Global linear solvation energy relationships for retention prediction in reversed-phase liquid chromatography

Improved hydrophobic subtraction model of reversed-phase liquid chromatography selectivity based on a large dataset with a focus on isomer selectivity

Reversed-phase (RP) liquid chromatography is an important tool for the characterization of materials and products in the pharmaceutical industry. Method development is still challenging in this application space, particularly when dealing with closely-related compounds. Models of chromatographic selectivity are useful for predicting which columns out of the hundreds that are available are likely to have very similar, or different, selectivity for the application at hand. The hydrophobic subtraction model (HSM1) has been widely employed for this purpose; the column database for this model currently stands at 750 columns. In previous work we explored a refinement of the original HSM1 (HSM2) and found that increasing the size of the dataset used to train the model dramatically reduced the number of gross errors in predictions of selectivity made using the model. In this paper we describe further work in this direction (HSM3), this time based on a much larger solute set (1014 solute/stationary phase combinations) containing selectivities for compounds covering a broader range of physicochemical properties compared to HSM1. The molecular weight range was doubled, and the range of the logarithm of the octanol/water partition coefficients was increased slightly. The number of active pharmaceutical ingredients and related synthetic intermediates and impurities was increased from four to 28, and ten pairs of closely related structures (e.g., geometric and cis-/trans- isomers) were included. The HSM3 model is based on retention measurements for 75 compounds using 13 RP stationary phases and a mobile phase of 40/60 acetonitrile/25 mM ammonium formate buffer at pH 3.2. This data-driven model produced predictions of ln α (chromatographic selectivity using ethylbenzene as the reference compound) with average absolute errors of approximately 0.033, which corresponds to errors in α of about 3 %. In some cases, the prediction of the trans-/cis- selectivities for positional and geometric isomers was relatively accurate, and the driving forces for the observed selectivity could be inferred by examination of the relative magnitudes of the terms in the HSM3 model. For some geometric isomer pairs the interactions mainly responsible for the observed selectivities could not be rationalized due to large uncertainties for particular terms in the model. This suggests that more work is needed in the future to explore other HSM-type models and continue expanding the training dataset in order to continue improving the predictive accuracy of these models. Additionally, we release with this paper a much larger data set (43,329 total retention measurements) at multiple mobile phase compositions, to enable other researchers to pursue their own lines of inquiry related to RP selectivity.

Evaluation of Hold-Up Volume Determination Methods and Markers in Hydrophilic Interaction Liquid Chromatography

Common methods for hold-up time and volume determination in Reversed-Phase Liquid Chromatography (RPLC) have been tested for Hydrophilic Interaction Liquid Chromatography (HILIC). A zwitterionic ZIC-HILIC column has been used for the testing. The pycnometric determination method, based on differences in column weight when filled with water or organic solvent, provides the overall volume of solvent inside the column. This includes the volume of eluent semi-sorbed on the packing of the column, which acts as the main stationary phase. The homologous series approach, based on the retention behavior of homologues in relation to their molecular volume, allows the determination of accurate hold-up volumes. However, the application of this method is time-consuming. In some cases, large neutral markers with poor dipolarity/polarizability and hydrogen bonding interactions can be used as hold-up volume markers. This is the case of dodecylbenzene and nonadecane-2-one in clearly HILIC behaving chromatographic systems, the use of decanophenone as a marker can be even extended to the boundary between HILIC and RPLC. The elution volume of the marker remains nearly unaffected by the concentration of ammonium acetate in the mobile phase up to 20 mM. The injection of pure solvents to produce minor base-line disturbance as hold-up markers is strongly discouraged, since solvent peaks are complex to interpret and depend on the ionic strength of the eluent.

Solute–Solvent Interactions in Hydrophilic Interaction Liquid Chromatography: Characterization of the Retention in a Silica Column by the Abraham Linear Free Energy Relationship Model

