Prediction of retention times and peak widths in temperature-programmed gas chromatography using the finite element method

Optimization of separations in gas chromatography is often a time-consuming task. However, computer simulations of chromatographic experiments may greatly reduce the time required. In this study, the finite element method was used to predict the retention times and peak widths of three analytes eluting from each of four columns during chromatographic separations with two temperature programs. The data acquired were displayed in predicted chromatograms that were then compared to experimentally acquired chromatograms. The differences between the predicted and measured retention times were typically less than 0.1%, although the experimental peak widths were typically 10% larger than expected from the idealized calculations. Input data for the retention and peak dispersion calculations were obtained from isothermal experiments, and converted to thermodynamic parameters.     

Evaluation of the Linear-Elution-Strength Model for the Prediction of Retention and Selectivity in Isothermal Gas Chromatography

Linear-elution strength theory and temperature-programmed gas chromatography is evaluated as a rapid method for predicting isothermal retention factors and column selectivity. Retention times for a wide range of compounds are determined at the program rates of 3 and 12 °C/min for the temperature range 60 to 160 °C on three open-tubular columns (DB-1701, DB-210 and EC-Wax) and used to predict isothermal retention factors for each column over the temperature range 60 to 140 °C. The temperature-program predicted isothermal retention factors are compared with experimental values using linear regression and the solvation parameter model. It is shown that isothermal retention factors predicted by the linear-elution-strength model only approximately represents the experimental data. The model fails to predict the slight curvature that exists in most plots of the experimental retention factor (log k) as a function of temperature. In addition, regression of the temperature-program predicted isothermal retention factors against the experimental values indicates that the slopes and intercepts deviate significantly from their target values of one and zero, respectively, in a manner which is temperature dependent. The temperature-program predicted isothermal retention factors result in system constants for the solvation parameter model that are different to those obtained from the experimental retention factors. These results are interpreted as indicating that linear-elution-strength theory predicts retention factors that fail to accurately model stationary phase interactions over a wide temperature range. It is concluded that temperature-program methods using linear-elution-strength theory are unsuitable for constructing system maps for isothermal separations.     

Ultrafiltration: separation enhancement by counter-current cascading

A model has been developed which predicts the performance of a counter-current ultrafiltration cascade. The model demonstrates that use of such a cascade can improve separations over those obtained with a single ultrafilter with respect to both separation factor and extraction. However, the model also shows that a high extraction and a high separation factor are mutually exclusive. The model predictions are compared with experimental data for the separation of S-ovalbumin and glucose by a three-stage cascade. The experimental separations were less than those predicted by the model. This discrepancy is most probably because of a failure in the approximation used to correct for concentration polarization as the volume extraction at individual stages increased. Nevertheless, the data show that the performance of the cascade is clearly superior to that obtained for a single ultrafilter     

A general strategy for performing temperature-programming in high performance liquid chromatography--prediction of segmented temperature gradients

In the present work it is shown that the linear elution strength (LES) model which was adapted from temperature-programming gas chromatography (GC) can also be employed to predict retention times for segmented-temperature gradients based on temperature-gradient input data in liquid chromatography (LC) with high accuracy. The LES model assumes that retention times for isothermal separations can be predicted based on two temperature gradients and is employed to calculate the retention factor of an analyte when changing the start temperature of the temperature gradient. In this study it was investigated whether this approach can also be employed in LC. It was shown that this approximation cannot be transferred to temperature-programmed LC where a temperature range from 60°C up to 180°C is investigated. Major relative errors up to 169.6% were observed for isothermal retention factor predictions. In order to predict retention times for temperature gradients with different start temperatures in LC, another relationship is required to describe the influence of temperature on retention. Therefore, retention times for isothermal separations based on isothermal input runs were predicted using a plot of the natural logarithm of the retention factor vs. the inverse temperature and a plot of the natural logarithm of the retention factor vs. temperature. It could be shown that a plot of lnk vs. T yields more reliable isothermal/isocratic retention time predictions than a plot of lnk vs. 1/T which is usually employed. Hence, in order to predict retention times for temperature-gradients with different start temperatures in LC, two temperature gradient and two isothermal measurements have been employed. In this case, retention times can be predicted with a maximal relative error of 5.5% (average relative error: 2.9%). In comparison, if the start temperature of the simulated temperature gradient is equal to the start temperature of the input data, only two temperature-gradient measurements are required. Under these conditions, retention times can be predicted with a maximal relative error of 4.3% (average relative error: 2.2%). As an example, the systematic method development for an isothermal as well as a temperature gradient separation of selected sulfonamides by means of the adapted LES model is demonstrated using a pure water mobile phase. Both methods are compared and it is shown that the temperature-gradient separation provides some advantages over the isothermal separation in terms of limits of detection and analysis time.     

