The Polarizable Atomic Multipole-based AMOEBA Force Field for Proteins

Refinement of the Drude Polarizable Force Field for Hexose Monosaccharides: Capturing Ring Conformational Dynamics with Enhanced Accuracy

We present a revised version of the Drude polarizable carbohydrate force field (FF), focusing on refining the ring and exocyclic torsional parameters for hexopyranose monosaccharides. This refinement addresses the previously observed discrepancies between calculated and experimental NMR 3J coupling values, particularly in describing ring dynamics and exocyclic rotamer populations within major hexose monosaccharides and their anomers. Specifically, α-MAN, β-MAN, α-GLC, β-GLC, α-GAL, β-GAL, α-ALT, β-ALT, α-IDO, and β-IDO were targeted for optimization. The optimization process involved potential energy scans (PES) of the ring and exocyclic dihedral angles computed using quantum mechanical (QM) methods. The target data for the reoptimization included PES of the inner ring dihedrals (C1-C2-C3-C4, C2-C3-C4-C5, C5-O5-C1-C2, C4-C5-O5-C1, O5-C1-C2-C3, C3-C4-C5-O5) and the exocyclic torsions, other than the pseudo ring dihedrals (O1-C1-O5-C5, O2-C2-C1-O5, and O4-C4-C5-O5) and hydroxyl torsions used in the previous parametrization efforts. These parameters, in conjunction with previously developed Drude parameters for hexopyranose monosaccharides, were validated against experimental observations, including NMR data and conformational energetics, in aqueous environments. The resulting polarizable model is shown to be in good agreement with a range of QM data, experimental NMR data, and conformational energetics of monosaccharides in aqueous solutions. This offers a significant improvement of the Drude carbohydrate force field, wherein the refinement enhances the accuracy of accessing the conformational dynamics of carbohydrates in biomolecular simulations.

Synergistic Integration of Physical Embedding and Machine Learning Enabling Precise and Reliable Force Field

Machine-learning force fields have achieved significant strides in accurately reproducing the potential energy surface with quantum chemical accuracy. However, this approach still faces several challenges, e.g., extrapolating to uncharted chemical spaces, interpreting long-range electrostatics, and mapping complex macroscopic properties. To address these issues, we advocate for a synergistic integration of physical principles and machine learning techniques within the framework of a physically informed neural network (PINN). This approach involves incorporating physical knowledge into the parameters of the neural network, coupled with an efficient global optimizer, the Tabu-Adam algorithm, proposed in this work to augment optimization under strict physical constraint. We choose the AMOEBA+ force field as the physics-based model for embedding and then train and test it using the diethylene glycol dimethyl ether (DEGDME) data set as a case study. The results reveal a breakthrough in constructing a precise and noise-robust machine learning force field. Utilizing two training sets with hundreds of samples, our model exhibits remarkable generalization and density functional theory (DFT) accuracy in describing molecular interactions and enables a precise prediction of the macroscopic properties such as the diffusion coefficient with minimal cost. This work provides valuable insight into establishing a fundamental framework of the PINN force field.

Polarizable atomic multipole-based force field for cholesterol

Cholesterol is one of the essential component of lipid in membrane. We present a polarizable atomic multipole force field (FF) for the molecular dynamic simulation of cholesterol. The FF building process follows the computational framework as the atomic multipole optimized energetics for biomolecular applications (AMOEBA) model. In this framework, the electronics parameters, including atomic monopole moments, dipole moments, and quadrupole moments calculated from ab initio calculations in the gas phase, are applied to represent the charge distribution. Furthermore, the many-body polarization is modeled by following the same pattern of distributed atomic polarizabilities. Then, the bilayers composed of two typical phospholipid molecules, 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), in a range of different cholesterol concentrations are built and implemented by molecular dynamics (MD) simulations based on the proposed polarizable FF. The simulation results are statistically analyzed to validate the feasibility of the proposed FF. The structural properties of the bilayers are calculated to compare with the related experimental values. The MD values show the same trend of experimental values changes.Communicated by Ramaswamy H. Sarma.

Water-glycan interactions drive the SARS-CoV-2 spike dynamics: insights into glycan-gate control and camouflage mechanisms

To develop therapeutic strategies against COVID-19, we introduce a high-resolution all-atom polarizable model capturing many-body effects of protein, glycan, solvent, and membrane components in SARS-CoV-2 spike protein open and closed states. Employing μs-long molecular dynamics simulations powered by high-performance cloud-computing and unsupervised density-driven adaptive sampling, we investigated the differences in bulk-solvent-glycan and protein-solvent-glycan interfaces between these states. We unraveled a sophisticated solvent-glycan polarization interaction network involving the N165/N343 glycan-gate patterns that provide structural support for the open state and identified key water molecules that could potentially be targeted to destabilize this configuration. In the closed state, the reduced solvent polarization diminishes the overall N165/N343 dipoles, yet internal interactions and a reorganized sugar coat stabilize this state. Despite variations, our glycan-solvent accessibility analysis reveals the glycan shield capability to conserve constant interactions with the solvent, effectively camouflaging the virus from immune detection in both states. The presented insights advance our comprehension of viral pathogenesis at an atomic level, offering potential to combat COVID-19.

