A solution to the 1D NMR alignment problem using an extended generalized fuzzy Hough transform and mode support

This paper approaches the problem of intersample peak correspondence in the context of later applying statistical data analysis techniques to 1D ¹H-nuclear magnetic resonance (NMR) data. Any data analysis methodology will fail to produce meaningful results if the analyzed data table is not synchronized, i.e., each analyzed variable frequency (Hz) does not originate from the same chemical source throughout the entire dataset. This is typically the case when dealing with NMR data from biological samples. In this paper, we present a new state of the art for solving this problem using the generalized fuzzy Hough transform (GFHT). This paper describes significant improvements since the method was introduced for NMR datasets of plasma in Csenki et al. (Anal Bioanal Chem 389:875-885, 15) and is now capable of synchronizing peaks from more complex datasets such as urine as well as plasma data. We present a novel way of globally modeling peak shifts using principal component analysis, a new algorithm for calculating the transform and an effective peak detection algorithm. The algorithm is applied to two real metabonomic ¹H-NMR datasets and the properties of the method are compared to bucketing. We implicitly prove that GFHT establishes the objectively true correspondence. Desirable features of the GFHT are: (1) intersample peak correspondence even if peaks change order on the frequency axis and (2) the method is symmetric with respect to the samples. Figure From chaos to order: heatmaps of a H-NMR spectral segment prior and post sorting on one peak position. Post sorting sample order reveals that peak positions exhibits distinctive patterns which are modeled by the GFHT to establish correspondence. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Proof of principle of a generalized fuzzy Hough transform approach to peak alignment of one-dimensional <Superscript>1</Superscript>H NMR data

In metabolic profiling, multivariate data analysis techniques are used to interpret one-dimensional (1D) ¹H NMR data. Multivariate data analysis techniques require that peaks are characterised by the same variables in every spectrum. This location constraint is essential for correct comparison of the intensities of several NMR spectra. However, variations in physicochemical factors can cause the locations of the peaks to shift. The location prerequisite may thus not be met, and so, to solve this problem, alignment methods have been developed. However, current state-of-the-art algorithms for data alignment cannot resolve the inherent problems encountered when analysing NMR data of biological origin, because they are unable to align peaks when the spatial order of the peaks changes—a commonly occurring phenomenon. In this paper a new algorithm is proposed, based on the Hough transform operating on an image representation of the NMR dataset that is capable of correctly aligning peaks when existing methods fail. The proposed algorithm was compared with current state-of-the-art algorithms operating on a selected plasma dataset to demonstrate its potential. A urine dataset was also processed using the algorithm as a further demonstration. The method is capable of successfully aligning the plasma data but further development is needed to address more challenging applications, for example urine data. Figure Traces of NMR peaks visualizing the Generalized Fuzzy Hough Transform (GFHT) method for elucidating peak correspondence between samples. The spectra are sorted according to one shift sensitive peak and reveals that other peaks exhibit a similar shift pattern. This pattern(s) can now be searched for using the GFHT. The red and black spectra in the figure are the most shifting spectra (top and bottom), by following the GFHT traces peak correspondence is easily established although peaks change spatial location Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Matrix-free analysis of aflatoxins in pistachio nuts using parallel factor modeling of liquid chromatography diode-array detection data

In the present study a second-order calibration strategy for high performance liquid chromatography with diode-array detection (HPLC-DAD) has been developed using parallel factor analysis (PARAFAC) and has been applied for simultaneous determination of aflatoxins B₁, B₂, G₁ and G₂ in pistachio nuts in the presence of matrix interferences. Sample preparation was based on solvent extraction (SE) followed by solid phase extraction (SPE) on Bond Elut C18 cartridges. Since the sample preparation procedure was not selective to the analytes of interest, exploiting second-order advantage to obtain concentrations of individual analytes in the presence of uncalibrated interfering compounds seemed necessary. Appropriate pre-processing steps have been applied to correct background signals and the effect of retention time shifts. Transferred calibration data set obtained from standardization of solvent based calibration data has been used in prediction step. The results of PARAFAC on a set of spiked and naturally contaminated pistachio nuts indicated that the four aflatoxins could be successfully determined. The method was validated and multivariate analytical figures of merit were calculated. The advantages of the proposed method are using a low-cost SPE step relative to standard method of aflatoxin analysis (immune affinity column assay), a unique and simple isocratic elution program for all samples and a calibration transfer for saving both chemicals and time of analysis. This study show that coupling of SPE-HPLC-DAD with PARAFAC as a powerful second-order calibration method can be considered as an alternative method for resolution and quantification of aflatoxins in the presence of unknown interferences obtained through analysis of highly complex matrix of pistachio samples and cost per analysis can be reduced significantly.     