The Abraham linear free energy relationship model has been used to characterize a hydrophilic interaction liquid chromatography (HILIC) silica column with acetonitrile/water and methanol/water mobile phases. Analysis by the model for acetonitrile/water mobile phases points to solute volume and hydrogen bond basicity as the main properties affecting retention, whereas solute hydrogen bond acidity, dipolarity and polarizability practically do not affect it. Formation of a cavity is easier in acetonitrile-rich mobile phases than in the aqueous stationary phase, and hence increase of solute volume decreases retention. Conversely, hydrogen bond acidity is stronger in the aqueous stationary phase than in the acetonitrile-rich mobile phase and thus an increase of solute hydrogen bond basicity increases retention. Results are similar for methanol/water mobile phases with the difference that solute hydrogen bond acidity is significant too. Increase in hydrogen bond acidity of the solute decreases retention showing that methanol mobile phases must be better hydrogen bond acceptors than acetonitrile ones, and even than water-rich stationary phases. The results are like the ones obtained in zwitterionic HILIC columns bonded to silica or polymer supports for acetonitrile/water mobile phases, but different for solute hydrogen bond acidity for a polymer bonded zwitterionic column with methanol/water mobile phases, indicating that bonding support plays an important role in HILIC retention. Comparison to RPLC characterized systems confirms the complementarity of HILIC systems to RPLC ones because the main properties affecting retention are the same but with reversed coefficients. The least retained solutes in RPLC are the most retained in HILIC.

Perspective on the Future Approaches to Predict Retention in Liquid Chromatography

The demand for rapid column screening, computer-assisted method development and method transfer, and unambiguous compound identification by LC/MS analyses has pushed analysts to adopt experimental protocols and software for the accurate prediction of the retention time in liquid chromatography (LC). This Perspective discusses the classical approaches used to predict retention times in LC over the last three decades and proposes future requirements to increase their accuracy. First, inverse methods for retention prediction are essentially applied during screening and gradient method optimization: a minimum number of experiments or design of experiments (DoE) is run to train and calibrate a model (either purely statistical or based on the principles and fundamentals of liquid chromatography) by a mere fitting process. They do not require the accurate knowledge of the true column hold-up volume V₀, system dwell volume V_dwell (in gradient elution), and the retention behavior (k versus the content of strong solvent φ, temperature T, pH, and ionic strength I) of the analytes. Their relative accuracy is often excellent below a few percent. Statistical methods are expected to be the most attractive to handle very complex retention behavior such as in mixed-mode chromatography (MMC). Fundamentally correct retention models accounting for the simultaneous impact of φ, I, pH, and T in MMC are needed for method development based on chromatography principles. Second, direct methods for retention prediction are ideally suited for accurate method transfer from one column/system configuration to another: these quality by design (QbD) methods are based on the fundamentals and principles of solid-liquid adsorption and gradient chromatography. No model calibration is necessary; however, they require universal conventions for the accurate determination of true retention factors (for 1 < k < 30) as a function of the experimental variables (φ, T, pH, and I) and of the true column/system parameters (V₀, V_dwell, dispersion volume, σ, and relaxation volume, τ, of the programmed gradient profile at the column inlet and gradient distortion at the column outlet). Finally, when the molecular structure of the analytes is either known or assumed, retention prediction has essentially been made on the basis of statistical approaches such as the linear solvation energy relationships (LSERs) and the quantitative structure retention relationships (QSRRs): their ability to accurately predict the retention remains limited within 10-30%. They have been combined with molecular similarity approaches (where the retention model is calibrated with compounds having structures similar to that of the targeted analytes) and artificial intelligence algorithms to further improve their accuracy below 10%. In this Perspective, it is proposed to adopt a more rigorous and fundamental approach by considering the very details of the solid-liquid adsorption process: Monte Carlo (MC) or molecular dynamics (MD) simulations are promising tools to explain and interpret retention data that are too complex to be described by either empirical or statistical retention models.

Measuring and using scanning-gradient data for use in method optimization for liquid chromatography

The use of scanning gradients can significantly reduce method-development time in reversed-phase liquid chromatography. However, there is no consensus on how they can best be used. In the present work we set out to systematically investigate various factors and to formulate guidelines. Scanning gradients are used to establish retention models for individual analytes. Different retention models were compared by computing the Akaike information criterion and the prediction accuracy. The measurement uncertainty was found to influence the optimum choice of model. The use of a third parameter to account for non-linear relationships was consistently found not to be statistically significant. The duration (slope) of the scanning gradients was not found to influence the accuracy of prediction. The prediction error may be reduced by repeating scanning experiments or - preferably - by reducing the measurement uncertainty. It is commonly assumed that the gradient-slope factor, i.e. the ratio between slopes of the fastest and the slowest scanning gradients, should be at least three. However, in the present work we found this factor less important than the proximity of the slope of the predicted gradient to that of the scanning gradients. Also, interpolation to a slope between that of the fastest and the slowest scanning gradient is preferable to extrapolation. For comprehensive two-dimensional liquid chromatography (LC × LC) our results suggest that data obtained from fast second-dimension gradients cannot be used to predict retention in much slower first-dimension gradients.

