Generic approach to the method development of intact protein separations using hydrophobic interaction chromatography

We describe a liquid chromatography method development approach for the separation of intact proteins using hydrophobic interaction chromatography. First, protein retention was determined as function of the salt concentration by isocratic measurements and modeled using linear regression. The error between measured and predicted retention factors was studied while varying gradient time (between 15 and 120 min) and gradient starting conditions, and ranged between 2 and 15%. To reduce the time needed to develop optimized gradient methods for hydrophobic interaction chromatography separations, retention‐time estimations were also assessed based on two gradient scouting runs, resulting in significantly improved retention‐time predictions (average error < 2.5%) when varying gradient time. When starting the scouting gradient at lower salt concentrations (stronger eluent), retention time prediction became inaccurate in contrast to predictions based on isocratic runs. Application of three scouting runs and a nonlinear model, incorporating the effects of gradient duration and mobile‐phase composition at the start of the gradient, provides accurate results (improved fitting compared to the linear solvent‐strength model) with an average error of 1.0% and maximum deviation of –8.3%. Finally, gradient scouting runs and retention‐time modeling have been applied for the optimization of a critical‐pair protein isoform separation encountered in a biotechnological sample.     

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.     

Development of an ion chromatographic gradient retention model from isocratic elution experiments

When facing separation problems in ion chromatography, chromatographers often lack guidelines to decide a priori if isocratic elution will give enough separation in a reasonable analysis time or a gradient elution will be required. This situation may be solved by the prediction of retention in gradient elution mode by using isocratic experimental data. This work describes the development of an ion chromatographic gradient elution retention model for fluoride, chloride, nitrite, bromide, nitrate, sulfate and phosphate by using isocratic experimental data. The isocratic elution retention model was developed by applying a polynomial relation between the logarithm of the retention factor and logarithm of the concentration of competing ions; the gradient elution retention model was based on the stepwise numerical integration of the corresponding differential equation. It was shown that the developed gradient elution retention model was not significantly affected by transferring data form isocratic experiment. The root mean squared prediction error for gradient elution retention model was between 0.0863 for fluoride and 0.7027 for bromide proving a very good predictive ability of developed gradient elution retention model.     

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。     

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.     

Recent applications of retention modelling in liquid chromatography

Recent applications of retention modelling in liquid chromatography (2015–2020) are comprehensively reviewed. The fundamentals of the field, which date back much longer, are summarized. Retention modeling is used in retention‐mechanism studies, for determining physical parameters, such as lipophilicity, and for various more‐practical purposes, including method development and optimization, method transfer, and stationary‐phase characterization and comparison. The review focusses on the effects of mobile‐phase composition on retention, but other variables and novel models to describe their effects are also considered. The five most‐common models are addressed in detail, i.e. the log‐linear (linear‐solvent‐strength) model, the quadratic model, the log–log (adsorption) model, the mixed‐mode model, and the Neue–Kuss model. Isocratic and gradient‐elution methods are considered for determining model parameters and the evaluation and validation of fitted models is discussed. Strategies in which retention models are applied for developing and optimizing one‐ and two‐dimensional liquid chromatographic separations are discussed. The review culminates in some overall conclusions and several concrete recommendations.     

Modeling of bispecific antibody elution in mixed‐mode cation‐exchange chromatography

The increasing demand for cost‐efficient manufacturing of biopharmaceuticals has been the main driving force for the development of novel chromatography resins, which resulted in the development of multimodal or mixed‐mode chromatographic resins. Most of them combine electrostatic and hydrophobic functionalities and are designed to deliver unique selectivity and increased binding capacities also at increased ionic strength. However, the mechanism of the protein–resin interaction in mixed‐mode chromatography is still not fully understood. The performance of protein separations in mixed‐mode chromatography is consequently difficult to predict. In this work, we present a model combining both salt and pH dependence to characterize and to predict protein retention in mixed‐mode chromatography. The model parameters are determined based on simple linear pH gradient elution experiments at different ionic strengths and they are directly transferable for the prediction of salt‐induced elution at fixed pH. Validity of the model is demonstrated for a bispecific antibody and its product‐related impurities.     