Spectrofluorimetric determination of chlorophylls and pheopigments using parallel factor analysis

In this study, parallel factor analysis (PARAFAC) was applied to fluorescence excitation emission matrices (EEM) of chlorophylls and pheopigments dissolved in acetone:water (9:1). The excitation wavelength range was from 350 to 500 nm and the emission was recorded from 600 to 730 nm. Nine standards, comprising mixtures of six analytes, were decomposed into a six-component PARAFAC model. Each component resembled the corresponding EEM of the pure analyte, demonstrating the uniqueness properties of PARAFAC. The score matrix obtained from the model was used for calibration and prediction of an independent set of standards and for eleven samples collected in the Baltic proper. The results obtained by the proposed method were compared to classical least squares (CLS) and to predictions by reference methods (HPLC and visible spectroscopy). For the independent set of standards the proposed method and CLS performed equal well in terms of predictive ability. But for the samples the proposed method yielded results that were in good agreement to the reference methods, whereas CLS failed. Also the so-called "second-order advantage" was examined, showing that not all constituents must be included in the calibration set. The concentration range was for chlorophyll a varied between 10 and 75 mug l(-1), and similar for the other analytes.     

Quantitative analysis of camptothecin derivatives in Nothapodytes foetida using 1H-NMR method

A quantitative analysis using (1)H-NMR has been developed for the determination of camptothecin derivatives and trigonelline in Nothapodytes foetida root, stems and leaves. In the region of delta 9.5-5.5, the signals of H-7 of camptothecin (1), H-10 of 9-methoxycamptothecin (2), H-19 of pumiloside (3) and H-2 of trigonelline (4), were well separated from each other in DMSO-d(6). The quantity of the compounds was calculated by the ratio of the intensity of each compound to the known amount of internal standard 3,4,5-trimethoxybenzaldehyde. These results were compared with the conventional HPLC method. The advantages of the method are that no reference compounds are required for calibration curves, the quantification could be directly realized on a crude extract, an overall profile of the preparation could be directly obtained, and a very significant time-gain could be achieved, in comparison to conventional HPLC methods, for instance.     

Classification of weathered petroleum oils by multi-way analysis of gas chromatography-mass spectrometry data using PARAFAC2 parallel factor analysis

The application of multi-way parallel factor analysis (PARAFAC2) is described for the classification of different kinds of petroleum oils using GC-MS. Oils were subjected to controlled weathering for 2, 7 and 15 days and PARAFAC2 was applied to the three-way GC-MS data set (MSxGCxsample). The classification patterns visualized in scores plots and it was shown that fitting multi-way PARAFAC2 model to the natural three-way structure of GC-MS data can lead to the successful classification of weathered oils. The shift of chromatographic peaks was tackled using the specific structure of the PARAFAC2 model. A new preprocessing of spectra followed by a novel use of analysis of variance (ANOVA)-least significant difference (LSD) variable selection method were proposed as a supervised pattern recognition tool to improve classification among the highly similar diesel oils. This lead to the identification of diagnostic compounds in the studied diesel oil samples.     

Metabolic fingerprinting of Ephedra species using 1H-NMR spectroscopy and principal component analysis

The metabolomic analysis of Ephedra species was performed using 1H-NMR spectroscopy and multivariate data analysis. A broad range of metabolites could be detected by 1H-NMR spectroscopy without any chromatographic separation. The principal component analysis used to reduce the huge data set obtained from the 1H-NMR spectra of the plant extracts clearly discriminated three different Ephedra species. The major differences in Ephedra sinica, Ephedra intermedia and Ephedra distachya var. distachya were found to be due to benzoic acid analogues in the aqueous fraction and ephedrine-type alkaloids in the organic fraction. Based on this metabolomic recognition, one of nine commercial Ephedra materials evaluated was shown to be a mixture of Ephedra species. This method will be a useful tool for chemotaxonomic analysis and authentification of Ephedra species including quality control of plant materials.     