Conformation-Dependent Hydrogen-Bonding Interactions in a Switchable Artificial Metalloprotein

Hydrogen-bonding (H-bonding) interactions in metalloprotein active sites can critically regulate enzyme function. Changes in the protein structure triggered by interplay with substrates, products, and partner proteins are often translated to the metallocofactor by way of specific changes in H-bond networks connected to the active site. However, the complexities of metalloprotein architecture and mechanism often preclude our ability to define the precise molecular interactions giving rise to these intricate regulatory pathways. To address this shortcoming, we have developed conformationally switchable artificial metalloproteins (swArMs) in which allosteric Gln-binding triggers protein conformational changes that impact the microenvironment surrounding an installed metallocofactor. Herein, we report a combined structural, spectroscopic, and computational approach to enhance the conformation-dependent changes in H-bond interactions surrounding the metallocofactor site of a swArM. Structure-informed molecular dynamics simulations were employed to predict point mutations that could enhance active site H-bond interactions preferentially in the Gln-bound holo-conformation of the swArM. Testing our predictions via the unique infrared spectral signals associated with the metallocofactor site, we have identified three key residues capable of imparting conformational control over the metallocofactor microenvironment. The resultant swArMs not only model biologically relevant structural regulation but also provide an enhanced Gln-responsive biological probe to be leveraged in future biosensing applications.

Electronic Polarizability Tunes the Function of the Human Bestrophin 1 Cl- Channel

Mechanisms of anion permeation within ion channels and nanopores remain poorly understood. Recent cryo-electron microscopy structures of the human bestrophin 1 Cl- channel (hBest1) provide an opportunity to evaluate ion interactions predicted by molecular dynamics (MD) simulations against experimental observations. Here, we implement the fully polarizable forcefield AMOEBA in MD simulations on different conformations of hBest1. This forcefield models multipole moments up to the quadrupole; therefore, it captures induced dipole and anion-π interactions. We show that key biophysical properties of the channel can only be simulated when electronic polarization is included in the molecular models and that Cl- permeation through the neck of the pore is achieved through hydrophobic solvation concomitant with partial ion dehydration. Furthermore, we demonstrate how such polarizable simulations can help determine the identity of ion-like densities within high-resolution cryo-EM structures and that neglecting polarization places Cl- at positions that do not correspond with their experimentally resolved location. Overall, our results demonstrate the importance of including electronic polarization in realistic and physically accurate models of biological systems, especially channels and pores that selectively permeate anions.

Dynamic interchange between two protonation states is characteristic of active sites of cholinesterases

Cholinesterases are well-known and widely studied enzymes crucial to human health and involved in neurology, Alzheimer's, and lipid metabolism. The protonation pattern of active sites of cholinesterases influences all the chemical processes within, including reaction, covalent inhibition by nerve agents, and reactivation. Despite its significance, our comprehension of the fine structure of cholinesterases remains limited. In this study, we employed enhanced-sampling quantum-mechanical/molecular-mechanical calculations to show that cholinesterases predominantly operate as dynamic mixtures of two protonation states. The proton transfer between two non-catalytic glutamate residues follows the Grotthuss mechanism facilitated by a mediator water molecule. We show that this uncovered complexity of active sites presents a challenge for classical molecular dynamics simulations and calls for special treatment. The calculated proton transfer barrier of 1.65 kcal/mol initiates a discussion on the potential existence of two coupled low-barrier hydrogen bonds in the inhibited form of butyrylcholinesterase. These findings expand our understanding of structural features expressed by highly evolved enzymes and guide future advances in cholinesterase-related protein and drug design studies.

Quantifying Induced Dipole Effects in Small Molecule Permeation in a Model Phospholipid Bilayer

The cell membrane functions as a semipermeable barrier that governs the transport of materials into and out of cells. The bilayer features a distinct dielectric gradient due to the amphiphilic nature of its lipid components. This gradient influences various aspects of small molecule permeation and the folding and functioning of membrane proteins. Here, we employ polarizable molecular dynamics simulations to elucidate the impact of the electronic environment on the permeation process. We simulated eight distinct amino-acid side chain analogs within a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer using the Drude polarizable force field (FF). Our approach includes both unbiased and umbrella sampling simulations. By using a polarizable FF, we sought to investigate explicit dipole responses in relation to local electric fields along the membrane normal. We evaluate molecular dipole moments, which exhibit variation based on their localization within the membrane, and compare the outcomes with analogous simulations using the nonpolarizable CHARMM36 FF. This comparative analysis aims to discern characteristic differences in the free energy surfaces of permeation for the various amino-acid analogs. Our results provide the first systematic quantification of the impact of employing an explicitly polarizable FF in this context compared to the fixed-charge convention inherent to nonpolarizable FFs, which may not fully capture the influence of the membrane dielectric gradient.

