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In this work, a new strategy for the chemometric analysis of two-dimensional liquid chromatography-high-resolution mass spectrometry (LC × LC-HRMS) data is proposed. This approach consists of a preliminary compression step along the mass spectrometry (MS) spectral dimension based on the selection of the regions of interest (ROI), followed by a further data compression along the chromatographic dimension by wavelet transforms. In a secondary step, the multivariate curve resolution alternating least squares (MCR-ALS) method is applied to previously compressed data sets obtained in the simultaneous analysis of multiple LC × LC-HRMS chromatographic runs from multiple samples. The feasibility of the proposed approach is demonstrated by its application to a large experimental data set obtained in the untargeted LC × LC-HRMS study of the effects of different environmental conditions (watering and harvesting time) on the metabolism of multiple rice samples. An untargeted chromatographic setup coupling two different liquid chromatography (LC) columns [hydrophilic interaction liquid chromatography (HILIC) and reversed-phase liquid chromatography (RPLC)] together with an HRMS detector was developed and applied to analyze the metabolites extracted from rice samples at the different experimental conditions. In the case of the metabolomics study taken as example in this work, a total number of 154 metabolites from 15 different families were properly resolved after the application of MCR-ALS. A total of 139 of these metabolites could be identified by their HRMS spectra. Statistical analysis of their concentration changes showed that both watering and harvest time experimental factors had significant effects on rice metabolism. The biochemical insight of the effects of watering and harvesting experimental factors on the changes in concentration of these detected metabolites in the investigated rice samples is attempted.

In this work, we present a novel probabilistic peak detection algorithm based on a Bayesian framework for forensic DNA analysis. The proposed method aims at an exhaustive use of raw electropherogram data from a laser-induced fluorescence multi-CE system. As the raw data are informative up to a single data point, the conventional threshold-based approaches discard relevant forensic information early in the data analysis pipeline. Our proposed method assigns a posterior probability reflecting the data point's relevance with respect to peak detection criteria. Peaks of low intensity generated from a truly existing allele can thus constitute evidential value instead of fully discarding them and contemplating a potential allele drop-out. This way of working utilizes the information available within each individual data point and thus avoids making early (binary) decisions on the data analysis that can lead to error propagation. The proposed method was tested and compared to the application of a set threshold as is current practice in forensic STR DNA profiling. The new method was found to yield a significant improvement in the number of alleles identified, regardless of the peak heights and deviation from Gaussian shape., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Comprehensive hyphenated two-dimensional liquid chromatography mass spectrometry (LC×LC-MS) is a very powerful analytical tool achieving high throughput resolution of highly complex natural samples. However, even using this approach there is still the possibility of not resolving some of the analytes of interest. For instance, triacylglycerols (TAGs) structural isomers in oil samples are extremely difficult to separate chromatographically due to their very similar structure and chemical properties. Traditional approaches based on current vendor chromatographic software cannot distinguish these isomers from their different mass spectral features. In this work, a chemometric approach is proposed to solve this problem. First, the experimental LC×LC-MS data structure is discussed, and results achieved by different methods based on the fulfilment of the trilinear model are compared. Then, the step-by-step resolution and identification of strongly coeluted compounds from different examples of triacylglycerols (TAGs) structural isomers in corn oil samples are described. As a conclusion, the separation power of two-dimensional chromatography can be significantly improved when it is combined with the multivariate curve resolution method., (Copyright © 2016 Elsevier B.V. All rights reserved.)

A novel peak tracking method based on Bayesian statistics is proposed. The method consists of assigning (i.e. tracking) peaks from two GCxGC-FID data sets of the same sample taken in different conditions. Opposed to traditional (i.e. deterministic) peak tracking algorithms, in which the assignment problem is solved with a unique solution, the proposed algorithm is probabilistic. In other words, we quantify the uncertainty of matching two peaks without excluding other possible candidates, ranking the possible peak assignments regarding their posterior probability. This represents a significant advantage over existing deterministic methods. Two algorithms are presented: the blind peak tracking algorithm (BPTA) and peak table matching algorithm (PTMA). PTMA method was able to assign correctly 78% of a selection of peaks in a GCxGC-FID chromatogram of a diesel sample and proved to be extremely fast., (Copyright © 2016 Elsevier B.V. All rights reserved.)

