A simple,fast, and accurate thermodynamic‐based approach for transfer and prediction of GC retention times between columns and instruments Part II: Estimation of target column geometry

The transfer of thermodynamic parameters governing retention of a molecule in gas chromatography from a reference column to a target column is a difficult problem. Successful transfer demands a mechanism whereby the column geometries of both columns can be determined with high accuracy. This is the second part in a series of three papers. In Part I of this work we introduced a new approach to determine the actual effective geometry of a reference column and thermodynamic‐based parameters of a suite of compounds on the column. Part II, presented here, illustrates the rapid estimation of the effective inner diameter (or length) and the effective phase ratio of a target column. The estimation model based on the principle of least squares; a fast Quasi‐Newton optimization algorithm was developed to provide adequate computational speed. The model and optimization algorithm were tested and validated using simulated and experimental data. This study, together with the work in Parts I and III, demonstrates a method that improves the transferability of thermodynamic models of gas chromatography retention between gas chromatography columns.     

A simple,fast, and accurate thermodynamic‐based approach for transfer and prediction of gas chromatography retention times between columns and instruments Part I: Estimation of reference column geometry and thermodynamic parameters

The transfer of retention times based on thermodynamic models between columns can aid in separation optimization and compound identification in gas chromatography. Although earlier investigations have been reported, this problem remains unsuccessfully addressed. One barrier is poor predictive accuracy when moving from a reference column or system to a new target column or system. This is attributed to challenges associated with the accurate determination of the effective geometric parameters of the columns. To overcome this, we designed least squares‐based models that account for geometric parameters of the columns and thermodynamic parameters of compounds as they partition between mobile and stationary phases. Quasi‐Newton‐based algorithms were then used to perform the numerical optimization. In this first of three parts, the model used to determine the geometric parameters of the reference column and the thermodynamic parameters of compounds subjected to separation is introduced. As will be shown, the overall approach significantly improves the predictive accuracy and transferability of thermodynamic data (and retention times) between columns of the same stationary phase chemistry. The data required for the determination of the thermodynamic parameters and retention time prediction are obtained from fast and simple experiments. The proposed model and optimization algorithms were tested and validated using simulated and experimental data.     

Thermodynamics‐based modelling of gas chromatography separations across column geometries and systems,including the prediction of peak widths

Thermodynamics‐based models have been demonstrated to be useful for predicting retention time and peak widths in gas chromatography and two‐dimensional gas chromatography separations. However, the collection of data to train the models can be time consuming, which lessens the practical utility of the method. In this contribution, a method for obtaining thermodynamic‐based data to predict peak widths in temperature‐programmed gas chromatography is presented. Experimental work to collect data for peak width prediction is identical to that required to collect data for retention time prediction using approaches that we have presented previously. Using this combined approach, chromatograms including retention times and peak widths are predicted with very high accuracy. Typical errors in retention time are < 0.5%, while errors in peak width are typically < 5% as demonstrated using polycycic aromatic hydrocarbons and a mixture containing compounds with aldehyde, ketone, alkene, alkane, alcohol, and ester functionalities.     

Updating chromatographic predictions by accounting ageing for single and tandem columns

The most efficient optimization methodologies in liquid chromatography are based on the modeling and prediction of the chromatographic behavior for each compound in the sample. However, when the column suffers some ageing after the modeling process, predictions may differ significantly from the actual separation. Repeating the modeling is especially troublesome when several columns are involved, as is the case of coupled columns. We propose a shortcut to correct the time and peak profiles in these situations, after evaluating the effects of ageing. The original models are corrected by introducing parameters accounting for column ageing, obtained using the data of a small subset of compounds from those used to model the brand‐new column. The ageing parameters are fitted from the discrepancies between the data predicted with the original retention models for the brand‐new column and the experimental data measured for the aged column. The approach was developed and tested to predict the chromatographic behavior of 15 sulfonamides, analyzed with individual and tandem columns, using isocratic and gradient elution. Chromatograms more in line with the aged column performance were predicted. The agreement between predictions and experimental data in the aged columns was excellent.     