Using computer modeling to predict and optimize separations for comprehensive two-dimensional gas chromatography

In order to fully realize the separation power of comprehensive two-dimensional gas chromatography (GC x GC), a means of predicting and optimizing separations based on operating variables was developed. This approach initially calculates the enthalpy (DeltaH) and entropy (DeltaS) for the target compounds from experimental input data, and then uses this information to simultaneously optimize all column and runtime variables, including stationary phase composition, by comparing the performance of large numbers of simulated separations. This use of computer simulation has been shown to be a useful aid in conventional separations. It becomes almost essential for GC x GC optimization because of the large number of variables involved and their very complex interaction. Agreement between experimental and predicted values of standard test samples (Grob mix) using GC x GC separation shows that this approach is accurate. We believe that this success can be extended to more challenging mixtures resulting in optimizations that are simpler and transferable between GC x GC instruments.     

Predictive Liquid Chromatography of Peptides Based on Hydrophilic Interactions for Mass Spectrometry-Based Proteomics

High-performance liquid chromatography (HPLC) is widely used for separation of complex peptide mixtures before mass spectrometry-based proteome analysis. In this analysis, reversed phase HPLC (RPHPLC) using non-polar stationary phases such as surface-modified silica containing alkyl groups (e.g., C18) is typically employed. Because of the high heterogeneity of proteomic samples, multidimensional separation approaches gained increasing attention recently to tackle this complexity and extremely high range of concentrations. In two-dimensional liquid chromatography, hydrophilic interaction chromatography (HILIC) is often a method of choice for combination with RP-HPLC because it uses reversed-phase type eluents and allows efficient separation of polar peptides. Due to the high degree of orthogonality in this two-dimensional separation space, it is tempting to develop approaches for predicting peptide retention times for HILIC-based separations similar to the ones for RP-HPLC. Recent successful efforts in this area were focused on developing retention coefficient (RC)-based approaches. Herein, we explored the feasibility of using a statistical thermodynamic model for prediction of peptide retention times in HILIC separations and determined the phenomenological parameters of the model for a bare silica column. The performance of the developed model was tested using HPLC-MS analysis of a set of synthetic peptides, as well as a tryptic peptide mixture.     

Optimization of artificial neural network for retention modeling in high-performance liquid chromatography

An artificial neural network (ANN) model for the prediction of retention times in high-performance liquid chromatography (HPLC) was developed and optimized. A three-layer feed-forward ANN has been used to model retention behavior of nine phenols as a function of mobile phase composition (methanol-acetic acid mobile phase). The number of hidden layer nodes, number of iteration steps and the number of experimental data points used for training set were optimized. By using a relatively small amount of experimental data (25 experimental data points in the training set), a very accurate prediction of the retention (percentage normalized differences between the predicted and the experimental data less than 0.6%) was obtained. It was shown that the prediction ability of ANN model linearly decreased with the reduction of number of experiments for the training data set. The results obtained demonstrate that ANN offers a straightforward way for retention modeling in isocratic HPLC separation of a complex mixture of compounds widely different in pK_a and log K_ow values.     