Applicable and cost-efficient microplastic analysis by quantitative 1H-NMR spectroscopy using benchtop NMR and NoD methods

In continuation of our work on the proof-of-concept that quantitative NMR spectroscopy may be a valuable tool in microplastic (MP) analysis and quantification, we present here investigations using low-field NMR spectrometers and nondeuterated solvents for the analysis of solutions of MP particles in suitable solvents. The use of low-field NMR spectrometers (benchtop NMR) that are considerably more cost-effective in terms of purchase and operating costs compared with high-field NMR spectrometers and the use of nondeuterated solvents (NoD method) leads to an applicable and cost-efficient method for mass-based MP analysis. For benchtop 80-MHz NMR, limits of detection for polyvinylchloride (PVC), polyethylene terephthalate (PET), and polystyrene (PS) are in the same range as if a high-field 500-MHz NMR spectrometer was used for quantification (500 MHz: PET 1 μg/ml, PVC 42 μg/ml, and PS 9 μg/ml; 80 MHz: PET 4 μg/ml, PVC 19 μg/ml, and PS 21 μg/ml) for polymers being dissolved in deuterated solvents. The same is true for the corresponding limits of quantification. Moreover, it is shown for the first time that quantitative determination of the mass concentration of PET, PVC, and PS is also possible using NoD methods by evaluating the integrals of polymer-specific signals relative to an internal or external standard. Detection limits for NoD methods are in a similar range as if deuterated solvents were used (PET 2 μg/ml, PVC 39 μg/ml, and PS 8 μg/ml) using a high-field 500-MHz spectrometer or the 80-MHz spectrometer (PET 5 μg/ml).     

On uniqueness and selectivity in three-component parallel factor analysis

Unambiguous recovery of profiles is a distinguishable advantage of Parallel Factor Analysis (PARAFAC) as a trilinear model and has made it a promising exploratory tool for data analysis. Linear dependency in profiles destroys trilinearity and will increase ambiguity in the curve resolution of three-way data sets. PARAFAC uniqueness deteriorates totally or partially in data sets with linearly dependent loadings. Exploiting a reliable method for determination and direct visualization of feasible bands in the PARAFAC model can be helpful not only in full characterization of uniqueness conditions but also in the investigation of the effects of constraints on the PARAFAC feasible solutions. The purpose of this paper is twofold. First, the calculation of rotational ambiguity in the PARAFAC model extends to three components system. The principle behind the algorithm is described in detail and tested for simulated and real data sets. Completely general and thoroughly investigated results are presented for the three component cases. Secondly, the effects of selective regions in the profiles on the resolution of systems that suffered from the rank deficiency problem, due to rank overlap, are emphasized. In the case of two-way data sets the effect of selectivity constraint on the unique recovery of profiles was investigated and applied. However, to our knowledge, in this report, for the first time, the effect of the presence of selective windows in the profiles, on the unique resolution of three-way data sets has been systematically investigated.     

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.     

NMR and pattern recognition methods in metabolomics: From data acquisition to biomarker discovery: A review

Metabolomics is the discipline where endogenous and exogenous metabolites are assessed, identified and quantified in different biological samples. Metabolites are crucial components of biological system and highly informative about its functional state, due to their closeness to functional endpoints and to the organism's phenotypes. Nuclear Magnetic Resonance (NMR) spectroscopy, next to Mass Spectrometry (MS), is one of the main metabolomics analytical platforms. The technological developments in the field of NMR spectroscopy have enabled the identification and quantitative measurement of the many metabolites in a single sample of biofluids in a non-targeted and non-destructive manner. Combination of NMR spectra of biofluids and pattern recognition methods has driven forward the application of metabolomics in the field of biomarker discovery. The importance of metabolomics in diagnostics, e.g. in identifying biomarkers or defining pathological status, has been growing exponentially as evidenced by the number of published papers. In this review, we describe the developments in data acquisition and multivariate analysis of NMR-based metabolomics data, with particular emphasis on the metabolomics of Cerebrospinal Fluid (CSF) and biomarker discovery in Multiple Sclerosis (MScl).     

Monitoring of molecular transformations in acid-base reactions by evolving factor analysis of Fourier transform infrared spectral data

An evolving factor analysis procedure with concentration constraints (gradient concentration window) was applied to the analysis of data sets of aqueous Fourier transform infrared (FT-IR) spectra of carboxylic acids (acetic, malonic and succinic acids) collected in experiments with varying pH. Besides the calculation of the number of acid-base systems, this procedure allowed the calculation of the FT-IR spectra of the acid-base species present in equilibrium as well as the corresponding pK(a) values.     

