Retention Index Units Research Articles

Machine Learning-Based Retention Time Prediction of Trimethylsilyl Derivatives of Metabolites.

In gas chromatography–mass spectrometry-based untargeted metabolomics, metabolites are identified by comparing mass spectra and chromatographic retention time with reference databases or standard materials. In that sense, machine learning has been used to predict the retention time of metabolites lacking reference data. However, the retention time prediction of trimethylsilyl derivatives of metabolites, typically analyzed in untargeted metabolomics using gas chromatography, has been poorly explored. Here, we provide a rationalized framework for machine learning-based retention time prediction of trimethylsilyl derivatives of metabolites in gas chromatography. We compared different machine learning paradigms, in addition to exploring the influence of the computational molecular structure representation to train the prediction models: fingerprint class and fingerprint calculation software. Our study challenged predicted retention time when using chemical ionization and electron impact ionization sources in simulated and real cases, demonstrating a good correct identity ranking capability by machine learning, despite observing a limited false identity filtering power in cases where a spectrum or a monoisotopic mass match to multiple candidates. Specifically, machine learning prediction yielded median absolute and relative retention index (relative retention time) errors of 37.1 retention index units and 2%, respectively. In addition, fingerprint class and fingerprint calculation software, as well as the molecular structural similarity between the training and test or real case sets, showed to be critical modulators of the prediction performance. Finally, we leveraged the structural similarity between the training and test or real case set to determine the probability that the prediction error is below a specific threshold. Overall, our study demonstrates that predicted retention time can provide insights into the true structure of unknown metabolites by ranking from the most to the least plausible molecular identity, and sets the guidelines to assess the confidence in metabolite identification using predicted retention time data.

Normalization of LC-MS mycotoxin determination using the N-alkylpyridinium-3-sulfonates (NAPS) retention index system

A major challenge for LC-MS analysis is the ability to compare data between laboratories and across instrument platforms. Currently, mycotoxin determination relies on dereplication strategies based on physicochemical properties such as the m/z of the precursor and product ions. Unlike these intrinsic properties, retention time (tR) is an extrinsic property impacted by LC conditions, including mobile phases and column chemistry, making exchange of data between groups difficult. To address this, we are introducing the concept of incorporating an electrospray compatible, retention index (RI) system based on a series of N-alkylpyridinium-3-sulfonates (NAPS) into routine mycotoxin determination. These standards of differing alkyl chain length span RI units from 100 to 2000, are UV active and have fixed positive and negative charges for electrospray ionization in either mode. Using high resolution LC-MS/MS, the RIs of 96 mycotoxins and fungal secondary metabolites were normalized as a proof of concept with the NAPS RI system under multiple pH, column and gradient chromatographic conditions. This method was then applied to the analysis of a crude extract of Penicillium roqueforti, where we were able to decrease the number of false positives by implementing an RI filter as well as a secondary correction factor. Additionally, we developed software that allows users to convert published RIs to a predicted tR values. Integration of the NAPS RI system into routine LC-MS analysis will improve compound identifications and help facilitate ease of data sharing.

Gradient boosting for the prediction of gas chromatographic retention indices

The estimation of gas chromatographic retention indices based on compounds structures is an importantproblem. Predicted retention indices can be used in a mass spectral library search for the identificationof unknowns. Various machine learning methods are used for this task, but methods based on decisiontrees, in particular gradient boosting, are not used widely. The aim of this work is to examine the usability ofthis method for the retention index prediction. 177 molecular descriptors computed with Chemistry Development Kit are used as the input representation of a molecule. Random subsets of the whole NIST 17 database are used as training, test and validation sets. 8000 trees with 6 leaves each are used. A neural network with one hidden layer (90 hidden nodes) is used for the comparison. The same data sets and the set of descriptors are used for the neural network and gradient boosting. The model based on gradient boosting outperforms the neural network with one hidden layer for subsets of NIST 17 and for the set of essential oils.The performance of this model is comparable or better than performance of other modern retention prediction models. The average relative deviation is ~3.0%, the median relative deviation is ~1.7% for subsets of NIST 17. The median absolute deviation is ~34 retention index units. Only non-polar liquid stationary phases (such as polydimethylsiloxane, 5% phenyl 95% polydimethylsiloxane, squalane) are considered. Errors obtained with different machine learning algorithms and with the same representation of the molecule strongly correlate with each other.

