Multivariate selectivity as a metric for evaluating comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry subjected to chemometric peak deconvolution

Two-dimensional gas chromatography (GC x GC) coupled to time-of-flight mass spectrometry (TOFMS) [GC x GC-TOFMS)] is a highly selective technique well suited to analyzing complex mixtures. The data generated is information-rich, making it applicable to multivariate quantitative analysis and pattern recognition. One separation on a GC x GC-TOFMS provides retention times on two chromatographic columns and a complete mass spectrum for each component within the mixture. In this report, we demonstrate how GC x GC-TOFMS combined with trilinear chemometric techniques, specifically parallel factor analysis (PARAFAC) initiated by trilinear decomposition (TLD), results in a powerful analytical methodology for multivariate deconvolution. Using PARAFAC, partially resolved components in complex mixtures can be deconvoluted and identified without requiring a standard data set, signal shape assumptions or any fully selective mass signals. A set of four isomers (iso-butyl, sec-butyl, tert-butyl, and n-butyl benzenes) is used to investigate the practical limitations of PARAFAC for the deconvolution of isomers at varying degrees of chromatographic resolution and mass spectral selectivity. In this report, multivariate selectivity was tested as a metric for evaluating GC x GC-TOFMS data that is subjected to PARAFAC peak deconvolution. It was found that deconvolution results were best with multivariate selectivities over 0.18. Furthermore, the application of GC x GC-TOFMS followed by TLD/PARAFAC is demonstrated for a plant metabolite sample. A region of GC x GC-TOFMS data from a complex natural sample of a derivatized metabolic plant extract from Huilmo (Sisyrinchium striatum) was analyzed using TLD/PARAFAC, demonstrating the utility of this analytical technique on a natural sample containing overlapped analytes without selective ions or peak shape assumptions.     

Two-dimensional analysis of tear protein patterns of diabetic patients.

In diabetic patients, dry eye and other ocular surface diseases occur more often than in healthy subjects. The aim of this study was to analyze the tear protein patterns of patients suffering from diabetes mellitus type II (dia) and to compare them to the patterns of healthy volunteers (ctrl). Tear proteins of nonstimulated tears of 20 patients (ctrl n=10, dia n=10) were separated using two-dimensional electrophoretic techniques. The protein patterns of each group were analyzed by a multivariate analysis of discriminance. Furthermore, for all spots of each gel, a 50 x 50 variables pH/Mr (molecular weight) array was generated and subsequently analyzed by a multivariate analysis of discriminance. Additionally, an artificial neural network was trained using the matrix data as input and a sensitivity analysis was performed to figure out, which spots were the most important to differentiate between the tear protein patterns. In both groups a complex staining pattern could be obtained. In diabetic patients significantly more spots were detected compared to the control group (P<0.02). The analysis of discriminance found a highly significant difference between dia and ctrl (P<0.00001). Using the matrix data, the analysis of discriminance showed a significant difference between the two groups, too (P<0.0001). The sensitivity analysis by means of the artificial neural network revealed several spots that were more expressed or more frequently present in the diabetic group. Our findings reveal that the composition of tear proteins of diabetic patients is different from that of healthy subjects. The use of the two-dimensional electrophoretic technique could give more insight into the diabetic-related changes in the tear film composition.     

Are biosensor arrays in one membrane possible? A combination of multifrequency impedance measurements and chemometrics

A novel concept of a membrane-based micro-array biosensor is presented. The methodology is based on a single lipid membrane interrogated with electrochemical impedance techniques followed by multivariate data analysis. A single membrane is designed so that relaxation processes with a range of time constants can be probed at different potentials. A range of other approaches cited in the literature is reviewed.     

Local covariance order diffusion-ordered spectroscopy: a powerful tool for mixture analysis

Diffusion-ordered spectroscopy (DOSY) is an important tool in NMR mixture analysis that has found use in most areas of chemistry, including organic synthesis, drug discovery, and supramolecular chemistry. Typically the aim is to disentangle the overlaid, and often overlapped, NMR spectra of individual mixture components and/or to obtain size and interaction information from their respective diffusion coefficients. The most common processing method, high-resolution DOSY, breaks down where component spectra overlap; here multivariate methods can be very effective, but only for small numbers (2-5) of components. In this study, we present a hybrid method, local covariance order DOSY (LOCODOSY), that breaks a spectral data set into suitable windows and analyzes each individually before combining the results. This approach uses a multivariate algorithm (e.g., SCORE or DECRA) to resolve only a small number of components in any given window. Because a small spectral region should contain signals from only a few components, even when the spectrum as a whole contains many more, the total number of resolvable chemical components rises dramatically. It is demonstrated here that complete resolution of component spectra can be achieved for mixtures that are much more complex than could previously be analyzed with DOSY. Thus, LOCODOSY is a powerful, flexible tool for processing NMR diffusion data of complex mixtures.     

