Predicting the chromatographic retention of polymers: poly(methyl methacrylate)s and polyacryate blends

The suitability of a retention model especially designed for polymers is investigated to describe and predict the chromatographic retention behavior of poly(methyl methacrylate)s as a function of mobile phase composition and gradient steepness. It is found that three simple yet rationally chosen chromatographic experiments suffice to extract the analyte specific model parameters necessary to calculate the retention volumes. This allows predicting accurate retention volumes based on a minimum number of initial experiments. Therefore, methods for polymer separations can be developed in relatively short time. The suitability of the virtual chromatography approach to predict the separation of polymer blend is demonstrated for the first time using a blend of different polyacrylates.     

液相色谱梯度洗脱中的谱带压缩效应

谱带压缩效应是梯度洗脱区别于等度洗脱的重要特征。经典的范德姆特(van Deemter)理论塔板高度方程基于等度洗脱推导得到,因此不能对谱带压缩效应进行描述。在梯度洗脱中,保留因子(k)会随流动相组成(φ)的改变而发生变化,这就使得对梯度洗脱机理的研究要比等度洗脱复杂许多。该文对近10年来谱带压缩效应的研究进展,特别是溶剂强度模型(即描述ln k与φ关系的数学表达式)的非线性特征对谱带压缩因子(G)的影响进行了述评,指出为了更好地认识谱带压缩效应需要将这种非线性因素考虑在内。     

Exact peak compression factor in linear gradient elution. I. Theory

The only existing expression for the peak compression factor in linear gradient elution chromatography assumes that the linear-solvent-strength model (LSSM) applies to the retention of the compound studied, that the column efficiency is independent of the mobile phase composition, and that, during gradient elution, the relative retention factor of a compound inside its band varies linearly with the distance from the band center. Because the retention factors of many analytes in reversed-phase liquid chromatography do not rigorously follow the LSSM, we extend the theoretical approach of Poppe et al. to the prediction of peak compression factors in linear gradient elution chromatography for any retention model, when column efficiency varies with the mobile phase composition. Only the contribution of the chromatographic column to the peak compression was taken into account, the contribution of the dwell volume being neglected. A second restriction is the linearity of the relative retention factor as a function of the position along the band width inside the column. These constraints could be the sources for the difference observed between experimental and theoretical values of peak compression factors. When the retention factor varies steeply with the mobile phase composition, such as with proteins or large peptides in RP-HPLC, it is found that the thermodynamic compression term, which tends to sharpen the peak, is coupled with the column dispersion term, which tends to broaden the peak. This coupling term acts as an apparent dispersion term, contributing to broaden the peak. This result is consistent with the measurements of peak compression factors found in the literature.     

Theoretical Aspects of Gradient Reversed-Phase High Performance Liquid Chromatography of Styrene – Butylacrylate Block Copolymers

Butylacrylate – styrene co-polymers prepared by atom transfer radical polymeratization were separated on an octadecyl silica column by gradient elution with tetrahydrofuran in water, up to the molar masses 10,000. In reversed-phase high performance liquid chromatography (RP-HPLC), the retention of macromolecules is affected very significantly even by change of a few tenths of per cent of the organic solvent in the aqueous-organic mobile phase. Therefore, gradient elution was used for the determination of the parameters of the equations describing the effects of the mobile phase on the retention behaviour of synthetic polymers. The retention parameters of homopolymers and copolymers were calculated from the gradient data using two retention models. The retention behaviour of the copolymers was described using the experimental gradient retention data for homopolymers.     

Predicting the behaviour of polydisperse polymers in liquid chromatography under isocratic and gradient conditions

In this paper we describe how the existing theories to describe retention and peak width in isocratic and gradient-elution liquid chromatography can be expanded to describe the retention behaviour of natural and synthetic repetitive polymers, which feature distributions of molecules with different masses (and often different structures) rather than unambiguous molecular formulas. For polydisperse samples, it is vital that the model accommodates (isocratic) elution of sample components before the onset of a gradient, elution during the gradient, and elution after the completion of the gradient. The expanded models can readily be implemented in standard spreadsheet software, such as Excel. We have created such spreadsheets based on the conventional model for retention in reversed-phase liquid chromatography (RPLC) and on two different models for retention in normal-phase liquid chromatography. The implementation allows an easy visualization of the theoretical concept. Up to three different polymeric series can be entered, with a total of up to 100 peaks being computed and displayed in isocratic or gradient-elution chromatograms. Also visualized are "retention models" (diagrams of isocratic retention vs. composition) and "calibration curves" (retention or elution composition vs. molecular mass or degree of polymerization). The coefficients in the isocratic retention model may be correlated, as has often been observed in RPLC. It is shown that under certain conditions such a correlation corresponds to the existence of so-called critical (isocratic) conditions, at which all the members of a given polymeric series (same composition and end groups, different number of repeat units) show co-elution.     

