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

The evolution of machine learning potentials for molecules, reactions and materials

Recent years have witnessed the fast development of machine learning potentials (MLPs) and their widespread applications in chemistry, physics, and material science. By fitting discrete ab initio data faithfully to continuous and symmetry-preserving mathematical forms, MLPs have enabled accurate and efficient atomistic simulations in a large scale from first principles. In this review, we provide an overview of the evolution of MLPs in the past two decades and focus on the state-of-the-art MLPs proposed in the last a few years for molecules, reactions, and materials. We discuss some representative applications of MLPs and the trend of developing universal potentials across a variety of systems. Finally, we outline a list of open challenges and opportunities in the development and applications of MLPs.

Methods for Theoretical Treatment of Local Fields in Proteins and Enzymes

Electric fields generated by protein scaffolds are crucial in enzymatic catalysis. This review surveys theoretical approaches for detecting, analyzing, and comparing electric fields, electrostatic potentials, and their effects on the charge density within enzyme active sites. Pioneering methods like the empirical valence bond approach rely on evaluating ionic and covalent resonance forms influenced by the field. Strategies employing polarizable force fields also facilitate field detection. The vibrational Stark effect connects computational simulations to experimental Stark spectroscopy, enabling direct comparisons. We highlight how protein dynamics induce fluctuations in local fields, influencing enzyme activity. Recent techniques assess electric fields throughout the active site volume rather than only at specific bonds, and machine learning helps relate these global fields to reactivity. Quantum theory of atoms in molecules captures the entire electron density landscape, providing a chemically intuitive perspective on field-driven catalysis. Overall, these methodologies show protein-generated fields are highly dynamic and heterogeneous, and understanding both aspects is critical for elucidating enzyme mechanisms. This holistic view empowers rational enzyme engineering by tuning electric fields, promising new avenues in drug design, biocatalysis, and industrial applications. Future directions include incorporating electric fields as explicit design targets to enhance catalytic performance and biochemical functionalities.

From Ab Initio to Instrumentation: A Field Guide to Characterizing Multivalent Liquid Electrolytes

In this field guide, we outline empirical and theory-based approaches to characterize the fundamental properties of liquid multivalent-ion battery electrolytes, including (i) structure and chemistry, (ii) transport, and (iii) electrochemical properties. When detailed molecular-scale understanding of the multivalent electrolyte behavior is insufficient we use examples from well-studied lithium-ion electrolytes. In recognition that coupling empirical and theory-based techniques is highly effective, but often nontrivial, we also highlight recent electrolyte characterization efforts that uncover a more comprehensive and nuanced understanding of the underlying structures, processes, and reactions that drive performance and system-level behavior. We hope the insights from these discussions will guide the design of future electrolyte studies, accelerate development of next-generation multivalent-ion batteries through coupling of modeling with experiments, and help to avoid pitfalls and ensure reproducibility of modeling results.

Application of modern artificial intelligence techniques in the development of organic molecular force fields

The molecular force field (FF) determines the accuracy of molecular dynamics (MD) and is one of the major bottlenecks that limits the application of MD in molecular design. Recently, artificial intelligence (AI) techniques, such as machine-learning potentials (MLPs), have been rapidly reshaping the landscape of MD. Meanwhile, organic molecular systems feature unique characteristics, and require more careful treatment in both model construction, optimization, and validation. While an accurate and generic organic molecular force field is still missing, significant progress has been made with the facilitation of AI, warranting a promising future. In this review, we provide an overview of the various types of AI techniques used in molecular FF development and discuss both the advantages and weaknesses of these methodologies. We show how AI methods provide unprecedented capabilities in many tasks such as potential fitting, atom typification, and automatic optimization. Meanwhile, it is also worth noting that more efforts are needed to improve the transferability of the model, develop a more comprehensive database, and establish more standardized validation procedures. With these discussions, we hope to inspire more efforts to solve the existing problems, eventually leading to the birth of next-generation generic organic FFs.

