Electrostatically embedded symmetry-adapted perturbation theory.

Symmetry-adapted perturbation theory (SAPT) is an ab initio approach that directly computes noncovalent interaction energies in terms of electrostatics, exchange repulsion, induction/polarization, and London dispersion components. Due to its high computational scaling, routine applications of even the lowest order of SAPT are typically limited to a few hundred atoms. To address this limitation, we report here the addition of electrostatic embedding to the SAPT (EE-SAPT) and ISAPT (EE-ISAPT) methods. We illustrate the embedding scheme using water trimer as a prototype example. Then, we show that EE-SAPT/EE-ISAPT can be applied for efficiently and accurately computing noncovalent interactions in large systems, including solvated dimers and protein-ligand systems. In the latter application, particular care must be taken to properly handle the quantum mechanics/molecular mechanics boundary when it cuts covalent bonds. We investigate various schemes for handling charges near this boundary and demonstrate which are most effective in the context of charge-embedded SAPT.

Discovery and Optimization of Aryl Piperidinone Ureas as Selective Formyl Peptide Receptor 2 Agonists.

We report the discovery and optimization of aryl piperidinone urea formyl peptide receptor 2 (FPR2) agonists from a weakly active high-throughput screening (HTS) hit to potent and selective agonists with favorable efficacy in acute in vivo models. A basis for the selectivity for FPR2 over FPR1 is proposed based on docking molecules into recently reported FPR2 and FPR1 cryoEM structures. Compounds from the new scaffold reported in this study exhibited superior potency and selectivity and favorable ADME profiles. Furthermore, select compounds were evaluated in an acute rat lipopolysaccharide (LPS) inflammation model and demonstrated robust dose-dependent induction of IL10, a marker for inflammation resolution, providing a valuable proof of concept for this class of FPR2 agonists.

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

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.

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.

A quantitative assessment of deformation energy in intermolecular interactions: How important is it?

Dimer interaction energies have been well studied in computational chemistry, but they can offer an incomplete understanding of molecular binding depending on the system. In the current study, we present a dataset of focal-point coupled-cluster interaction and deformation energies (summing to binding energies, De) of 28 organic molecular dimers. We use these highly accurate energies to evaluate ten density functional approximations for their accuracy. The best performing method (with a double-ζ basis set), B97M-D3BJ, is then used to calculate the binding energies of 104 organic dimers, and we analyze the influence of the nature and strength of interaction on deformation energies. Deformation energies can be as large as 50% of the dimer interaction energy, especially when hydrogen bonding is present. In most cases, two or more hydrogen bonds present in a dimer correspond to an interaction energy of -10 to -25 kcal mol-1, allowing a deformation energy above 1 kcal mol-1 (and up to 9.5 kcal mol-1). A lack of hydrogen bonding usually restricts the deformation energy to below 1 kcal mol-1 due to the weaker interaction energy.

Discovery of Heteroaryl Urea Isosteres for Formyl Peptide Receptor 2 Agonists.

Formyl peptide receptor 2 (FPR2) agonists have shown efficacy in inflammatory-driven animal disease models and have the potential to treat a range of diseases. Many reported synthetic agonists contain a phenylurea, which appears to be necessary for activity in the reported chemotypes. We set out to find isosteres for the phenylurea and focused our efforts on heteroaryl rings. The wide range of potencies with heterocyclic isosteres demonstrates how electronic effects of the heteroatom placement impact molecular recognition. Herein, we report our discovery of benzimidazole and aminophenyloxadiazole FPR2 agonists with low nanomolar activity.

The influence of a solvent environment on direct non-covalent interactions between two molecules: A symmetry-adapted perturbation theory study of polarization tuning of π-π interactions by water.

