Directional ΔG Neural Network (DrΔG-Net): A Modular Neural Network Approach to Binding Free Energy Prediction.

The protein-ligand binding free energy is a central quantity in structure-based computational drug discovery efforts. Although popular alchemical methods provide sound statistical means of computing the binding free energy of a large breadth of systems, they are generally too costly to be applied at the same frequency as end point or ligand-based methods. By contrast, these data-driven approaches are typically fast enough to address thousands of systems but with reduced transferability to unseen systems. We introduce DrΔG-Net (or simply Dragnet), an equivariant graph neural network that can blend ligand-based and protein-ligand data-driven approaches. It is based on a 3D fingerprint representation of the ligand alone and in complex with the protein target. Dragnet is a global scoring function to predict the binding affinity of arbitrary protein-ligand complexes, but can be easily tuned via transfer learning to specific systems or end points, performing similarly to common 2D ligand-based approaches in these tasks. Dragnet is evaluated on a total of 28 validation proteins with a set of congeneric ligands derived from the Binding DB and one custom set extracted from the ChEMBL Database. In general, a handful of experimental binding affinities are sufficient to optimize the scoring function for a particular protein and ligand scaffold. When not available, predictions from physics-based methods such as absolute free energy perturbation can be used for the transfer learning tuning of Dragnet. Furthermore, we use our data to illustrate the present limitations of data-driven modeling of binding free energy predictions.

A quantum chemical interaction energy dataset for accurately modeling protein-ligand interactions.

Fast and accurate calculation of intermolecular interaction energies is desirable for understanding many chemical and biological processes, including the binding of small molecules to proteins. The Splinter ["Symmetry-adapted perturbation theory (SAPT0) protein-ligand interaction"] dataset has been created to facilitate the development and improvement of methods for performing such calculations. Molecular fragments representing commonly found substructures in proteins and small-molecule ligands were paired into >9000 unique dimers, assembled into numerous configurations using an approach designed to adequately cover the breadth of the dimers' potential energy surfaces while enhancing sampling in favorable regions. ~1.5 million configurations of these dimers were randomly generated, and a structurally diverse subset of these were minimized to obtain an additional ~80 thousand local and global minima. For all >1.6 million configurations, SAPT0 calculations were performed with two basis sets to complete the dataset. It is expected that Splinter will be a useful benchmark dataset for training and testing various methods for the calculation of intermolecular interaction energies.

Benchmark coupled-cluster lattice energy of crystalline benzene and assessment of multi-level approximations in the many-body expansion.

The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller-Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod-Teller-Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol-1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol-1. Our CCSD(T)/CBS best estimate of the 0 K lattice energy is -54.01 kJ mol-1, compared to an estimated experimental value of -55.3 ± 2.2 kJ mol-1.

Benchmarking two-body contributions to crystal lattice energies and a range-dependent assessment of approximate methods.

Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol-1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%.

Range-dependence of two-body intermolecular interactions and their energy components in molecular crystals.

Routinely assessing the stability of molecular crystals with high accuracy remains an open challenge in the computational sciences. The many-body expansion decomposes computation of the crystal lattice energy into an embarrassingly parallel collection of computations over molecular dimers, trimers, and so forth, making quantum chemistry techniques tractable for many crystals of small organic molecules. By examining the range-dependence of different types of energetic contributions to the crystal lattice energy, we can glean qualitative understanding of solid-state intermolecular interactions as well as practical, exploitable reductions in the number of computations required for accurate energies. Here, we assess the range-dependent character of two-body interactions of 24 small organic molecular crystals by using the physically interpretable components from symmetry-adapted perturbation theory (electrostatics, exchange-repulsion, induction/polarization, and London dispersion). We also examine correlations between the convergence rates of electrostatics and London dispersion terms with molecular dipole moments and polarizabilities, to provide guidance for estimating convergence rates in other molecular crystals.

Electron-Passing Neural Networks for Atomic Charge Prediction in Systems with Arbitrary Molecular Charge.

Atomic charges are critical quantities in molecular mechanics and molecular dynamics, but obtaining these quantities requires heuristic choices based on atom typing or relatively expensive quantum mechanical computations to generate a density to be partitioned. Most machine learning efforts in this domain ignore total molecular charges, relying on overfitting and arbitrary rescaling in order to match the total system charge. Here, we introduce the electron-passing neural network (EPNN), a fast, accurate neural network atomic charge partitioning model that conserves total molecular charge by construction. EPNNs predict atomic charges very similar to those obtained by partitioning quantum mechanical densities but at such a small fraction of the cost that they can be easily computed for large biomolecules. Charges from this method may be used directly for molecular mechanics, as features for cheminformatics, or as input to any neural network potential.

AP-Net: An atomic-pairwise neural network for smooth and transferable interaction potentials.

Intermolecular interactions are critical to many chemical phenomena, but their accurate computation using ab initio methods is often limited by computational cost. The recent emergence of machine learning (ML) potentials may be a promising alternative. Useful ML models should not only estimate accurate interaction energies but also predict smooth and asymptotically correct potential energy surfaces. However, existing ML models are not guaranteed to obey these constraints. Indeed, systemic deficiencies are apparent in the predictions of our previous hydrogen-bond model as well as the popular ANI-1X model, which we attribute to the use of an atomic energy partition. As a solution, we propose an alternative atomic-pairwise framework specifically for intermolecular ML potentials, and we introduce AP-Net-a neural network model for interaction energies. The AP-Net model is developed using this physically motivated atomic-pairwise paradigm and also exploits the interpretability of symmetry adapted perturbation theory (SAPT). We show that in contrast to other models, AP-Net produces smooth, physically meaningful intermolecular potentials exhibiting correct asymptotic behavior. Initially trained on only a limited number of mostly hydrogen-bonded dimers, AP-Net makes accurate predictions across the chemically diverse S66x8 dataset, demonstrating significant transferability. On a test set including experimental hydrogen-bonded dimers, AP-Net predicts total interaction energies with a mean absolute error of 0.37 kcal mol-1, reducing errors by a factor of 2-5 across SAPT components from previous neural network potentials. The pairwise interaction energies of the model are physically interpretable, and an investigation of predicted electrostatic energies suggests that the model "learns" the physics of hydrogen-bonded interactions.

Approaches for machine learning intermolecular interaction energies and application to energy components from symmetry adapted perturbation theory.

Accurate prediction of intermolecular interaction energies is a fundamental challenge in electronic structure theory due to their subtle character and small magnitudes relative to total molecular energies. Symmetry adapted perturbation theory (SAPT) provides rigorous quantum mechanical means for computing such quantities directly and accurately, but for a computational cost of at least O(N5), where N is the number of atoms. Here, we report machine learned models of SAPT components with a computational cost that scales asymptotically linearly, O(N). We use modified multi-target Behler-Parrinello neural networks and specialized intermolecular symmetry functions to address the idiosyncrasies of the intermolecular problem, achieving 1.2 kcal mol-1 mean absolute errors on a test set of hydrogen bound complexes including structural data extracted from the Cambridge Structural Database and Protein Data Bank, spanning an interaction energy range of 20 kcal mol-1. Additionally, we recover accurate predictions of the physically meaningful SAPT component energies, of which dispersion and induction/polarization were the easiest to predict and electrostatics and exchange-repulsion are the most difficult.