Retention models in ion chromatography and their use in computer optimization of eluent composition

Computer optimization of eluent composition in ion chromatography can be performed using a retention model to predict elution behaviour of solutes. Approaches to optimization are outlined and some of the more recently published retention models are discussed in terms of the experimental parameters necessary for their implementation and the complexity of calculation necessary to solve the appropriate mathematical relationships in the models.     

Application of the reversed-phase liquid chromatographic model to describe the retention behaviour of polydisperse macromolecules in gradient and isocratic liquid chromatography

This paper illustrates how conventional models of chromatographic behaviour can be used to predict the separation behaviour of polydisperse macromolecules. Using polystyrene and polymethylmethacrylate homo- and co-polymeric standards, the models were validated by comparing experimental retention behaviour with that predicted by the chromatographic model. The experimental retention time of each of the samples was entered into a spreadsheet application, which calculated the parameters that best described retention (for a given model). When a correlation between the relevant parameters and molecular mass was established, that correlation was used to predict the change in retention behaviour over the molecular-mass range. An expression introduced in a previous paper, to calculate the critical mobile-phase composition of a homopolymer was validated using polystyrene homopolymers. A second expression, which can predict the elution behaviour of copolymers, was also validated. This expression can predict the retention of a copolymer, based solely onthe retention of the homopolymeric units that make up the copolymer.     

New practical algorithm for modelling retention times in gradient reversed-phase high-performance liquid chromatography

Computer models have been widely used to predict the chromatographic behaviour of liquid chromatography systems. With the introduction of mass spectrometric detection and the use of lower mobile phase flow rates with conventional LC equipment, the influence of the dwell volume on the shape of the gradient curve becomes an issue in predicting the retention times. A new straight forward algorithm is proposed for the modelling of retention times in reversed-phase LC, taking the effect of the dwell volume on the gradient shape into account. The results show that the dwell volume has a large effect at lower flow rates and on the retention times of the analytes eluting at the end of fast gradient curves. The proposed model is able to make reliable predictions and can be helpful in LC-MS method development.     

Modelling and prediction of retention in high-performance liquid chromatography by using neural networks

Summary Multi-layer feed-forward neural networks trained with an error back-propagation algorithm have been used to model retention behaviour of liquid chromatography as a function of the composition of the mobile phases. Conventional hydro-organic and micellar mobile phases were considered. Accurate retention modelling and prediction have been achieved using mobile phases defined by two, three and four parameters. With micellar mobile phases, the parameters involved included the concentrations of surfactant and organic modifier, pH and temperature. It is shown that neural networks provide a competitive tool to model varied inherent nonlinear relationships of retention behaviour with respect to the mobile phase parameters. The soft models defined by the weights of the networks are capable of accommodating all types of linear and nonlinear relationships, neural networks being specially useful when the relationships between retention behaviour and the mobile phase parameters are unknown. However, to train neural networks more experimental points than with hard-modelling methods are required, hence the use of the networks is recommended only for those cases where adequate theoretical or empirical models do not exist.     

Response surface methodology and support vector machine for the optimization of separation in linear gradient elution

Experimental design methodology was used to optimize the linear gradient elution chromatography. The effect of initial mobile phase composition (φ_in), initial isocratic time (t_in), and gradient time (t_G) on the retention times of phenyl thiohydantoin aminoacids (PTH‐amino acids) was investigated. The experiments were performed according to Box–Behnken experimental design to map the chromatographic response surface. Then multiple linear regression and support vector machine (SVM) methods were used to fit the retention times of solutes. Results shows the SVM models have better ability to predict retention time and used for grid search in factor space. The SVM models were verified, as good agreement was observed between the predicted and experimental values of retention time in the optimal condition.     

Multi-criteria decision making in micellar liquid chromatographic separation of chlorophenols

Simultaneous optimization of separation quality and analysis time of the micellar liquid chromatography of nine chlorophenol isomers was investigated. The effect on retention of three experimental parameters was studied using multivariate analysis. The factors studied were the concentration of sodium dodecyl sulfate, propanol content, and pH of the mobile phase. The experiments were performed according to the face-centered cube central composite design and the inverse form of the experimental retention times of analytes was fitted to polynomial models. The results of the analysis of variance showed that the models obtained explain over 99% of the variance observed in the chromatograms. The good predictive ability of the models was verified by high correlation coefficient (R2 > 0.99) and F ratio values for the plots of predicted cross-validated versus experimental retention times. The study showed that the use of the Pareto-Optimality method, an approach from multi-criteria decision making, allows selection of the best possible combinations of separation quality and analysis time in micellar liquid chromatography of chlorophenols.     

