Simulating protein-ligand binding with neural network potentials

Quantum-level machine learning calculations of Levodopa

Many drug molecules contain functional groups, resulting in a torsional barrier corresponding to rotation around the bond linking the fragments. In medicinal chemistry and pharmaceutical sciences, inclusive of drug design studies, the exact calculation of the potential energy surface (PES) of these molecular torsions is extremely important and precious. Machine learning (ML), including deep learning (DL), is currently one of the most rapidly evolving tools in computer-aided drug discovery and molecular simulations. In this work, we used ANI-1x neural network potential as a quantum-level ML to predict the PESs of the L-3,4-dihydroxyphenylalanine (Levodopa) antiparkinsonian drug molecule. The electronic energies and structural parameters calculated by density functional theory (DFT) using the wB97X method and all possible Pople's basis sets indicated the 6-31G(d) basis set, when used with the wB97X functional, exhibits behavior similar to that of the ANI-1x model. The vibrational frequencies investigation showed a linear correlation between DFT and ML data. All ANI-1x calculations were completed quickly in a very short computing time. From this perspective, we expect the ANI-1x dataset applied in this work to be appreciably efficient and effective in computational structure-based drug design studies.

Stable and accurate atomistic simulations of flexible molecules using conformationally generalisable machine learned potentials

Computational simulation methods based on machine learned potentials (MLPs) promise to revolutionise shape prediction of flexible molecules in solution, but their widespread adoption has been limited by the way in which training data is generated. Here, we present an approach which allows the key conformational degrees of freedom to be properly represented in reference molecular datasets. MLPs trained on these datasets using a global descriptor scheme are generalisable in conformational space, providing quantum chemical accuracy for all conformers. These MLPs are capable of propagating long, stable molecular dynamics trajectories, an attribute that has remained a challenge. We deploy the MLPs in obtaining converged conformational free energy surfaces for flexible molecules via well-tempered metadynamics simulations; this approach provides a hitherto inaccessible route to accurately computing the structural, dynamical and thermodynamical properties of a wide variety of flexible molecular systems. It is further demonstrated that MLPs must be trained on reference datasets with complete coverage of conformational space, including in barrier regions, to achieve stable molecular dynamics trajectories.

FeNNol: An efficient and flexible library for building force-field-enhanced neural network potentials

Neural network interatomic potentials (NNPs) have recently proven to be powerful tools to accurately model complex molecular systems while bypassing the high numerical cost of ab initio molecular dynamics simulations. In recent years, numerous advances in model architectures as well as the development of hybrid models combining machine-learning (ML) with more traditional, physically motivated, force-field interactions have considerably increased the design space of ML potentials. In this paper, we present FeNNol, a new library for building, training, and running force-field-enhanced neural network potentials. It provides a flexible and modular system for building hybrid models, allowing us to easily combine state-of-the-art embeddings with ML-parameterized physical interaction terms without the need for explicit programming. Furthermore, FeNNol leverages the automatic differentiation and just-in-time compilation features of the Jax Python library to enable fast evaluation of NNPs, shrinking the performance gap between ML potentials and standard force-fields. This is demonstrated with the popular ANI-2x model reaching simulation speeds nearly on par with the AMOEBA polarizable force-field on commodity GPUs (graphics processing units). We hope that FeNNol will facilitate the development and application of new hybrid NNP architectures for a wide range of molecular simulation problems.

A neural network potential based on pairwise resolved atomic forces and energies

Molecular simulations have become a key tool in molecular and materials design. Machine learning (ML)-based potential energy functions offer the prospect of simulating complex molecular systems efficiently at quantum chemical accuracy. In previous work, we have introduced the ML-based PairF-Net approach to neural network potentials, that adopts a pairwise interatomic scheme to predicting forces within a molecular system. Here, we further develop the PairF-Net model to intrinsically incorporate energy conservation and couple the model to a molecular mechanical (MM) environment within the OpenMM package. The updated PairF-Net model yields energy and force predictions and dynamical distributions in good agreement with the rMD17 dataset of ten small organic molecules in the gas-phase. We further show that these in vacuo ML models of small molecules can be applied to force predictions in aqueous solution via hybrid ML/MM simulations. We present a new benchmark dataset for these ten molecules in solution, obtained from QM/MM simulations, which we denote as rMD17-aq (https://zenodo.org/records/10048644); and assess the ability of PairF-Net to reproduce the molecular energy, atomic forces and dynamical distributions of these solution conformations via ML/MM simulations.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

