A comprehensive two-dimensional retention time alignment algorithm to enhance chemometric analysis of comprehensive two-dimensional separation data

A comprehensive two-dimensional (2D) retention time alignment algorithm was developed using a novel indexing scheme. The algorithm is termed comprehensive because it functions to correct the entire chromatogram in both dimensions and it preserves the separation information in both dimensions. Although the algorithm is demonstrated by correcting comprehensive two-dimensional gas chromatography (GC x GC) data, the algorithm is designed to correct shifting in all forms of 2D separations, such as LC x LC, LC x CE, CE x CE, and LC x GC. This 2D alignment algorithm was applied to three different data sets composed of replicate GC x GC separations of (1) three 22-component control mixtures, (2) three gasoline samples, and (3) three diesel samples. The three data sets were collected using slightly different temperature or pressure programs to engender significant retention time shifting in the raw data and then demonstrate subsequent corrections of that shifting upon comprehensive 2D alignment of the data sets. Thirty 12-min GC x GC separations from three 22-component control mixtures were used to evaluate the 2D alignment performance (10 runs/mixture). The average standard deviation of first column retention time improved 5-fold from 0.020 min (before alignment) to 0.004 min (after alignment). Concurrently, the average standard deviation of second column retention time improved 4-fold from 3.5 ms (before alignment) to 0.8 ms (after alignment). Alignment of the 30 control mixture chromatograms took 20 min. The quantitative integrity of the GC x GC data following 2D alignment was also investigated. The mean integrated signal was determined for all components in the three 22-component mixtures for all 30 replicates. The average percent difference in the integrated signal for each component before and after alignment was 2.6%. Singular value decomposition (SVD) was applied to the 22-component control mixture data before and after alignment to show the restoration of trilinearity to the data, since trilinearity benefits chemometric analysis. By applying comprehensive 2D retention time alignment to all three data sets (control mixtures, gasoline samples, and diesel samples), classification by principal component analysis (PCA) substantially improved, resulting in 100% accurate scores clustering.     

Dependence of effective peak capacity in comprehensive two-dimensional separations on the distribution of peak capacity between the two dimensions

One of the basic tenets of comprehensive two-dimensional chromatography is that the total peak capacity is simply the product of the first- and second-dimension peak capacities. As formulated, the total peak capacity does not depend on the relative values of the individual dimensions but only on the product of the two. This concept is tested here for the experimentally realistic situation wherein the first-dimension separation is undersampled. We first propose that a relationship exists between the number of observed peaks in a two-dimensional separation and the effective peak capacity. We then show here for a range of reasonable total peak capacities (500-4000) and various contributions of peak capacity in each dimension (10-150) that the number of observed peaks is only slightly dependent on the relative contributions over a reasonable and realistic range in sampling times (equal to the first-dimension peak standard deviation, multiplied by 0.2-16). Most of this work was carried out under the assumption of totally uncorrelated retention times. For uncorrelated separations, the small deviations from the product rule are due to the "edge effect" of statistical overlap theory and a recently introduced factor that corrects for the broadening of first-dimension peaks by undersampling them. They predict that relatively more peaks will be observed when the ratio of the first- to the second-dimension peak capacity is much less than unity. Additional complications are observed when first- and second-dimension retention times show some correlation, but again the effects are small. In both cases, deviations from the product rule are measured by the relative standard deviations of the number of observed peaks, which are typically 10 or less. Thus, although the basic tenet of two-dimensional chromatography is not exact when the first dimension is undersampled, the deviations from the product rule are sufficiently small as to be unimportant in practical work. Our results show that practitioners have a high degree of flexibility in designing and optimizing experimental comprehensive two-dimensional separations.     

