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.     

Theoretical opportunities and actual limitations of pH gradient HPLC

In a series of reports published recently by our laboratory comprehensive theory and experimental conditions were established for reversed-phase high-performance liquid chromatography (RP HPLC) employing the programmed pH gradient of mobile phase. A procedure was developed providing, rapidly and conveniently, the acidity (pK_a) of weak acids and bases and their lipophilicity (hydrophobicity) log k_w. The basis of the double-gradient RP HPLC, employing simultaneous gradients of organic modifier content and mobile phase pH, was also elaborated. The fundamentals of the approach are presented briefly and systematically and its advantages and limitations are discussed. It is demonstrated that the newly introduced pH gradient method increases the analytical versatility of RP HPLC and our understanding of its physicochemical basis.     

pH gradient high-performance liquid chromatography: theory and applications

pH gradient high-performance liquid chromatography (HPLC) is a method of reversed-phase high-performance liquid chromatography suitable for ionogenic substances. It consists in programmed increase during the chromatographic process of the eluting strength of eluent with respect to the analytes separated. On the analogy of the conventional organic modifier gradient reversed-phase HPLC, in the pH gradient approach the eluting strength of the mobile phase increases due to its changing pH: increasing in case of acids or decreasing in case of bases. At the same time the content of organic modifier remains constant. A theory of the pH gradient HPLC has been elaborated. The resulting mathematical model is easily manageable. Its ability to predict changes in retention and separation of analytes following the changes in chromatographic conditions is demonstrated. The pH gradient method is uniquely suitable to determine pKa values of analytes. An equation is presented allowing to calculate pKa values basing on appropriate retention data. The effects on pKa are discussed of the concentration of methanol in the mobile phase. The RP HPLC-derived pKa data correlate to the reference pKa values (w(w)pKa) but are not identical. That may be explained by the effects on the chromatographically determined pKa of the specific interactions of analytes with stationary phases. The proposed pH gradient RP HPLC procedure offers a fast and convenient means to get comparable acidity parameters for larger series of compounds, like drug candidates, also when the analytes are available only in minute amounts and/or as complex mixtures.     

The application of gradient reversed-phase high-performance liquid chromatography to the pK(a) and log k(w) determination of polyprotic analytes

The purpose of this work was to propose a theoretical model of the combined pH/organic modifier gradient in reversed-phase high-performance liquid chromatography (RP HPLC) with special emphasis on its applicability to polyprotic analytes. The model was developed and approximated to be useful for a data set comprising organic modifier gradients obtained at different pH changes and different gradient durations. It was evaluated regarding its ability to describe experimental data. The chromatographic pK(a) and lipophilicity parameter, log k(w), were obtained by fitting to the proposed model and comparing to the literature values.     

Effects of pH in reversed-phase liquid chromatography

The effects of concomitant variations in pH and organic modifier concentration on retention, efficiency and peak symmetry are considered for reversed-phase liquid chromatography (RPLC) on octadecyl-modified silica (ODS) columns. A number of factors are discussed, which make the systematic exploitation of pH effects in RPLC more complicated than the optimization of solvent composition. If the pH is varied, a second factor (usually the concentration of organic modifier) will need to be varied simultaneously to maintain retention (capacity factors) in the optimum range. When pH is considered as a parameter in RPLC, not only its effects on retention, but also the variations in efficiency (plate count) and peak shape (asymmetry) need to be considered. These parameters turn out to vary drastically between individual solutes and between different experimental conditions. The results of a study involving a number of acidic, basic and neutral solutes, two different ODS columns and mixtures of either methanol or acetonitrile with aqueous buffers are reported. In the earlier part of the study, using methanol as the organic modifier, reproducible data for retention, peak width and peak symmetry were obtained and these data are reported. In the later part of the study, using acetonitrile, a gradual change in retention as a function of time was observed, this effect coinciding with a decrease in column efficiency. It is concluded that ODS columns are subject to considerable degradation during studies in which the pH is varied. Although this effect can be described mathematically, the preferred solution is thought to be the use of pH-stable columns.     