Surface fitting for calculating the second dimension retention index in comprehensive two-dimensional gas chromatography mass spectrometry

Comprehensive two-dimensional gas chromatography mass spectrometry (GC × GC–MS) has been widely used for analysis of volatile compounds. However, the second dimension retention index (I) of each compound is not widely used to aid compound identification owing to the limited accuracy of I calculation. We report a surface fitting approach to the calculation of I using n-alkanes (C7–C30) as references, where the second dimension retention time (2tR) and the second dimension column temperature (2Te) formed the X-Y plane and the I was the Z-axis to form the I surface. Compared to the conventional approach for calculating I using isovolatility curves, the surface fitting approach eliminated the construction of isovolatility curves for the reference compounds and gives better reproducibility. The goodness of the proposed surface fitting achieved R2 = 0.9999 and RMSE = 6.1 retention index units (iu). Ten-fold cross validation demonstrated the surface fitting approach had a good predictability with average R2 = 0.9999 and RMSE = 6.6 iu. The developed method was also applied to calculate the second dimension retention indices of compound standards in two commercial mixtures MegaMix A and MegaMix B. The mean standard deviation of the calculated I was only 1.6 iu for compounds in MegaMix A and 3.4 iu for compounds in MegaMix B. Compared with the literature results, the small value of standard deviation in the calculated retention index using surface fitting method shows that the surface fitting method has less measurement variability than the conventional isovolatility curve approach.

Chromatographic efficiency of polar capillary columns applied for the analysis of fatty acid methyl esters by gas chromatography.

The chromatographic efficiency that could be achieved in temperature-programmed gas chromatography was compared for four capillary columns that are typically applied for analysis of fatty acid methyl esters (FAME). Three different carrier gases, hydrogen, helium and nitrogen, were applied. For each experiment, the carrier gas velocities and the temperature rates were varied with a full 9 × 3 design, with nine levels on the carrier gas velocity and temperature rates of 1, 2 or 3°C/min. Response surface methodology was used to create models of chromatographic efficiency as a function of temperature rate and carrier gas velocity. The chromatographic efficiency was defined as the inverse of peak widths measured in retention index units. The final results were standardized so that the efficiencies that could be achieved within a certain time frame, defined by the retention time of the last compound in the chromatogram, could be compared. The results show that there were clear differences in the efficiencies that could be achieved with the different columns and that the efficiency decreased with increasing polarity of the stationary phase. The differences can be explained by higher resistance to mass transfer in the stationary phase in the most polar columns.

A regression model for calculating the second dimension retention index in comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry

Comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC/TOF–MS) system has become a key analytical technology in high-throughput analysis. Retention index has been approved to be helpful for compound identification in one-dimensional gas chromatography, which is also true for two-dimensional gas chromatography. In this work, a novel regression model was proposed for calculating the second dimension retention index of target components where n-alkanes were used as reference compounds. This model was developed to depict the relationship among adjusted second dimension retention time, temperature of the second dimension column and carbon number of n-alkanes by an exponential nonlinear function with only five parameters. Three different criteria were introduced to find the optimal values of parameters. The performance of this model was evaluated using experimental data of n-alkanes (C7–C31) at 24 temperatures which can cover all 0–6s adjusted retention time area. The experimental results show that the mean relative error between predicted adjusted retention time and experimental data of n-alkanes was only 2%. Furthermore, our proposed model demonstrates a good extrapolation capability for predicting adjusted retention time of target compounds which located out of the range of the reference compounds in the second dimension adjusted retention time space. Our work shows the deviation was less than 9 retention index units (iu) while the number of alkanes were added up to 5. The performance of our proposed model has also been demonstrated by analyzing a mixture of compounds in temperature programmed experiments.

Optimizing the relationship between chromatographic efficiency and retention times in temperature-programmed gas chromatography.