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

Condensed Matter Systems Exposed to Radiation: Multiscale Theory, Simulations, and Experiment

This roadmap reviews the new, highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The Review highlights several recent advances in the field and provides a roadmap for the development of the field over the next decade. Condensed matter systems exposed to radiation can be inorganic, organic, or biological, finite or infinite, composed of different molecular species or materials, exist in different phases, and operate under different thermodynamic conditions. Many of the key phenomena related to the behavior of irradiated systems are very similar and can be understood based on the same fundamental theoretical principles and computational approaches. The multiscale nature of such phenomena requires the quantitative description of the radiation-induced effects occurring at different spatial and temporal scales, ranging from the atomic to the macroscopic, and the interlinks between such descriptions. The multiscale nature of the effects and the similarity of their manifestation in systems of different origins necessarily bring together different disciplines, such as physics, chemistry, biology, materials science, nanoscience, and biomedical research, demonstrating the numerous interlinks and commonalities between them. This research field is highly relevant to many novel and emerging technologies and medical applications.

Developing a Differentiable Long-Range Force Field for Proteins with E(3) Neural Network-Predicted Asymptotic Parameters

Accurately describing long-range interactions is a significant challenge in molecular dynamics (MD) simulations of proteins. High-quality long-range potential is also an important component of the range-separated machine learning force field. This study introduces a comprehensive asymptotic parameter database encompassing atomic multipole moments, polarizabilities, and dispersion coefficients. Leveraging active learning, our database comprehensively represents protein fragments with up to 8 heavy atoms, capturing their conformational diversity with merely 78,000 data points. Additionally, the E(3) neural network (E3NN) is employed to predict the asymptotic parameters directly from the local geometry. The E3NN models demonstrate exceptional accuracy and transferability across all asymptotic parameters, achieving an R2 of 0.999 for both protein fragments and 20 amino acid dipeptide test sets. The long-range electrostatic and dispersion energies can be obtained using the E3NN-predicted parameters, with an error of 0.07 and 0.02 kcal/mol, respectively, when compared to symmetry-adapted perturbation theory (SAPT). Therefore, our force fields demonstrate the capability to accurately describe long-range interactions in proteins, paving the way for next-generation protein force fields.

Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment

Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid-base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.

Intrinsic Conformational Dynamics of Glycine and Alanine in Polarizable Molecular Dynamics Force Fields: Comparison to Spectroscopic Data

Molecular dynamics (MD) is a great tool for elucidating conformational dynamics of proteins and peptides in water at the atomistic level that often surpasses the level of detail available experimentally. Structure predictions, however, are limited by the accuracy of the underlying MD force field. This limitation is particularly stark in the case of intrinsically disordered peptides and proteins, which are characterized by solvent-accessible and disordered peptide regions and domains. Recent studies show that most additive MD force fields, including CHARMM36m, do not reproduce the intrinsic conformational distributions of guest amino acid residues x in cationic GxG peptides in water in line with experimental data. Positing that a lack of polarizability in additive MD force fields may be the culprit for the reported discrepancies, we here examine the conformational dynamics of guest glycine and alanine residues in cationic GxG peptides in water using two polarizable MD force fields, CHARMM Drude and AMOEBA. Our results indicate that while AMOEBA captures the experimental data better than CHARMM Drude, neither of the two polarizable force fields offers an improvement of the Ramachandran distributions of glycine and alanine residues in cationic GGG and GAG peptides, respectively, over CHARMM36m.

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.

Exploring Biomolecular Conformational Dynamics with Polarizable Force Field AMOEBA and Enhanced Sampling Method Milestoning

Conformational dynamics play a crucial role in determining the behavior of the biomolecules. Polarizable force fields, such as AMOEBA, can accurately capture electrostatic interactions underlying the conformational space. However, applying a polarizable force field in molecular dynamics (MD) simulations can be computationally expensive, especially in studying long-time-scale dynamics. To overcome this challenge, we incorporated the AMOEBA potential with Milestoning, an enhanced sampling method in this work. This integration allows us to efficiently sample the rare and important conformational states of a biomolecule by using many short and independent molecular dynamics trajectories with the AMOEBA force field. We applied this method to investigate the conformational dynamics of alanine dipeptide, DNA, and RNA A-B form conversion. Well-converged thermodynamic and kinetic properties were obtained, including the free energy difference, mean first passage time, and critical transitions between states. Our results demonstrate the power of integrating polarizable force fields with enhanced sampling methods in quantifying the thermodynamic and kinetic properties of biomolecules at the atomic level.