The emergence of machine learning force fields in drug design

In the field of molecular simulation for drug design, traditional molecular mechanic force fields and quantum chemical theories have been instrumental but limited in terms of scalability and computational efficiency. To overcome these limitations, machine learning force fields (MLFFs) have emerged as a powerful tool capable of balancing accuracy with efficiency. MLFFs rely on the relationship between molecular structures and potential energy, bypassing the need for a preconceived notion of interaction representations. Their accuracy depends on the machine learning models used, and the quality and volume of training data sets. With recent advances in equivariant neural networks and high-quality datasets, MLFFs have significantly improved their performance. This review explores MLFFs, emphasizing their potential in drug design. It elucidates MLFF principles, provides development and validation guidelines, and highlights successful MLFF implementations. It also addresses potential challenges in developing and applying MLFFs. The review concludes by illuminating the path ahead for MLFFs, outlining the challenges to be overcome and the opportunities to be harnessed. This inspires researchers to embrace MLFFs in their investigations as a new tool to perform molecular simulations in drug design.

Incorporating Neural Networks into the AMOEBA Polarizable Force Field

Neural network potentials (NNPs) offer significant promise to bridge the gap between the accuracy of quantum mechanics and the efficiency of molecular mechanics in molecular simulation. Most NNPs rely on the locality assumption that ensures the model's transferability and scalability and thus lack the treatment of long-range interactions, which are essential for molecular systems in the condensed phase. Here we present an integrated hybrid model, AMOEBA+NN, which combines the AMOEBA potential for the short- and long-range noncovalent atomic interactions and an NNP to capture the remaining local covalent contributions. The AMOEBA+NN model was trained on the conformational energy of the ANI-1x data set and tested on several external data sets ranging from small molecules to tetrapeptides. The hybrid model demonstrated substantial improvements over the baseline models in term of accuracy as the molecule size increased, suggesting its potential as a next-generation approach for chemically accurate molecular simulations.

Implementation and Validation of an OpenMM Plugin for the Deep Potential Representation of Potential Energy

Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field.

DP/MM: A Hybrid Model for Zinc-Protein Interactions in Molecular Dynamics

Zinc-containing proteins are vital for many biological processes, yet accurately modeling them using classical force fields is hindered by complicated polarization and charge transfer effects. This study introduces DP/MM, a hybrid force field scheme that utilizes a deep potential model to correct the atomic forces of zinc ions and their coordinated atoms, elevating them from MM to QM levels of accuracy. Trained on the difference between MM and QM atomic forces across diverse zinc coordination groups, the DP/MM model faithfully reproduces structural characteristics of zinc coordination during simulations, such as the tetrahedral coordination of Cys4 and Cys3His1 groups. Furthermore, DP/MM allows water exchange in the zinc coordination environment. With its unique blend of accuracy, efficiency, flexibility, and transferability, DP/MM serves as a valuable tool for studying structures and dynamics of zinc-containing proteins and also represents a pioneering approach in the evolving landscape of machine learning potentials for molecular modeling.

NNP/MM: Accelerating Molecular Dynamics Simulations with Machine Learning Potentials and Molecular Mechanics

Machine learning potentials have emerged as a means to enhance the accuracy of biomolecular simulations. However, their application is constrained by the significant computational cost arising from the vast number of parameters compared with traditional molecular mechanics. To tackle this issue, we introduce an optimized implementation of the hybrid method (NNP/MM), which combines a neural network potential (NNP) and molecular mechanics (MM). This approach models a portion of the system, such as a small molecule, using NNP while employing MM for the remaining system to boost efficiency. By conducting molecular dynamics (MD) simulations on various protein-ligand complexes and metadynamics (MTD) simulations on a ligand, we showcase the capabilities of our implementation of NNP/MM. It has enabled us to increase the simulation speed by ∼5 times and achieve a combined sampling of 1 μs for each complex, marking the longest simulations ever reported for this class of simulations.

Drug Design in the Exascale Era: A Perspective from Massively Parallel QM/MM Simulations

The initial phases of drug discovery - in silico drug design - could benefit from first principle Quantum Mechanics/Molecular Mechanics (QM/MM) molecular dynamics (MD) simulations in explicit solvent, yet many applications are currently limited by the short time scales that this approach can cover. Developing scalable first principle QM/MM MD interfaces fully exploiting current exascale machines - so far an unmet and crucial goal - will help overcome this problem, opening the way to the study of the thermodynamics and kinetics of ligand binding to protein with first principle accuracy. Here, taking two relevant case studies involving the interactions of ligands with rather large enzymes, we showcase the use of our recently developed massively scalable Multiscale Modeling in Computational Chemistry (MiMiC) QM/MM framework (currently using DFT to describe the QM region) to investigate reactions and ligand binding in enzymes of pharmacological relevance. We also demonstrate for the first time strong scaling of MiMiC-QM/MM MD simulations with parallel efficiency of ∼70% up to >80,000 cores. Thus, among many others, the MiMiC interface represents a promising candidate toward exascale applications by combining machine learning with statistical mechanics based algorithms tailored for exascale supercomputers.

