A physics-aware neural network for protein-ligand interactions with quantum chemical accuracy

Abstract

Quantifying intermolecular interactions with quantum chemistry (QC) is useful for many chemical problems, including understanding the nature of protein-ligand interactions. Unfortunately, QC computations on protein-ligand systems are too computationally expensive for most use cases. The flourishing field of machine-learned (ML) potentials is a promising solution, but it is limited by an inability to easily capture long range, non-local interactions. In this work we develop an atomic-pairwise neural network (AP-Net) specialized for modeling intermolecular interactions. This model benefits from a number of physical constraints, including a two-component equivariant message passing neural network architecture that predicts interaction energies via an intermediate prediction of monomer electron densities. The AP-Net model is trained on a comprehensive dataset composed of paired ligand and protein fragments. This model accurately predicts QC-quality interaction energies of protein-ligand systems at a computational cost reduced by orders of magnitude. Applications of the AP-Net model to molecular crystal structure prediction are explored, as well as limitations in modeling highly polarizable systems.

Fig. 1. An overview of the AP-Net architecture where (A) is the atomic property module and (B) is the interaction energy module. AP-Net predicts the four physically meaningful components of a protein–ligand interaction: electrostatics (E_elst), exchange (E_exch), induction/polarization (E_ind), and London dispersion (E_disp).

Fig. 2. (A) Depiction of the Splinter dimer dataset. This dataset was constructed by exhaustively pairing small protein and ligand fragments. Between 50 and 500 dimer configurations were generated for each pair of fragments. (B) Distribution of interaction energies (left) and AP-Net errors with respect to interaction energies (right) over 150 000 validation dimers of the Splinter dataset, in kcal mol⁻¹. The respective mean absolute interaction energies and mean absolute errors of the two sets of distributions are labeled.

Fig. 3. An example dimer from the SAPT-PDB-13K dataset. A small molecule inhibitor interacts with the nearest amino acid, a tyrosine, of an Escherichia coli sliding clamp protein. This dimer was extracted from PDB entry 4PNU.

Fig. 4. Correlation between AP-Net predicted interaction energies and computed SAPT0/aDZ interaction energies on the 13 216 dimers in the SAPT-PDB-13K dataset.

Fig. 5. Example of an alchemical ΔΔE_int experiment. The chlorine group of the P1 substructure of the Factor Xa inhibitor, BAY 59-7939, is mutated to a methyl. The structure is extracted from PDB entry 2W26.

Fig. 6. (Top Right) Visualization of a two-dimensional interaction energy scan (kcal mol⁻¹) for the NMA dimer, varying the hydrogen bond distance (r) and angle (θ). (Top Left) The NMA dimer interaction energy surface computed at the cheaper SAPT0/aDZ level of theory. (Bottom Left) The NMA dimer interaction energy surface computed at the expensive CCSD(T)/CBS level of theory. (Top Center) The NMA dimer interaction energy surface predicted by an AP-Net model trained on ∼1.7 million SAPT0/aDZ data points. (Bottom Center) The NMA dimer interaction energy surface predicted by an AP-Net model trained on one hundred CCSD(T)/CBS data points. (Bottom Right) The NMA dimer interaction energy surface predicted by an AP-Net model trained on ∼1.7 million SAPT0/aDZ data points and then re-trained with one hundred CCSD(T)/CBS data points. All energies in kcal mol⁻¹.

Fig. 7. (Left) The experimentally observed form II of the 5-fluorouracil crystal. (Center) Comparison between computed and predicted relative crystal lattice energies. (Right) Relative crystal lattice energies as a function of density.