Effect of first-dimension undersampling on effective peak capacity in comprehensive two-dimensional separations

The objective of this work is to establish a means of correcting the theoretical maximum peak capacity of comprehensive two-dimensional (2D) separations to account for the deleterious effect of undersampling first-dimension peaks. Simulations of comprehensive 2D separations of hundreds of randomly distributed sample constituents were carried out, and 2D statistical overlap theory was used to calculate an effective first-dimension peak width based on the number of observed peaks in the simulated separations. The distinguishing feature of this work is the determination of the effective first-dimension peak width using the number of observed peaks in the entire 2D separation as the defining metric of performance. We find that the ratio of the average effective first-dimension peak width after sampling to its width prior to sampling (defined as ) is a simple function of the ratio of the first-dimension sampling time (t(s)) to the first-dimension peak standard deviation prior to sampling (1sigma): = square root1+0.21(t /(s)(1) sigma(2) This is valid for 2D separations of constituents having either randomly distributed or weakly correlated retention times, over the range of 0.2 on t(s)/1 sigma from this expression is in qualitative agreement with previous work based on the effect of undersampling on the effective width of a single first-dimension peak, but predicts up to 35% more broadening of first-dimension peaks than is predicted by previous models. This simple expression and accurate estimation of the effect of undersampling first-dimension peaks should be very useful in making realistic corrections to theoretical 2D peak capacities, and in guiding the optimization of 2D separations.     

Data reduction in comprehensive two-dimensional gas chromatography for rapid and repeatable automated data analysis

A rapid approach for comprehensive two-dimensional gas chromatographic data analysis is introduced, providing important environmental metrics including total petroleum hydrocarbon concentration as well as chemical-class distribution. The approach, comprising transformation of exported data files to two-dimensional retention time arrays, blank subtraction, alignment and projection onto new axes, subdivision of the aligned two-dimensional data matrix, and compilation of summary data is able to be performed without user intervention. The approach satisfies critical goals of rapid batch analysis with repeatability and traceability. Application to assessment of petroleum hydrocarbon contaminated soil samples from Macquarie Island, a remote Southern Ocean island, is shown to illustrate the utility of this new data analysis strategy.     

Nondestructive analysis and dating of historical paper based on IR spectroscopy and chemometric data evaluation

Sampling restrictions in analysis of cultural heritage materials narrow the choice of appropriate analytical methods considerably. In this work, near- and mid-FT-IR reflectance data were related to paper properties determined with classical analytical methods using partial least-squares. Nondestructive determination of properties, which are of importance for evaluation of the long-term stability of historical paper, i.e., ash content, lignin content, degree of polymerization of cellulose, pH, and aluminum content, is possible. With the use of a considerable sample set, satisfactory reliability was achieved for all properties but aluminum content. Considering that with age, chemical properties of paper change, dating of historical documents was attempted for the first time, also with success.     

Limits of detection and quantification in comprehensive multidimensional separations. 1. A theoretical look

Comprehensive multidimensional separations (e.g., GC×GC, LC×LC, etc.) are increasingly popular tools for the analysis of complex samples, due to their many advantages, such as vastly increased peak capacity, and improvements in sensitivity. The most well-established of these techniques, GC×GC, has revolutionized analytical separations in fields as diverse as petroleum, environmental research, food and flavors, and metabolic profiling. Using multidimensional approaches, analytes can be quantified at levels substantially lower than those possible by one-dimensional techniques. However, it has also been shown that the modulation process introduces a new source of error to the measurement. In this work, we present the results of a study into the limits of quantification and detection (LOQ and LOD) in comprehensive multidimensional separations using GC×GC and the more popular "two-step" integration algorithm as an example. Simulation of chromatographic data permits precise control of relevant parameters of peak geometry and modulation phase. Results are expressed in terms of the dimensionless parameter of signal-to-noise ratio of the base peak (S/N(BP)) making them transportable to any result where quantification is performed using a two-step algorithm. Based on these results, the LOD is found to depend upon the modulation ratio used for the experiment and vary between a S/N(BP) of 10-17, while the LOQ depends on both the modulation ratio and the phase of the modulation for the peak and ranges from a S/N(BP) of 10 to 50, depending on the circumstances.     

Detection of albumin unfolding preceding proteolysis using Fourier transform infrared spectroscopy and chemometric data analysis

The hydrolysis of bovine serum albumin with protease K at 60 degrees C has been studied by means of infrared spectroscopy. Two-dimensional correlation spectroscopy (2DCoS) has been used to study spectral changes in the reaction. The use of the multivariate curve resolution-alternating least-squares method applied to infrared measurements allowed the recovery of pure infrared spectra and concentration profiles of the different species involved in the reaction. Special attention was paid to the careful inspection of residuals again using 2DCoS. In this way, a heat-induced unfolding step previous to protein hydrolysis was identified. The infrared spectra of the intermediate species showed a more disordered structure than native albumin, the decrease in alpha-helix conformation being especially noticeable. The formation of beta-sheet aggregates due to heating was detected too.     