Quantitative analysis of bilobalide and ginkgolides from Ginkgo biloba leaves and Ginkgo products using (1)H-NMR

1H-NMR spectrometry was applied to the quantitative analysis of the bilobalide, ginkgolides A, B, and C in Ginkgo biloba leaves and six kinds of commercial Ginkgo products without any chromatographic purification. The experiment was performed by the analysis of each singlet H-12, which were well separated in the range of delta 6.0-7.0 in the (1)H-NMR spectrum. However, the H-12 protons of bilobalide and ginkgolides may have overlapped with H-6 or H-8 protons of the Ginkgo flavonoids. Therefore, the optimum (1)H-NMR solvent for the analysis of the compound was selected through the evaluation of solvent effects on the resolution of these signals from the compounds. Acetone-d(6)-benzene-d(6) (50 : 50) was found to be the best one among the solvents evaluated. The quantity of the compounds was calculated by the relative ratio of the intensity of each compound to the known amount of internal standard (25 microgram), phloroglucinol. This method allows rapid and simple quantitation of underivatized bilobalide and ginkgolides in 5 min without any pre-purification steps.     

Quantitative analysis of isoprene units in natural rubber and synthetic polyisoprene using 1H-NMR spectroscopy with an internal standard

Isoprene units in natural rubber (NR) and its synthetic analogues were quantified by ¹H-NMR spectroscopy using polyethylene glycol (PEG) as an internal standard. The effect of PEG and rubber concentrations, molar ratio of rubber/PEG, measuring temperature and scan number on the quantification was investigated to establish the respective working range. Analysis of commercial grades of NR revealed that the differences in 1,4 isoprene content is caused by the production process and feedstock, in which proteins and lipids were found to be the major impurity in NR. Gel fraction of NR has insignificant effect on the measurement of 1,4 isoprene content. Furthermore, the new method was found to produce good results for the quantification of 1,4 and 3,4 units of synthetic polyisoprenes.     

Simultaneous mixture analysis by using non-linear spectrophotometric data and linear iterative target transformation factor analysis

Non-linear absorption spectral data obtained from ternary mixtures of analytes are analyzed by using a linear model, iterative target transformation factor analysis (ITTFA). The use of transformed original variables is used to correct non-linearities in the original data. Absorbance below a certain limit (k) is described as linear and above this limit as non-linear. The extension of the regressor variables is the squared absorbances above the linear range. The variation of the prediction error as a function of the number of the factors and the k-values were considered and the minimum prediction error was evaluated for reaching to optimum. Except the natural non-negativity constraint the correlation constraint also is used on concentration vector in each iteration of ITTFA algorithm. The reliability of the method is evaluated using model data for ternary mixtures by spectral overlapping and different degrees of non-linearity. Simultaneous spectrophotometric determination of Eu³⁺, UO₂²⁺ and Th⁴⁺ with arsenazo III as chromogenic reagent is used as experimental model systems with non-linearity behavior of Eu³⁺and UO₂²⁺ components. The application to both synthetic and real data sets with different degrees of non-linearity demonstrate the ability of the proposed methodology to obtain better results than original data and ITTFA. The relative standard errors of prediction for proposed method in comparison with using the PLS calibration on original and extended data are nearly smaller.     

Diagnosis of early stage nasopharyngeal carcinoma using ultraviolet autofluorescence excitation-emission matrix spectroscopy and parallel factor analysis

We report the diagnostic ability of ultraviolet (UV)-excited autofluorescence (AF) excitation-emission matrix (EEM) spectroscopy associated with parallel factor (PARAFAC) analysis for differentiating cancer from normal nasopharyngeal tissue. A bifurcated fiber-optic probe coupled with an EEM system was used to acquire tissue AF EEMs using excitation wavelengths between 260 and 400 nm, and emission collection between 280 and 500 nm. A total of 152 AF EEM landscapes were acquired from 13 normal and 16 nasopharyngeal carcinoma (NPC) thawed ex vivo tissue samples from 23 patients. PARAFAC was introduced for curve resolution of individual AF EEM landscapes associated with the endogenous tissue constituents. The significant factors were further fed to a support vector machine (SVM) and cross-validated to construct diagnostic algorithms. Both the EEM intensity landscapes and the PARAFAC model revealed tryptophan, collagen, and elastin to be the three major endogenous fluorophores responsible for the AF signal from normal and NPC tissues. The EEM intensity distribution and PARAFAC factors suggest an increase of tryptophan and a decrease of collagen and elastin in NPC tissues compared to the normal. The classification results obtained from the PARAFAC-SVM modeling yielded a diagnostic accuracy of 94.7% (sensitivity of 95.0% (76/80); specificity of 94.4% (68/72)) for normal and NPC tissue differentiation. This study suggests that UV-excited AF EEM spectroscopy integrated with PARAFAC algorithms has the potential to provide clinical diagnostics of early onset and progression of NPC.     