A novel method for compound identification in liquid chromatography-high resolution mass spectrometry (LC-HRMS) is proposed. The method, based on Bayesian statistics, accommodates all possible uncertainties involved, from instrumentation up to data analysis into a single model yielding the probability of the compound of interest being present/absent in the sample. This approach differs from the classical methods in two ways. First, it is probabilistic (instead of deterministic); hence, it computes the probability that the compound is (or is not) present in a sample. Second, it answers the hypothesis "the compound is present", opposed to answering the question "the compound feature is present". This second difference implies a shift in the way data analysis is tackled, since the probability of interfering compounds (i.e., isomers and isobaric compounds) is also taken into account.

The application of GC×GC-FID and GC×GC-MS for the chemical analysis and profiling of neat white spirit is explored and the benefit of the enhanced peak capacity offered by comprehensive two-dimensional gas chromatography is demonstrated. An extensive sampling exercise was conducted throughout The Netherlands and the production and logistics in terms of bottling and distribution of white spirits were studied. An exploratory approach based on target-peak tables and principal component analysis was employed to study the brand-to-brand differences and production variations over time. Despite the complex chemical composition of white spirit samples this study shows that chemical variation during productions is actually quite limited. Hence care has to be taken with the chemical comparison for forensic purposes. Although some clustering was noticed on brand level, the large scale production process leads to a very consistent composition across stores and brands. However, because of the broad specifications of this commodity product, substantial chemical variation was found over time. This temporal discrimination could be of forensic value when considering white spirits supplies in individual households., (Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.)

In this work, we introduce an automated, efficient, and elegant model to combine all pieces of evidence (e.g., expected retention times, peak shapes, isotope distributions, fragment-to-parent ratio) obtained from liquid chromatography-tandem mass spectrometry (LC-MS/MS/MS) data for screening purposes. Combining all these pieces of evidence requires a careful assessment of the uncertainties in the analytical system as well as all possible outcomes. To-date, the majority of the existing algorithms are highly dependent on user input parameters. Additionally, the screening process is tackled as a deterministic problem. In this work we present a Bayesian framework to deal with the combination of all these pieces of evidence. Contrary to conventional algorithms, the information is treated in a probabilistic way, and a final probability assessment of the presence/absence of a compound feature is computed. Additionally, all the necessary parameters except the chromatographic band broadening for the method are learned from the data in training and learning phase of the algorithm, avoiding the introduction of a large number of user-defined parameters. The proposed method was validated with a large data set and has shown improved sensitivity and specificity in comparison to a threshold-based commercial software package.

The challenge of fully optimizing LC×LC separations is horrendous. Yet, it is essential to address this challenge if sophisticated LC×LC instruments are to be utilized to their full potential in an efficient manner. Currently, lengthy method development is a major obstacle to the proliferation of the technique, especially in industry. A program was developed for the rigorous optimization of LC×LC separations, using gradient-elution in both dimensions. The program establishes two linear retention models (one for each dimension) based on just two LC×LC experiments. It predicts LC×LC chromatograms using a simple van-Deemter model to generalize band-broadening. Various objectives (analysis time, resolution, orthogonality) can be implemented in a Pareto-optimization framework to establish the optimal conditions. The program was successfully applied to a separation of a complex mixture of 54 aged, authentic synthetic dyestuffs, separated by ion-exchange chromatography and ion pair chromatography. The main limitation experienced was the retention-time stability in the first (ion-exchange) dimension. Using the PIOTR program LC×LC method development can be greatly accelerated, typically from a few months to a few days., (Copyright © 2016 Elsevier B.V. All rights reserved.)

A new method for comparison of GCxGC-MS is proposed. The method is aimed at spotting the differences between two GCxGC-MS injections, in order to highlight the differences between two samples, in order to flag differences in composition, or to spot compounds only present in one of the samples. The method is based on application of the Jensen-Shannon divergence (JS) analysis combined with Bayesian hypothesis testing. In order to make the method robust against misalignment in both time dimensions, a moving-window approach is proposed. Using a Bayesian framework, we provide a probabilistic visual map (i.e., log likelihood ratio map) of the significant differences between two data sets consequently excluding the deterministic (i.e., "yes" or "no") decision. We proved this approach to be a versatile tool in GCxGC-MS data analysis, especially when the differences are embedded inside a complex matrix. We tested the approach to spot contamination of diesel samples.