Investigation of the interaction of carbofuran and DNA by voltammetry and fluorescence with the aid of chemometrics

<正>The interactions of carbofuran and DNA were studied using voltammetry and fluorescence spectroscopy.The formation of carbofuran-DNA makes the current peak of DNA decreased by voltammetry method.The binding number(n) and constant(K_a) for complex carbofuran-DNA were calculated to be 1.06±0.04 and 0.11±0.03mol~(-1) L,respectively by fluorescence measurement.Chemometrics approach,such as singular value decomposition(SVD) was used to evaluate the number of spectral species in the drug-DNA binding process.And the pure spectra and concentration profiles in the kinetic system were clearly deduced by multivariate curve resolution alternating least squares(MCR-ALS) with the initial estimates by evolving factor analysis(EFA).     

Detailed analysis and group-type separation of natural fats and oils using comprehensive two-dimensional gas chromatography

Comprehensive gas chromatography (GC x GC) is an adequate methodology for the separation and identification of very complex samples. It is based on the coupling of two capillary columns that each give a different but substantial contribution to the unprecedented resolving power of this technique. The 2D space chromatograms that derive from GC x GC analysis have great potential for identification. This is due to the fact that the contour plot positions, pinpointed by two retention time coordinates, give characteristic patterns for specific families of compounds that can be mathematically translated. This investigation concerned the application of this principle to fatty acid methyl esters that were grouped on an equal double bond number basis. The ester samples were derived from various lipids and all underwent bidimensional analysis on two sets of columns. Peak attribution was supported by mass spectra, linear retention indices and information reported in the literature.     

Gramicidin conducting dimers in lipid bilayers are stabilized by single-file ionic flux along them

Gramicidin D was incorporated in a biomimetic membrane consisting of a lipid bilayer tethered to a mercury electrode via a hydrophilic spacer, and its behavior was investigated in aqueous 0.1 M KCl by potential-step chronocoulometry and electrochemical impedance spectroscopy. The impedance spectra, recorded from 0.1 to 1 x 10(5) Hz over a potential range of 0.7 V, were fitted to a series of RC meshes, which were related to the different substructural elements of the biomimetic membrane. These impedance spectra were compared with those obtained by incorporating valinomycin, under otherwise identical conditions. The potential dependence of the stationary currents reported on bilayer lipid membranes by Bamberg and L?uger (Bamberg, E.; L?uger, P. J. Membrane Biol. 1973, 11, 177-194) as well as those extracted from potential-step chronocoulometric measurements was interpreted by relating the increase in gramicidin dimerization to a progressive increase in single-file K+ flux along the dimeric channels. An analogous approach was adopted in explaining the difference between the impedance spectra obtained with gramicidin D and those obtained with valinomycin. It is concluded that gramicidin has a low tendency to form dimers in the absence of ionic flux.     

A Critical Evaluation and Modification of the Padé–Laplace Method for Deconvolution of Viscoelastic Spectra

This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations. Analysis of different sets of generated data points from known multi-exponential functions indicates that by increasing the level of Padé approximants, the condition number of a matrix whose entries are coefficients of a Taylor series in the Laplace space grows rapidly. When higher levels of Padé approximants need to be computed to achieve stable modes for separation of exponentials, the problem of generating matrices with large condition numbers becomes more pronounced. The analysis in this paper discusses the origin of ill-posedness of the PL method and it was shown that ill-posedness may be regularized by reconstructing the system of equations and using singular value decomposition (SVD) for computation of the Padé table. Moreover, it is shown that after regularization, the PL method can deconvolute the exponential decays even when the input parameter of the method is out of its optimal range.     

Automated resolution of overlapping peaks in chromatographic data

Parallel factor analysis 2 (PARAFAC2) has been shown to be a powerful tool for resolution of complex overlapping peaks in chromatographic analyses. It is particularly useful because of its ability to handle shifts in the elution time mode and peak shape changes. Like all curve resolution techniques, PARAFAC2 will only find chemically meaningful parameters (elution time profiles and mass spectra) if the correct number of factors are determined. So far, the primary way to determine an appropriate number of factors, when using PARAFAC2, is to calculate models with different number of factors and then inspect the models manually. This approach is time consuming, and the result may be biased because of the manual assessment of the model quality, making PARAFAC2 inaccessible for analytical chemists in general. Here, we develop a method that can determine an appropriate number of factors in an automated way. The automation is based on a number of model diagnostics (quality criteria) collected from models with different numbers of factors. Combining these diagnostics, it is possible to assess what the appropriate number of components is. In this work, only gas chromatography–mass spectrometry data are considered. However, it will most likely be fairly straightforward to expand the work to also cover liquid chromatography data (with a multivariate detector). Automating the model quality evaluation of the PARAFAC2 model enables both the inexperienced and trained user to perform comprehensive and advanced analysis of chromatographic data with a minimum of manual work. © 2013 The Authors. Journal of Chemometrics Published by John Wiley & Sons Ltd.     