Simultaneous analysis of the photocatalytic degradation of polycyclic aromatic hydrocarbons using three-dimensional excitation-emission matrix fluorescence and parallel factor analysis

Polycyclic aromatic hydrocarbons (PAHs) may be photochemically degraded. Monitoring of degradation process of PAHs is carried out by traditional methods, which normally imply time-consuming procedures that do not allow the chemical process to be analyzed in real time. In the present study, photodegradation kinetics of dibenz[a,h]anthracene, benz[a]anthracene, benz[a]pyrene and benz[k]fluorantene were investigated in aqueous solutions under different conditions. A 2³ factorial design was used for optimizing the degradation process.Fluorescence spectroscopy is a fast, cheap and sensitive analytical method, attractive for use in conjunction with chemometric methods; in this case three-way analytical methodology based on fluorescence excitation-emission matrix (EEM) and parallel factor analysis (PARAFAC) was employed. A four-factor PARAFAC model made it possible to resolve the species presents in the degradation mixture and quantify the relative concentration of the analytes throughout the degradation. Several different parameters, such as core consistency, percentage of fit and correlation coefficients between recovered and reference spectra were employed to determine the suitable number of factors for the PARAFAC model. This new methodology allows us to determine satisfactorily the PAHs concentration during the photodegradation in mixtures of arbitrary composition, representing an interesting alternative to the conventional techniques normally used for the monitoring of degradation reactions.     

Rapid, non-targeted discovery of biochemical transformation and biomarker candidates in oncovirus-infected cell lines using LAESI mass spectrometry

Finding insights into how viruses hijack metabolic processes and biomarkers for viral diseases often require hypotheses about target compounds and/or labelling techniques. Here we present a method based on laser ablation electrospray ionization mass spectrometry to rapidly identify potential protein and metabolite biomarkers of oncovirus infection in B lymphocytes.     

Pattern recognition analysis for classification of hypertensive model rats and diurnal variation using 1H-NMR spectroscopy of urine.

Urine samples were collected during the daytime and nighttime from spontaneously hypertensive model rats and normal rats without dosing. The 1H NMR spectra were measured for their urine samples, and analyzed by a pattern recognition method, known as Principal Component Analysis (PCA) and Soft Independent Modeling of Class Analogy (SIMCA). The separation of urinary data due to the diurnal variation (daytime and nighttime) and also to the difference between the two strains of rat was achieved in the PCA score plot. Differences of the urinary profiles in the respective separation were effectively extracted as marker variables by the SIMCA method. NMR measurements coupled with pattern recognition methods provide a straightforward approach to inspect the disease metabolic status and the preliminary screening tool of marker candidates for further development.     

Comparison of oil spillages using mid-IR indexes and 3-way procrustes rotation, matrix-augmented principal components analysis and parallel factor analysis

Three different approaches for 3-way analyses, namely, Procrustes rotation, parallel factor analysis (PARAFAC) and matrix-augmented principal component analysis (MA-PCA), have been used to compare six different oil spillages made under controlled conditions (one of them corresponding to the heavy oil released after the sunk of the Prestige tanker off the Galician coast-NW Spain on November 2002). Each spillage was monitored during three and a half months by attenuated total reflectance (ATR) mid-IR spectroscopy. Ten characteristic band ratios were defined. Results showed that the three 3-way chemometric techniques lead to essentially the same conclusions, where from it was concluded that the most relevant pattern defining the oil weathering was related to ‘total aromaticity’, i.e., the total number of CC bonds in the molecules which form the products. In addition, weathering of the samples got clearly characterized by a steady evolution on the scores (sample weights), with a clear increase after 11-14 days. Differentiation of the products (slices of the data cube) was also possible due to their intrinsic characteristics as, in general, heavy products oppose to the lightest ones.