A methodology that can maximise the chromatographic efficiency that can be achieved within a defined time frame in temperature-programmed gas chromatography is described. The efficiency can be defined as the inverse of peak widths measured in retention index units. This parameter can be described by a model similar to the van Deemter equation, which is expanded to account for the effect of the temperature rate in addition to the effect of carrier gas velocity. The model of efficiency is found by response surface methodology, where the temperature rates and the carrier gas velocities are systematically varied in the experiments. A second model that accurately explains the retention time of the last eluting compound can be found from the same experiments, and optimal conditions are found by combining the two models. The methodology has been evaluated with four capillary columns and three carrier gases, using fatty acid methyl esters as analytes. All experiments showed that there is a fairly linear decrease in efficiency with increasing temperature rates. At any temperature rate, optimal velocity is only marginally higher than the velocity that maximises chromatographic efficiency, since the carrier gas velocity has a limited effect on the retention times.

Optimizing artificial neural network models for metabolomics and systems biology: an example using HPLC retention index data.

Artificial Neural Networks (ANN) are extensively used to model 'omics' data. Different modeling methodologies and combinations of adjustable parameters influence model performance and complicate model optimization. We evaluated optimization of four ANN modeling parameters (learning rate annealing, stopping criteria, data split method, network architecture) using retention index (RI) data for 390 compounds. Models were assessed by independent validation (I-Val) using newly measured RI values for 1492 compounds. The best model demonstrated an I-Val standard error of 55 RI units and was built using a Ward's clustering data split and a minimally nonlinear network architecture. Use of validation statistics for stopping and final model selection resulted in better independent validation performance than the use of test set statistics.

Gas Chromatographic and Mass Spectrometric Characterization of Trimethylsilyl Derivatives of Some Terpene Alcohol Phenylpropenoids

This paper reports mass spectra and linear temperature programmed retention indices (I(T)) for 31 esters of mono- and sesquiterpene alcohols with hydroxycinnamic acids. In this study, 14 phenylpropenoids were synthesized by esterification of terpenols with p-coumaric, ferulic, caffeic and sinapinic acids. Other phenylpropenoids were semi-quantitatively isolated by column chromatography from exudates covering the buds of two birch species (Betula pubescens and B. litwinowii). Main diagnostic ions in phenylpropenoids mass spectra were determined by GC/MS analysis. The possibility of predicting I(T) values was demonstrated with standard error of prediction between 3 and 11 of retention index units.

Development of Ecom50 and Retention Index Models for Nontargeted Metabolomics: Identification of 1,3-Dicyclohexylurea in Human Serum by HPLC/Mass Spectrometry

The goal of many metabolomic studies is to identify the molecular structure of endogenous molecules that are differentially expressed among sampled or treatment groups. The identified compounds can then be used to gain an understanding of disease mechanisms. Unfortunately, despite recent advances in a variety of analytical techniques, small molecule (<1000 Da) identification remains difficult. Rarely can a chemical structure be determined from experimental "features" such as retention time, exact mass, and collision induced dissociation spectra. Thus, without knowing structure, biological significance remains obscure. In this study, we explore an identification method in which the measured exact mass of an unknown is used to query available chemical databases to compile a list of candidate compounds. Predictions are made for the candidates using models of experimental features that have been measured for the unknown. The predicted values are used to filter the candidate list by eliminating compounds with predicted values substantially different from the unknown. The intent is to reduce the list of candidates to a reasonable number that can be obtained and measured for confirmation. To facilitate this exploration, we measured data and created models for two experimental features; MS Ecom₅₀ (the energy in electronvolts required to fragment 50% of a selected precursor ion) and HPLC retention index. Using a data set of 52 compounds, Ecom₅₀ models were developed based on both Molconn and CODESSA structural descriptors. These models gave r² values of 0.89 to 0.94 depending on the number of inputs, the modeling algorithm chosen, and whether neutral or protonated structures were used. The retention index model was developed with 400 compounds using a back-propagation artificial neural network and 33 Molconn structure descriptors. External validation gave a v² = 0.87 and standard error of 38 retention index units. As a test of the validity of the filtering approach, the Ecom₅₀ and retention index models, along with exact mass and collision induced dissociation spectra matching, were used to identify 1,3-dicyclohexylurea in human plasma. This compound was not previously known to exist in human biofluids and its elemental formula was identical to 315 other candidate compounds downloaded from PubChem. These results suggest that the use of Ecom₅₀ and retention index predictive models can improve nontargeted metabolite structure identification using HPLC/MS derived structural features.

