Applicability of linear and nonlinear retention‐time models for reversed‐phase liquid chromatography separations of small molecules,peptides, and intact proteins

The applicability and predictive properties of the linear solvent strength model and two nonlinear retention‐time models, i.e., the quadratic model and the Neue model, were assessed for the separation of small molecules (phenol derivatives), peptides, and intact proteins. Retention‐time measurements were conducted in isocratic mode and gradient mode applying different gradient times and elution‐strength combinations. The quadratic model provided the most accurate retention‐factor predictions for small molecules (average absolute prediction error of 1.5%) and peptides separations (with a prediction error of 2.3%). An advantage of the Neue model is that it can provide accurate predictions based on only three gradient scouting runs, making tedious isocratic retention‐time measurements obsolete. For peptides, the use of gradient scouting runs in combination with the Neue model resulted in better prediction errors (<2.2%) compared to the use of isocratic runs. The applicability of the quadratic model is limited due to a complex combination of error and exponential functions. For protein separations, only a small elution window could be applied, which is due to the strong effect of the content of organic modifier on retention. Hence, the linear retention‐time behavior of intact proteins is well described by the linear solvent strength model. Prediction errors using gradient scouting runs were significantly lower (2.2%) than when using isocratic scouting runs (3.2%).     

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.     

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.     

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.     

Altering efficiency of hydrophobic interaction chromatography by combined salt and temperature effects

The coupled effect of salt concentration and temperature on the retention behavior of proteins in hydrophobic interaction chromatography has been studied. The retention data of four model proteins, i.e., myoglobin, lysozyme, α-chymotrypsinogen and bovine serum albumin, have been acquired by isocratic experiments of chromatographic elution within the temperature range 5–25 °C at different ammonium sulphate concentrations in the mobile phase. The retention dependencies quantified as functions of the salt concentration and temperature have been exploited in designing the process of gradient elution. The propagation velocity of proteins under conditions of the step gradient of salt and temperature has been determined by use of the equilibrium theory. To evaluate kinetic effects accompanying the band propagation the transport-dispersive model has been employed. It has been shown that altering the propagation of the salt and temperature waves in a proper manner allows improving the separation efficiency. Moreover, manipulation of specific kinetics effects can also be exploited in protein separations.     

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.     

Rapid analysis of pyridinoline and deoxypyridinoline in biological samples by liquid chromatography with mass spectrometry and a silica hydride column

Pyridinoline and deoxypyridinoline crosslinks are biomarkers found in urine for collagen degradation in bone turnover. For the first time, a rapid, sensitive, and ion‐pairing free method is described for the analysis of pyridinoline and deoxypyridinoline using ultra‐high performance liquid chromatography with Cogent Diamond Hydride column and detection by Q Exactive hybrid quadrupole‐orbitrap high resolution accurate mass spectrometry. The separation was achieved using both isocratic and gradient conditions and run time <5 min under isocratic conditions of 20% acetonitrile in water containing 0.1% formic acid. Pyridoxine was used as an internal standard and relative standard deviation of the retention times of both pyridinoline and deoxypyridinoline were <1%. The limit of detection was 0.082 ± 0.023 μM for pyridinoline and 0.118 ± 0.052 μM for deoxypyridinoline. The limit of quantitation was 0.245 ± 0.070 μM for pyridinoline and 0.354 ± 0.157 μM for deoxypyridinoline. The method was validated by the detection and quantitation of both pyridinoline and deoxypyridinoline in skin and urine samples.     

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.     

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).     

Mixed‐mode chromatography integrated with high‐performance liquid chromatography for protein analysis and separation: Using bovine serum albumin and lysozyme as the model target

A type of mixed‐mode chromatography was integrated with high‐performance liquid chromatography for protein analysis and separation. The chromatographic behavior was tested using bovine serum albumin and lysozyme as model proteins. For the mixed‐mode column, the silica beads were activated with γ‐(2,3‐epoxypropoxy)‐propytrimethoxysilane and coupled with 4‐mercaptopyridine as the functional ligand. The effects of pH, salt, and the organic solvent conditions of the mobile phase on the retention behavior were studied, which provided valuable clues for separation strategy. When eluted with a suitable pH gradient, salt concentration gradient, and acetonitrile content gradient, the separation behavior of bovine serum albumin and lysozyme could be controlled by altering the conditions of the mobile phase. The results indicated this type of chromatography might be a useful method for protein analysis and separation.     