Combination of dynamic time warping and multivariate analysis for the comparison of comprehensive two-dimensional gas chromatograms: application to plant extracts

Comprehensive two-dimensional gas chromatography (GC x GC) is now recognized as the preferred technique for the detailed analysis and characterization of complex mixtures of volatile compounds. However, for comparison purposes, taking into account all the information contained in the chromatogram is far from trivial. In this paper, it is shown that the combination of peak alignment by dynamic time warping and multivariate analysis facilitated the comparison of complex chromatograms of tobacco extracts. The comparison is shown to be efficient enough to provide a clear discrimination among three types of tobacco. A tentative interpretation of loadings is presented in order to give access to the compounds which differ from one sample to another. Once located, mass spectrometry was used to identify markers of tobacco type.     

Characterization and determination of stability constants of copper(II)-l-histidine complexation system by using multivariate curve resolution method of visible spectra and two hard modeling methods in aqueous solutions

Multivariate curve resolution, alternating least-squares is applied to spectra data obtained in the study of Cu(II) complexation by l-histidine. The combination of several chemometric techniques based on factor analysis (FA), singular value decomposition (SVD), evolving factor analysis (EFA), and multivariate curve resolution with constrained alternating least-squares (ALS) is used to determine the number of species and their distribution diagram. This multivariate analysis data treatment simultaneously reveals the species Cu, CuL, CuLH, CuL₂, CuL₂H, and CuLOH, through the calculated concentration profiles and allows the assignment of numerically obtained pure individual spectra. Formation constants of these species were calculated by hard-modeling methods applied potentiometric and spectrophotometric measurements.     

Multivariate data analysis for enhanced interpretation of electrochemical impedance spectra of gramicidin-ion interactions in phospholipid monolayers

This article describes a multifrequency electrochemical impedance study of phospholipid monolayers on a mercury drop electrode in solutions containing electrolytes and gramicidin derivatives: gramicidin A (gA), gramicidin-BOC (g-BOC), and desformylgramicidin (g-des). The impedance spectra have been studied individually (univariate approach) and also transformed using a multivariate data reduction method (multivariate approach). It was shown that the two approaches are complementary. Thus the formation of K+-conducting channels is observed in gA only, and these channels can be distinguished from an interaction of all gramicidin derivatives with Mg2+. An unknown peptide interaction in the monolayer was observed on a slow time scale.     

High speed multi-frequency impedance analysis of single particles in a microfluidic cytometer using maximum length sequences

A novel impedance spectroscopy technique has been developed for high speed single biological particle analysis. A microfluidic cytometer is used to measure the impedance of single micrometre sized latex particles at high speed across a range of frequencies. The setup uses a technique based on maximum length sequence (MLS) analysis, where the time-dependent response of the system is measured in the time domain and transformed into the impulse response using fast M-sequence transform (FMT). Finally fast Fourier transform (FFT) is applied to the impulse response to give the transfer-function of the system in the frequency domain. It is demonstrated that the MLS technique can give multi-frequency (broad-band) measurement in a short time period (ms). The impedance spectra of polystyrene micro-beads are measured at 512 evenly distributed frequencies over a range from 976.5625 Hz to 500 kHz. The spectral information for each bead is obtained in approximately 1 ms. Good agreement is shown between the MLS data and both circuit simulations and conventional AC single frequency measurements.     

Utilization of characteristics of fast linear prediction based on the lattice algorithm in an analysis of time domain magnetic resonance

We examined details of the fast linear prediction (FLP) analysis of time domain data. The FLP method is introduced by Gesmar and Hansen [J. Magn. Reson., Ser. A 106 (1994) 236] to improve computational efficiency of the LP analysis. We focused on two characteristic features of FLP inherited from the lattice algorithm. The first is bi-directional prediction. One can obtain both forward and backward prediction models by single execution of FLP. It is found that distances between the forward and backward prediction roots in a complex plane can be used to determine a number of resonance lines. We showed that the method utilizing the distance is as effective as that using the singular value of the singular value decomposition (SVD) analysis. Secondly, the FLP method gives prediction models for all of smaller prediction orders than some given value. This character enables one to examine a prediction order dependence of spectral parameters estimated by the analysis. We found that there were significant differences in the order dependence of the estimated frequencies between true and false resonance signals.     