High-level quantum chemical computations have provided significant insight into the fundamental physical nature of non-covalent interactions. These studies have focused primarily on gas-phase computations of small van der Waals dimers; however, these interactions frequently take place in complex chemical environments, such as proteins, solutions, or solids. To better understand how the chemical environment affects non-covalent interactions, we have undertaken a quantum chemical study of π-π interactions in an aqueous solution, as exemplified by T-shaped benzene dimers surrounded by 28 or 50 explicit water molecules. We report interaction energies (IEs) using second-order Møller-Plesset perturbation theory, and we apply the intramolecular and functional-group partitioning extensions of symmetry-adapted perturbation theory (ISAPT and F-SAPT, respectively) to analyze how the solvent molecules tune the π-π interactions of the solute. For complexes containing neutral monomers, even 50 explicit waters (constituting a first and partial second solvation shell) change total SAPT IEs between the two solute molecules by only tenths of a kcal mol-1, while significant changes of up to 3 kcal mol-1 of the electrostatic component are seen for the cationic pyridinium-benzene dimer. This difference between charged and neutral solutes is attributed to large non-additive three-body interactions within solvated ion-containing complexes. Overall, except for charged solutes, our quantum computations indicate that nearby solvent molecules cause very little "tuning" of the direct solute-solute interactions. This indicates that differences in binding energies between the gas phase and solution phase are primarily indirect effects of the competition between solute-solute and solute-solvent interactions.

CLIFF: A component-based, machine-learned, intermolecular force field.

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug-protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol-1 in both total and component energies across a diverse dimer test set. For the side chain-side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol-1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug-protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes.

Cartesian message passing neural networks for directional properties: Fast and transferable atomic multipoles.

The message passing neural network (MPNN) framework is a promising tool for modeling atomic properties but is, until recently, incompatible with directional properties, such as Cartesian tensors. We propose a modified Cartesian MPNN (CMPNN) suitable for predicting atom-centered multipoles, an essential component of ab initio force fields. The efficacy of this model is demonstrated on a newly developed dataset consisting of 46 623 chemical structures and corresponding high-quality atomic multipoles, which was deposited into the publicly available Molecular Sciences Software Institute QCArchive server. We show that the CMPNN accurately predicts atom-centered charges, dipoles, and quadrupoles and that errors in the predicted atomic multipoles have a negligible effect on multipole-multipole electrostatic energies. The CMPNN is accurate enough to model conformational dependencies of a molecule's electronic structure. This opens up the possibility of recomputing atomic multipoles on the fly throughout a simulation in which they might exhibit strong conformational dependence.

Optimized damping parameters for empirical dispersion corrections to symmetry-adapted perturbation theory.

Symmetry-adapted perturbation theory (SAPT) has become an invaluable tool for studying the fundamental nature of non-covalent interactions by directly computing the electrostatics, exchange (steric) repulsion, induction (polarization), and London dispersion contributions to the interaction energy using quantum mechanics. Further application of SAPT is primarily limited by its computational expense, where even its most affordable variant (SAPT0) scales as the fifth power of system size [O(N5)] due to the dispersion terms. The algorithmic scaling of SAPT0 is reduced from O(N5)→O(N4) by replacing these terms with the empirical D3 dispersion correction of Grimme and co-workers, forming a method that may be termed SAPT0-D3. Here, we optimize the damping parameters for the -D3 terms in SAPT0-D3 using a much larger training set than has previously been considered, namely, 8299 interaction energies computed at the complete-basis-set limit of coupled cluster through perturbative triples [CCSD(T)/CBS]. Perhaps surprisingly, with only three fitted parameters, SAPT0-D3 improves on the accuracy of SAPT0, reducing mean absolute errors from 0.61 to 0.49 kcal mol-1 over the full set of complexes. Additionally, SAPT0-D3 exhibits a nearly 2.5× speedup over conventional SAPT0 for systems with ∼300 atoms and is applied here to systems with up to 459 atoms. Finally, we have also implemented a functional group partitioning of the approach (F-SAPT0-D3) and applied it to determine important contacts in the binding of salbutamol to G-protein coupled ß1-adrenergic receptor in both active and inactive forms. SAPT0-D3 capabilities have been added to the open-source Psi4 software.