Study of the gas chromatographic behavior of selected alcohols and amines

The gas chromatographic behavior of selected linear and non-linear alcohols and amines was investigated using four capillary columns containing phenyl substitution levels of 0%, 5%, and 50% and 50% cyanopropyl substitution. In a previous study, the positions of specific compounds inside the capillary column were iteratively modeled using only two thermodynamic parameters (ΔH and ΔS). The present study addresses the validation of the two-parameter model for retention time prediction for selected alcohols and amines using thermodynamic data obtained from as few as two data points. The difference between predicted and observed retention times under different temperature conditions was generally less than 1% of the experimental value and the predicted order of elution was correct in the used model.     

Application of thermodynamic‐based retention time prediction to ionic liquid stationary phases

First‐ and second‐dimension retention times for a series of alkyl phosphates were predicted for multiple column combinations in GC×GC. This was accomplished through the use of a three‐parameter thermodynamic model where the analytes’ interactions with the stationary phases in both dimensions are known. Ionic liquid columns were employed to impart unique selectivity for alkyl phosphates, and it was determined that for alkyl phosphate compounds, ionic liquid columns are best used in the primary dimension. Retention coordinates for unknown phosphates are predicted from the thermodynamic parameters of a set standard alkyl phosphates. Additionally, we present changing retention properties of alkyl phosphates on some ionic liquid columns, due to suspected reaction between the analyte and column. This makes it difficult to accurately predict their retention properties, and in general poses a problem for ionic liquid columns with these types of analytes.     

Comparing columns for gas chromatography with the two-parameter model for retention prediction

The retention times of selected compounds in temperature programmed gas chromatography were predicted using a two-parameter model, on the basis of thermodynamic data obtained from isothermal runs on seven capillary columns, primarily substituted with 5% diphenylsiloxane. The scope for using thermodynamic data obtained from isothermal runs on one column to optimize separation on a different column or a different instrument setup was investigated. Additionally, the predictive utility of thermodynamic data obtained using a DB-5 column that had been in use for three years was compared to that of a new column of the same model. It was found that satisfactory separation could be achieved on one capillary column or instrument setup on the basis of thermodynamic data obtained using a different column or instrument set-up.     

Retention time prediction of compounds in Grob standard mixture for apolar capillary columns in temperature-programmed gas chromatography

This paper presents an extension of a previous investigation in which the behavior of nonpolar compounds in temperature-programmed gas chromatographic runs was predicted using thermodynamic (entropy and enthalpy) parameters derived from isothermal runs. In a similar manner, entropy and enthalpy parameters were determined for a Grob standard mixture of compounds with widely varying chemical characteristics. These parameters were used to predict the retention times and chromatographic behaviors of the compounds on four gas chromatography capillary columns: three that had phenyl-based stationary phases (with degrees of substitution of 0%, 5% and 50%) and one with (50%) cyanopropyl substitution. The predictions matched data empirically obtained from temperature-programmed chromatographic runs for all of the compounds extremely well, despite the wide variations in polarity of both the compounds and stationary phases. Thus, the results indicate that such simulations could greatly reduce the time and material costs of chromatographic optimizations.     

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 0-6s 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.     

基于深度学习的保留时间预测方法的研究进展及应用

在基于液相色谱-质谱联用的蛋白质组学研究中,肽段的保留时间作为有效区分不同肽段的特征参数,可以根据肽段自身的序列等信息对其进行预测。使用预测得到的保留时间辅助质谱数据鉴定肽段序列可以提高鉴定的准确性,因此对保留时间预测的工作一直受到领域内的广泛关注。传统的保留时间预测方法通常是根据氨基酸序列计算肽段的理化性质,进而计算肽段在特定色谱条件下的保留时间。近年来,深度学习方法取得了极大的进展,在蛋白质组学研究中发挥着越来越重要的作用。目前已发展出了多种基于深度学习的保留时间预测方法,与传统的保留时间预测方法相比有着更高的准确度,易于跨平台使用,并且能对修饰肽段的保留时间进行预测。但对某些复杂的修饰,如糖基化修饰等的预测结果还不够准确。如何进一步提高对修饰肽段预测的准确性是基于深度学习的保留时间预测方法的重要研究方向。这些预测的保留时间被应用于肽段鉴定的质量控制和方法评估,以及与预测的二级质谱谱图结合,建立模拟谱图库等方面。该文综述了深度学习方法在保留时间预测领域的最新研究进展以及应用成果,同时对其发展趋势和未来的应用方向进行了展望,以期为保留时间预测研究以及蛋白质组鉴定工作提供参考。     