化合物色谱保留参数与其三维结构关系的研究

利用比较分子场分析(CoMFA)方法,建立了烷基取代苯、氯代苯、多环芳烃和二硝基取代芳烃等4类结构相近的化合物在甲醇／水体系中反相C18柱上的保留参数a,c值与其三维结构之间关系的定量模型。前3类化合物所得到的3个模型的交叉验证相关系数q2均大于0.5,其中针对烷基取代苯、氯代苯所建立的两个模型的非交叉验证相关系数r2大于0.995,表明模型具有较好的预测能力。该研究结果对进一步开展化合物液相色谱保留参数与其三维结构关系的研究提供了思路和方法。     

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.     

Theoretical background of monolithic short layer ion-exchange chromatography for separation of charged large biomolecules or bioparticles

The retention and peak spreading in linear gradient elution of charged large biomolecules were investigated by using numerical simulations. Oligo-DNA separation by monolithic anion-exchange chromatography was chosen as a model system. The peak width and the retention were well predicted by using the parameters obtained by gradient elution experiments at different gradient slopes. As the distribution coefficient at the peak retention volume K_R decreases with increasing molecular size, the peak became sharper for larger DNAs. This is due to very large effective charge (binding site) values of large DNAs (20–60). The peak width was well correlated with K_R based on the model equation developed for linear gradient elution of proteins. It was shown that the monolithic disk is best suited for very large charged biomolecule separations at high flow velocities with shallow gradients slopes.     

Hydrophilic interaction ultra performance liquid chromatography retention prediction under gradient elution

The development and application of new separation mechanisms such as hydrophilic interaction chromatography (HILIC) is of high importance for the simultaneous analysis of polar molecules such as primary metabolites. However the retention mechanism in HILIC is not fully understood and as a result retention prediction tools are not at hand for this chromatographic approach. In the present report we study the utility of a simple algorithm, based on a simple linear and/or a simple logarithmic retention model, for retention prediction in HILIC gradient separation of a mixture of 23 selected compounds including (poly)amines, amino acids, saccharides, and other molecules. Utilizing two types of gradient elution programs with or without an isocratic part, retention data were collected in order to build prediction models. Starting from at least three gradient runs the prediction of analyte retention was very satisfactory for all gradient programs tested, providing useful evidence of the value of such retention time prediction methodologies.     

On the utility of predictive chromatography to complement mass spectrometry based intact protein identification

The amino acid sequence determines the individual protein three-dimensional structure and its functioning in an organism. Therefore, “reading” a protein sequence and determining its changes due to mutations or post-translational modifications is one of the objectives of proteomic experiments. The commonly utilized approach is gradient high-performance liquid chromatography (HPLC) in combination with tandem mass spectrometry. While serving as a way to simplify the protein mixture, the liquid chromatography may be an additional analytical tool providing complementary information about the protein structure. Previous attempts to develop “predictive” HPLC for large biomacromolecules were limited by empirically derived equations based purely on the adsorption mechanisms of the retention and applicable to relatively small polypeptide molecules. A mechanism of the large biomacromolecule retention in reversed-phase gradient HPLC was described recently in thermodynamics terms by the analytical model of liquid chromatography at critical conditions (BioLCCC). In this work, we applied the BioLCCC model to predict retention of the intact proteins as well as their large proteolytic peptides separated under different HPLC conditions. The specific aim of these proof-of-principle studies was to demonstrate the feasibility of using “predictive” HPLC as a complementary tool to support the analysis of identified intact proteins in top-down, middle-down, and/or targeted selected reaction monitoring (SRM)-based proteomic experiments.     

Prediction of peptide retention times in normal-phase liquid chromatography with only a single gradient run.

Previous studies of peptide separation by normal-phase liquid chromatography have shown a linear relationship between the logarithm of the capacity factor and the logarithm of the volume fraction of modifier in the mobile phase. This permitted the use of a model to predict isocratic and gradient retention times based on data obtained by two initial gradient runs. In the present study, chromatographic behavior of 25 peptides in normal-phase liquid chromatography with isocratic elution have been studied and a linear relationship between the slope (S) and intercept [log k(0)] was obtained. This relationship was combined with the algorithm of prediction reported in the previous paper. The prediction of peptide retention times with only a single experimental gradient retention data was investigated.