As part of forensic toxicological investigation of cases involving unexpected death of an individual, targeted or untargeted xenobiotic screening of post-mortem samples is normally conducted. To this end, liquid chromatography (LC) coupled to high-resolution mass spectrometry (MS) is typically employed. For data analysis, almost all commonly applied algorithms are threshold-based (frequentist). These algorithms examine the value of a certain measurement (e.g., peak height) to decide whether a certain xenobiotic of interest (XOI) is present/absent, yielding a binary output. Frequentist methods pose a problem when several sources of information [e.g., shape of the chromatographic peak, isotopic distribution, estimated mass-to-charge ratio (m/z), adduct, etc.] need to be combined, requiring the approach to make arbitrary decisions at substep levels of data analysis. We hereby introduce a novel Bayesian probabilistic algorithm for toxicological screening. The method tackles the problem with a different strategy. It is not aimed at reaching a final conclusion regarding the presence of the XOI, but it estimates its probability. The algorithm effectively and efficiently combines all possible pieces of evidence from the chromatogram and calculates the posterior probability of the presence/absence of XOI features. This way, the model can accommodate more information by updating the probability if extra evidence is acquired. The final probabilistic result assists the end user to make a final decision with respect to the presence/absence of the xenobiotic. The Bayesian method was validated and found to perform better (in terms of false positives and false negatives) than the vendor-supplied software package.

Accurate analysis of chromatographic data often requires the removal of baseline drift. A frequently employed strategy strives to determine asymmetric weights in order to fit a baseline model by regression. Unfortunately, chromatograms characterized by a very high peak saturation pose a significant challenge to such algorithms. In addition, a low signal-to-noise ratio (i.e. s/n<40) also adversely affects accurate baseline correction by asymmetrically weighted regression. We present a baseline estimation method that leverages a probabilistic peak detection algorithm. A posterior probability of being affected by a peak is computed for each point in the chromatogram, leading to a set of weights that allow non-iterative calculation of a baseline estimate. For extremely saturated chromatograms, the peak weighted (PW) method demonstrates notable improvement compared to the other methods examined. However, in chromatograms characterized by low-noise and well-resolved peaks, the asymmetric least squares (ALS) and the more sophisticated Mixture Model (MM) approaches achieve superior results in significantly less time. We evaluate the performance of these three baseline correction methods over a range of chromatographic conditions to demonstrate the cases in which each method is most appropriate., (Copyright © 2016 Elsevier B.V. All rights reserved.)

We introduce a novel Bayesian probabilistic peak detection algorithm for liquid chromatography-mass spectroscopy (LC-MS). The final probabilistic result allows the user to make a final decision about which points in a chromatogram are affected by a chromatographic peak and which ones are only affected by noise. The use of probabilities contrasts with the traditional method in which a binary answer is given, relying on a threshold. By contrast, with the Bayesian peak detection presented here, the values of probability can be further propagated into other preprocessing steps, which will increase (or decrease) the importance of chromatographic regions into the final results. The present work is based on the use of the statistical overlap theory of component overlap from Davis and Giddings (Davis, J. M.; Giddings, J. Anal. Chem. 1983, 55, 418-424) as prior probability in the Bayesian formulation. The algorithm was tested on LC-MS Orbitrap data and was able to successfully distinguish chemical noise from actual peaks without any data preprocessing.

Forensic chemical analysis of fire debris addresses the question of whether ignitable liquid residue is present in a sample and, if so, what type. Evidence evaluation regarding this question is complicated by interference from pyrolysis products of the substrate materials present in a fire. A method is developed to derive a set of class-conditional features for the evaluation of such complex samples. The use of a forensic reference collection allows characterization of the variation in complex mixtures of substrate materials and ignitable liquids even when the dominant feature is not specific to an ignitable liquid. Making use of a novel method for data imputation under complex mixing conditions, a distribution is modeled for the variation between pairs of samples containing similar ignitable liquid residues. Examining the covariance of variables within the different classes allows different weights to be placed on features more important in discerning the presence of a particular ignitable liquid residue. Performance of the method is evaluated using a database of total ion spectrum (TIS) measurements of ignitable liquid and fire debris samples. These measurements include 119 nominal masses measured by GC-MS and averaged across a chromatographic profile. Ignitable liquids are labeled using the American Society for Testing and Materials (ASTM) E1618 standard class definitions. Statistical analysis is performed in the class-conditional feature space wherein new forensic traces are represented based on their likeness to known samples contained in a forensic reference collection. The demonstrated method uses forensic reference data as the basis of probabilistic statements concerning the likelihood of the obtained analytical results given the presence of ignitable liquid residue of each of the ASTM classes (including a substrate only class). When prior probabilities of these classes can be assumed, these likelihoods can be connected to class probabilities. In order to compare the performance of this method to previous work, a uniform prior was assumed, resulting in an 81% accuracy for an independent test of 129 real burn samples., (Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.)