Scalable hybrid deep neural networks/polarizable potentials biomolecular simulations including long-range effects

Deep-HP is a scalable extension of the Tinker-HP multi-GPU molecular dynamics (MD) package enabling the use of Pytorch/TensorFlow Deep Neural Network (DNN) models. Deep-HP increases DNNs' MD capabilities by orders of magnitude offering access to ns simulations for 100k-atom biosystems while offering the possibility of coupling DNNs to any classical (FFs) and many-body polarizable (PFFs) force fields. It allows therefore the introduction of the ANI-2X/AMOEBA hybrid polarizable potential designed for ligand binding studies where solvent-solvent and solvent-solute interactions are computed with the AMOEBA PFF while solute-solute ones are computed by the ANI-2X DNN. ANI-2X/AMOEBA explicitly includes AMOEBA's physical long-range interactions via an efficient Particle Mesh Ewald implementation while preserving ANI-2X's solute short-range quantum mechanical accuracy. The DNN/PFF partition can be user-defined allowing for hybrid simulations to include key ingredients of biosimulation such as polarizable solvents, polarizable counter ions, etc.… ANI-2X/AMOEBA is accelerated using a multiple-timestep strategy focusing on the model's contributions to low-frequency modes of nuclear forces. It primarily evaluates AMOEBA forces while including ANI-2X ones only via correction-steps resulting in an order of magnitude acceleration over standard Velocity Verlet integration. Simulating more than 10 μs, we compute charged/uncharged ligand solvation free energies in 4 solvents, and absolute binding free energies of host-guest complexes from SAMPL challenges. ANI-2X/AMOEBA average errors are discussed in terms of statistical uncertainty and appear in the range of chemical accuracy compared to experiment. The availability of the Deep-HP computational platform opens the path towards large-scale hybrid DNN simulations, at force-field cost, in biophysics and drug discovery.

In-Silico Approaches for the Screening and Discovery of Broad-Spectrum Marine Natural Product Antiviral Agents Against Coronaviruses

The urgent need for SARS-CoV-2 controls has led to a reassessment of approaches to identify and develop natural product inhibitors of zoonotic, highly virulent, and rapidly emerging viruses. There are yet no clinically approved broad-spectrum antivirals available for beta-coronaviruses. Discovery pipelines for pan-virus medications against a broad range of betacoronaviruses are therefore a priority. A variety of marine natural product (MNP) small molecules have shown inhibitory activity against viral species. Access to large data caches of small molecule structural information is vital to finding new pharmaceuticals. Increasingly, molecular docking simulations are being used to narrow the space of possibilities and generate drug leads. Combining in-silico methods, augmented by metaheuristic optimization and machine learning (ML) allows the generation of hits from within a virtual MNP library to narrow screens for novel targets against coronaviruses. In this review article, we explore current insights and techniques that can be leveraged to generate broad-spectrum antivirals against betacoronaviruses using in-silico optimization and ML. ML approaches are capable of simultaneously evaluating different features for predicting inhibitory activity. Many also provide a semi-quantitative measure of feature relevance and can guide in selecting a subset of features relevant for inhibition of SARS-CoV-2.

Does a Machine-Learned Potential Perform Better Than an Optimally Tuned Traditional Force Field? A Case Study on Fluorohydrins

We present a comparative study that evaluates the performance of a machine learning potential (ANI-2x), a conventional force field (GAFF), and an optimally tuned GAFF-like force field in the modeling of a set of 10 γ-fluorohydrins that exhibit a complex interplay between intra- and intermolecular interactions in determining conformer stability. To benchmark the performance of each molecular model, we evaluated their energetic, geometric, and sampling accuracies relative to quantum-mechanical data. This benchmark involved conformational analysis both in the gas phase and chloroform solution. We also assessed the performance of the aforementioned molecular models in estimating nuclear spin-spin coupling constants by comparing their predictions to experimental data available in chloroform. The results and discussion presented in this study demonstrate that ANI-2x tends to predict stronger-than-expected hydrogen bonding and overstabilize global minima and shows problems related to inadequate description of dispersion interactions. Furthermore, while ANI-2x is a viable model for modeling in the gas phase, conventional force fields still play an important role, especially for condensed-phase simulations. Overall, this study highlights the strengths and weaknesses of each model, providing guidelines for the use and future development of force fields and machine learning potentials.

SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials

Machine learning potentials are an important tool for molecular simulation, but their development is held back by a shortage of high quality datasets to train them on. We describe the SPICE dataset, a new quantum chemistry dataset for training potentials relevant to simulating drug-like small molecules interacting with proteins. It contains over 1.1 million conformations for a diverse set of small molecules, dimers, dipeptides, and solvated amino acids. It includes 15 elements, charged and uncharged molecules, and a wide range of covalent and non-covalent interactions. It provides both forces and energies calculated at the ωB97M-D3(BJ)/def2-TZVPPD level of theory, along with other useful quantities such as multipole moments and bond orders. We train a set of machine learning potentials on it and demonstrate that they can achieve chemical accuracy across a broad region of chemical space. It can serve as a valuable resource for the creation of transferable, ready to use potential functions for use in molecular simulations.