Prediction of retention times and efficiency in linear gradient programmed pressure analysis on capillary columns

A method for the prediction of the retention time and the resolution of chromatographic peaks in different experimental conditions by starting from few experimental data measured in isothermal and isobaric analyses was published previously. In this paper, the same mathematical model was implemented for calculating the retention times and the column efficiency in programmed pressure runs. Some models originated from the Golay equation and reported in the literature are compared, and a new modified equation for the calculation of the peak width at half height is proposed. The procedure for the prediction of the retention time and the peak width at half height at programmed pressure of the carrier gas and different column temperature and linear gradient by using retention data of different compounds obtained in few isobaric runs is described. The prediction of the retention time and the separation efficiency of compounds with different polarity gave good results for the programmed pressure runs with linear gradient. The effect of the variation of the initial parameters of the experimental analyses and of the mathematical model on the accuracy of the prediction has been evaluated.     

反相高效液相色谱中流动相线性梯度洗脱条件下溶质保留时间预测的新方法

 在计算溶质的梯度保留时间时 ,根据流动相在色谱柱内的分布规律 ,对溶质在色谱柱内的迁移距离和流动相梯度同时进行校正 ,从而建立了一种预测溶质线性梯度洗脱条件下保留时间的新方法。该方法在不同的仪器系统中 ,对于弱保留和强保留溶质在不同线性梯度洗脱条件下保留时间的预测 ,都具有良好的准确度。以 15种氨基酸和 8种苯的同系物为例 ,该方法对于弱保留溶质保留时间的预测 ,相对平均误差分别为 3 70 %和 4 90 % ,远小于文献方法得到的结果 (2 3 6 1%和 31 16 % ) ;对于强保留溶质保留时间的预测 ,相对平均误差分别为 0 2 1%和6 0 1% ,略小于文献 。     

Strategies for compound identification and quantification using fused silica capillary column GC/MS

A test mixture containing 28 compounds plus their stable isotopically labeled analogs was analyzed on a daily basis for one month during a series of routine fused silica capillary column GC/MS analyses in order to establish the precision with which retention times and responses were produced. These long-term precision data were evaluated to determine how to best predict retention times and how to best reproduce quantification. Results clearly indicate that relative retention times should be calculated using the reference compound eluted most closely to the target compound and that quantification should be based on relative response using a chemically “similar” compound.     

Methodology for porting retention prediction data from old to new columns and from conventional-scale to miniaturised ion chromatography systems

Several procedures are available for simulating and optimising separations in ion chromatography (IC), based on the application of retention models to an extensive database of analyte retention times on a wide range of columns. These procedures are subject to errors arising from batch-to-batch variability in the synthesis of stationary phases, or when using a column having a different diameter to that used when the database was acquired originally. Approaches are described in which the retention database can be recalibrated to accommodate changes in the stationary phase (ion-exchange selectivity coefficient and ion-exchange capacity) or in the column diameter which lead to changes in phase ratio. The entire database can be recalibrated for all analytes on a particular column by performing three isocratic separations with two analyte ions. The retention data so obtained are then used to derive a "porting" equation which is employed to generate the required simulated separation. Accurate prediction of retention times is demonstrated for both anions and cations on 2mm and 0.4mm diameter columns under elution conditions which consist of up to five sequential isocratic or linear gradient elution steps. The proposed approach gives average errors in retention time prediction of less than 3% and the correlation coefficient was 0.9849 between predicted and observed retention times for 344 data points comprising 33 anionic or cationic analytes, 5 column internal diameters and 8 complex elution profiles.     