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.     

Theory and applications of a novel ion exchange chromatographic technology using controlled pH gradients for separating proteins on anionic and cationic stationary phases

pISep is a major new advance in low ionic strength ion exchange chromatography. It enables the formation of externally controlled pH gradients over the very broad pH range from 2 to 12. The gradients can be generated on either cationic or anionic exchangers over arbitrary pH ranges wherein the stationary phases remain totally charged. Associated pISep software makes possible the calculation of either linear, nonlinear or combined, multi-step, multi-slope pH gradients. These highly reproducible pH gradients, while separating proteins and glycoproteins in the order of their electrophoretic pIs, provide superior chromatographic resolution compared to salt. This paper also presents a statistical mechanical model for protein binding to ion exchange stationary phases enhancing the electrostatic interaction theory for the general dependence of retention factor k, on both salt and pH simultaneously. It is shown that the retention factors computed from short time isocratic salt elution data of a model protein can be used to accurately predict its salt elution concentration in varying slope salt elution gradients formed at varying isocratic pH as well as the pH at which it will be eluted from an anionic exchange column by a pISep pH gradient in the absence of salt.     

Prediction of the effects of methanol and competing ion concentration on retention in the ion chromatographic separation of anionic and cationic pharmaceutically related compounds

The mixed-mode separation of a selection of anionic and cationic pharmaceutically related compounds is studied using ion-exchange columns and eluents consisting of ionic salts (potassium hydroxide or methanesulfonic acid) and an organic modifier (methanol). All separations were performed using commercially available ion-exchange columns and an ion chromatography instrument modified to allow introduction of methanol into the eluent without introducing compatibility problems with the eluent generation system. Isocratic retention prediction was undertaken over the two-dimensional space defined by the concentration of the competing ion and the percentage of organic modifier in the eluent. Various empirical models describing the observed relationships between analyte retention and both the competing ion concentration and the percentage of methanol were evaluated, with the resultant model being capable of describing the separation, including peak width, over the entire experimental space based on six initial experiments. Average errors in retention time and peak width were less than 6% and 27%, respectively, for runs taken from both inside and outside of the experimental space. Separations performed under methanol gradient conditions (while holding the competing ion concentration constant) were also modelled. The observed effect on retention of varying the methanol composition differed between analytes with several analytes exhibiting increased retention with increased percentage methanol in the eluent. An empirical model was derived based on integration of the observed t_R vs. %methanol plot for each analyte. A combination of the isocratic and gradient models allowed for the prediction of retention time using multi-step methanol gradient profiles with average errors in predicted retention times being less than 4% over 30 different 2- and 3-step gradient profiles for anions and less than 6% over 14 different 2- and 3-step gradient profiles for cations. A modified peak compression model was used to estimate peak widths under these conditions. This provided adequate width prediction with the average error between observed and predicted peak widths being less than 15% for 40 1-, 2- and 3-step gradients for anions and less than 13% over 14 1-, 2- and 3-step gradients for cations.     

A new approach to the prediction of RP-HPLC retention times in gradient elution from isocratic data

Summary A general chromatographic model has been set up starting from a set of equations based on the concept of the velocity of a solute along the column. The composition of the mobile phase is taken into account solely as a numerical factor entering into suitable equations and totally independent of the chemical-properties of the constituents. A few isocratic experimental runs are necessary as input data, and subsequently a small amount of computational effort is sufficient to make predictions of retention times under gradient elution conditions for solutes of whatever chemical structure. The prediction errors are dependent on the steepness of the linear gradient chosen but are, in any case, acceptably low.     