Modeling pyranose ring pucker in carbohydrates using machine learning and semi-empirical quantum chemical methods

Pyranose ring pucker is a key coordinate governing the structure, interactions and reactivity of carbohydrates. We assess the ability of the machine learning potentials, ANI-1ccx and ANI-2x, and the GFN2-xTB semiempirical quantum chemical method, to model ring pucker conformers of five monosaccharides and oxane in the gas phase. Relative to coupled-cluster quantum mechanical calculations, we find that ANI-1ccx most accurately reproduces the ring pucker energy landscape for these molecules, with a correlation coefficient r2 of 0.83. This correlation in relative energies lowers to values of 0.70 for ANI-2x and 0.60 for GFN2-xTB. The ANI-1ccx also provides the most accurate estimate of the energetics of the 4 C1 -to-1 C4 minimum energy pathway for the six molecules. All three models reproduce chair more accurately than non-chair geometries. Analysis of small model molecules suggests that the ANI-1ccx model favors puckers with equatorial hydrogen bonding substituents; that ANI-2x and GFN2-xTB models overstabilize conformers with axially oriented groups; and that the endo-anomeric effect is overestimated by the machine learning models and underestimated via the GFN2-xTB method. While the pucker conformers considered in this study correspond to a gas phase environment, the accuracy and computational efficiency of the ANI-1ccx approach in modeling ring pucker in vacuo provides a promising basis for future evaluation and application to condensed phase environments.

Application of Computational Biology and Artificial Intelligence in Drug Design

Traditional drug design requires a great amount of research time and developmental expense. Booming computational approaches, including computational biology, computer-aided drug design, and artificial intelligence, have the potential to expedite the efficiency of drug discovery by minimizing the time and financial cost. In recent years, computational approaches are being widely used to improve the efficacy and effectiveness of drug discovery and pipeline, leading to the approval of plenty of new drugs for marketing. The present review emphasizes on the applications of these indispensable computational approaches in aiding target identification, lead discovery, and lead optimization. Some challenges of using these approaches for drug design are also discussed. Moreover, we propose a methodology for integrating various computational techniques into new drug discovery and design.

An open-source molecular builder and free energy preparation workflow

Automated free energy calculations for the prediction of binding free energies of congeneric series of ligands to a protein target are growing in popularity, but building reliable initial binding poses for the ligands is challenging. Here, we introduce the open-source FEgrow workflow for building user-defined congeneric series of ligands in protein binding pockets for input to free energy calculations. For a given ligand core and receptor structure, FEgrow enumerates and optimises the bioactive conformations of the grown functional group(s), making use of hybrid machine learning/molecular mechanics potential energy functions where possible. Low energy structures are optionally scored using the gnina convolutional neural network scoring function, and output for more rigorous protein-ligand binding free energy predictions. We illustrate use of the workflow by building and scoring binding poses for ten congeneric series of ligands bound to targets from a standard, high quality dataset of protein-ligand complexes. Furthermore, we build a set of 13 inhibitors of the SARS-CoV-2 main protease from the literature, and use free energy calculations to retrospectively compute their relative binding free energies. FEgrow is freely available at https://github.com/cole-group/FEgrow, along with a tutorial.

How Robust Is the Reversible Steric Shielding Strategy for Photoswitchable Organocatalysts?

A highly appealing strategy to modulate a catalyst's activity and/or selectivity in a dynamic and noninvasive way is to incorporate a photoresponsive unit into a catalytically competent molecule. However, the description of the photoinduced conformational or structural changes that alter the catalyst's intrinsic reactivity is often reduced to a handful of intuitive static representations, which can struggle to capture the complexity of flexible organocatalysts. Here, we show how a comprehensive exploration of the free energy landscape of N-alkylated azobenzene-tethered piperidine catalysts is essential to unravel the conformational characteristics of each configurational state and explain the experimentally observed reactivity trends. Mapping the catalysts' conformational space highlights the existence of false ON or OFF states that lower their switching ability. Our findings expose the challenges associated with the realization of a reversible steric shielding for the photocontrol of Brønsted basicity of piperidine photoswitchable organocatalysts.