Evaluating aliphatic CF, CF2, and CF3 groups as vibrational Stark effect reporters

Given the extensive use of fluorination in molecular design, it is imperative to understand the solvation properties of fluorinated compounds and the impact of the C-F bond on electrostatic interactions. Vibrational spectroscopy can provide direct insights into these interactions by using the C-F bond stretching [v(C-F)] as an electric field probe through the vibrational Stark effect (VSE). In this work, we explore the VSE of the three basic patterns of aliphatic fluorination, i.e., mono-, di-, and trifluorination in CF, CF2, and CF3 groups, respectively, and compare their response to the well-studied aromatic v(C-F). Magnitudes (i.e., Stark tuning rates) and orientations of the difference dipole vectors of the v(C-F)-containing normal modes were determined using density functional theory and a molecular dynamics (MD)-assisted solvatochromic analysis of model compounds in solvents of varying polarity. We obtain Stark tuning rates of 0.2-0.8 cm-1/(MV/cm), with smallest and largest electric field sensitivities for CFaliphatic and CF3,aliphatic, respectively. While average electric fields of solvation were oriented along the main symmetry axis of the CFn, and thus along its static dipole, the Stark tuning rate vectors were tilted by up to 87° potentially enabling to map electrostatics in multiple dimensions. We discuss the influence of conformational heterogeneity on spectral shifts and point out the importance of multipolar and/or polarizable MD force fields to describe the electrostatics of fluorinated molecules. The implications of this work are of direct relevance for studies of fluorinated molecules as found in pharmaceuticals, fluorinated peptides, and proteins.

Evaluating Polarizable Biomembrane Simulations against Experiments

Owing to the increase of available computational capabilities and the potential for providing a more accurate description, polarizable molecular dynamics force fields are gaining popularity in modeling biomolecular systems. It is, however, crucial to evaluate how much precision is truly gained with increasing cost and complexity of the simulation. Here, we leverage the NMRlipids open collaboration and Databank to assess the performance of available polarizable lipid models─the CHARMM-Drude and the AMOEBA-based parameters─against high-fidelity experimental data and compare them to the top-performing nonpolarizable models. While some improvement in the description of ion binding to membranes is observed in the most recent CHARMM-Drude parameters, and the conformational dynamics of AMOEBA-based parameters are excellent, the best nonpolarizable models tend to outperform their polarizable counterparts for each property we explored. The identified shortcomings range from inaccuracies in describing the conformational space of lipids to excessively slow conformational dynamics. Our results provide valuable insights for the further refinement of polarizable lipid force fields and for selecting the best simulation parameters for specific applications.

Impact of an Ionic Liquid Solution on Horseradish Peroxidase Activity

Horseradish peroxidase (HRP) is an enzyme that oxidizes pollutants from wastewater. A previous report indicated that peroxidases can have an enhancement in initial enzymatic activity in an aqueous solution of 0.26 M 1-ethyl-3-methylimidazolium ethyl sulfate ([EMIm][EtSO4]) at neutral pH. However, the atomistic details remain elusive. In the enzymatic landscape of HRP, compound II (Cpd II) plays a key role and involves a histidine (H42) residue. Cpd II exists as oxoferryl (2a) or hydroxoferryl (2b(FeIV)) forms, where 2a is the predominantly observed form in experimental studies. Intriguingly, the ferric 2b(FeIII) form seen in synthetic complexes has not been observed in HRP. Here, we have investigated the structure and dynamics of HRP in pure water and aqueous [EMIm][EtSO4] (0.26 M), as well as the reaction mechanism of 2a to 2b conversion using polarizable molecular dynamics (MD) simulations and quantum mechanics/molecular mechanics (QM/MM) calculations. When HRP is solvated in aq [EMIm][EtSO4], the catalytic water displaces, and H42 directly orients over the ferryl moiety, allowing a direct proton transfer (PT) with a significant energy barrier reduction. Conversely, in neat water, the reaction of 2a to 2b follows the previously reported mechanism. We further investigated the deprotonated form of H42. Analysis of the electric fields at the active site indicates that the aq [EMIm][EtSO4] medium facilitates the reaction by providing a more favorable environment compared with the system solvated in neat water. Overall, the atomic level supports the previous experimental observations and underscores the importance of favorable electric fields in the active site to promote catalysis.

Seamless integration of GEM, a density based-force field, for QM/MM simulations via LICHEM, Psi4, and Tinker-HP

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations have become an essential tool in computational chemistry, particularly for analyzing complex biological and condensed phase systems. Building on this foundation, our work presents a novel implementation of the Gaussian Electrostatic Model (GEM), a polarizable density-based force field, within the QM/MM framework. This advancement provides seamless integration, enabling efficient and optimized QM/GEM calculations in a single step using the LICHEM Code. We have successfully applied our implementation to water dimers and hexamers, demonstrating the ability to handle water systems with varying numbers of water molecules. Moreover, we have extended the application to describe the double proton transfer of the aspartic acid dimer in a box of water, which highlights the method's proficiency in investigating heterogeneous systems. Our implementation offers the flexibility to perform on-the-fly density fitting or to utilize pre-fitted coefficients to estimate exchange and Coulomb contributions. This flexibility enhances efficiency and accuracy in modeling molecular interactions, especially in systems where polarization effects are significant.

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.