Optimization of stepwise gradient elution in reversed-phase chromatography

Summary Equations describing multi-step gradient elution with a mobile phase of constant composition in each step were derived. These equations useful for calculating the retention volumes in both gradient HPLC and TLC were derived on the basis of the relationship between the isocratic capacity factor and the volume fraction of the organic modifier. The validity of the equations was experimentally verified in a LiChrosorbRP-18-water/methanol system for 11 methyl- and chlorobenzenes and phenols. A satisfactory agreement between the theoretical and experimental k′ values was found.     

Axial temperature gradient and mobile phase gradient in microcolumn high-performance liquid chromatography

The effect of axial temperature gradient (ATG) along a microcolumn on the separation performance at both isocratic and gradient elution mode was investigated. A thermostat system was designed to form an ATG along the packed column. Polycyclic aromatic hydrocarbons (PAHs) were separated on a 0.53 mm  × 150 mm i.d. 5 μm C₁₈ microcolumn, with water and acetonitrile as mobile phase. The separation results obtained at mobile phase gradient (MPG) and ATG in microcolumn HPLC were compared with the results performed at ambient conditions. Extrapolated curves of peak width at half height (wh)versus lnk showed that wh is narrower at the same retention time when ATG was applied in addition to MPG. The column efficiency was enhanced 20-30% and the resolution was slightly reduced because of reduction of selectivity at elevated temperature at ATG condition. The RSD of retention time in ATG mode was less than 2.5%.     

Determination of testosterone and its metabolites using liquid chromatography with elevated column temperature and flow-rate gradient

A rapid high performance liquid chromatography (HPLC) method for determination of testosterone and its metabolites in biological samples is described. The method combines a flow-rate gradient with elevated column temperature to obtain a complete separation of testosterone and its metabolites. The flow-rate gradient method dramatically reduces the analysis time (17 min) compared with isocratic elution (35 min). This method is simple and reproducible with relative standard deviations (R.S.D.) of <0.1% for retention time and 1-4% for peak area. It provides limits of detection (LOD) in the range of 0.05-0.1 μM for testosterone and its five major metabolites. We applied the method to analyze rat liver microsome samples incubated with testosterone, demonstrating a testosterone metabolic profile due to enzymatic activities in the microsome. Analysis of testosterone and its metabolites is important because metabolism of testosterone is a surrogate measure for cytochrome P-450 (CYP) enzymatic activity.     

Retention modeling and simultaneous optimization of pH value and gradient steepness in RP‐HPLC using feed‐forward neural networks

A novel approach is proposed for the simultaneous optimization of mobile phase pH and gradient steepness in RP‐HPLC using artificial neural networks. By presetting the initial and final concentration of the organic solvent, a limited number of experiments with different gradient time and pH value of mobile phase are arranged in the two‐dimensional space of mobile phase parameters. The retention behavior of each solute is modeled using an individual artificial neural network. An “early stopping” strategy is adopted to ensure the predicting capability of neural networks. The trained neural networks can be used to predict the retention time of solutes under arbitrary mobile phase conditions in the optimization region. Finally, the optimal separation conditions can be found according to a global resolution function. The effectiveness of this method is validated by optimization of separation conditions for amino acids derivatised by a new fluorescent reagent.     

Optimisation technique for stepwise gradient elution in reversed-phase liquid chromatography

An optimisation technique of reversed-phase liquid chromatographic separations based on gradient elution with a stepwise variation pattern of the volume fraction phi of the organic modifier in the water-organic mobile phase is presented. It uses a non-linear least-squares programme with a Monte-Carlo search for initial estimates in order to determine the best variation pattern that leads to the optimum separation of a mixture of solutes. The validity of the above methodology was tested by separating eight catechol-related solutes with mobile phases modified by methanol or acetonitrile and variation patterns of two, three or four steps in the psi values. It was found in all cases a very satisfactory accuracy of the predicted gradient elution times, which is of the same order with the accuracy of the retention times predicted under isocratic or linear gradient conditions. In addition, it was shown that the proposed optimisation technique is both effective and flexible but well-shaped chromatograms are obtained under electrochemical detection only if steps with increasing psi are used and the change in psi is programmed to occur at the intermediate of the predicted peaks.     