Application of linear gradient elution in countercurrent chromatography for the separation of triterpenoid saponins from the roots of Pulsatilla koreana Nakai

A linear gradient elution method using countercurrent chromatography was developed for the separation of four triterpenoid saponins from the roots of Pulsatilla koreana Nakai, including hederacolchiside E, which is responsible for the neuroprotective activity of this plant. The target fraction was obtained by 80% methanol elution of solid phase column chromatography. The partition coefficients of the target compounds were very different, which means they are difficult to separate with a single biphasic solvent system. Several important parameters for gradient elution, such as addition of alcohol content to the solvent system, starting point of the second mobile phase, and the time for the gradient change were logically determined and optimized. Four triterpenoid saponins could ultimately be separated, analyzed by high‐performance liquid chromatography, and their structures were identified by comparing the mass spectra and NMR spectra with the literature data. The compounds and yields were: hederasaponin B ( 1 ; 21.3 mg/100 mg), hederacolchiside E ( 2 ; 19.8 mg/100 mg), cernuoside A ( 3 ; 18.4 mg/100 mg), and cernuoside B ( 4 ; 17.3 mg/100 mg). Gradient‐elution countercurrent chromatography allows the effective separation of compounds with a wide polarity range.     

Analysis of linear and cyclic oligomers in polyamide-6 without sample preparation by liquid chromatography using the sandwich injection method. III. Separation mechanism and gradient optimization

The first six linear and cyclic oligomers of polyamide-6 can be quantitatively determined in the polymer using HPLC with the sandwich injection method and an aqueous acetonitrile gradient. In this final part of the triptych concerning the determination of the oligomers in polyamide-6, the irregular elution behavior of the cyclic monomer compared to the cyclic oligomers was investigated. We also optimized the separation of the involved polyamide oligomers, with respect to gradient steepness, stationary phase, column temperature and mobile phase pH. The irregular elution behavior of the cyclic monomer could be caused by its relatively large exposed/accessible hydrophobic surface, which permits relatively easy penetration into the hydrophobic stationary phase giving extra retention. The dipole moment of the different oligomers was used as a measure for this exposed/accessible hydrophobic area to correlate the retention factors using quantitative structure-retention relationships. We also studied the retention behavior of the polyamide, which is injected each run directly onto the column and modifies the stationary phase. Using a 250-microl post gradient injection zone of formic acid on a 250x3 mm Zorbax SB-C18 column, the polyamide could be effectively removed from the stationary phase after each separation. The linear solvent strength (LSS) model was used to optimize the separation of the first six linear and cyclic oligomers. As the LSS model assumes a linear correlation between the modifier concentration and the logarithm of the retention factor and the cyclic monomer and dimer show extreme curvation of this relation in the eluting region, we investigated different models to predict gradient elution from isocratic data. A direct translation of the isocratic data to gradient retention times did not yield adequate retention times using the LSS model. It was found that the LSS model worked acceptably if gradient retention times were used as input data. Even for fast non-linearly eluting components, an average error of 0.4 resolution units of 4sigma was obtained. Using the LSS model in combination with different column temperatures and mobile phase pH values, a separation of the first six linear and cyclic oligomers was accomplished.     

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。     

Hydrophilic interaction liquid chromatography for the separation of acidic agricultural compounds

Organic acids with very low pK_a require extremely low pH conditions to achieve adequate retention in reversed‐phase liquid chromatography, but an extremely low pH mobile phase can cause instrument reliability problems and limit the choice of columns. Hydrophilic interaction chromatography is a potential alternative to reversed‐phase liquid chromatography for the separation of organic acids using more moderate conditions. However, the hydrophilic interaction chromatography separation mechanism is known to be very complex and involves multiple competing mechanisms. In the present study, a hydrophilic interaction chromatography column packed with bare silica core–shell particles was used as the separation column and six agricultural organic acids were used as model analytes to evaluate the effects of buffer concentration, buffer pH, and temperature on sample loading capacity, selectivity, retention, and repeatability. It was found that using a higher concentration of buffer can lead to a significant improvement in the overall performance and reproducibility of the separation. Investigation of column equilibration time revealed that a very long equilibration time is needed when changing mobile phase conditions in between runs. This limitation needs to be acknowledged in hydrophilic interaction chromatography method development and sufficient equilibration time needs to be allowed in method scouting.