QM/MM-Based Energy Decomposition Analysis Method for Large Systems

In this work, a QM/MM-based EDA method, called GKS-EDA(QM/MM), is proposed. As an extension of GKS-EDA, this scheme divides the total interaction energy into electrostatic, exchange-repulsion, polarization, and correlation/dispersion terms. GKS-EDA(QM/MM) can be applied to describe the interactions of large-scale systems combined with various QM/MM platforms. By using the examples of a hydrated hydronium ion complex in water solution, the barnase-barstar complex, and MMP-13-pyrimidinetrione in a metalloprotein, the capability of GKS-EDA(QM/MM) for various interactions in large systems is validated.

Vibrational Circular Dichroism Spectroscopy with a Classical Polarizable Force Field: Alanine in the Gas and Condensed Phases

Polarizable force fields are an essential component for the chemically accurate modeling of complex molecular systems with a significant degree of fluxionality, beyond harmonic or perturbative approximations. In this contribution we examine the performance of such an approach for the vibrational spectroscopy of the alanine amino acid, in the gas and condensed phases, from the Fourier transform of appropriate time correlation functions generated along molecular dynamics (MD) trajectories. While the infrared (IR) spectrum only requires the electric dipole moment, the vibrational circular dichroism (VCD) spectrum further requires knowledge of the magnetic dipole moment, for which we provide relevant expressions to be used with polarizable force fields. The AMOEBA force field was employed here to model alanine in the neutral and zwitterionic isolated forms, solvated by water or nitrogen, and as a crystal. Within this framework, comparison of the electric and magnetic dipole moments to those obtained with nuclear velocity perturbation theory based on density-functional theory for the same MD trajectories are found to agree well with one another. The statistical convergence of the IR and VCD spectra is examined and found to be more demanding in the latter case. Comparisons with experimental frequencies are also provided for the condensed phases.

Constant-pH Simulations with the Polarizable Atomic Multipole AMOEBA Force Field

Accurately predicting protein behavior across diverse pH environments remains a significant challenge in biomolecular simulations. Existing constant-pH molecular dynamics (CpHMD) algorithms are limited to fixed-charge force fields, hindering their application to biomolecular systems described by permanent atomic multipoles or induced dipoles. This work overcomes these limitations by introducing the first polarizable CpHMD algorithm in the context of the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. Additionally, our implementation in the open-source Force Field X (FFX) software has the unique ability to handle titration state changes for crystalline systems including flexible support for all 230 space groups. The evaluation of constant-pH molecular dynamics (CpHMD) with the AMOEBA force field was performed on 11 crystalline peptide systems that span the titrating amino acids (Asp, Glu, His, Lys, and Cys). Titration states were correctly predicted for 15 out of the 16 amino acids present in the 11 systems, including for the coordination of Zn2+ by cysteines. The lone exception was for a HIS-ALA peptide where CpHMD predicted both neutral histidine tautomers to be equally populated, whereas the experimental model did not consider multiple conformers and diffraction data are unavailable for rerefinement. This work demonstrates the promise polarizable CpHMD simulations for pKa predictions, the study of biochemical mechanisms such as the catalytic triad of proteases, and for improved protein-ligand binding affinity accuracy in the context of pharmaceutical lead optimization.

The OpenMMPol library for polarizable QM/MM calculations of properties and dynamics

We present a new library designed to provide a simple and straightforward way to implement QM/AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) and other polarizable QM/MM (Molecular Mechanics) methods based on induced point dipoles. The library, herein referred to as OpenMMPol, is free and open-sourced and is engineered to address the increasing demand for accurate and efficient QM/MM simulations. OpenMMPol is specifically designed to allow polarizable QM/MM calculations of ground state energies and gradients and excitation properties. Key features of OpenMMPol include a modular architecture facilitating extensibility, parallel computing capabilities for enhanced performance on modern cluster architectures, a user-friendly interface for intuitive implementation, and a simple and flexible structure for providing input data. To show the capabilities offered by the library, we present an interface with PySCF to perform QM/AMOEBA molecular dynamics, geometry optimization, and excited-state calculation based on (time-dependent) density functional theory.

Relative cooperativity in neutral and charged molecular clusters using QM/MM calculations

QM/MM methods have been used to study electronic structure properties and chemical reactivity in complex molecular systems where direct electronic structure calculations are not feasible. In our previous work, we showed that non-polarizable force fields, by design, describe intermolecular interactions through pairwise interactions, overlooking many-body interactions involving three or more particles. In contrast, polarizable force fields account partially for many-body effects through polarization, but still handle van der Waals and permanent electrostatic interactions pairwise. We showed that despite those limitations, polarizable and non-polarizable force fields can reproduce relative cooperativity achieved using density functional theory due to error compensation mechanisms. In this contribution, we assess the performance of QM/MM methods in reproducing these phenomena. Our study highlights the significance of the QM region size and force field choice in QM/MM calculations, emphasizing the importance of parameter validation to obtain accurate interaction energy predictions.