Post-polymerization photografting is a versatile tool to alter the surface chemistry of organic-based monoliths so as to obtain desired stationary phase properties. In this study, 2-acrylamido-2-methyl-1-propanesulfonic acid was grafted to a hydrophobic poly(butyl methacrylate-co-ethylene glycol dimethacrylate) monolith to create a strong cation exchange stationary phase. Both single-step and two-step photografting were addressed, and the effects of grafting conditions were assessed. An experimental design has been applied in an attempt to optimize three of the key parameters of the two-step photografting chemistry, i.e. the grafting time of the initiator, the monomer concentration and the monomer irradiation time. The photografted columns were implemented in a comprehensive two-dimensional column liquid chromatography ( (t) LC ×  (t) LC) workflow and applied for the separation of intact proteins and peptides. A baseline separation of 11 intact proteins was obtained within 20 min by implementing a gradient across a limited RP composition window in the second dimension. (t) LC ×  (t) LC with UV detection was used for the separation of cytochrome c digest, bovine serum insulin digest and a digest of a complex protein mixture. A semi-quantitative estimation of the occupation of separation space, the orthogonality, of the (t) LC ×  (t) LC system yielded 75%. The (t) LC ×  (t) LC setup was hyphenated to a high-resolution Fourier transform ion cyclotron resonance mass spectrometer instrument to identify the bovine serum insulin tryptic peptides and to demonstrate the compatibility with MS analysis.

In this paper we present a model relating experimental factors (column lengths, diameters and thickness, modulation times, pressures and temperature programs) with retention times. Unfortunately, an analytical solution to calculate the retention in temperature programmed GC × GC is impossible, making thus necessary to perform a numerical integration. In this paper we present a computational physical model of GC × GC, capable of predicting with a high accuracy retention times in both dimensions. Once fitted (e.g., calibrated), the model is used to make predictions, which are always subject to error. In this way, the prediction can result rather in a probability distribution of (predicted) retention times than in a fixed (most likely) value. One of the most common problems that can occur when fitting unknown parameters using experimental data is overfitting. In order to detect overfitting situations and assess the error, the K-fold cross-validation technique was applied. Another technique of error assessment proposed in this article is the use of error propagation using Jacobians. This method is based on estimation of the accuracy of the model by the partial derivatives of the retention time prediction with respect to the fitted parameters (in this case entropy and enthalpy for each component) in a set of given conditions. By treating the predictions of the model in terms of intervals rather than as precise values, it is possible to considerably increase the robustness of any optimization algorithm., (Copyright © 2014 Elsevier B.V. All rights reserved.)

Mathematical deconvolution methods can separate co-eluting peaks in samples for which (chromatographic) separation fail. However, these methods often heavily rely on manual user-input and interpretation. This is not only time-consuming but also error-prone and automation is needed if such methods are to be applied in a routine manner. One major hurdle when automating deconvolution methods is the selection of the correct number of components used for building the model. We propose a new method for the automatic determination of the optimum number of components when applying multivariate curve resolution (MCR) to comprehensive two-dimensional gas chromatography-mass spectrometry (GC×GC-MS) data. It is based on a two-fold cross-validation scheme. The obtained overall cross-validation error decreases when adding components and increases again once over-fitting of the data starts to occur. The turning point indicates that the optimum number of components has been reached. Overall, the method is at least as good as and sometimes superior to the inspection of the eigenvalues when performing singular-value decomposition. However, its strong point is that it can be fully automated and it is thus more efficient and less prone to subjective interpretation. The developed method has been applied to two different-sized regions in a GC×GC-MS chromatogram. In both regions, the cross-validation scheme resulted in selecting the correct number of components for applying MCR. The pure concentration and mass spectral profiles obtained can then be used for identification and/or quantification of the compounds. While the method has been developed for applying MCR to GC×GC-MS data, a transfer to other deconvolution methods and other analytical systems should only require minor modifications., (Copyright © 2013 Elsevier B.V. All rights reserved.)