The Robustness and Comparability of a Novel Rapid Reversed‐phase HPLC Drug‐screening Method Compared with Existing Systems

Acidic and basic drugs have been run on a novel non-buffered reversed-phase HPLC system. Variations in eluent pH, column temperature and eluent composition were used to demonstrate the excellent robustness of the system. The repeatability of the 16 nitro-n-alkanes used to assign index values to the retention times of acidic and basic drugs were not affected by the varied applied conditions (mean standard deviation less than 0.1 min). Due to the low operating pH of the system (2.2) the largest variation in retention index was seen to occur with the basic standard drug set, 7 retention index units between the two extremes of pH. Retention indices of 73 drugs run on different HPLC equipment using an ODS column from a different manufacturer, gave a correlation r = 0.990 with the retention indices of the same drugs run on the system used here. A correlation r = 0.977 was obtained for 48 common retention indices given by a buffered system published by other workers. A data set of 168 drugs run on the previous ODS system was used to generate a database of retention indices. These retention indices were obtained from the equations that described the correlations between this data set and that of other workers. For 115 drugs run on the system described here that are also present in this compilation, a correlation r = 0.945 was obtained from linear regression between them.

A method of calculating the second dimension retention index in comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry

A method was developed to calculate the second dimension retention index of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC × GC/TOF-MS) data using n-alkanes as reference compounds. The retention times of the C 7–C 31 alkanes acquired during 24 isothermal experiments cover the 0–6 s retention time area in the second dimension retention time space, which makes it possible to calculate the retention indices of target compounds from the corresponding retention time values without the extension of the retention space of the reference compounds. An empirical function was proposed to show the relationship among the second dimension retention time, the temperature of the second dimension column, and the carbon number of the n-alkanes. The proposed function is able to extend the second dimension retention time beyond the reference n-alkanes by increasing the carbon number. The extension of carbon numbers in reference n-alkanes up to two more carbon atoms introduces <10 retention index units (iu) of deviation. The effectiveness of using the proposed method was demonstrated by analyzing a mixture of compound standards in temperature programmed experiments using 6 different initial column temperatures. The standard deviation of the calculated retention index values of the compound standards fluctuated from 1 to 12 iu with a mean standard deviation of 5 iu.

Retention index thresholds for compound matching in GC–MS metabolite profiling

The generation of retention index (RI) libraries is an expensive and time-consuming effort. Procedures for the transfer of RI properties between chromatography variants are, therefore, highly relevant for a shared use. The precision of RI determination and accuracy of RI transfer between 8 method variants employing 5%-phenyl-95%-dimethylpolysiloxane capillary columns was investigated using a series of 9 n-alkanes (C 10–C 36). The precision of the RI determination of 13 exemplary fatty acid methyl esters (C 8 ME–C 30 ME) was 0.22–0.33 standard deviation (S.D.) expressed in RI units in low complexity samples. In the presence of complex biological matrices this precision may deteriorate to 0.75–1.11. Application of the previously proposed Kováts, van den Dool or 3rd–5th order polynomial regression algorithms resulted in similar precision of RI calculation. For transfer of empirical van den Dool-RI properties between the chromatography variants 3rd order regression was found to represent the minimal necessary assumption. The range of typical regression coefficients was r 2 = 0.9988–0.9998 and accuracy of RI prediction between chromatography variants varied between 5.1 and 19.8 (0.29–0.69%) S.D. of residual RI error, RI predicted − RI determined ( n > 64). Accuracy of prediction was enhanced when subsets of chemically similar compound classes were used for regression, for example organic acids and sugars exhibited 0.78 ( n = 29) and 3.74 ( n = 37) S.D. of residual RI error, respectively. In conclusion, we suggest use of percent RI error rather than absolute RI units for the definition of matching thresholds. Thresholds of 0.5–1.0% may apply to most transfers between chromatography variants. These thresholds will not solve all matching ambiguities in complex samples. Therefore, we recommend co-analysis of reference substances with each GC–MS profiling experiment. Composition of these defined reference mixtures may best approximate or mimic the quantitative and qualitative composition of the biological matrix under investigation.