Type Label Framework for Bonded Force Fields in LAMMPS

New functionality is added to the LAMMPS molecular simulation package, which increases the versatility with which LAMMPS can interface with supporting software and manipulate information associated with bonded force fields. We introduce the "type label" framework that allows atom types and their higher-order interactions (bonds, angles, dihedrals, and impropers) to be represented in terms of the standard atom type strings of a bonded force field. Type labels increase the human readability of input files, enable bonded force fields to be supported by the OpenKIM repository, simplify the creation of reaction templates for the REACTER protocol, and increase compatibility with external visualization tools, such as VMD and OVITO. An introductory primer on the forms and use of bonded force fields is provided to motivate this new functionality and serve as an entry point for LAMMPS and OpenKIM users unfamiliar with bonded force fields. The type label framework has the potential to streamline modeling workflows that use LAMMPS by increasing the portability of software, files, and scripts for preprocessing, running, and postprocessing a molecular simulation.

Solvation of Model Biomolecules in Choline-Aminoate Ionic Liquids: A Computational Simulation Using Polarizable Force Fields

One can foresee a very near future where ionic liquids will be used in applications such as biomolecular chemistry or medicine. The molecular details of their interaction with biological matter, however, are difficult to investigate due to the vast number of combinations of both the biological systems and the variety of possible liquids. Here, we provide a computational study aimed at understanding the interaction of a special class of biocompatible ionic liquids (choline-aminoate) with two model biological systems: an oligopeptide and an oligonucleotide. We employed molecular dynamics with a polarizable force field. Our results are in line with previous experimental and computational evidence on analogous systems and show how these biocompatible ionic liquids, in their pure form, act as gentle solvents for protein structures while simultaneously destabilizing DNA structure.

Unraveling Water Solvation Effects with Quantum Mechanics/Molecular Mechanics Semiclassical Vibrational Spectroscopy: The Case of Thymidine

We introduce a quantum mechanics/molecular mechanics semiclassical method for studying the solvation process of molecules in water at the nuclear quantum mechanical level with atomistic detail. We employ it in vibrational spectroscopy calculations because this is a tool that is very sensitive to the molecular environment. Specifically, we look at the vibrational spectroscopy of thymidine in liquid water. We find that the C═O frequency red shift and the C═C frequency blue shift, experienced by thymidyne upon solvation, are mainly due to reciprocal polarization effects, that the molecule and the water solvent exert on each other, and nuclear zero-point energy effects. In general, this work provides an accurate and practical tool to study quantum vibrational spectroscopy in solution and condensed phase, incorporating high-level and computationally affordable descriptions of both electronic and nuclear problems.

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.

Critical Evaluation of Polarizable and Nonpolarizable Force Fields for Proteins Using Experimentally Derived Nitrile Electric Fields

Molecular dynamics (MD) simulations are frequently carried out for proteins to investigate the role of electrostatics in their biological function. The choice of force field (FF) can significantly alter the MD results, as the simulated local electrostatic interactions lack benchmarking in the absence of appropriate experimental methods. We recently reported that the transition dipole moment (TDM) of the popular nitrile vibrational probe varies linearly with the environmental electric field, overcoming well-known hydrogen bonding (H-bonding) issues for the nitrile frequency and, thus, enabling the unambiguous measurement of electric fields in proteins (J. Am. Chem. Soc. 2022, 144 (17), 7562-7567). Herein, we utilize this new strategy to enable comparisons of experimental and simulated electric fields in protein environments. Specifically, previously determined TDM electric fields exerted onto nitrile-containing o-cyanophenylalanine residues in photoactive yellow protein are compared with MD electric fields from the fixed-charge AMBER FF and the polarizable AMOEBA FF. We observe that the electric field distributions for H-bonding nitriles are substantially affected by the choice of FF. As such, AMBER underestimates electric fields for nitriles experiencing moderate field strengths; in contrast, AMOEBA robustly recapitulates the TDM electric fields. The FF dependence of the electric fields can be partly explained by the presence of additional negative charge density along the nitrile bond axis in AMOEBA, which is due to the inclusion of higher-order multipole parameters; this, in turn, begets more head-on nitrile H-bonds. We conclude by discussing the implications of the FF dependence for the simulation of nitriles and proteins in general.

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features in simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations with only a modest increase in cost.

Cooperativity and Frustration Effects (or Lack Thereof) in Polarizable and Non-polarizable Force Fields

Understanding cooperativity and frustration is crucial for studying biological processes such as molecular recognition and protein aggregation. Force fields have been extensively utilized to explore cooperativity in the formation of protein secondary structures and self-assembled systems. Multiple studies have demonstrated that polarizable force fields provide more accurate descriptions of this phenomenon compared to fixed-charge pairwise nonpolarizable force fields, thanks to the incorporation of polarization effects. In this study, we assess the performance of the AMOEBA polarizable force field and the AMBER and OPLS nonpolarizable pairwise force fields in capturing positive and negative cooperativity recently explored in neutral and charged molecular clusters using density functional theory. Our findings show that polarizable and nonpolarizable force fields qualitatively reproduce the relative cooperativity observed in electron structure calculations. However, AMBER and OPLS fail to describe absolute cooperativity. In contrast, AMOEBA accounts for the absolute cooperativity by considering interactions beyond pairwise interactions. According to the energy decomposition analysis, it is observed that the electrostatic interactions calculated with the AMBER and OPLS force fields seem to play an important and counterintuitive role in reproducing the adiabatic interaction energies calculated with density functional theory. However, it is important to note that these force fields, due to their nature, do not explicitly incorporate many-body effects, which limits their ability to accurately describe cooperativity. On the other hand, frustration in polarizable and nonpolarizable force fields is caused by changes in bond stretching and angle bending terms of the building blocks when they are forming a complex.

