Ensemble hologram quantitative structure activity relationship model of the chromatographic retention index of aldehydes and ketones

Chromatographic retention index (RI) is an important parameter for describing the retention behavior of substances in chromatographic analysis. Experimentally determining the RI values of different aldehyde and ketone compounds in all kinds of polar stationary phases is expensive and time consuming. Quantitative structure activity relationship (QSAR) is an important chemometric technique that has been widely used to correlate the properties of chemicals to their molecular structures. Irrespective of whether the properties of a molecule have been experimentally determined, they can be calculated using QSAR models. It is therefore necessary and advisable to establish the QSAR model for predicting the RI value of aldehydes and ketones. Hologram QSAR (HQSAR) is a highly efficient QSAR approach that can easily generate QSAR models with good statistics and high prediction accuracy. A specific fragment of fingerprint, known as a molecular hologram, is proposed in the HQSAR approach and used as a structural descriptor to build the proposed QSAR model. In general, individual HQSAR models are built in QSAR researches. However, individual QSAR models are usually affected by underfitting and overfitting. The ensemble modeling method, which integrate several individual models through certain consensus strategies, can overcome the shortcomings of individual models. It is worth studying whether ensemble modeling can improve the prediction ability of the HQSAR method in order to build more accurate and reliable QSAR models.Therefore, this study investigates the QSAR model for chromatographic RI of aldehydes and ketones using ensemble modeling and the HQSAR method. Two individual HQSAR models comprising 34 compounds in two stationary phases, DB-210 and HP-Innowax, were established. The prediction ability of the two established models was assessed by external test set validation and leave-one-out cross validation (LOO-CV). The investigated 34 compounds were randomly assigned into two groups. Group Ⅰ comprised 26 compounds, and Group Ⅱ comprised 8 compounds. In the validation of the external test set, Group Ⅰ was employed to manually optimize the two fragment parameters (fragment distinction (FD) and fragment size (FS)) and build the HQSAR models. Group Ⅱ was used as the test set to assess the predictive performance of the developed models. For the DB-210 stationary phase, the optimal individual HQSAR model was obtained while setting the FD and FS to “donor/acceptor atoms (DA)” and 1-9, respectively. For the HP-Innowax stationary phase, the optimal individual HQSAR model was obtained by setting the FD and FS to “DA” and 4-7 respectively. The squared correlation coefficient of cross validation ( q cv 2 ), concordance correlation coefficient (CCC), squared correlation coefficient of external validation ( q ext 2 ), predictive squared correlation coefficient ( Q F 2 2 and Q F 3 2 ) of the two models for predicting the RI value were 0.935 and 0.909, 0.953 and 0.960, 0.925 and 0.927, 0.922 and 0.918, and 0.931 and 0.927, respectively. The results of the two validations show that there is a quantitative relationship between the molecular structure of these compounds and the RI value, and the HQSAR model is capable of modeling this relationship. Second, the ensemble HQSAR models were established using the four individual HQSAR models with the highest accuracy as the sub-models through arithmetic averaging. The ensemble HQSAR models were validated by external test set validation and LOO-CV. The q cv 2 , CCC, q ext 2 , Q F 2 2 , and Q F 3 2 for predicting the RI values of the DB-210 and HP-Innowax stationary phases were 0.927 and 0.919, 0.956 and 0.979, 0.929 and 0.963, 0.927 and 0.958, and 0.935 and 0.963, respectively. Compared to the individual HQSAR models, the established ensemble HQSAR models show better robustness and accuracy, thus establishing that ensemble modeling is an effective approach. The combination of HQSAR and the ensemble modeling method is a practicable and promising method for studying and predicting the RI values of aldehydes and ketones.