Linear free energy relationship models for the retention of partially ionized acid-base compounds in reversed-phase liquid chromatography

The LFER model of Abraham is applied to the retention of the neutral and ionic forms of 94 solutes in a C18 column and 40% v/v acetonitrile/water mobile phase. The results show that polarizability and cavity formation interactions increase retention, whereas dipole and hydrogen bonding interactions favours partition to the mobile phase and thus, they decrease retention. The coefficients of the ionic descriptors measure the effect of the electrostatic interactions and their contribution to partition of the cation or anion between the two mobile and stationary chromatographic phases. A new LFER model for application to the retention of partially dissociated acids and bases is derived averaging the descriptors of the neutral and ionic forms according to their degrees of ionization in the mobile phase. This new LFER model is satisfactorily compared to other literature modified Abraham models for a set of 498 retention data of partially dissociated acids and bases. All tested models require the calculation of the ionization degrees of the compounds at the measuring pH. Calculation of the ionization degrees in the chromatographic mobile phase (i.e. from pH and pK_a in the eluent) give good correlations for all tested models. However, estimation of these ionization degrees from pH - pK_a data in pure water gives biased estimations of the retention of the partially ionized solutes.

Novel computational approaches to retention modeling in dual hydrophilic interactions/reversed phase chromatography

The mixed-mode chromatographic behavior was estimated for imidazoline and serotonin receptor ligands, and their related compounds on dual hydrophilic/reversed phase stationary phase. The Box-Cox transformation was used to obtain the most suitable mathematical equations which describe the mixed-mode retention. Optimal equations were found for the optimization parameter (λ): λ = -1, λ = -0.5, λ = 0, λ = 0.5, and λ = 1. The proposed equations show satisfactory characteristics compared to standard multimodal and quadratic approaches. For a wide range of volume fractions of the mobile phase modifier, crossing between hydrophilic and reversed phase interactions (the turning point) was defined in terms of the minimal retention and the minimum value of the volume fraction of the aqueous eluent in the mobile phase. The cubic spline interpolation was used as a reference method for estimation of the turning point. It was found out that the newly proposed equations can be used as alternative mathematical forms for the description of the dual retention mechanism and for the evaluation of the turning point. Three new experimental descriptors of the mixed-mode retention were proposed. Two descriptors quantitatively characterize hydrophilic (log k_H) and reversed phase (log k_R) interactions, while the third one (log k_A) refers to the average retention for the whole HILIC/RP range. It was established that the main factors which control dual nature of the mixed-mode retention are lipophilicity, dipol-dipol, van der Waals and hydrogen bonding interactions. It was concluded that the newly proposed estimations of the retention data reliably characterize the mixed-mode chromatographic behavior.

Comparison of the Retention of Aliphatic Hydrocarbons with Polar Groups in RP-HPLC Systems with Different Modifiers of the Binary Eluent

The retention of aliphatic hydrocarbons with polar groups has been compared in respect to the separation selectivity changes in reversed-phase high-performance liquid chromatography with C18 stationary phase type and binary water eluent composed of methanol, acetonitrile, or tetrahydrofuran as modifiers. The changes in separation selectivity when one modifier is replaced by another in the eluent is explained, taking into consideration molecular interactions of the solutes with components of the stationary phase region, i.e., extracted modifier, and ordering of the stationary phase by the modifier.

Retention mechanism of a cholesterol-coated C18 stationary phase: van't Hoff and Linear Solvation Energy Relationships (LSER) approaches

This study examines the effect of temperature on the dynamic cholesterol coating of a C18 stationary phase and the effect of this coating on the retention mechanism. In general, an increase in temperature results in a decrease in the mass of cholesterol coated on the stationary phase. Typically, an increase in temperature from 25°C to 55°C results in a nearly 60% reduction in the mass of cholesterol loaded. The inclusion of temperature, along with loading solvent composition and cholesterol concentration in the loading solvent, allows for loading a targeted amount of cholesterol on the stationary phase over an order-of-magnitude range. In addition to loading studies, the retention mechanism of small non-ionizable solutes was examined on cholesterol-coated stationary phases. A van't Hoff analysis was performed to assess retention thermodynamics, while a LSER approach was used to examine retention mechanism. With 50/50 water/organic mobile phases, the addition of cholesterol results in an increase in the entropic contribution to retention, with a decrease in the enthalpic contribution. The opposite trend is seen with 40/60 water/organic mobile phases. LSER system constants are also affected by a cholesterol coating on the stationary phase, with some changing to favor elution and others changing to favor retention.