Application of the FFLUX Force Field to Molecular Crystals: A Study of Formamide

In this work, we present the first application of the quantum chemical topology force field FFLUX to the solid state. FFLUX utilizes Gaussian process regression machine learning models trained on data from the interacting quantum atom partitioning scheme to predict atomic energies and flexible multipole moments that change with geometry. Here, the ambient (α) and high-pressure (β) polymorphs of formamide are used as test systems and optimized using FFLUX. Optimizing the structures with increasing multipolar ranks indicates that the lattice parameters of the α phase differ by less than 5% to the experimental structure when multipole moments up to the quadrupole are used. These differences are found to be in line with the dispersion-corrected density functional theory. Lattice dynamics calculations are also found to be possible using FFLUX, yielding harmonic phonon spectra comparable to dispersion-corrected DFT while enabling larger supercells to be considered than is typically possible with first-principles calculations. These promising results indicate that FFLUX can be used to accurately determine properties of molecular solids that are difficult to access using DFT, including the structural dynamics, free energies, and properties at finite temperature.

Structure and Dynamics of Confined Water Inside Diphenylalanine Peptide Nanotubes

Diphenylalanine (FF) peptides exhibit a unique ability to self-assemble into nanotubes with confined water molecules playing pivotal roles in their structure and function. This study investigates the structure and dynamics of diphenylalanine peptide nanotubes (FFPNTs) using all-atom molecular dynamics (MD) and grand canonical Monte Carlo combined with MD (GCMC/MD) simulations with both the CHARMM additive and Drude polarizable force fields. The occupancy and dynamics of confined water molecules were also examined. It was found that less than 2 confined water molecules per FF help stabilize the FFPNTs on the x-y plane. Analyses of the kinetics of confined water molecules revealed distinctive transport behaviors for bound and free water, and their respective diffusion coefficients were compared. Our results validate the importance of polarizable force field models in studying peptide nanotubes and provide insights into our understanding of nanoconfined water.

From bonds to interactions: comprehensive molecular characterization via polarizable bond-dipole approach

Accurately characterizing molecular interactions stands as a pivotal requirement for ensuring the reliability of molecular dynamics simulations. In line with our bond-dipole-based interaction model proposed by Gao et al. [X.-C. Gao, Q. Hao and C.-S. Wang, J. Chem. Theory Comput., 2017, 13, 2730-2741.], we have implemented an efficient and concise approach to compute electrostatic potential. This methodology capitalizes on the polarizable nature of chemical bond dipoles, resulting in a model of remarkable simplicity. In this study, we have revised the polarizable bond-dipole-based force field (PBFF) through the meticulous curation of quantum chemical data sets. These data sets encompass a comprehensive collection of 40 000 conformations, including those of water, methylamine, methanol, and N-methylacetamide. Additionally, we incorporate 520 hydrogen-bonded dimers into our data sets. In pursuit of enhanced accuracy in molecular dynamics simulations and a more faithful representation of potential energy landscapes, we undertook the re-optimization of the nonbonded parameters within the PBFF framework. Concurrently, we intricately fine-tuned the bonded parameters. The results of our comprehensive evaluation denote that this newly optimized force field method adeptly and efficiently computes structural characteristics, harmonic frequencies, and interaction energies. Overall, this study provides further validation for the applicability of PBFF in molecular dynamics simulations.

The effect of the electronic structure method and basis set on the accuracy of the electric multipoles computed with the distributed multipole analysis (DMA)