Rapid prediction and optimization of concentration conditions for preparative fractions by solid-phase extraction

SPE is an effective tool for concentrating preparative fractions isolated from a complex sample. To guarantee high efficiency and recovery of concentration, the concentration conditions could be optimized by predicting the breakthrough volume (V(B)). In this study, a method of predicting V(B )of unknown compounds in preparative fractions at any isocratic mobile phase composition with the analytical retention parameters a and c is described. The a and c values and the relationship between half peak width (W(1/2)) and retention time of a model analyte were measured using the analytical elution mode on an SPE column, and the V(B )and retention volume (V(R)) predicted with the a and c values were validated with breakthrough experiments. However, it is impossible to measure the a and c values of multiple compounds in a complex system directly on an SPE column with a low number of theoretical plates. The correlation of the a and c values between the SPE and analytical columns was developed so that the analytical data could be transferred to the SPE column. With the calculated a and c values, we could optimize the concentration conditions on the basis of the predicted V(B )and the volume of the preparative fraction.     

Retention Prediction System of O‐Aryl,O‐(1‐methylthioethylidene‐amino)phosphates on RP‐HPLC

Using factor analysis and stepwise linear regression methods, two parameters – CMR and ECCR – were selected from eight solute‐related structure parameters as the most retention‐influencing parameters. The relationships between the retention data (k ´) and the two structure parameters were established for 13 O‐aryl,O‐(1‐methylthioethylideneamino)phosphate compounds under a wide range of experimental conditions. The retention data (k ´) of another seven compounds with similar structures were predicted using these QSRR equations. Good agreement was obtained between the experimental k ´ values and predicted ones.     

Molecular Distance‐Edge Vector (μ) and Chromatographic Retention Index of Alkanes

A new method of quantitative structure‐retention relationship (QSRR) is proposed for estimating and predicting gas chromatographic retention indices of alkanes by using a novel molecular distance‐edge vector, called μ vector, containing 10 elements. The QSRR model (Ml), between the μ vector and chromatographic retention indices of 64 alkanes, was developed by using multiple linear regression (MLR) with the correlation coefficient being R = 0.9992 and the root mean square (RMS) error between the estimated and measured retention indices being RMS = 5.938. In order to explain the equation stability and prediction abilities of the M1 model, it is essential to perform a cross‐validation (CV) procedure. Satisfactory CV results have been obtained by using one external predicted sample every time with the average correlation coefficient being R = 0.9988 and average RMS = 7.128. If 21 compounds, about one third drawn from all 64 alkanes, construct an external prediction set and the 43 remaining construct an internal calibration set, the second QSRR model (M2) can be created by using calibration set data with statistics being R = 0.9993 and RMS = 5.796. The chromatographic retention indices of 21 compounds in the external testing set can be predicted by the M2 model and good prediction results are obtained with R = 0.9988 and RMS = 6.508.     

Easy and accurate high-performance liquid chromatography retention prediction with different gradients, flow rates, and instruments by back-calculation of gradient and flow rate profiles

Isocratic retention data should make a suitable foundation for an accurate, cross-instrument LC retention prediction system. Our previous work suggested that in order to accurately calculate (or "project") gradient retention times on a wide range of HPLC systems using a single set of isocratic retention data, the precise shape of both the gradient and flow rate profiles produced by each instrument must be properly taken into account. However, accurate measurement of these system properties is difficult and time-consuming. In this work, we describe an approach that uses the measured gradient retention times of a set of standard solutes spiked into the sample along with their known isocratic retention vs. eluent composition relationships to determine the effective gradient and flow rate profiles by back-calculation. Retention "projections" of 20 other solutes using these back-calculated profiles, under various chromatographic conditions typical of metabolomics experiments, were remarkably accurate (as good as 0.23% of the gradient time, R2 up to 0.99996), being very near the level of retention reproducibility. Our calculations suggest that this level of accuracy will allow a quadrupole MS to identify 38-fold more compounds out of a simulated mixture of 7307; it would allow an FTICR-MS to improve its identification rate nearly two-fold with the same mixture. Moreover, very little effort is required of the user. This approach provides a simple way to correct for all instrument-related factors affecting retention, allowing dramatically streamlined and improved retention projection across gradients, flow rates, and HPLC instruments.