Integration of machine learning with computational structural biology of plants

Computational structural biology of proteins has developed rapidly in recent decades with the development of new computational tools and the advancement of computing hardware. However, while these techniques have widely been used to make advancements in human medicine, these methods have seen less utilization in the plant sciences. In the last several years, machine learning methods have gained popularity in computational structural biology. These methods have enabled the development of new tools which are able to address the major challenges that have hampered the wide adoption of the computational structural biology of plants. This perspective examines the remaining challenges in computational structural biology and how the development of machine learning techniques enables more in-depth computational structural biology of plants.

First Principles Calculation of Protein-Protein Dimer Affinities of ALS-Associated SOD1 Mutants

Cu,Zn superoxide dismutase (SOD1) is a 32 kDa homodimer that converts toxic oxygen radicals in neurons to less harmful species. The dimerization of SOD1 is essential to the stability of the protein. Monomerization increases the likelihood of SOD1 misfolding into conformations associated with aggregation, cellular toxicity, and neuronal death in familial amyotrophic lateral sclerosis (fALS). The ubiquity of disease-associated mutations throughout the primary sequence of SOD1 suggests an important role of physicochemical processes, including monomerization of SOD1, in the pathology of the disease. Herein, we use a first-principles statistical mechanics method to systematically calculate the free energy of dimer binding for SOD1 using molecular dynamics, which involves sequentially computing conformational, orientational, and separation distance contributions to the binding free energy. We consider the effects of two ALS-associated mutations in SOD1 protein on dimer stability, A4V and D101N, as well as the role of metal binding and disulfide bond formation. We find that the penalty for dimer formation arising from the conformational entropy of disordered loops in SOD1 is significantly larger than that for other protein-protein interactions previously considered. In the case of the disulfide-reduced protein, this leads to a bound complex whose formation is energetically disfavored. Somewhat surprisingly, the loop free energy penalty upon dimerization is still significant for the holoprotein, despite the increased structural order induced by the bound metal cations. This resulted in a surprisingly modest increase in dimer binding free energy of only about 1.5 kcal/mol upon metalation of the protein, suggesting that the most significant stabilizing effects of metalation are on folding stability rather than dimer binding stability. The mutant A4V has an unstable dimer due to weakened monomer-monomer interactions, which are manifested in the calculation by a separation free energy surface with a lower barrier. The mutant D101N has a stable dimer partially due to an unusually rigid β-barrel in the free monomer. D101N also exhibits anticooperativity in loop folding upon dimerization. These computational calculations are, to our knowledge, the most quantitatively accurate calculations of dimer binding stability in SOD1 to date.

Computer simulation of the Receptor-Ligand Interactions of Mannose Receptor CD206 in Comparison with the Lectin Concanavalin A Model

Computer modeling of complexation of mono- and oligosaccharide ligands with the main (fourth) carbohydrate-binding domain of the mannose receptor CD206 (CRD4), as well as with the model receptor concanavalin A (ConA), was carried out for the first time, using methods of molecular dynamics and neural network analysis. ConA was shown to be a relevant model of CD206 (CRD4) due to similarity of the structural organization of the binding sites and high correlation of the values of free energies of complexation between the literature data and computer modeling (r > 0.9). Role of the main factors affecting affinity of the ligand–receptor interactions is discussed: the number and nature of carbohydrate residues, presence of Me-group in the O1 position, type of the glycoside bond in dimannose. Complexation of ConA and CD206 with ligands is shown to be energetically caused by electrostatic interactions (E) of the charged residues (Asn, Asp, Arg) with oxygen and hydrogen atoms in carbohydrates; contributions of hydrophobic and van der Waals components is lower. Possibility of the additional stabilization of complexes due to the CH–π stacking interactions of Tyr with the Man plane is discussed. The role of calcium and manganese ions in binding ligands has been studied. The values of free energies of complexation calculated in the course of molecular dynamics simulation correlate with experimental data (published for the model ConA): correlation coefficient r = 0.68. The Pafnucy neural network was trained based on the set of PDBbind2020 ligand–receptor complexes, which significantly increased accuracy of the energy predictions to r = 0.8 and 0.82 for CD206 and ConA receptors, respectively. A model of normalization of the complexation energy values for calculating the relevant values of ΔG_bind, K_d is proposed. Based on the developed technique, values of the dissociation constants of a series of CD206 complexes with nine carbohydrate ligands of different structures were determined, which were not previously known. The obtained data open up possibilities for using computer modeling for the development of optimal drug carriers capable of active macrophage targeting, and also determine the limits of applicability of using ConA as a relevant model for studying parameters of the CD206 binding to various carbohydrate ligands.