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.

Assessment of Density Functional Methods for Geometry Optimization of Bimolecular van der Waals Complexes.

We explore the suitability of three popular density functionals (B97-D3, B3LYP-D3, M05-2X) for producing accurate equilibrium geometries of van der Waals (vdW) complexes with diverse binding motifs. For these functionals, optimizations using Dunning's aug-cc-pVDZ basis set best combine accuracy and a reasonable computational expense. Each DFT/aug-cc-pVDZ combination produces optimized equilibrium geometries for 21 small vdW complexes of organic molecules (up to four non-hydrogen atoms total) that agree with high-level CCSD(T)/CBS reference geometries to within ±0.1 Å for the averages of the center-of-mass displacement and the mean least root-mean-squared displacement. The DFT/aug-cc-pVDZ combinations are also able to reproduce the optimal center-of-mass displacements interpolated from CCSD(T)/CBS radial potential energy surfaces in both NBC7x and HBC6 test sets to within ±0.1 Å. We therefore conclude that each of these denisty functional methods, together with the aug-cc-pVDZ basis set, is suitable for producing equilibrium geometries of generic nonbonded complexes.

Improving Accuracy, Diversity, and Speed with Prime Macrocycle Conformational Sampling.

A novel method for exploring macrocycle conformational space, Prime macrocycle conformational sampling (Prime-MCS), is introduced and evaluated in the context of other available algorithms (Molecular Dynamics, LowModeMD in MOE, and MacroModel Baseline Search). The algorithms were benchmarked on a data set of 208 macrocycles which was curated for diversity from the Cambridge Structural Database, the Protein Data Bank, and the Biologically Interesting Molecule Reference Dictionary. The algorithms were evaluated in terms of accuracy (ability to reproduce the crystal structure), diversity (coverage of conformational space), and computational speed. Prime-MCS most reliably reproduced crystallographic structures for RMSD thresholds >1.0 Å, most often produced the most diverse conformational ensemble, and was most often the fastest algorithm. Detailed analysis and examination of both typical and outlier cases were performed to reveal characteristics, shortcomings, expected performance, and complementarity of the methods.

Neutral macrocyclic factor VIIa inhibitors.

Factor VIIa (FVIIa) inhibitors have shown strong antithrombotic efficacy in preclinical thrombosis models with limited bleeding liabilities. Discovery of potent, orally active FVIIa inhibitors has been largely unsuccessful due to the requirement of a basic P1 group to interact with Asp189 in the S1 binding pocket, limiting their membrane permeability. We have combined recently reported neutral P1 binding substituents with a highly optimized macrocyclic chemotype to produce FVIIa inhibitors with low nanomolar potency and enhanced permeability.

The Surprising Importance of Peptide Bond Contacts in Drug-Protein Interactions.

The study of noncovalent interactions, notably including drug-protein binding, relies heavily on the language of localized functional group contacts: hydrogen bonding, π-π interactions, CH-π contacts, halogen bonding, etc. Applying the state-of-the-art functional group symmetry-adapted perturbation theory (F-SAPT) to an important question of chloro versus methyl aryl substitution in factor Xa inhibitor drugs, we find that a localized contact model provides an incorrect picture for the origin of the enhancement of chloro-containing ligands. Instead, the enhancement is found to originate from many intermediate-range contacts distributed throughout the binding pocket, particularly including the peptide bonds in the protein backbone. The contributions from these contacts are primarily electrostatic in nature, but require ab initio computations involving nearly the full drug-protein pocket system to be accurately quantified.

Design and Synthesis of Novel Meta-Linked Phenylglycine Macrocyclic FVIIa Inhibitors.

Two novel series of meta-linked phenylglycine-based macrocyclic FVIIa inhibitors have been designed to improve the rodent metabolic stability and PK observed with the precursor para-linked phenylglycine macrocycles. Through iterative structure-based design and optimization, the TF/FVIIa Ki was improved to subnanomolar levels with good clotting activity, metabolic stability, and permeability.