Maximum A Posteriori Bayesian Estimation of Chromatographic Parameters by Limited Number of Experiments

The aim of this work was to develop a nonlinear mixed-effect chromatographic model able to describe the retention times of weak acids and bases in all possible combinations of organic modifier content and mobile-phase pH. Further, we aimed to identify the influence of basic covariates, like lipophilicity (log P), dissociation constant (pK(a)), and polar surface area (PSA), on the intercompound variability of chromatographic parameters. Lastly, we aimed to propose the optimal limited experimental design to the estimation process of parameters through a maximum a posteriori (MAP) Bayesian method to facilitate the method development process. The data set comprised retention times for two series of organic modifier content collected at different pH for a large series of acids and bases. The obtained typical parameters and their distribution were subsequently used as priors to improve the estimation process from reduced design with a variable number of preliminary experiments. The MAP Bayesian estimator was validated using two external-validation data sets. The common literature model was used to relate analyte retention time with mobile-phase pH and organic modifier content. A set of QSRR-based covariate relationships was established. It turned out that four preliminary experiments and prior information that includes analyte pK(a), log P, acid/base type, and PSA are sufficient to accurately predict analyte retention in virtually all combined changes of pH and organic modifier content. The MAP Bayesian estimator of all important chromatographic parameters controlling retention in pH/organic modifier gradient was developed. It can be used to improve parameter estimation using limited experimental design.