Application of retention modelling to the simulation of separation of organic anions in suppressed ion chromatography

The ion-exchange separation of organic anions of varying molecular mass has been demonstrated using ion chromatography with isocratic, gradient and multi-step eluent profiles on commercially available columns with UV detection. A retention model derived previously for inorganic ions and based solely on electrostatic interactions between the analytes and the stationary phase was applied. This model was found to accurately describe the observed elution of all the anions under isocratic, gradient and multi-step eluent conditions. Hydrophobic interactions, although likely to be present to varying degrees, did not limit the applicability of the ion-exchange retention model. Various instrumental configurations were investigated to overcome problems associated with the use of organic modifiers in the eluent which caused compatibility issues with the electrolytically derived, and subsequently suppressed, eluent. The preferred configuration allowed the organic modifier stream to bypass the eluent generator, followed by subsequent mixing before entering the injection valve and column. Accurate elution prediction was achieved even when using 5-step eluent profiles with errors in retention time generally being less than 1% relative standard deviation (RSD) and all being less than 5% RSD. Peak widths for linear gradient separations were also modelled and showed good agreement with experimentally determined values.     

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.     

Prediction of the chromatographic signal in gradient elution ion chromatography

This study describes the development of a signal prediction model in gradient elution ion chromatography. The proposed model is based on a retention model and generalized logistic peak shape function which guarantees simplicity of the model and its easy implementation in method development process. Extensive analysis of the model predictive ability has been performed for ion chromatographic determination of bromate, nitrite, bromide, iodide, and perchlorate, using KOH solutions as eluent. The developed model shows good predictive ability (average relative error of gradient predictions 1.94%). The developed model offers short calculation times as well as low experimental effort (only nine isocratic runs are used for modeling).     

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.     

Retention prediction of a set of amino acids under gradient elution conditions in hydrophilic interaction liquid chromatography

The analysis of amino acids presents significant challenges to contemporary analytical separations. The present paper investigates the possibility of retention prediction in hydrophilic interaction chromatography (HILIC) gradient elution based on the analytical solution of the fundamental equation of the multilinear gradient elution derived for reversed‐phase systems. A simple linear dependence of the logarithm of the solute retention (ln k) upon the volume fraction of organic modifier (φ) in a binary aqueous‐organic mobile is adopted. Utility of the developed methodology was tested on the separation of a mixture of 21 amino acids carried out with 14 different gradient elution programs (from simple linear to multilinear and curved shaped) using ternary eluents in which a mixture of methanol and water (1:1, v/v) was the strong eluting member and acetonitrile was the weak solvent. Starting from at least two gradient runs, the prediction of solute retention obtained under all the rest gradients was excellent, even when curved gradient profiles were used. Development of such methodologies can be of great interest for a wide range of applications.     

From Isocratic Data to a Gradient Elution Retention Model in IC: An Artificial Neural Network Approach

Gradient elution is used in ion chromatography to achieve rapid analysis with reasonable separation. Optimization and prediction of the gradient is clearly a multidimensional problem, however. One approach to prediction of gradient retention behavior is based on isocratic experimentation. In this work, a gradient model for simultaneous prediction of the retention behavior of fluoride, chlorite, chloride, chlorate, nitrate, and sulfate ions, on the basis of isocratic experimental data, is proposed. An artificial neural network was used to predict isocratic results; the network was optimized with regard to the number of data in the training set (25) and number of neurons in the hidden layer (6). A slight systematic error was observed in the isocratic prediction, but this did not effect gradient prediction. Good predictions were achieved for all the anions investigated (average error 1.79%). Deviations were somewhat higher for prediction of sulfate retention than for the other anions, probably because of the higher charge and larger size of sulfate in comparison with the other ions examined.     

Evaluation of a reversed-phase column (supelcosil LC-ABZ) under isocratic and gradient elution conditions for estimating octanol-water partition coefficients

The solvation parameter model is used to identify suitable chromatographic models for estimating the octanol-water partition coefficient for neutral compounds of varied structure by reversed-phase liquid chromatography. The stationary phase Supelcosil LC-ABZ with methanol-water mobile phases affords a series of suitable correlation models for estimating the octanol-water partition coefficient (log KOW) under isocratic and gradient elution conditions. Isocratic separations with mobile phase compositions containing from about 25 to 40% (v/v) methanol provide the most accurate results for log KOW values in the range -0.1 to 4.0. Gradient separations programmed from 5 to 100% (v/v) methanol are suitable for faster separations of compounds with large log KOW values. The standard error in the estimate for the regression models of the predicted log KOW values against literature values are 0.135 log units for the 30% (v/v) methanol-water isocratic system and 0.263 log units for the methanol-water gradient system. Isocratic retention factors predicted from two gradient separations with gradient times of 15 and 45 min afford a poorer fit for the correlation models between log KOW and the estimated retention factors than that of either the above isocratic and gradient models. Plots of the retention factor (log k) as a function of mobile phase composition are generally non-linear. Values of log kw obtained by non-linear extrapolation to a volume fraction of 0% (v/v) methanol do not afford a useful model for estimating log KOW.     

