Combining the Fragmentation Approach and Neural Network Potential Energy Surfaces of Fragments for Accurate Calculation of Protein Energy

Accurate and efficient all-atom quantum mechanical (QM) calculations for biomolecules still present a challenge to computational physicists and chemists. In this study, an extensible generalized molecular fractionation with a conjugate caps method combined with neural networks (NN-GMFCC) is developed for efficient QM calculation of protein energy. In the NN-GMFCC scheme, the total energy of a given protein is calculated by taking a proper combination of the high-precision neural network potential energies of all capped residues and overlapping conjugate caps. In addition, the two-body interaction energies of residue pairs are calculated by molecular mechanics (MM). With reference to the GMFCC/MM calculation at the ωB97XD/6-31G* level, the overall mean unsigned errors of the energy deviations and atomic force root-mean-squared errors calculated by NN-GMFCC are only 2.01 kcal/mol and 0.68 kcal/mol/Å, respectively, for 14 proteins (containing up to 13,728 atoms). Meanwhile, the NN-GMFCC approach is about 4 orders of magnitude faster than the GMFCC/MM method. The NN-GMFCC method could be systematically improved by inclusion of two-body QM interaction and multibody electronic polarization effect. Moreover, the NN-GMFCC approach can also be applied to other macromolecular systems such as DNA/RNA, and it is capable of providing a powerful and efficient approach for exploration of structures and functions of proteins with QM accuracy.