Contribution to linearly programmed temperature gas chromatography: Further application of the Van den Dool–Kratz equation, and a new utilization of the Sadtler retention index library

Programmed temperature retention indices (PTRIs) calculated according to the equations of Van den Dool and Kratz, Golovnya and Uraletz, and Erdey et al. (also referred to as Antoine's integrated equation) are used in this work. Precalculation of isotherm retention indices from the results of a linearly programmed temperature GC is also presented. Deviations between experimental and calculated isothermal retention indices are below 2 retention index units. A relative “volatility” retention index is defined, as a function of the “volatilities”of the solute and the bracket reference n-alkanes. The comparison of the “volatility” retention indices with the PTRIs obtained with the other above equations shows absolute deviations of up to 4 retention index units. Based on an earlier “equivalent” temperature concept and on Tekler's proviso, a novel way for the utilization of Sadtler's retention index database, which takes advantage of the 3 data supplied by the library, is proposed.

Conversion of programmed-temperature retention indices from one set of conditions to another

In order to make programmed-temperature retention index (PTRI) data be shared by other chromatographers and laboratories, conversion of PTRI from one set of experimental conditions to another is investigated in detail in this work. It was found that the differences between the PTRIs at different heating rates are structurally dependent, especially the number of ring in molecules. Thus, with the help of molecule constitutional descriptors, equations of PTRI conversion to certain initial temperature, heating rate, and stationary phase were obtained with high correlation coefficients and low standard deviations. Calculation errors of PTRI conversion between different heating rates and between different initial temperatures were from 1.1 to 2.9 retention index units (i.u.), which is in the same order with experiment errors. It is well known that reproducibility of PTRI on a polar column is not as good as that on an apolar column because of the apolarity of the n-alkane homologues. Thus, topological descriptors were used for PTRI conversion between two columns with different polar stationary phases, giving better results than those obtained by constitutional descriptors. This shows that topological descriptors could provide more molecular structural information than constitutional descriptors. However, as constitutional descriptor has the advantages of clear physical meaning and very simple calculation, it is our first selection when the PTRI calculation accuracy is satisfied. The method developed is simple in calculation, easy to be performed with high accuracy.

An accurate and easy procedure to obtain isothermal Kováts retention indices in gas chromatography

Isothermal Kováts retention indices may be used in GC for identification purposes, but they are also useful in characterisation of stationary phases and for studying structural and physico-chemical properties of both the analyte and the stationary phase. They are currently reported as whole numbers with an accuracy of one index unit for non-polar stationary phases. The method recommended for their calculation uses a linear regression model, although non-linear models have also been applied with good results. In both cases, a computer programme and the retention times of a series of n-alkanes that elute correctly and resolved from the other compounds are needed, conditions which cannot always be fulfilled. However, it is possible to calculate retention indices with an accuracy of 0.1 retention index units (0.2 units for packed columns) with the help of only three n-alkanes using just a pocket calculator or a computer spreadsheet. The main requirement is that at least one of the n-alkanes has a retention index differing by no more than one hundred retention index units from that of the analyte being investigated. Examples are given for different stationary phases.