The maximum achievable performance of possible types of three-dimensional chromatographic systems (LC×LC×LC) has been investigated. The Pareto-optimization approach was applied to establish a trade-off between three main objectives (total peak capacity, analysis time and dilution of the sample) and Pareto-front values were obtained. The performances of (x)LC×(x)LC×(x)LC (three-dimensional separation in space), (t)LC×(t)LC×(t)LC (three-dimensional separation in time) and the hybrid (x)LC×(x)LC×(t)LC system were compared mutually and with two-dimensional chromatographic systems. It was found that (x)LC×(x)LC×(x)LC performs best in terms of maximum achievable peak capacity in shortest analysis time. Based on current thin-layer-chromatography performance it should be possible to obtain a peak capacity of 50,000 within 20min. If contemporary column-packing standards can be upheld the achievable limit is approximately 50% higher. However, in an (x)LC×(x)LC×(x)LC chromatographic system analytes remain in the separation domain after the analysis, which complicates the detection. Use of an (x)LC×(x)LC×(t)LC system with elution in the last dimension alleviates the detection problem. The maximum achievable peak capacity in the same analysis time is lower for (x)LC×(x)LC×(t)LC than for (x)LC×(x)LC×(x)LC. Using the same (reasonable) length of the separation domain (e.g. a cube 200×200×200 mm) for both systems, it is possible to achieve peak capacities of 78,000 for (x)LC×(x)LC×(t)LC operated in the gradient mode, which is twice higher than for an (x)LC×(x)LC×(x)LC system. A three-dimensional (three-column) time-based (t)LC×(t)LC×(t)LC system does not greatly improve the performance of (t)LC×(t)LC in terms of (maximum) peak capacity and (minimum) analysis time. Dilution factors in (t)LC×(t)LC×(t)LC are very high. Decreasing the dilution has a detrimental influence on the peak capacity. The trade-off between these objectives is of crucial importance. The influence of several parameters (length of the separation domain, particle size, etc.) on the performance of chromatographic systems was investigated, optimal ranges were found., (Copyright © 2012. Published by Elsevier B.V.)

The expected performance of spatial ("flat-bed") two-dimensional liquid chromatography ((x)LC×(x)LC) has been calculated using the Pareto-optimality strategy. This approach allowed different objectives (total peak capacity, total analysis time, and total dilution) to be considered simultaneously and to establish optimal parameters (pressure drop, particle size, bed length, and initial spot size). The performance of spatial two-dimensional chromatographic systems was compared with that of conventional on-line, real-time two-dimensional column-liquid-chromatography systems ((t)LC×(t)LC). The potential gain in peak capacity and/or analysis time of the spatial configuration was confirmed. By restricting the spatial parameters to realistic chromatographic conditions (limiting the stress, as counterbalance for the pressure drop through the sorbent bed, to 2500 kg) it was found that (x)LC×(x)LC is attractive for very fast analysis of complex samples, rather than for extremely efficient separations. For example, a peak capacity of 780 may be achieved in only 2.7 min using a 100×100 mm sorbent bed of a quality currently encountered thin-layer chromatography. Furthermore, if beds can be packed as efficiently as contemporary columns, the predicted peak capacity increases to around 1000, corresponding to a peak-production rate of about 6.3 peaks/s. Possibilities to boost the performance of (x)LC×(x)LC further are briefly discussed. Unless we can overcome the severe stress requirements of high-performance (x)LC×(x)LC, conventional (t)LC×(t)LC may be more amenable to very complex separations, thanks to the very high peak capacities. However, (t)LC×(t)LC separations will require long analysis times (e.g. 10,000 peaks in 37 h, corresponding to 0.075 peaks/s at a pressure drop of 40 MPa). The best trade-off between total peak capacity, total analysis time, and total dilution under restricted (realistic) conditions was obtained using high pressures, small chromatographic beds, small particles, and relatively large sample spots., (Copyright © 2012 Elsevier B.V. All rights reserved.)

A new method for peak detection in two-dimensional chromatography is presented. In a first step, the method starts with a conventional one-dimensional peak detection algorithm to detect modulated peaks. In a second step, a sophisticated algorithm is constructed to decide which of the individual one-dimensional peaks have been originated from the same compound and should then be arranged in a two-dimensional peak. The merging algorithm is based on Bayesian inference. The user sets prior information about certain parameters (e.g., second-dimension retention time variability, first-dimension band broadening, chromatographic noise). On the basis of these priors, the algorithm calculates the probability of myriads of peak arrangements (i.e., ways of merging one-dimensional peaks), finding which of them holds the highest value. Uncertainty in each parameter can be accounted by adapting conveniently its probability distribution function, which in turn may change the final decision of the most probable peak arrangement. It has been demonstrated that the Bayesian approach presented in this paper follows the chromatographers' intuition. The algorithm has been applied and tested with LC × LC and GC × GC data and takes around 1 min to process chromatograms with several thousands of peaks.