Machine Learning-Assisted Hybrid ReaxFF Simulations

We have developed a machine learning (ML)-assisted Hybrid ReaxFF simulation method ("Hybrid/Reax"), which alternates reactive and non-reactive molecular dynamics simulations with the assistance of ML models to simulate phenomena that require longer time scales and/or larger systems than are typically accessible to ReaxFF. Hybrid/Reax uses a specialized tracking tool during the reactive simulations to further accelerate chemical reactions. Non-reactive simulations are used to equilibrate the system after the reactive simulation stage. ML models are used between reactive and non-reactive stages to predict non-reactive force field parameters of the system based on the updated bond topology. Hybrid/Reax simulation cycles can be continued until the desired chemical reactions are observed. As a case study, this method was used to study the cross-linking of a polyethylene (PE) matrix analogue (decane) with the cross-linking agent dicumyl peroxide (DCP). We were able to run relatively long simulations [>20 million molecular dynamics (MD) steps] on a small test system (4660 atoms) to simulate cross-linking reactions of PE in the presence of DCP. Starting with 80 PE molecules, more than half of them cross-linked by the end of the Hybrid/Reax cycles on a single Xeon processor in under 48 h. This simulation would take approximately 1 month if run with pure ReaxFF MD on the same machine.

Adaptive partitioning molecular dynamics using an extended Hamiltonian approach

A recently proposed extended Hamiltonian approach to switching interaction potentials is generalized to enable adaptive partitioning molecular dynamics simulations. Switching is performed along a fictitious classical degree of freedom whose value determines the mixing ratio of the two potentials on a time scale determined by its associated mass. We propose to choose this associated fictitious mass adaptively so as to ensure a constant time scale for all switching processes. For different model systems, including a harmonic oscillator and a Lennard-Jones fluid, we investigate the window of switching time scales that guarantees the conservation of the extended Hamiltonian for a large number of switching events. The methodology is first applied in the microcanonical ensemble and then generalized to the canonical ensemble using a Nosé-Hoover chain thermostat. It is shown that the method is stable for thousands of consecutive switching events during a single simulation, with constant temperature and a conserved extended Hamiltonian. A slight modification of the original Hamiltonian is introduced to avoid accumulation of small numerical errors incurred after each switching process.

Probing the Suitability of Different Ca2+ Parameters for Long Simulations of Diisopropyl Fluorophosphatase

Organophosphate hydrolases are promising as potential biotherapeutic agents to treat poisoning with pesticides or nerve gases. However, these enzymes often need to be further engineered in order to become useful in practice. One example of such enhancement is the alteration of enantioselectivity of diisopropyl fluorophosphatase (DFPase). Molecular modeling techniques offer a unique opportunity to address this task rationally by providing a physical description of the substrate-binding process. However, DFPase is a metalloenzyme, and correct modeling of metal cations is a challenging task generally coming with a tradeoff between simulation speed and accuracy. Here, we probe several molecular mechanical parameter combinations for their ability to empower long simulations needed to achieve a quantitative description of substrate binding. We demonstrate that a combination of the Amber19sb force field with the recently developed 12-6 Ca2+ models allows us to both correctly model DFPase and obtain new insights into the DFP binding process.

Fitting quantum machine learning potentials to experimental free energy data: predicting tautomer ratios in solution

The computation of tautomer ratios of druglike molecules is enormously important in computer-aided drug discovery, as over a quarter of all approved drugs can populate multiple tautomeric species in solution. Unfortunately, accurate calculations of aqueous tautomer ratios—the degree to which these species must be penalized in order to correctly account for tautomers in modeling binding for computer-aided drug discovery—is surprisingly difficult. While quantum chemical approaches to computing aqueous tautomer ratios using continuum solvent models and rigid-rotor harmonic-oscillator thermochemistry are currently state of the art, these methods are still surprisingly inaccurate despite their enormous computational expense. Here, we show that a major source of this inaccuracy lies in the breakdown of the standard approach to accounting for quantum chemical thermochemistry using rigid rotor harmonic oscillator (RRHO) approximations, which are frustrated by the complex conformational landscape introduced by the migration of double bonds, creation of stereocenters, and introduction of multiple conformations separated by low energetic barriers induced by migration of a single proton. Using quantum machine learning (QML) methods that allow us to compute potential energies with quantum chemical accuracy at a fraction of the cost, we show how rigorous relative alchemical free energy calculations can be used to compute tautomer ratios in vacuum free from the limitations introduced by RRHO approximations. Furthermore, since the parameters of QML methods are tunable, we show how we can train these models to correct limitations in the underlying learned quantum chemical potential energy surface using free energies, enabling these methods to learn to generalize tautomer free energies across a broader range of predictions.

We show how alchemical free energies can be calculated with QML potentials to identify deficiencies in RRHO approximations for computing tautomeric free energies, and how these potentials can be learned from experiment to improve prediction accuracy.