Improved Description of Environment and Vibronic Effects with Electrostatically Embedded ML Potentials

Incorporation of environment and vibronic effects in simulations of optical spectra and excited state dynamics is commonly done by combining molecular dynamics with excited state calculations, which allows to estimate the spectral density describing the frequency-dependent system-bath coupling strength. The need for efficient sampling, however, usually leads to the adoption of classical force fields despite well-known inaccuracies due to the mismatch with the excited state method. Here, we present a multiscale strategy that overcomes this limitation by combining EMLE simulations based on electrostatically embedded ML potentials with the QM/MMPol polarizable embedding model to compute the excited states and spectral density of 3-methyl-indole, the chromophoric moiety of tryptophan that mediates a variety of important biological functions, in the gas phase, in water solution, and in the human serum albumin protein. Our protocol provides highly accurate results that faithfully reproduce their ab initio QM/MM counterparts, thus paving the way for accurate investigations on the interrelation between the time scales of biological motion and the photophysics of tryptophan and other biosystems.

ANI/EFP: Modeling Long-Range Interactions in ANI Neural Network with Effective Fragment Potentials

Deep learning Neural Networks (NN) have been developed in the field of molecular modeling for the purpose of circumventing the high computational cost of quantum-mechanical calculations while rivaling their accuracies. Although these networks have found great success, they generally lack the ability to accurately describe long-range interactions, which makes them unusable for extended molecular systems. Herein, we provide a method for partially retraining the deep learning general-use neural network ANI, in which the long-range interactions are represented via atomic electrostatic potentials. The electrostatic potentials, generated with polarizable effective fragment potentials (EFP), are used as an additional input feature for the network. This new ANI/EFP network can predict solute-solvent interaction energies on a trained data set with a kcal/mol accuracy. It also shows promise in predicting the interaction energies of a solute in solvent environments that have not been included in a training data set. The proposed protocol can be taken as an example and further developed, leading to highly accurate and transferable neural network potentials capable of handling long-range interactions and extended molecular systems.

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.

Advancing Force Fields Parameterization: A Directed Graph Attention Networks Approach

Force fields (FFs) are an established tool for simulating large and complex molecular systems. However, parametrizing FFs is a challenging and time-consuming task that relies on empirical heuristics, experimental data, and computational data. Recent efforts aim to automate the assignment of FF parameters using pre-existing databases and on-the-fly ab initio data. In this study, we propose a graph-based force field (GB-FFs) model to directly derive parameters for the Generalized Amber Force Field (GAFF) from chemical environments and research into the influence of functional forms. Our end-to-end parametrization approach predicts parameters by aggregating the basic information in directed molecular graphs, eliminating the need for expert-defined procedures and enhances the accuracy and transferability of GAFF across a broader range of molecular complexes. Simulation results are compared to the original GAFF parametrization. In practice, our results demonstrate an improved transferability of the model, showcasing its improved accuracy in modeling intermolecular and torsional interactions, as well as improved solvation free energies. The optimization approach developed in this work is fully applicable to other nonpolarizable FFs as well as to polarizable ones.

Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation

We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.

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.

From Organic Fragments to Photoswitchable Catalysts: The OFF-ON Structural Repository for Transferable Kernel-Based Potentials

Structurally and conformationally diverse databases are needed to train accurate neural networks or kernel-based potentials capable of exploring the complex free energy landscape of flexible functional organic molecules. Curating such databases for species beyond "simple" drug-like compounds or molecules composed of well-defined building blocks (e.g., peptides) is challenging as it requires thorough chemical space mapping and evaluation of both chemical and conformational diversities. Here, we introduce the OFF-ON (organic fragments from organocatalysts that are non-modular) database, a repository of 7869 equilibrium and 67,457 nonequilibrium geometries of organic compounds and dimers aimed at describing conformationally flexible functional organic molecules, with an emphasis on photoswitchable organocatalysts. The relevance of this database is then demonstrated by training a local kernel regression model on a low-cost semiempirical baseline and comparing it with a PBE0-D3 reference for several known catalysts, notably the free energy surfaces of exemplary photoswitchable organocatalysts. Our results demonstrate that the OFF-ON data set offers reliable predictions for simulating the conformational behavior of virtually any (photoswitchable) organocatalyst or organic compound composed of H, C, N, O, F, and S atoms, thereby opening a computationally feasible route to explore complex free energy surfaces in order to rationalize and predict catalytic behavior.