Metabolic profiling based on two-dimensional J-resolved 1H NMR data and parallel factor analysis

Metabolic profiling of natural products is used to map correlated concentration variances of known and unknown secondary metabolites in extracts. NMR-spectroscopy is in this respect regarded as a convenient and reproducible technique with the ability to detect a wide range of small organic compounds. Two-dimensional J-resolved NMR-spectra are used in this context to resolve overlapping signals by separating the effect of J-coupling from the effect of chemical shifts. Often one-dimensional projections of these data are used as input for standard multivariate statistical methods, and only the intensity variances along the chemical shift axis are taken into account. Here, we describe the use of parallel factor analysis (PARAFAC) as a tool to preprocess a set of two-dimensional J-resolved spectra with the aim of keeping the J-coupling information intact. PARAFAC is a mathematical decomposition method that fits three-way experimental data to a model whose parameters in this case reflect concentrations and individual component spectra along the chemical shift axis and corresponding profiles along the J-coupling axis. A set of saffron samples, directly extracted with methanol-d(4), were used as a model system to evaluate the feasibility and merits of the method. To successfully use PARAFAC, the two-dimensional spectra (n = 96) had to be aligned and processed in narrow windows (0.04 ppm wide) along the chemical shift axis. Selection of windows and number of components for each PARAFAC-model was done automatically by evaluating amount of explained variance and core consistency values. Score plots showing the distribution of objects in relation to each other, and loading plots in the form of two-dimensional pseudospectra with the same appearance as the original J-resolved spectra but with positive and negative contributions are presented. Loadings are interpreted not only in terms of signals with different chemical shifts but also the associated J-coupling profiles.     

Objective assessment of image quality. V. Photon-counting detectors and list-mode data

A theoretical framework for detection or discrimination tasks with list-mode data is developed. The object and imaging system are rigorously modeled via three random mechanisms: randomness of the object being imaged, randomness in the attribute vectors, and, finally, randomness in the attribute vector estimates due to noise in the detector outputs. By considering the list-mode data themselves, the theory developed in this paper yields a manageable expression for the likelihood of the list-mode data given the object being imaged. This, in turn, leads to an expression for the optimal Bayesian discriminant. Figures of merit for detection tasks via the ideal and optimal linear observers are derived. A concrete example discusses detection performance of the optimal linear observer for the case of a known signal buried in a random lumpy background.     

Modulator design for comprehensive two-dimensional gas chromatography: quantitative analysis of polyaromatic hydrocarbons and polychlorinated biphenyls

A novel cryogenic modulator was constructed for comprehensive two-dimensional gas chromatography (GC x GC). The modulator is based on two-step cryogenic trapping with CO2 and thermal desorption with electric heating. The GC x GC system included a nonpolar first-dimension column and two semipolar second-dimension columns, one connected to a flame ionization detector and the other one to a electron capture detector. A Matlab-based program, which allowed determination of peak heights and volumes, was written for the data analysis. The GC x GC system was applied for the analysis of polyaromatic hydrocarbons and polychlorinated biphenyls. The functioning of the modulator and the quantitativity of the method were studied with both peak volumes and peak heights from a three-dimensional plot. The separate peak areas from the modulated chromatogram were calculated as a comparison. The quantitative results were compared with those obtained with the same system but without the thermal modulation. The method was found to be repeatable and linear with use of peak volumes as well as peak heights. There was also good agreement with the results obtained by integration of separate peak areas. The developed GC x GC method was applied to the analysis of a Soxhlet extract of a certified sediment sample. The results were compared with the certified values.     