Characterisation of stationary phases in supercritical fluid chromatography with the solvation parameter model

Characterisation of chromatographic systems with the solvation parameter model provides satisfactory information on the main non-ionic interactions developed in a chromatographic system. The procedure requires the analysis of a large number of compounds to warrant the relevance and the accuracy of the calculated models, and even if retention time is lower in supercritical fluid chromatography (SFC) than in HPLC (3-5 times lower), a decrease in the time required for that procedure would favour the use of this model in method development. Consequently, in order to establish a rapid testing procedure that would provide equivalent information, nine key solutes were carefully selected among the hundred we classically use. The separation factors calculated between these key solutes, taken two by two to establish new equations, allow the calculation of the model coefficients. The normal testing procedure is thus reduced from one or two days down to 2h. Precision and accuracy of the models provided are assessed through back-calculation of the coefficients that served for the establishment of the procedure, then through calculation of the coefficients of 13 new SFC systems. The applicability of the rapid testing procedure in SFC is evidenced with three examples: the elaboration of a system map, by varying the modifier concentration in the mobile phase, and the comparison of six ODS phases bonded on the same silica base. The simplified procedure presented here does not pretend to characterize the chromatographic systems as precisely as the complete testing procedure does, but is only aimed at rapidly evaluating the chromatographic retention characteristics when operating parameters are varied.

Investigation of retention behaviour of non-steroidal anti-inflammatory drugs in high-performance liquid chromatography by using quantitative structure–retention relationships

In this paper, a quantitative structure-retention relationship (QSRR) method is employed to model the retention behaviour in reversed-phase high-performance liquid chromatography of arylpropionic acid derivatives, largely used non-steroidal anti-inflammatory drugs (NSAIDs). Computed molecular descriptors and the organic modifier content in the mobile phase are associated into a comprehensive model to describe the effect of both solute structure and eluent composition on the isocratic retention of these drugs in water-acetonitrile mobile phases. Multilinear regression (MLR) combined with genetic algorithm (GA) variable selection is used to extract from a large set of computed 3D descriptors an optimal subset. Based on GA-MLR analysis, a five-dimensional QSRR model is identified. All the four selected molecular descriptors belong to the category of GEometry, Topology, and Atom-Weights AssemblY (GETAWAY) descriptors. The related multilinear model exhibits a quite good fitting and predictive performance. This model is further improved using an artificial neural network (ANN) learned by error back-propagation. Finally, the ANN-based model displays a remarkably better performance as compared with the MLR counterpart and, based on external validation, is able to predict with good accuracy the behaviour of unknown arylpropionic NSAIDs in the range of mobile phase composition of analytical interest (between 35 and 75% acetonitrile (v/v)).

Could linear solvation energy relationships give insights into chiral recognition mechanisms?

Linear solvation energy relationships (LSER) have been used for years in liquid chromatography to access the factors that lead to retention and, more recently, to selectivity. In chiral separations, two enantiomers will receive exactly the same descriptors correctly predicting that they will not be separated by any non-chiral stationary phase. However, LSER studies could be used considering that each enantiomer sees a chiral stationary phase (CSP) differently. Working with the enantioselectivity factor, k'2lk'1 could give interesting information on the chiral recognition mechanisms. The b and v system parameters always predominantly contribute to a solute's retention in reversed phase liquid chromatography (RPLC) compared to the a, e and s parameters. However, these minor parameters for retention may become the essential ones for enantiomeric separations where a minimum of three simultaneous interactions is needed for an enantioseparation to occur. In this non-chiral study, six different stationary phases, a classical C(18), a diphenyl bonded stationary phase (DP), a polystyrene-divinylbenzene (DVB), a polar embedded new stationary phase, an anion exchanger (SAX) and a teicoplanin aglycone (TAG) CSP were studied with achiral test solutes. Significantly higher e terms were obtained for the SAX and TAG columns. It seems that the ability of stationary surface charges to induce dipoles in polarizable molecules is encoded mainly in the e term. Since the DP and DVB columns did not produce e parameters significantly higher than the C(18) column, it seems that pi-pi interactions are (a) extremely weak in RPLC or (b) they are not simply encoded in this single e system parameter but spread in at least three parameters. The TAG CSP produced logically very different parameters when used in the reversed phase mode compared to the normal phase mode showing the critical role of the mobile phase.