Various hydroxyl-propylmethylcellulose (HPMC) polymers were characterized according to size and compositional distributions (percentage of methoxyl and hydroxyl-propoxyl substitution) by means of comprehensive two-dimensional liquid chromatography (LC×LC) using reversed-phase (RP) liquid chromatography in the first dimension and aqueous size-exclusion chromatography (aq-SEC) in the second dimension. RP separation was carried out in gradient-elution mode applying 0.05% TFA in water and 1-propanol, while 0.05% TFA in water was used as mobile phase in aqueous SEC. A two-position ten-port switching valve equipped with two storage loops was used to realize LC×LC. Detection of HPMC was accomplished by charged-aerosol detection (CAD). Data processing to visualize chromatograms was carried out using Matlab software. The significant influence of the LC×LC temperature on (the retention of) HPMC was studied using a column oven which allowed accurate temperature control. Due to the phenomenon of thermal gelation, which is a result of methyl and hydroxypropyl substitution of anhydroglucose units from the cellulose backbone, we were able to obtain additional, specific information on compositional characteristics of various HPMC samples. As the retention behaviour of gelated and non-gelated polymer proved to be different, the fraction of the polymer that is gelated in the chromatographic column could be monitored at different temperatures. Moreover, the temperature at which half of the polymer is gelated could be correlated with the cloud-point temperature. As a result, differences in inherent cloud points of modified cellulose can be used as a further distinguishing property in "temperature-responsive" LC×LC., (Copyright © 2011 Elsevier B.V. All rights reserved.)

A new strategy for biomarker discovery is presented that is based on multi-dose kinetic metabolomics data. Gas chromatography-mass spectrometry (GC-MS) data sets recorded in the full scan mode are scanned for compounds showing a meaningful trend following the different doses and sampling time points. From a biological point of view, a meaningful trend denotes a compound that responds similarly at all doses and follows a smooth trend along the time points. This type of information can be used to distinguish relevant metabolites from those compounds not following the expected trends. The method is based on analysing the time and dosage trends of each compound via principal component analysis. As only local information is analysed at a time (meaning no correlation with other metabolites is taken into account), the proposed model flags relevant metabolites even if their trend is different from that of any other compound. The new method is therefore an attractive way to reduce the long list of detected compounds in a metabolomics sample set to include only those having the expected smooth time profile that is common for all doses. The new strategy is tested on a sample set obtained from a gut fermentation study of a polyphenol-rich diet. For this study, the initial list of over 25,000 potentially interesting features was reduced to less than 250, thus significantly reducing the expensive and time-consuming manual examination., (Copyright © 2010 Elsevier B.V. All rights reserved.)

A method aimed to obtain the relative abundances of all molecular species in highly overlapped mass spectra is presented. Its performance is demonstrated with an example of matrix-assisted laser desorption ionization (MALDI) spectra obtained from a polysterene-co-polyisoprene sample, retrieving the full co-polymer architecture. The method is based on a multiple regression operation, applied locally at consecutive regions. The method is designed in such a way that it is not necessary to locate regions in the spectrum that are not influenced by adjacent ones. This increases its applicability, since the method is able to tackle the analysis of highly complex spectra, tending to minimise the need of user intervention. The method allows to correct for non-idealities (such as wrong calibration) or to adjust the variations of spectral resolution with mass. Additionally, the algorithm calculates the precision of the computation in a straightforward way., (Copyright (c) 2010 Elsevier B.V. All rights reserved.)

A new strategy for biomarker discovery is presented that uses time-series metabolomics data. Data sets from samples analysed at different time points after an intervention are searched for compounds that show a meaningful trend following the intervention. Obviously, this requires new data-analytical tools to distinguish such compounds from those showing only random variation. Two univariate methods, autocorrelation and curve-fitting, are used either as stand-alone methods or in combination to discover unknown metabolites in data sets originating from target-compound analysis. Both techniques reduce the long list of detected compounds in the kinetic sample set to include only those having a pre-defined interesting time profile. Thus, new metabolites may be discovered within data structures that are usually only used for target-compound analysis. The new strategy is tested on a sample set obtained from a gut fermentation study of a polyphenol-rich diet. For this study, the initial list of over 9000 potentially interesting features was reduced to less than 150, thus significantly reducing the expensive and time-consuming manual examination., (Copyright 2010 Elsevier B.V. All rights reserved.)

