How Much Can We Learn from a Single Chromatographic Experiment? A Bayesian Perspective

Uncertainty management for In Silico screening of reversed-phase liquid chromatography methods for small compounds

The process of developing new reversed-phase liquid chromatography methods can be both time-consuming and challenging. To meet this challenge, statistics-based strategies have emerged as cost-effective, efficient and flexible solutions. In the present study, we use a Bayesian response surface methodology, which takes advantage of the knowledge of the pKa values of the compounds present in the analyzed sample to model their retention behavior. A multi-criteria decision analysis (MCDA) was then developed to exploit the uncertainty information inherent in the model distributions. This strategic approach is designed to integrate seamlessly with quantitative structure retention relationship (QSRR) models, forming an initial in-silico screening phase. Of the two methods presented for MCDA, one showed promising results. The method development process was carried out with the optimization phase, generating a design space that corroborates the results of the selection phase.

User-Driven Strategy for In Silico Screening of Reversed-Phase Liquid Chromatography Conditions for Known Pharmaceutical-Related Small Molecules

In the pharmaceutical field, and more precisely in quality control laboratories, robust liquid chromatographic methods are needed to separate and analyze mixtures of compounds. The development of such chromatographic methods for new mixtures can result in a long and tedious process even while using the design of experiments methodology. However, developments could be accelerated with the help of in silico screening. In this work, the usefulness of a strategy combining response surface methodology (RSM) followed by multicriteria decision analysis (MCDA) applied to predictions from a quantitative structure-retention relationship (QSRR) model is demonstrated. The developed strategy shows that selecting equations for the retention time prediction models based on the pKa of the compound allows flexibility in the models. The MCDA developed is shown to help to make decisions on different criteria while being robust to the user's decision on the weights for each criterion. This strategy is proposed for the screening phase of the method lifecycle. The strategy offers the possibility to the user to select chromatographic conditions based on multiple criteria without being too sensitive to the importance given to them. The conditions with the highest desirability are defined as the starting point for further optimization steps.

Application of Bayesian Multilevel Modeling in the Quantitative Structure-Retention Relationship Studies of Heterogeneous Compounds

Quantitative structure-retention relationships (QSRRs) are used in the field of chromatography to model the relationship between an analyte structure and chromatographic retention. Such models are typically difficult to build and validate for heterogeneous compounds because of their many descriptors and relatively limited analyte-specific data. In this study, a Bayesian multilevel model is proposed to characterize the isocratic retention time data collected for 1026 heterogeneous analytes. The QSRR considers the effects of the molecular mass and 100 functional groups (substituents) on analyte-specific chromatographic parameters of the Neue model (i.e., the retention factor in water, the retention factor in acetonitrile, and the curvature coefficient). A Bayesian multilevel regression model was used to smooth noisy parameter estimates with too few data and to consider the uncertainties in the model parameters. We discuss the benefits of the Bayesian multilevel model (i) to understand chromatographic data, (ii) to quantify the effect of functional groups on chromatographic retention, and (iii) to predict analyte retention based on various types of preliminary data. The uncertainty of isocratic and gradient predictions was visualized using uncertainty chromatograms and discussed in terms of usefulness in decision making. We think that this method will provide the most benefit in providing a unified scheme for analyzing large chromatographic databases and assessing the impact of functional groups and other descriptors on analyte retention.

The application of Box-Behnken-Design in the optimization of HPLC separation of fluoroquinolones

Box-Behnken Design is a useful tool for the optimization of the chromatographic analysis. The goal of this study was to select the most significant factors that influenced the following parameters of the chromatographic separation: retention time, relative retention time, symmetry of the peaks, tailing factor, a number of theoretical plates, Foley – Dorsey parameter, resolution factor, peak width at half height. The results underwent the ANOVA test to find the statistically significant variables and interactions between them. The level of significance was for p < 0.05. The polynomial equations described quantitatively the statistically significant parameters and the interactions between them. The statistical analysis indicated both the best conditions for the separation of the compounds and the variables that were most influential for peaks’ parameters. The four-factor analysis performed for LEVO and MOXI indicated that ACN, TEA and pH are the most significant factors that influence the separation. The analysis for the pair CIPRO and LEVO required six factors. The statistical analysis proved that the most significant factors are ACN, MeOH and TEA. In the separation of these two compounds on the HPLC column, the interaction ACN × MeOH was also significant.

Chemometric-assisted method development in hydrophilic interaction liquid chromatography: A review

With an enormous growth in the application of hydrophilic interaction liquid chromatography (HILIC), there has also been significant progress in HILIC method development. HILIC is a chromatographic method that utilises hydro-organic mobile phases with a high organic content, and a hydrophilic stationary phase. It has been applied predominantly in the determination of small polar compounds. Theoretical studies in computer-aided modelling tools, most importantly the predictive, quantitative structure retention relationship (QSRR) modelling methods, have attracted the attention of researchers and these approaches greatly assist the method development process. This review focuses on the application of computer-aided modelling tools in understanding the retention mechanism, the classification of HILIC stationary phases, prediction of retention times in HILIC systems, optimisation of chromatographic conditions, and description of the interaction effects of the chromatographic factors in HILIC separations. Additionally, what has been achieved in the potential application of QSRR methodology in combination with experimental design philosophy in the optimisation of chromatographic separation conditions in the HILIC method development process is communicated. Developing robust predictive QSRR models will undoubtedly facilitate more application of this chromatographic mode in a broader variety of research areas, significantly minimising cost and time of the experimental work.

Rapid Method Development in Hydrophilic Interaction Liquid Chromatography for Pharmaceutical Analysis Using a Combination of Quantitative Structure-Retention Relationships and Design of Experiments

A design-of-experiment (DoE) model was developed, able to describe the retention times of a mixture of pharmaceutical compounds in hydrophilic interaction liquid chromatography (HILIC) under all possible combinations of acetonitrile content, salt concentration, and mobile-phase pH with R² > 0.95. Further, a quantitative structure-retention relationship (QSRR) model was developed to predict retention times for new analytes, based only on their chemical structures, with a root-mean-square error of prediction (RMSEP) as low as 0.81%. A compound classification based on the concept of similarity was applied prior to QSRR modeling. Finally, we utilized a combined QSRR-DoE approach to propose an optimal design space in a quality-by-design (QbD) workflow to facilitate the HILIC method development. The mathematical QSRR-DoE model was shown to be highly predictive when applied to an independent test set of unseen compounds in unseen conditions with a RMSEP value of 5.83%. The QSRR-DoE computed retention time of pharmaceutical test analytes and subsequently calculated separation selectivity was used to optimize the chromatographic conditions for efficient separation of targets. A Monte Carlo simulation was performed to evaluate the risk of uncertainty in the model's prediction, and to define the design space where the desired quality criterion was met. Experimental realization of peak selectivity between targets under the selected optimal working conditions confirmed the theoretical predictions. These results demonstrate how discovery of optimal conditions for the separation of new analytes can be accelerated by the use of appropriate theoretical tools.