Machine Learning Force Fields

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

A critical overview of computational approaches employed for COVID-19 drug discovery

COVID-19 has resulted in huge numbers of infections and deaths worldwide and brought the most severe disruptions to societies and economies since the Great Depression. Massive experimental and computational research effort to understand and characterize the disease and rapidly develop diagnostics, vaccines, and drugs has emerged in response to this devastating pandemic and more than 130 000 COVID-19-related research papers have been published in peer-reviewed journals or deposited in preprint servers. Much of the research effort has focused on the discovery of novel drug candidates or repurposing of existing drugs against COVID-19, and many such projects have been either exclusively computational or computer-aided experimental studies. Herein, we provide an expert overview of the key computational methods and their applications for the discovery of COVID-19 small-molecule therapeutics that have been reported in the research literature. We further outline that, after the first year the COVID-19 pandemic, it appears that drug repurposing has not produced rapid and global solutions. However, several known drugs have been used in the clinic to cure COVID-19 patients, and a few repurposed drugs continue to be considered in clinical trials, along with several novel clinical candidates. We posit that truly impactful computational tools must deliver actionable, experimentally testable hypotheses enabling the discovery of novel drugs and drug combinations, and that open science and rapid sharing of research results are critical to accelerate the development of novel, much needed therapeutics for COVID-19.

Learning protein-ligand binding affinity with atomic environment vectors

Scoring functions for the prediction of protein-ligand binding affinity have seen renewed interest in recent years when novel machine learning and deep learning methods started to consistently outperform classical scoring functions. Here we explore the use of atomic environment vectors (AEVs) and feed-forward neural networks, the building blocks of several neural network potentials, for the prediction of protein-ligand binding affinity. The AEV-based scoring function, which we term AEScore, is shown to perform as well or better than other state-of-the-art scoring functions on binding affinity prediction, with an RMSE of 1.22 pK units and a Pearson’s correlation coefficient of 0.83 for the CASF-2016 benchmark. However, AEScore does not perform as well in docking and virtual screening tasks, for which it has not been explicitly trained. Therefore, we show that the model can be combined with the classical scoring function AutoDock Vina in the context of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta$$\end{document}Δ-learning, where corrections to the AutoDock Vina scoring function are learned instead of the protein-ligand binding affinity itself. Combined with AutoDock Vina, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta$$\end{document}Δ-AEScore has an RMSE of 1.32 pK units and a Pearson’s correlation coefficient of 0.80 on the CASF-2016 benchmark, while retaining the docking and screening power of the underlying classical scoring function.

Compact atomic descriptors enable accurate predictions via linear models

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors.

Confronting pitfalls of AI-augmented molecular dynamics using statistical physics

Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.

Profiling SARS-CoV-2 Main Protease (MPRO) Binding to Repurposed Drugs Using Molecular Dynamics Simulations in Classical and Neural Network-Trained Force Fields

The current COVID-19 pandemic caused by a novel coronavirus SARS-CoV-2 urgently calls for a working therapeutic. Here, we report a computation-based workflow for efficiently selecting a subset of FDA-approved drugs that can potentially bind to the SARS-CoV-2 main protease MPRO. The workflow started with docking (using Autodock Vina) each of 1615 FDA-approved drugs to the MPRO active site. This step selected 62 candidates with docking energies lower than -8.5 kcal/mol. Then, the 62 docked protein-drug complexes were subjected to 100 ns of molecular dynamics (MD) simulations in a molecular mechanics (MM) force field (CHARMM36). This step reduced the candidate pool to 26, based on the root-mean-square-deviations (RMSDs) of the drug molecules in the trajectories. Finally, we modeled the 26 drug molecules by a pseudoquantum mechanical (ANI) force field and ran 5 ns hybrid ANI/MM MD simulations of the 26 protein-drug complexes. ANI was trained by neural network models on quantum mechanical density functional theory (wB97X/6-31G(d)) data points. An RMSD cutoff winnowed down the pool to 12, and free energy analysis (MM/PBSA) produced the final selection of 9 drugs: dihydroergotamine, midostaurin, ziprasidone, etoposide, apixaban, fluorescein, tadalafil, rolapitant, and palbociclib. Of these, three are found to be active in literature reports of experimental studies. To provide physical insight into their mechanism of action, the interactions of the drug molecules with the protein are presented as 2D-interaction maps. These findings and mappings of drug-protein interactions may be potentially used to guide rational drug discovery against COVID-19.

Deep Learning in Protein Structural Modeling and Design

Deep learning is catalyzing a scientific revolution fueled by big data, accessible toolkits, and powerful computational resources, impacting many fields, including protein structural modeling. Protein structural modeling, such as predicting structure from amino acid sequence and evolutionary information, designing proteins toward desirable functionality, or predicting properties or behavior of a protein, is critical to understand and engineer biological systems at the molecular level. In this review, we summarize the recent advances in applying deep learning techniques to tackle problems in protein structural modeling and design. We dissect the emerging approaches using deep learning techniques for protein structural modeling and discuss advances and challenges that must be addressed. We argue for the central importance of structure, following the "sequence → structure → function" paradigm. This review is directed to help both computational biologists to gain familiarity with the deep learning methods applied in protein modeling, and computer scientists to gain perspective on the biologically meaningful problems that may benefit from deep learning techniques.

