Analysis of Isocratic-Chromatographic-Retention Data using Bayesian Multilevel Modeling

Performance of global retention models in the optimisation of the chromatographic separation (I): Simple multi-analyte samples

Conventional retention models lead to accurate descriptions of the elution behaviour from the fitting of data for single solutes or from a set of solutes, one by one. However, the simultaneous fitting of several solutes through a regression process that separates the contributions of column and solvent from those of each solute is also possible. The result is a global retention model constituted by a set of equations with some common parameters (those associated with column and solvent), whereas others, specific to each solute, differ for each equation. This work explores the possibilities, advantages, and limitations of global models when they are applied to the optimisation of chromatographic resolution. A set constituted by 13 drugs (diuretics and β-blockers) and a training experimental design of seven multi-linear gradients are considered. Since standards for all compounds were available, the optimisation based on global models could be compared with the conventional optimisation, which is based on individual models. In their current state, global models do not predict changes in elution order, but they do allow for incorporating additional solutes (e.g., new analytes or matrix peaks) with only one new experiment. This possibility is explored by extending the model for the 13 analytes to include 26 peaks associated with a contamination in the injector. The combination of individual and global models allows an optimisation where the effects of matrix peaks on the separation of analytes can be integrated.

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.