Thermodynamic characterization of weak association equilibria accompanied with spectral overlapping by a SVD-based chemometric method

A singular value decomposition (SVD)-based chemometric method is used for deconvolution of spectral information obtained from a single sample containing an equilibrium system with spectral overlapping at different temperatures. The output of analysis is the association constants at each temperature, thermodynamic parameters and the component spectral profiles. Thermodynamic characterization of charge-transfer complex formation between chloranil and some aromatic hydrocarbons are used as a model system for weak association equilibria and strong component spectral overlapping. The approach can be successfully applied for studying equilibrium systems, which cannot be treated with classical methods like Benesi-Hildebrand method due to the presence of systematic errors.     

A strategy for ranking environmentally occurring chemicals. Part VI. QSARs for the mutagenic effects of halogenated aliphatics.

A strategy for the systematic analysis and priority ranking of environmental chemicals has been applied to a class of 58 halogenated aliphatic hydrocarbons. A training set of ten compounds representing this class, was selected by statistical design. The training set compounds were then subjected to biological testing in the Salmonella typhimurium reverse mutation assay (Ames test). The measured biological data, recorded as dose-response curves, were analyzed to determine the mutagenic potency (slope of the initial portion) and the mutagen dose (MD 50) required to increase the number of revertants above the background by 50%. For each compound, four mutagenic potency estimates and four MD 50 values were determined, all originating from the tester strains TA 100 and TA 1535 with and without metabolic activation. The obtained responses were analyzed with multivariate techniques to give QSAR models relating the mutagenic potency data to the physico-chemical properties of the compounds. Finally, the derived QSARs were used to predict the mutagenic potencies and the MD 50S for the non-tested compounds in the class.     

Automatic analysis of mixed spectra : Generalised spectral subtraction applied to electron spin resonance spectroscopy

A new technique is described for estimating the pure component spectra from a set of linearly independent spectra. The process is one of generalised spectral subtraction in which an iterative combination of multivariate linear least-squares analysis and matrix transformation is applied to the input data to give estimates of the number of independent components in the original mixed spectra. This technique is applicable to bipolar data (e.g. from e.p.r. spectra) as well as absorption spectra determined by any spectroscopic technique, provided that the spectra may be reasonably assumed to be an additive mixture of unknown pure components. Numerical model examples are given together with an experimental application to electron spin resonance.     

Coordination Numbers of Central Atoms in Coordination Compounds

A sample of structurally characterized 10000 complexes (X-ray diffraction data) was carefully selected from available databases for analysis of coordination numbers (CNs) of their central atoms (complexing agents). The coordination numbers of various chemical elements are tabulated for their different oxidation numbers (ONs). Variations in CN with the ordinal number of an element in the Periodic Table were followed. A general distribution of the sample complexes over the CNs of the central atom, as well as their distributions for particular ONs, is displayed. References to particular coordination compounds are given for extreme and very uncommon CNs of a central atom with different ONs. A general pattern of the observed variations in the CN of chemical elements can be useful for predicting the properties of complexes, constructing their stability models, designing compounds with rich and unique properties, and developing retrieval and graphic tools for chemical databases.     

A tutorial review: Metabolomics and partial least squares-discriminant analysis – a marriage of convenience or a shotgun wedding

The predominance of partial least squares-discriminant analysis (PLS-DA) used to analyze metabolomics datasets (indeed, it is the most well-known tool to perform classification and regression in metabolomics), can be said to have led to the point that not all researchers are fully aware of alternative multivariate classification algorithms. This may in part be due to the widespread availability of PLS-DA in most of the well-known statistical software packages, where its implementation is very easy if the default settings are used. In addition, one of the perceived advantages of PLS-DA is that it has the ability to analyze highly collinear and noisy data. Furthermore, the calibration model is known to provide a variety of useful statistics, such as prediction accuracy as well as scores and loadings plots. However, this method may provide misleading results, largely due to a lack of suitable statistical validation, when used by non-experts who are not aware of its potential limitations when used in conjunction with metabolomics. This tutorial review aims to provide an introductory overview to several straightforward statistical methods such as principal component-discriminant function analysis (PC-DFA), support vector machines (SVM) and random forests (RF), which could very easily be used either to augment PLS or as alternative supervised learning methods to PLS-DA. These methods can be said to be particularly appropriate for the analysis of large, highly-complex data sets which are common output(s) in metabolomics studies where the numbers of variables often far exceed the number of samples. In addition, these alternative techniques may be useful tools for generating parsimonious models through feature selection and data reduction, as well as providing more propitious results. We sincerely hope that the general reader is left with little doubt that there are several promising and readily available alternatives to PLS-DA, to analyze large and highly complex data sets.