Evaluation of sequential Bayesian-based method development procedures for chromatographic problems involving one, two, and three analytes

Assisted Active Learning for Model-Based Method Development in Liquid Chromatography

In recent decades, there has been a growing interest in fully automated methods for tackling complex optimization problems across various fields. Active learning (AL) and its variant, assisted active learning (AAL), incorporating guidance or assistance from external sources into the learning process, play key roles in this automation by enabling the autonomous selection of optimal experimental conditions to efficiently explore the problem space. These approaches are particularly valuable in situations wherein experimentation is costly or time-consuming. This study explores the application of AAL in model-based method development (MD) for liquid chromatography (LC) by using Bayesian statistics to incorporate historical data and analyte information for the generation of initial retention models. The process involves updating the model parameters based on new experiments, coupled with an active data selection method to choose the most informative experiment to run in a subsequent step. This iterative process balances model exploitation and experimental exploration until a satisfactory separation is achieved. The effectiveness of this approach is demonstrated via two practical examples, resulting in optimized separations in a limited number of experiments by optimizing the gradient slope. It is shown that the ability of AAL to leverage past knowledge and compound information to improve accuracy and reduce experimental runs offers a flexible alternative approach to fixed design methods.

Comparison of Chromatographic Stationary Phases Using a Bayesian-Based Multilevel Model

Herein, we used a Bayesian multilevel model of chromatographic retention to compare five reversed-phase high-performance liquid chromatography stationary phases: XBridge Shield RP18, XTerra MS C18, XBridge Phenyl, XBridge C8, and Xterra MS C8. For this, we used a large data set of retention times collected using chromatographic techniques coupled with mass spectrometry. The experiments were conducted in gradient mode for an initial mixture of 300 small analytes for a wide range of pH values in methanol and acetonitrile at two temperatures and for three gradient durations. Our analysis was based on a mechanistic model derived from the principles and fundamentals of liquid chromatography and utilized previously reported chromatographic parameters. The data and model were used to characterize the between-column differences in the chromatographic parameters of the neutral, acidic, and basic analytes. The analysis provides an interpretable summary of stationary-phase properties that can be used in decision-making, i.e., finding the best chromatographic conditions using limited experimental data. The proposed approach is an interesting alternative to the existing approaches used to compare chromatographic stationary phases.

Toward the General Mechanistic Model of Liquid Chromatographic Retention

Large datasets of chromatographic retention times are relatively easy to collect. This statement is particularly true when mixtures of compounds are analyzed under a series of gradient conditions using chromatographic techniques coupled with mass spectrometry detection. Such datasets carry much information about chromatographic retention that, if extracted, can provide useful predictive information. In this work, we proposed a mechanistic model that jointly explains the relationship between pH, organic modifier type, temperature, gradient duration, and analyte retention based on liquid chromatography retention data collected for 187 small molecules. The model was built utilizing a Bayesian multilevel framework. The model assumes (i) a deterministic Neue equation that describes the relationship between retention time and analyte-specific and instrument-specific parameters, (ii) the relationship between analyte-specific descriptors (log P, pK_a, and functional groups) and analyte-specific chromatographic parameters, and (iii) stochastic components of between-analyte and residual variability. The model utilizes prior knowledge about model parameters to regularize predictions which is important as there is ample information about the retention behavior of analytes in various stationary phases in the literature. The usefulness of the proposed model in providing interpretable summaries of complex data and in decision making is discussed.

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.