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.

Force-field-enhanced neural network interactions: from local equivariant embedding to atom-in-molecule properties and long-range effects

We introduce FENNIX (Force-Field-Enhanced Neural Network InteraXions), a hybrid approach between machine-learning and force-fields. We leverage state-of-the-art equivariant neural networks to predict local energy contributions and multiple atom-in-molecule properties that are then used as geometry-dependent parameters for physically-motivated energy terms which account for long-range electrostatics and dispersion. Using high-accuracy ab initio data (small organic molecules/dimers), we trained a first version of the model. Exhibiting accurate gas-phase energy predictions, FENNIX is transferable to the condensed phase. It is able to produce stable Molecular Dynamics simulations, including nuclear quantum effects, for water predicting accurate liquid properties. The extrapolating power of the hybrid physically-driven machine learning FENNIX approach is exemplified by computing: (i) the solvated alanine dipeptide free energy landscape; (ii) the reactive dissociation of small molecules.

Combining Force Fields and Neural Networks for an Accurate Representation of Chemically Diverse Molecular Interactions

A key goal of molecular modeling is the accurate reproduction of the true quantum mechanical potential energy of arbitrary molecular ensembles with a tractable classical approximation. The challenges are that analytical expressions found in general purpose force fields struggle to faithfully represent the intermolecular quantum potential energy surface at close distances and in strong interaction regimes; that the more accurate neural network approximations do not capture crucial physics concepts, e.g., nonadditive inductive contributions and application of electric fields; and that the ultra-accurate narrowly targeted models have difficulty generalizing to the entire chemical space. We therefore designed a hybrid wide-coverage intermolecular interaction model consisting of an analytically polarizable force field combined with a short-range neural network correction for the total intermolecular interaction energy. Here, we describe the methodology and apply the model to accurately determine the properties of water, the free energy of solvation of neutral and charged molecules, and the binding free energy of ligands to proteins. The correction is subtyped for distinct chemical species to match the underlying force field, to segment and reduce the amount of quantum training data, and to increase accuracy and computational speed. For the systems considered, the hybrid ab initio parametrized Hamiltonian reproduces the two-body dimer quantum mechanics (QM) energies to within 0.03 kcal/mol and the nonadditive many-molecule contributions to within 2%. Simulations of molecular systems using this interaction model run at speeds of several nanoseconds per day.

Computational Framework Combining Quantum Mechanics, Molecular Dynamics, and Deep Neural Networks to Evaluate the Intrinsic Properties of Materials

The design and evaluation of future nanomaterials with specific properties is a challenging task as the current traditional methods rely on trial and error approaches that are time-consuming and expensive. On the computational front, design tools such as molecular dynamics (MD) simulations help us reduce the costs and times. However, nonbonded potential parameters, the key input parameters for an MD simulation, are usually not available for designing and studying new materials. Resolving this, quantum mechanics (QM) calculations could be used to evaluate the system's energy as a function of the nonbonded distances, and the resulting data set could be fit to a generic potential equation to obtain the fitting constants (potential parameters). However, fitting this massive data set containing thousands of unknown parameters using traditional mathematical formulations is not feasible. Hence, most computational frameworks in the literature utilize several simplifications, leading to a severe loss of accuracy. Addressing this deficiency, in this work, we propose a multi-scale framework that couples QM calculations and MD with advanced deep neural networks to determine the potential parameters. This advanced framework has been extensively validated by employing it to predict properties such as the density, boiling point, and melting point of five different types of molecules that are well-understood, namely, the polar molecule H2O, ionic compound LiPF6, ethanol (C2H5OH), long-chain molecule C8H18, and the complex molecular system ethylene carbonate (EC).