Geographic classification of extra virgin olive oils from the eastern Mediterranean by chemometric analysis of visible and near-infrared spectroscopic data

Visible and near-infrared reflectance spectra have been examined for their ability to classify extra virgin olive oils from the eastern Mediterranean on the basis of their geographic origin. Classification strategies investigated were partial least-squares regression, factorial discriminant analysis, and k-nearest neighbors analysis. Discriminant models were developed and evaluated using spectral data in the visible (400-750 nm), near-infrared (1100-2498 nm), and combined (400-2498 nm) wavelength ranges. A variety of data pretreatments was applied. Best results were obtained using factorial discriminant analysis on raw spectral data over the combined wavelength range; a correct classification rate of 93.9% was obtained on a prediction sample set. Though the overall sample set was limited in numbers, these results demonstrate the potential of near-infrared spectroscopy to classify extra virgin olive oils on the basis of their geographic origin.     

Group-type analysis of oxygenated compounds with a silica gel porous layer open tubular column and comprehensive two-dimensional supercritical fluid and gas chromatography

A porous layer open tubular (PLOT) silica gel column was used together with subcritical CO2 as the mobile phase to effect the group separation of polar oxygenated compounds. Aliphatic and aromatic compounds were shown to elute together. This group was followed by ethers and aldehydes, which were separated from compounds containing an alcohol functional group. Compounds with a carboxylic acid moiety could also be eluted from the silica gel. The group separation obtained when a silica gel PLOT column is used together with subcritical CO2 was also demonstrated to be valuable as the first dimension of a comprehensive two-dimensional SFCxGC analysis where the GC analysis in the second dimension is performed with a fast and independently heated temperature programmed gas chromatograph. With this combination of SFC and GC, many of the oxygenated compounds, routinely found in petroleum samples, could successfully be separated and identified.     

Vapor recognition with small arrays of polymer-coated microsensors. A comprehensive analysis.

A comprehensive analysis of vapor recognition as a function of the number of sensors in a vapor-sensor array is presented. Responses to 16 organic vapors collected from six polymer-coated surface acoustic wave (SAW) sensors were used in Monte Carlo simulations coupled with pattern recognition analyses to derive statistical estimates of vapor recognition rates as a function of the number of sensors in the array (< or = 6), the polymer sensor coatings employed, and the number and concentration of vapors being analyzed. Results indicate that as few as two sensors can recognize individual vapors from a set of 16 possibilities with < 6% average recognition error, as long as the vapor concentrations are > 5 x LOD for the array. At lower concentrations, a minimum of three sensors is required, but arrays of 3-6 sensors provide comparable results. Analyses also revealed that individual-vapor recognition hinges more on the similarity of the vapor response patterns than on the total number of possible vapors considered. Vapor mixtures were also analyzed for specific 2-, 3-, 4-, 5-, and 6-vapor subsets where all possible combinations of vapors within each subset were considered simultaneously. Excellent recognition rates were obtainable for mixtures of up to four vapors using the same number of sensors as vapors in the subset. Lower recognition rates were generally observed for mixtures that included structurally homologous vapors. Acceptable recognition rates could not be obtained for the 5- and 6-vapor subsets examined, due, apparently, to the large number of vapor combinations considered (i.e., 31 and 63, respectively). Importantly, increasing the number of sensors in the array did not improve performance significantly for any of the mixture analyses, suggesting that for SAW sensors and other sensors whose responses rely on equilibrium vapor-polymer partitioning, large arrays are not necessary for accurate vapor recognition and quantification.     

Enhanced synchronous spectrofluorometric determination of tetracycline in blood serum by chemometric analysis. Comparison of partial least-squares and hybrid linear analysis calibrations.

Tetracycline has been determined in human serum samples by a combination of: (1) synchronous fluorescence spectra of whole sera treated with Mg2+, and (2) the multivariate calibration methods of partial least-squares (PLS-1) and a variant of the recently introduced hybrid linear analysis (HLA), which does not require the knowledge of pure-component spectra. The calibration set was designed with 50 sera spiked with concentrations of tetracycline in the range 0.0-4.0 micrograms mL-1'. Studies concerning validation, precision, accuracy and figures of merit (selectivity, sensitivity and limit of determination) were also carried out. A novel wavelength-selection procedure was applied to minimize the effect of nonmodeled interferents present in serum samples containing bilirubin, triglycerides, and salicylate. Overall, the performance of the newly developed HLA approach seems to be better than that of PLS-1.     