Development of Gradient Retention Model in Ion Chromatography. Part I: Conventional QSRR Approach

New retention methodology that integrates the conventional quantitative structure-retention relationship (QSRR) approach and gradient retention modeling based on isocratic retention data is developed and presented in this paper. Such an integrated approach removes the general QSRR limitation of highly predefined application conditions (i.e., QSRR are generally applicable only under the conditions used during model development) and allows the prediction of retentions over a wide range of different elution conditions (practically for any isocratic or gradient elution profile). At the same time, it retains the ability to predict retention of components unknown to the model, i.e., the components that have not been used in modeling. Ion-exchange chromatography (IC) analysis of carbohydrates was selected as modeling environment. Three regression techniques were applied and compared during QSRR modeling, namely: stepwise multiple linear regression, partial least squares (PLS), and uninformative variable elimination–PLS regression. The obtained prediction results of the best QSRR model (root-mean-square error of prediction = 22.69 %) were similar to those found in the literature. The upgrade from QSRR to the integrated model did not diminish the predictive ability of the model, indicating an excellent potential of the developed methodology not only in IC but also in chromatography in general.     

Optimizing gradient conditions in online comprehensive two‐dimensional reversed‐phase liquid chromatography by use of the linear solvent strength model

The linear solvent strength model was used to predict coverage in online comprehensive two‐dimensional reversed‐phase liquid chromatography. The prediction model uses a parallelogram to describe the separation space covered with peaks in a system with limited orthogonality. The corners of the parallelogram are assumed to behave like chromatographic peaks and the position of these pseudo‐compounds was predicted. A mix of 25 polycyclic aromatic compounds were used as a test. The precision of the prediction, span 0–25, was tested by varying input parameters, and was found to be acceptable with root mean square errors of 3. The accuracy of the prediction was assessed by comparing with the experimental coverages. Less than half of experimental coverages were outside prediction ± 1 × root mean square error and none outside prediction ± 2 × root mean square error. Accuracy was lower when retention factors were low, or when gradient conditions affected parameters not included in the model, e.g. second dimension gradient time affects the second dimension equilibration time. The concept shows promise as a tool for gradient optimization in online comprehensive two‐dimensional liquid chromatography, as it mitigates the tedious registration and modeling of all sample constituents, a circumstance that is particularly appealing when dealing with complex samples.     

Retention prediction of small peptides in reversed-phase liquid chromatography

Summary Retention prediction of small peptides (up to four residues) in reversed-phase liquid chromatography has been investigated, considering the contributions of side chains in each position to the peptide retention. In isocratic elution the retention of peptides could be predicted within about 8% relative error.     

Multi-linear gradient elution optimization for separation of phenylthiohydantoin amino acids using pareto optimality method

Multi-linear gradient elution was applied for simultaneous optimization of resolution and analysis times for ten phenylthiohydantoin amino acids (PTH-AAs) in liquid chromatography. Relation of lnK upon φ for each analyte was determined using isocratic retention time data, and gradient retention time of analytes was predicted using fundamental equation of gradient elution. Then a grid search program was used to predict retention time of solutes in variable space. Two different chromatographic goals-analysis time and minimum difference between adjacent peaks- were simultaneously evaluated using Pareto optimality method. Gradient program in optimum condition was: initially 24% CH₃OH/Water for 10 min, linear ramp to 34% over 5 min, to 29% over 5 min, and to 70% over 20 min. The average of calculated relative error in the prediction of the retention time in optimal conditions was -1.67% that shows a good agreement between predicted and experimental values of the chromatographic retention time in optimal condition.     

Retention models for isocratic and gradient elution in reversed-phase liquid chromatography

One- and multi-variable retention models proposed for isocratic and/or gradient elution in reversed-phase liquid chromatography are critically reviewed. The thermodynamic, exo-thermodynamic or empirical arguments adopted for their derivation are presented and discussed. Their connection to the retention mechanism is also indicated and the assumptions and approximations involved in their derivation are stressed. Special attention is devoted to the fitting performance of the various models and its impact on the final predicted error between experimental and calculated retention times. The possibility of using exo-thermodynamic retention models for prediction under gradient elution is considered from a practical point of view. Finally, the use of statistical weights in the fitting procedure of a retention model and its effect on the calculated elution times as well as the transferability of retention data among isocratic and gradient elution modes are also examined and discussed.