The watershed algorithm is the most common method used for peak detection and integration in two-dimensional chromatography. However, the retention time variability in the second dimension may render the algorithm to fail. A study calculating the probabilities of failure of the watershed algorithm was performed. The main objective was to calculate the maximum second-dimension retention time variability, Delta(2)t(R,crit), above which the algorithm fails. Several models to calculate Delta(2)t(R,crit) were developed and evaluated: (a) exact model; (b) simplified model and (c) simple-modified model. Model (c) gave the best performance and allowed to deduce an analytical expression for the probability of failure of the watershed algorithm as a function of experimental Delta(2)t(R), modulation time and peak width in the first and second dimensions. It could be demonstrated that the probability of failure of the watershed algorithm under normal conditions in GCxGC is around 15-20%. Small changes of Delta(2)t(R), modulation time and/or peak width in the first and second dimension could induce subtle changes in the probability of failure of the watershed algorithm. Theoretical equations were verified with experimental results from a diesel sample injected in GC x GC and were found to be in good agreement with the experiments., (Copyright 2009 Elsevier B.V. All rights reserved.)

A comprehensive study of the applicability of multivariate curve resolution (MCR) methods to series of T2-relaxation filtered 1H NMR spectra of a cross-linked polymer network is presented. A collection of Hahn-echo NMR spectra is obtained at different echo times, yielding two-way data. In this study the applicability of two different types of orthogonal-projection approach (OPA1 and OPA2) (column-wise and row-wise) were tested. Four different strategies of alternating least squares methods were also examined (ALS1, ALS2, ALS3 and ALS4). These strategies differed on the order of measurement for which the constraints were applied in the final output, and the way in which SSR was calculated to monitor for convergence. In the spectral order of measurement, a non-negativity constraint was imposed, whereas in the time order of measurement, the signal was forced to follow an exponential decay. This yielded up to eight MCR configurations, giving different results. For solid-state NMR, the dissimilarity in NMR profiles is significantly lower than the dissimilarity in signal decays, and therefore OPA2 performed better. A final output with a constrained solution in relaxation time was preferred (instead of a constrained solution in NMR spectra) for practical purposes. Differences between the solutions given from the two ALS configurations can be interpreted as a sign of lack of fit.

An improved comprehensive two-dimensional (LC x LC) HPLC system for the analysis of triacylglycerols was developed. In the first-dimension, a Ag(I)-coated cation exchanger (250 mm x 2.1 mm, 5 microm) was employed with a gradient from 100% MeOH to 6% MeCN in MeOH at 20 microL/min. Using a 10-way valve with two switching loops, 1 min sections of the first-dimension were introduced in the second-dimension consisting of a 30 mm x 4.6 mm C18 (1.8 microm) column with an isocratic mobile phase of methanol-methyl tert-butyl ether (70:30) at 3.0 mL/min. As the second-dimension solvent was stronger than the first-dimension solvent, focusing in the second-dimension took place, leading to better separations than in previously reported analyses in which hexane was the main constituent of the first-dimension eluent. Compounds differing by 2 in their partition number were baseline separated in the second-dimension. Detection took place by UV at 210 nm, evaporative light scattering and (+)-atmospheric pressure chemical ionisation-MS with the latter giving the best results. Corn oil was investigated and 44 compounds could be detected: 34 triacylglycerols (TAGs), 8 oxygenated TAGs, and 2 TAGs containing a trans double bond. Data manipulation allowed the construction of contour plots and the automated calculation of the first- and second-dimension retention times and peak areas. Quantitative results are compared with a fatty acid methyl ester analysis, and with literature data.

A method for peak detection in two-dimensional chromatography is presented. The algorithm applies first the methods developed for peak detection in one-dimensional chromatography to detect peaks in one dimension. In a second step, a decision tree is applied to decide which one-dimensional peaks are originated from the same compound and have to be 'merged' into one two-dimensional peak. To this end, different features of the peaks (second-dimension peak regions and second-dimension retention times) are compared and different criteria (common peak regions, retention time differences, unimodality in the first dimension) are applied. Different options can be used, depending on the nature of the data. The user controls this decision tree by establishing several options and "switches". The algorithm was tested with GCxGC chromatograms obtained for a commercial air-freshener sample, detecting and merging the modulated peaks belonging to the same compound. Recommendations for the set of options and switches are given. A utility that calculates and sums peak areas from merged peaks is added to facilitate automated quantification. Although the algorithm was developed for GCxGC, its application to comprehensive two-dimensional liquid chromatography (LCxLC) data should at most require minor modifications.