Prediction of protein retention times in gradient hydrophobic interaction chromatographic systems

A two-step methodology has been developed for the prediction of protein retention time in linear-gradient HIC systems. Isocratic retention parameters were determined from ln(k')-salt concentration plots for a number of commercially available proteins with a range of properties. Quantitative structure property relationship (QSPR) models based on a support vector machine (SVM) approach were generated for predicting isocratic retention parameters for proteins not included in the model generation. The predicted parameters were then used to calculate protein gradient retention times and the results indicate that this approach is well suited for predicting experimental gradient retention data. The approach presented in this paper may have implications for HIC methods development at both the bench and process scales.     

反相高效液相三元流动相台阶梯度分离条件的快速优化方法

 根据溶质在柱内的迁移规律 ,建立了一种利用线性梯度实验快速获得溶质保留值方程系数 ,然后以串行响应函数为优化指标进行多台阶梯度分离条件优化的方法。与利用等度实验获得保留值方程的方法相比 ,该法可以大大缩短优化时间。通过该方法对芳香胺和衍生化氨基酸样品进行了分离 ,获得了满意的分离度 ,表明该方法的预测精度很好。     

Predictions of Reversed-Phase Gradient Elution LC Separations Supported by QSRR

Previous studies demonstrated that quantitative structure-retention relationships (QSRR) combined with the linear solvent strength (LSS) model allow for prediction of gradient reversed-phase liquid chromatography retention time for any analyte of a known molecular structure under defined LC conditions. A QSRR model derived at the selected gradient time and at the same gradient time was tested. The aim the present study was to evaluate the accuracy of QSRR predictions used during the predictions of LC gradient retention times with variable gradient times. For this purpose, predictions of retention times at two gradient times were used to find the optimal, different gradient times. In the first step, experimental retention data for the model set of analytes were used to derive appropriate QSRR models at two gradient times. These QSRR models were further used to predict gradient retention times for another set of testing analytes at the two selected above gradient times. Then, applying linear solvent-strength (LSS) theory, the predicted retention times for test analytes were used to find other optimal gradient times for those analytes. Satisfactory predictions of gradient retention times for test analytes were obtained at gradient times different from those applied for model analytes.     

Retention time and peak width in the combined pH/organic modifier gradient high performance liquid chromatography

The purpose of this work was to test the applicability of the current theory to predict the peak retention time and the peak width in the combined pH/organic modifier gradient reversed phase high performance liquid chromatography (RP HPLC). A series of 38 isocratic measurements have been conducted for a wide range of pH and methanol contents for ketoprofen (weak acid) and papaverine (weak base). It served to find the model describing dependence of retention factor and the height equivalent of a theoretical plate (HETP) on pH and organic modifier content. The information gathered in the isocratic mode was used to simulate retention times and peak widths for 30 various methanol gradients, 25 pH gradients, and 3 combined pH/methanol gradients. The simulations were compared with the experimental data. We also proposed a simplified version of this model that was parameterized based on 12 initial organic modifier gradients carried out for different pHs and for the 20 min and 60 min gradient development times. The full and the simplified model described the experimental data very well. In conclusion, the proposed modeling approach allowed predicting analyte retention times and peak width for various pH and organic modifier changes. Its simplified version required only 12 initial experiments and seems to be very promising in the optimization RP HPLC separations for complex samples and for conditions providing peak compression.     