New approach to linear gradient elution used for optimisation in reversed-phase liquid chromatography

A new mathematical treatment concerning the gradient elution in reversed-phase liquid chromatography when the volume fraction psi of an organic modifier in the water-organic mobile phase varies linearly with time is presented. The experimental ln k versus psi curve, where k is the retention factor under isocratic conditions in a binary mobile phase, is subdivided into a finite number of linear portions and the solute gradient retention time tR is calculated by means of an analytical expression arising from the fundamental equation of gradient elution. The validity of the proposed analytical expression and the methodology followed for the calculation of tR was tested using eight catechol-related solutes with mobile phases modified by methanol or acetonitrile. It was found that in all cases the accuracy of the predicted gradient retention times is very satisfactory because it is the same with the accuracy of the retention times predicted under isocratic conditions. Finally, the above method for estimating gradient retention times was used in an optimisation algorithm, which determines the best variation pattern of psi that leads to the optimum separation of a mixture of solutes at different values of the total elution time.     

Effects of stationary phase structure on retention and selectivity in reversed-phase liquid chromatography of flavonoid compounds with methanol as organic modifier

Summary Retention of an extended set of flavonoid compounds by octyl, octadecyl, phenyl and cyanopropyl-bonded, reversed-phase columns, with methanol, as the organic mobile phase modifier and acetic acid as the acid modifier is reported. Solvent strengths and useful ranges for both isocratic and gradient elution are determined. Relative retention is found to be independent of methanol volume fraction in the mobile phase for all the columns examined. Correlations between retention on different columns, specific selectivity effects and their dependence on molecular structure are analyzed. Practical applications for separation and identification are discussed.     

Combined effect of temperature and organic modifier concentration on the retention under single mode gradient conditions in reversed-phase HPLC

The combined effect of temperature, T, and organic modifier concentration, phi, on the retention under gradient conditions in RPLC is studied by considering, both theoretically and experimentally gradients, of phi at constant T and gradients of T at constant phi. Two approaches are examined: in the first approach the prediction of the elution time of a sample solute is based on the isocratic/isothermal properties of this solute. The second approach is based on a direct fitting procedure of a proper retention model to 2-D isocratic/T-gradient or isothermal/phi-gradient retention data. These approaches were tested using alkylbenzes in eluting systems modified by ACN. We found that both approaches can give excellent predictions under certain prerequisites. However, the first approach exhibits the notable advantage that it can be used effectively to predict retention times under any kind of phi-gradients at constant T or T-gradients at constant phi. The second approach has the advantage that it is relatively simple but its applicability is very restricted since its predictions are satisfactory only if the gradients are of the same kind with those used in the fitting procedure and the conditions lie within those used for fitting.     

Designing polymer matrix for microchip-based double-stranded DNA capillary electrophoresis

An optimization strategy for ternary solvent-strength gradient elution RP chromatography is described in which a two-dimensional model of gradient time (2 levels) against ternary proportions of organic modifiers (4 levels) was constructed. From the resolution surface the optimum ratio of organic modifiers could be selected. Excellent retention time and acceptable peak width and resolution simulations were obtained. The separation could be further optimized from the same input data by using a standard one-dimensional model in order to optimize for gradient slope, duration and shape. Excellent retention time and acceptable peak width and resolution simulations were obtained (< 1, 2 and 6% error, respectively).     