Retention in gas–liquid chromatography with a polyethylene oxide stationary phase: Molecular simulation and experiment

Configurational-bias Monte Carlo simulations in the isobaric–isothermal Gibbs ensemble were carried out to investigate the partitioning of normal alkanes, primary and secondary alcohols, symmetric alkyl ethers and arenes between a helium vapor phase and a polyethylene oxide stationary phase ( M W = 382 g mol −1). The united-atom version of the transferable potentials for phase equilibria force field was used to model all solutes, polyethylene oxide and helium. The Gibbs free energies of transfer and Kovats retention indices of the solutes were calculated directly from the partition constants at two different temperatures, 353 and 393 K. Chromatographic experiments on a Carbowax 20M retentive phase were performed for the same set of solutes and temperatures ranging from 333 to 413 K. The predicted retention indices for alcohols, ethers and arenes are overestimated by about 120, 70 and 20 retention index units, respectively, pointing to an overestimation of the first-order electrostatic interactions in the model system. Molecular-level analysis shows that hydrogen-bonding and dipole–dipole interactions lead to orientational ordering for the alcohol and ether analytes, whereas the weaker dipole–quadrupole interactions for the arene solutes are not sufficient to induce orientational ordering. The retention indices of alcohols and ethers decrease with increasing temperature because of the large entropic cost of hydrogen-bonding and orientational ordering. In contrast, the retention indices for arenes increase with increasing temperature because the entropic cost of cavity formation is smaller for arenes than for comparable alkanes.

Prediction of gas chromatographic retention indices of a diverse set of toxicologically relevant compounds

For a set of 846 organic compounds, relevant in forensic analytical chemistry, with highly diverse chemical structures, the gas chromatographic Kovats retention indices have been quantitatively modeled by using a large set of molecular descriptors generated by software Dragon. Best and very similar performances for prediction have been obtained by a partial least squares regression (PLS) model using all considered 529 descriptors, and a multiple linear regression (MLR) model using only 15 descriptors obtained by a stepwise feature selection. The standard deviations of the prediction errors (SEP), were estimated in four experiments with differently distributed training and prediction sets. For the best models SEP is about 80 retention index units, corresponding to 2.1–7.2% of the covered retention index interval of 1110–3870. The molecular properties known to be relevant for GC retention data, such as molecular size, branching and polar functional groups are well covered by the selected 15 descriptors. The developed models support the identification of substances in forensic analytical work by GC–MS in cases the retention data for candidate structures are not available.

Mosaic increments for predicting the gas chromatographic retention data of the chlorobenzenes

The chlorinated organic compounds are very important from the point of view of the chemical industry and environmental protection, and therefore the gas chromatographic analysis of these compounds is very interesting for analytical chemists. In this paper we studied the relationship between the molecular structure and gas chromatographic retention on several stationary phases having different polarity and at several temperatures of benzene and 12 chlorobenzene compounds as model compounds. A coding system involving primary (mosaic increments) and secondary (bond increments) calculation methods was developed. The retention indices of benzene and the chlorobenzenes calculated on HP-5 at 120 °C shows a better performance of the mosaic increments (average absolute deviation δ of 1.7 retention index units) compared with the bond increments ( δ=11.7 retention index units). Retention factors, k, calculated with mosaic increments for chlorobenzenes on SPB-1 and WAX-10, at 140 °C, yield average relative errors of ϵ=0.9 and 3.5%, respectively. Therefore, the presented paper provides a new possibility for precalculation of the retention data.

Temperature effects on the retention of n-alkanes and arenes in helium–squalane gas–liquid chromatography : Experiment and molecular simulation

Experiments and molecular simulations were carried out to study temperature effects (in the range of 323 to 383 K) on the absolute and relative retention of n-hexane, n-heptane, n-octane, benzene, toluene and the three xylene isomers in gas–liquid chromatography. Helium and squalane were used as the carrier gas and retentive phase, respectively. Both the experiments and the simulations show a markedly different temperature dependence of the retention for the n-alkanes compared to the arenes. For example, over the 60 K temperature range studied, the Kovats retention index of benzene is found to increase by about 16 or 18±10 retention index units determined from the experiments or simulations, respectively. For toluene and the xylenes, the experimentally measured increases are similar in magnitude and range from 14 to 17 retention index units for m-xylene to o-xylene. The molecular simulation data provide an independent method of obtaining the transfer enthalpies and entropies. The change in retention indices is shown to be the result of the larger entropic penalty and the larger heat capacity for the transfer of the alkane molecules.