Chemometric resolution and quantification of four-way data arising from comprehensive 2D-LC-DAD analysis of human urine

Two-dimensional liquid chromatography (LC × LC) is quickly becoming an important technique for the analysis of complex samples, owing largely to the relatively high peak capacities attainable by this analytical technique. With the increase in the complexity of the sample comes a corresponding increase in the complexity of the collected data. Thus the need for chemometric methods capable of resolving and quantifying such data is ever more urgent in order to obtain the maximum information available from the data. To this end, we have developed a chemometric method that combines iterative key set factor analysis and multivariate curve resolution-alternating least squares analysis with a spectral selectivity constraint that is shown to be capable of resolving chromatographically rank deficient, non-multilinear data. (spectrally rank deficient compounds can only be quantified if the peaks having the same spectra are chromatographically resolved). Over 50 chromatographic peaks were found in a relatively small section of a LC × LC-diode array data set of replicate urine samples (a four-way data set) using the developed method. The relative concentrations for 34 of the 50 peaks were determined with % RSD values ranging from 0.09% to 16%.     

Robust analysis of two-way models with repeated measures on both factors

Summary A robust analysis of two-way models with repeated measures on both factors is developed using a dispersion function. This robust analysis gives users a complete inference: Estimation, tests for the general linear hypotheses, and multiple comparison procedures. Asymptotic relative efficiencies of the rank tests with respect to the least-squares counterpart are discussed. Analyses of two real life examples from medical and pharmaceutical studies are presented.     

Modular two-dimensional analysis of SAW filters. II. Analysis and compensation results

For pt.I see ibid vol.39, no.1, pp.61-72 (1992). Physical effects causing distortions of the transfer function of a broadband (36% fractional bandwidth) spectrum shaping filter for digital radio with 16 quadrature amplitude modulation (QAM) are analyzed separately and connected with the modular two-dimensional (2-D) model described in Part I, demonstrating the importance of every single effect. A compensation of the second-order effects is performed, yielding an agreement between simulation and measurement in amplitude and phase of more than +/-0.1 dB and +/-1 degrees all over the passband. The stopband is also predicted with high accuracy.     

Nonlinear data alignment for UPLC-MS and HPLC-MS based metabolomics: quantitative analysis of endogenous and exogenous metabolites in human serum

A nonlinear alignment strategy was examined for the quantitative analysis of serum metabolites. Two small-molecule mixtures with a difference in relative concentration of 20-100% for 10 of the compounds were added to human serum. The metabolomics protocol using UPLC and XCMS for LC-MS data alignment could readily identify 8 of 10 spiked differences among more than 2700 features detected. Normalization of data against a single factor obtained through averaging the XCMS integrated response areas of spiked standards increased the number of identified differences. The original data structure was well preserved using XCMS, but reintegration of identified differences in the original data reduced the number of false positives. Using UPLC for separation resulted in 20% more detected components compared to HPLC. The length of the chromatographic separation also proved to be a crucial parameter for a number of detected features. Moreover, UPLC displayed better retention time reproducibility and signal-to-noise ratios for spiked compounds over HPLC, making this technology more suitable for nontargeted metabolomics applications.     

Robust algorithm for alignment of liquid chromatography-mass spectrometry analyses in an accurate mass and time tag data analysis pipeline

Liquid chromatography coupled to mass spectrometry (LC-MS) and tandem mass spectrometry (LC-MS/MS) has become a standard technique for analyzing complex peptide mixtures to determine composition and relative abundance. Several high-throughput proteomics techniques attempt to combine complementary results from multiple LC-MS and LC-MS/MS analyses to provide more comprehensive and accurate results. To effectively collate and use results from these techniques, variations in mass and elution time measurements between related analyses need to be corrected using algorithms designed to align the various types of data: LC-MS/MS versus LC-MS/MS, LC-MS versus LC-MS/MS, and LC-MS versus LC-MS. Described herein are new algorithms referred to collectively as liquid chromatography-based mass spectrometric warping and alignment of retention times of peptides (LCMSWARP), which use a dynamic elution time warping approach similar to traditional algorithms that correct for variations in LC elution times using piecewise linear functions. LCMSWARP is compared to the equivalent approach based upon linear transformation of elution times. LCMSWARP additionally corrects for temporal drift in mass measurement accuracies. We also describe the alignment of LC-MS results and demonstrate their application to the alignment of analyses from different chromatographic systems, showing the suitability of the present approach for more complex transformations.