Abstract :
[en] 1 Introduction
Reverse phase liquid chromatography (RPLC) is still one of the most used analytical technique for the analysis of chemical mixtures. The development step can be very extensive given the different possible stationary phases, mobile phases and other analysis parameters. A thorough screening takes a lot of time and requires many consumables even with a systematic approach using experimental planification. The development of quantitative structure-retention relationship (QSRR) models can advantageously replace this experimental screening phase with in silico chromatograms simulations.
QSRR models are statistically derived relationships between chromatographic parameters and computed molecular descriptors characterizing the analytes. Several linear and nonlinear models have been used to build such models (Partial least squares (PLS), Bayesian, Ridge, Lasso, K-nearest neighbors (KNN), support vector machines (SVR), artificial neural network (ANN), etc.) [1]. Ensemble machine-learning models covering boosting, bagging and stacking have shown to generally outperform other algorithms [2].
In the presented work, QSRR models will be built for different chromatographic conditions (pH and gradient time). Subsequently, a response surface model (RSM) will be used allowing predictions of retention times in new conditions within the studied space [3, 4, 5].
2 Material and methods
Ninety-eight molecules were selected to cover a wide range in LogP values (-3.22 – 6.45), molecular weight (46 – 454 g/mol) and includes both non-charged and charged molecules (25 non-charged and 73 charged). Experimental retention times were acquired in house on three different HPLC systems (Waters Alliance) with gradients from 100% buffer to 5% buffer in 20 and 60 minutes considering five different pH levels (2.7, 3.5, 5, 6.5 and 8). These two gradients and five pH conditions represent the ten datasets that will be analyzed. Methanol was selected as the organic modifier.
At first, the weighted average of the molecular descriptors of each present form of the compound are calculated. Then, four machine-learning models were fitted on the ten datasets using the 26
features selected using stepwise regression methods. RMSE and R² values were used to compare the different models. Finally, a RSM is fitted for each compound based on the predicted retention times starting from equation (1) while removing pH terms for neutral.
log(𝑡𝑅)=𝛽0+𝛽1×𝑝𝐻+𝛽2×𝑡𝑔𝑟𝑎𝑑+𝛽12×𝑝𝐻×𝑡𝑔𝑟𝑎𝑑+𝛽11×𝑝𝐻2+𝛽111×𝑝𝐻3 (1)
3 Results and discussion
Out of the tested models, XGBoost and Lasso were the best performing ones showing R² values as high as 0.99 for the training set and R² higher than 0.95 for the prediction set shown in Figure1. Their blended prediction performed better over single model predictions.
Using those predictions, RSM models were built. The different predictions of ibuprofen from the external test set can be seen on Figure2.
Figure 1: Plot of observed vs. predicted retention times for best prediction model (XGBoost)
Figure 2: Observed (hollow points), ML predicted (filled points) and RSM predicted (curves) retention times of ibuprofen for 20, 40 and 60 minutes gradients
4 Conclusion
The RPLC retention times predicted by QSRR models followed by a RSM model were close to the experimental ones. This demonstrates that the combination of QSRR and RSM offers the possibility to replace usefully the experimental screening phase by computational methods when developing chromatographic techniques for known sets of molecules. The presented results concern a limited set of test molecules and will be further extended to new molecules and chromatographic modes.
