Quantum Chemical Calculations with Machine Learning for Multipolar Electrostatics Prediction in RNA: An Application to Pentose.

To develop a realistic electrostatic model that allows for the anisotropy of the atomic electron density, high-rank atomic multipole moments computed by quantum chemical calculations have been studied extensively. However, it is hard to process huge RNA systems only relying on quantum chemical calculations due to its highly computational cost. In this study, we employ five machine learning methods of Gaussian process regression with automatic relevance determination (ARDGPR), Kriging, radial basis function neural networks, Bagging, and generalized regression neural network to predict atomic multipole moments. Atom-atom electrostatic interaction energies are subsequently computed using the predicted atomic multipole moments in the pilot system pentose of RNA. Here, the performance of the five methods is compared in terms of both the multipole moment prediction errors and the electrostatic energy prediction errors. For the predicted high-rank multipole moments of the four elements (O, C, N, and H) in capped pentose, ARDGPR and Kriging consistently outperform the other three methods. Therefore, the multipole moments predicted by the two best methods of ARDGPR and Kriging are then used to predict electrostatic interaction energy of each pentose. Finally, the absolute average energy errors of ARDGPR and Kriging are 1.83 and 4.33 kJ mol, respectively. Compared to Kriging, the ARDGPR method achieves a 58% decrease in the absolute average energy error. These satisfactory results demonstrated that the ARDGPR method with the strong feature extraction ability can predict the electrostatic interaction energy of pentose in RNA correctly and reliably.