PCA method and PARAllel FACtor analysis 2 (PARAFAC2) multiway analysis. A comparison of the different methods is conducted and the advantages of the different methods highlighted. All methods provide valuable interpretations of the time-intensity data and lead to similar conclusions. The multiway analysis provides a comprehensive overview of the data, but more experience with different datasets is needed to provide definite advices as to which methods are preferable.

Application of PARAFAC2 to fault detection and diagnosis in semiconductor etch

AbstractMonitoring and fault detection of batch chemical processes are complicated by stretching of the time axis, resulting in batches of different length. This paper offers an approach to the unequal time axis problem using the parallel factor analysis 2 (PARAFAC2) model. Unlike PARAFAC, the PARAFAC2 model does not assume parallel proportional profiles, but only that the matrix of profiles preserves its ‘inner product structure’ from sample to sample. PARAFAC2 also allows each matrix in the multiway array to have a different number of rows. It has previously been demonstrated how the PARAFAC2 model can be used to model chromatographic data with retention time shifts. Fault detection and, to a lesser extent, diagnosis in a semiconductor etch process are considered in this paper. It is demonstrated that PARAFAC2 can effectively model batch process data from semiconductor manufacture with unequal dimension in one of the orders, such as the unequal batch length problem. It is shown that the PARAFAC2 model has approximately the same sensitivity to faults as other competing methods, including principal component analysis (PCA), unfold PCA (often referred to as multiway PCA), trilinear decomposition (TLD) and conventional PARAFAC. The advantage of PARAFAC2 is that it is easier to apply than MPCA, TLD and PARAFAC, because unequal batch lengths can be handled directly rather than through preprocessing methods. It also provides additional diagnostic information: the recovered batch profiles. It is likely, however, that it is less sensitive to faults than conventional PARAFAC. Copyright © 2001 John Wiley & Sons, Ltd.