Methacrylate monolithic capillary columns for gradient peptide separations

For the separation of peptides with gradient-elution liquid chromatography a poly(butyl methacrylate-co-ethylene dimethacrylate) (BMA) monolithic capillary column was prepared and tested. The conditional peak capacity was used as a metric for the performance of this column, which was compared with a capillary column packed with C18-modified silica particles. The retention of the peptides was found to be smaller on the BMA column than on the particulate C18 column. To obtain the same retention in isocratic elution an approximately 15% (v/v) lower acetonitrile concentration had to be used in the mobile phase. The retention window in gradient elution was correspondingly smaller with the BMA column. The relation between peak width and retention under gradient conditions was studied in detail. It was found that in shallow gradients, with gradient times of 30min and more, the peak widths of the least retained compounds are strongly increased with the BMA column. This was attributed to the fact that these compounds migrate and elute with an unfavorable high retention factor. More retained compounds are eluted later in the gradient, but with a lower effective retention factor. With shallow gradients the peak capacity of the BMA column ( approximately 90) was clearly lower than that of a conventional packed column ( approximately 150). On the other hand, with steep gradients, when components elute with a low effective retention factor, the performance of the BMA column is relatively good. With a gradient time of 15min similar peak widths and thus similar peak capacities ( approximately 75) were found for the packed and the monolithic column. Two strategies were investigated to obtain higher peak capacities with methacrylate monolithic columns. The use of lauryl methacrylate (LMA) instead of butyl methacrylate (BMA) gave an increase in retention and narrower peaks for early eluting peptides. The peak capacity of the LMA column was approximately 125 in a 60min gradient. Another approach was to use a longer BMA column which resulted in a peak capacity of approximately 135 could be obtained in 60min.     

Optimizing the peak capacity per unit time in one-dimensional and off-line two-dimensional liquid chromatography for the separation of complex peptide samples

To obtain the best compromise between peak capacity and analysis time in one-dimensional and two-dimensional (2D) liquid chromatography (LC), column technology and operating conditions were optimized. The effects of gradient time, flow rate, column temperature, and column length were investigated in one-dimensional reversed-phase (RP) gradient nano-LC, with the aim of maximizing the peak per unit time for peptide separations. An off-line two-dimensional LC approach was developed using a micro-fractionation option of the autosampler, which allowed automatic fractionation of peptides after a first-dimension ion-exchange separation and re-injection of the fractions onto a second-dimension RP nano-LC column. Under the applied conditions, which included a preconcentration/desalting time of 5 min, and a column equilibration time of 12.5 min, the highest peak capacity per unit time in the 2D-LC mode was obtained when applying a short (10 min) first-dimension gradient and second-dimension RP gradients of 20 min duration. For separations requiring a maximum peak capacity of 375, one-dimensional LC was found to be superior to the off-line strong cation-exchange/×/RPLC approach in terms of analysis time. Although a peak capacity of 450 could be obtained in one-dimensional LC when applying 120-min gradients on 500-mm long columns packed with 3-μm particles, for separations requiring a peak capacity higher than 375 2D-LC experiments provide a higher peak capacity per unit time. Finally, the potential of off-line 2D-LC coupled to tandem mass spectrometry detection is demonstrated with the analysis of a tryptic digest of a mixture of nine proteins and an Escherichia coli digest.     

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.     

Probing the kinetic performance limits for ion chromatography. II. Gradient conditions for small ions

A gradient kinetic plot method is used for theoretical characterisation of the performance of polymeric particulate anion exchange columns for gradient separations of small inorganic anions. The method employed requires only information obtained from a series of isocratic column performance measurements and in silico predictions of retention time and peak width under gradient conditions. Results obtained under practically constrained conditions provide parameters for the generation of high peak capacities and rapid peak production for fast analysis to be determined. Using this prediction method, a maximum theoretical peak capacity of 84 could be used to achieve separation of 26 components using a 120 min gradient (R_s > 1). This approach provides a highly convenient tool for development of both mono- and multidimensional ion chromatography (IC) methodologies as it yields comprehensive understanding of the influence of gradient slope, analysis time, column length and temperature upon kinetically optimised gradient performance.     

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%).