A new resolution metric for two-dimensional chromatography is proposed and tested. This resolution measurement is based on the concept of the (one-dimensional) valley-to-peak ratio, which has been adapted and modified for two-dimensional chromatography. Two questions are considered related to the computation of the resolution of a given (two-dimensional) peak. First, the concept of peak neighbourhood is revised, since it changes drastically from one- to two-dimensional chromatography. In a chromatogram resulting from a two-dimensional analysis, one peak may be surrounded by more than two neighbouring peaks. However, the neighbouring peaks can be remote from the peak or some interfering peaks may be in between. In these cases, it is not meaningful to compute the resolution between them. A method is proposed to determine whether a resolution measurement between two two-dimensional peaks is reasonable. Second, a measurement of the valley-to-peak ratio in two-dimensional chromatography is proposed. The measurement is based on the concept of the saddle point (which is defined for two-dimensional surface plots). A study of the correlation of the valley-to-peak ratio with the error obtained for quantification is presented. The new metric can be used as an estimator of the quantification errors. Also, valley-to-peak ratios can be calculated for one or more target peak(s) to estimate the separation quality of the entire chromatogram. This makes the proposed measurement suitable for optimisation purposes. Although the algorithm was developed for GC x GC, preliminary studies suggested that its application to other two-dimensional separation methods (e.g. LC x LC) should only require minor modification (if any).

In this paper a protocol is proposed for establishing suitable column dimensions (length and diameters), particle sizes, flow rates, and second-dimension injection volumes (i.e. loop sizes) in comprehensive two-dimensional liquid chromatography (LC x LC). The chromatographer should select the maximum allowable first-dimension retention time, which is approximately equal to the overall analysis time. Also, (s)he should define the maximum allowable pressure in both dimensions and the (minimum) diameter of the first-dimension column. The proposed protocol provides design parameters corresponding to the ideal (theoretically optimal) conditions or to realistic practical conditions. The protocol also allowed us to study the implications of contemporary developments in LC, such as the use of high temperatures (implying reduced viscosities and increased diffusion coefficients), monolithic columns (implying smaller flow-resistance factors), and ultra-high-pressure LC. The combination of (reversed-phase or normal-phase) liquid chromatography with size-exclusion chromatography (LC x SEC) is frequently employed for analysing complex polymers. The proposed protocol is used to design a suitable LC x SEC system under realistic conditions. The results resemble the systems that have been designed and implemented by expert chromatographers, but they also indicate how current practice can be improved.

A new method is presented for the analysis of comprehensive two-dimensional data. The approach complements existing chemometric methods for analysing these kinds of data (e.g. multivariate-curve-resolution methods, MCR), and is especially suited for the analysis of families of compounds. The method is based on finding a new pair of axes (replacing the retention time axes) to represent the data. A drop in the matrix rank is observed when one of the axes collects all the variance for a certain family of compounds. This is achieved by introducing retention models (in both chromatographic dimensions) that describe the behaviour of a family of compounds as a function of the property that varies between the members. After this transformation, a single family of compounds gives rise to a single source of variance. This suggests the application of MCR techniques in a second step to separate the contributions of different (overlapped) families of compounds. For the latter application, more research has to be performed. The approach is illustrated using the separation of families of functional poly(methyl-methacrylate) polymers with different numbers of hydroxyl end groups and degrees of polymerisation or, equivalently, with the molecular weight as the key descriptive property within one family.

A method to select the optimal window size of the Savitzky-Golay (SG) algorithm is presented. The approach is based on a comparison of the fitting residuals (i.e., the differences between the input signal and the smoothed signal) with the noise of the instrument. The window size that yields an autocorrelation of the residuals closest to the autocorrelation of the noise of the instrument is considered optimal. The method is applied in two steps. In a first step, the lag-one autocorrelation value of the noise of the instrument is computed through the study of a blank signal. In a second step, the SG algorithm is applied to "smooth" the signal using different window sizes. The method was applied to data from NMR, chromatography, and mass spectrometry and was shown to be robust. It finds the optimal window size for different signal features. This allows the method to be used in an unsupervised way, embedded in a more complex algorithm in which smoothing and/or differentiation of signals is required, provided that the lag-one autocorrelation value of the instrument noise does not change.

A method is proposed for the comprehensive characterization and comparison of columns in the high-performance liquid chromatographic (HPLC) and capillary electrochromatographic (CEC) modes. Using this approach, column parameters such as the number of plates, the eddy-diffusion and mass-transfer contributions to peak broadening, the permeability, and the analysis time are incorporated in a single graph and a comparison in terms of efficiency and speed is obtained. The chromatographic performance of silica-based and polymer-based monolithic capillary columns is discussed and a comparison is made with the performance of packed columns. Also, the potential of ultra-high-pressure liquid chromatography is discussed in this context. In the HPLC mode, the best results were obtained with silica monoliths; in the CEC mode, the low-density methacrylate-ester-based monoliths showed the best performance.