反相液相色谱中同系物体系实验点与预测方程参数间的匹配研究

以波相色谱中溶质计量置换统一保留模型（SDM-R）的二参数、三参数和四参数方程为基础,研究了在预测同系物保留值时实验点与预测方程参数间的匹配关系。用两个实验点,分别以二、三和四参数方程对反相色谱中同系物保留值进行预测,发现预测值与实验值基本相符,但以二参数方程预测结果为最佳。又与其它保留方程的预测结果进行了比较,证实了上述结论。当实验点数增加到4～5个时,多参数方程预测同系物的准确度增加,且明显高于二参数方程。同时还讨论了方程中各参数与同系物碳数间的线性关系,发现二参数方程中的参数遵循同系物变化规律。     

Application of optimization procedures for the separation of anabolic compounds by high-performance liquid chromatography

A simple systematic approach is presented for optimizing high-performance liquid chromatographic separations of anabolics with multi-component isocratic mobile phases. A computer program was obtained and adjusted for use with an IBM-compatible XT personal computer. The program requires experimental retention data with three quaternary solvent mixtures to calculate the optimum solvent composition using a geometric model of a prism. For each possible composition of the mobile phase the set of retention data can be calculated. Applications are shown for mixtures of anabolic compounds using a mobile phase composed of methanol, tetrahydrofuran and acetonitrile. The predicted retention data agreed very well with the experimental data.     

Development of an inorganic cations retention model in ion chromatography by means of artificial neural networks with different two-phase training algorithms

This paper describes development of artificial neural network (ANN) retention model, which can be used for method development in variety of ion chromatographic applications. By using developed retention model it is possible both to improve performance characteristic of developed method and to speed up new method development by reducing unnecessary experimentation. Multilayered feed forward neural network has been used to model retention behaviour of void peak, lithium, sodium, ammonium, potassium, magnesium, calcium, strontium and barium in relation with the eluent flow rate and concentration of methasulphonic acid (MSA) in eluent. The probability of finding the global minimum and fast convergence at the same time were enhanced by applying a two-phase training procedure. The developed two-phase training procedure consists of both first and second order training. Several training algorithms were applied and compared, namely: back propagation (BP), delta-bar-delta, quick propagation, conjugate gradient, quasi Newton and Levenberg-Marquardt. It is shown that the optimized two-phase training procedure enables fast convergence and avoids problems arisen from the fact that every new weight initialization can be regarded as a new starting position and yield irreproducible neural network if only second order training is applied. Activation function, number of hidden layer neurons and number of experimental data points used for training set were optimized in order to insure good predictive ability with respect to speeding up retention modelling procedure by reducing unnecessary experimental work. The predictive ability of optimized neural networks retention model was tested by using several statistical tests. This study shows that developed artificial neural network are very accurate and fast retention modelling tool applied to model varied inherent non-linear relationship of retention behaviour with respect to mobile phase parameters.     

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...     

Reverse osmosis of multicomponent electrolyte solutions Part II. Experimental verification

A variety of single salt experiments were performed over a wide range of concentration and pH using NaCl and CaCl₂, to test the model developed in Part I. The model was shown to be effective in producing the same type of separation behaviors as was experimentally observed. Using the parameters obtained from single salt experiments, separations of mixtures of NaCl and CaCl₂ were predicted and experimentally confirmed. Agreement between the predictions and experimental data was quite good, and confirms that the model is useful for prediction of multicomponent separations using data from single salt experiments.     

Prediction of retention times for anions in linear gradient elution ion chromatography with hydroxide eluents using artificial neural networks

The feasibility of using an artificial neural network (ANN) to predict the retention times of anions when eluted from a Dionex AS11 column with linear hydroxide gradients of varying slope was investigated. The purpose of this study was to determine whether an ANN could be used as the basis of a computer-assisted optimisation method for the selection of optimal gradient conditions for anion separations. Using an ANN with a (1, 10, 19) architecture and a training set comprising retention data obtained with three gradient slopes (1.67, 2.50 and 4.00 mM/min) between starting and finishing conditions of 0.5 and 40.0 mM hydroxide, respectively, retention times for 19 analyte anions were predicted for four different gradient slopes. Predicted and experimental retention times for 133 data points agreed to within 0.08 min and percentage normalised differences between the predicted and experimental data averaged 0.29% with a standard deviation of 0.29%. ANNs appear to be a rapid and accurate method for predicting retention times in ion chromatography using linear hydroxide gradients.