Benchmarking Force Field and the ANI Neural Network Potentials for the Torsional Potential Energy Surface of Biaryl Drug Fragments

Many drug molecules contain biaryl fragments, resulting in a torsional barrier corresponding to rotation around the bond linking the aryls. The potential energy surfaces of these torsions vary significantly because of steric and electronic effects, ultimately affecting the relative stability of the molecular conformations in the protein-bound and solution states. Simulations of protein-ligand binding require accurate computational models to represent the intramolecular interactions to provide accurate predictions of the structure and dynamics of binding. In this article, we compare four force fields [generalized AMBER force field (GAFF), open force field (OpenFF), CHARMM general force field (CGenFF), optimized potentials for liquid simulations (OPLS)] and two neural network potentials (ANI-2x and ANI-1ccx) for their ability to predict the torsional potential energy surfaces of 88 biaryls extracted from drug fragments. The root mean square deviation (rmsd) over the full potential energy surface and the mean absolute deviation of the torsion rotational barrier height (MADB) relative to high-level ab initio reference data (CCSD(T1)*) were used as the measure of accuracy. Uncertainties in these metrics due to the composition of the data set were estimated using bootstrap analysis. In comparison to high-level ab initio data, ANI-1ccx was most accurate for predicting the barrier height (rmsd: 0.5 ± 0.0 kcal/mol, MADB: 0.8 ± 0.1 kcal/mol), followed closely by ANI-2x (rmsd: 0.5 ± 0.0 kcal/mol, MADB: 1.0 ± 0.2 kcal/mol), then CGenFF (rmsd: 0.8 ± 0.1 kcal/mol, MADB: 1.3 ± 0.1 kcal/mol) and OpenFF (rmsd: 0.7 ± 0.1 kcal/mol, MADB: 1.3 ± 0.1 kcal/mol), then GAFF (rmsd: 1.2 ± 0.2 kcal/mol, MADB: 2.6 ± 0.5 kcal/mol), and finally OPLS (rmsd: 3.6 ± 0.3 kcal/mol, MADB: 3.6 ± 0.3 kcal/mol). Significantly, the neural network potentials (NNPs) are systematically more accurate and more reliable than any of the force fields. As a practical example, the NNP/molecular mechanics method was used to simulate the isomerization of ozanimod, a drug used for multiple sclerosis. Multinanosecond molecular dynamics (MD) simulations in an explicit aqueous solvent were performed, as well as umbrella sampling and adaptive biasing force-enhanced sampling techniques. The rate constant for this isomerization calculated using transition state theory was 4.30 × 10^-1 ns^-1, which is consistent with direct MD simulations.

Flexible Fitting of Small Molecules into Electron Microscopy Maps Using Molecular Dynamics Simulations with Neural Network Potentials

Despite significant advances in resolution, the potential for cryo-electron microscopy (EM) to be used in determining the structures of protein-drug complexes remains unrealized. Determination of accurate structures and coordination of bound ligands necessitates simultaneous fitting of the models into the density envelopes, exhaustive sampling of the ligand geometries, and, most importantly, concomitant rearrangements in the side chains to optimize the binding energy changes. In this article, we present a flexible-fitting pipeline where molecular dynamics flexible fitting (MDFF) is used to refine structures of protein-ligand complexes from 3 to 5 Å electron density data. Enhanced sampling is employed to explore the binding pocket rearrangements. To provide a model that can accurately describe the conformational dynamics of the chemically diverse set of small-molecule drugs inside MDFF, we use QM/MM and neural-network potential (NNP)/MM models of protein-ligand complexes, where the ligand is represented using the QM or NNP model, and the protein is represented using established molecular mechanical force fields (e.g., CHARMM). This pipeline offers structures commensurate to or better than recently submitted high-resolution cryo-EM or X-ray models, even when given medium to low-resolution data as input. The use of the NNPs makes the algorithm more robust to the choice of search models, offering a radius of convergence of 6.5 Å for ligand structure determination. The quality of the predicted structures was also judged by density functional theory calculations of ligand strain energy. This strain potential energy is found to systematically decrease with better fitting to density and improved ligand coordination, indicating correct binding interactions. A computationally inexpensive protocol for computing strain energy is reported as part of the model analysis protocol that monitors both the ligand fit as well as model quality.

A machine learning based intramolecular potential for a flexible organic molecule

Here, we employ the kernel regression machine learning technique to construct an analytical potential that reproduces the quantum mechanical potential energy surface of a small, flexible, drug-like molecule, 3-(benzyloxy)pyridin-2-amine.