CONTEXT

An accurate description of the molecular charge density is crucial for investigating intra- and inter-molecular properties. Among the different ways of describing and analyzing it, the widely used distributed multipole analysis (DMA) is an accurate method for decomposing the molecular charge density into atom-centered electric multipoles (monopole, dipole, quadrupole, and so on) that have a direct chemical interpretation. In this work, DMA was employed to decompose the molecular charge density of six chemically distinct molecules, namely, (2R)-2-amino-3-[(S)-prop-2-enylsulfinyl] propanoic acid (AAP), 4-amine-2-nitro-1,3,5 triazole (ANTA), (RS)-Propan-2-yl methylphosphonofluoridate (SARIN), chloromethane (CLMET), and 2-aminoacetic acid (GLY) into monopole, dipole, and quadrupole values. A hypothetical variation of ANTA built by exchanging all the nitrogen atoms with phosphorus that we named 4-phosphine-2-phosphite-1,3,5-phosphorine (ANTAP) was also studied. These molecules have different chemical structures bearing distinct carbon skeletons, electronegative atoms, and electron-withdrawing/donating groups. We found that although DFT multipole values can depend considerably on the exchange-correlation functional for specific atomic sites, the associated root-mean-square errors (RMSEs) compared to benchmark MP4 mainly were about [Formula: see text] The most significant variations were for monopoles and dipoles of sites highly polarized by adjacent atoms, and to a lesser degree, for the quadrupoles. The double hybrid B2PLYP and the hybrid meta M06-2X functionals, as expected in the framework of Jacob's ladder, overall give the most accurate results among the DFT methods. The MP2 DMA multipole values have an RMSE in relation to the MP4 benchmark mainly in the range [Formula: see text], thus representing a lower computational cost to obtain results with similar good accuracy without the ambiguity of choosing a DFT functional. The deviations of the HF multipoles from the benchmark in most cases were less than 20%, in agreement with the well-known fact that non-correlated charge densities have a slight dependence on the electronic correlation. We also confirmed that DMA values have a small dependence on the size of the basis set: deviations did not exceed 5% in most cases. However, the dependence of the DMA values on the size of the basis set increases with the rank of the electric multipole. To compute accurate values of DMA multipoles of an atom bonded to very electronegative atoms, especially dipoles and quadrupoles, a large basis set including diffuse functions is necessary. Despite that, for a given polarized basis set, the choice of the basis set to compute accurate DMA multipole values is not critical.

METHODS

The molecular charge densities were computed using the electronic structure methods Hartree-Fock (HF), MP2, MP4, DFT/PBE, DFT/B3LYP, DFT/B3PW91, DFT/M06-2X, and DFT/B2PLYP implemented in the Gaussian 09 package. MP4 was the benchmark method. The DMA multipoles were obtained with the GDMA program of Stone. The 6-311G +  + (d,p) basis set was used for the production calculations, and the augmented correlation-consistent Dunning's hierarchy of basis sets was employed to evaluate the dependence of the DMA multipoles on the basis set size.

Crystallization of FAPbI3: Polytypes and stacking faults

Molecular dynamics simulations are performed to study the crystallization of formamidinium lead iodide. From all-atom simulations of the crystal growth process and the δ-α-phase transitions, we try to reveal the formation of various stack-faulted intermediate defected structures and report various polytypes of formamidinium lead iodide that are observed from simulations.

Perspectives on Ligand/Protein Binding Kinetics Simulations: Force Fields, Machine Learning, Sampling, and User-Friendliness

Computational techniques applied to drug discovery have gained considerable popularity for their ability to filter potentially active drugs from inactive ones, reducing the time scale and costs of preclinical investigations. The main focus of these studies has historically been the search for compounds endowed with high affinity for a specific molecular target to ensure the formation of stable and long-lasting complexes. Recent evidence has also correlated the in vivo drug efficacy with its binding kinetics, thus opening new fascinating scenarios for ligand/protein binding kinetic simulations in drug discovery. The present article examines the state of the art in the field, providing a brief summary of the most popular and advanced ligand/protein binding kinetics techniques and evaluating their current limitations and the potential solutions to reach more accurate kinetic models. Particular emphasis is put on the need for a paradigm change in the present methodologies toward ligand and protein parametrization, the force field problem, characterization of the transition states, the sampling issue, and algorithms' performance, user-friendliness, and data openness.

Assessment of an Electrostatic Energy-Based Charge Model for Modeling the Electrostatic Interactions in Water Solvent

The protein force field based on the restrained electrostatic potential (RESP) charges has limitations in accurately describing hydrogen bonding interactions in proteins. To address this issue, we propose an alternative approach called the electrostatic energy-based charges (EEC) model, which shows improved performance in describing electrostatic interactions (EIs) of hydrogen bonds in proteins. In this study, we further investigate the performance of the EEC model in modeling EIs in water solvent. Our findings demonstrate that the fixed EEC model can effectively reproduce the quantum mechanics/molecular mechanics (QM/MM)-calculated EIs between a water molecule and various water solvent environments. However, to achieve the same level of computational accuracy, the electrostatic potential (ESP) charge model needs to fluctuate according to the electrostatic environment. Our analysis indicates that the requirement for charge adjustments depends on the specific mathematical and physical representation of EIs as a function of the environment for deriving charges. By comparing with widely used empirical water models calibrated to reproduce experimental properties, we confirm that the performance of the EEC model in reproducing QM/MM EIs is similar to that of general purpose TIP4P-like water models such as TIP4P-Ew and TIP4P/2005. When comparing the computed 10,000 distinct EI values within the range of -40 to 0 kcal/mol with the QM/MM results calculated at the MP2/aug-cc-pVQZ/TIP3P level, we noticed that the mean unsigned error (MUE) for the EEC model is merely 0.487 kcal/mol, which is remarkably similar to the MUE values of the TIP4P-Ew (0.63 kcal/mol) and TIP4P/2005 (0.579 kcal/mol) models. However, both the RESP method and the TIP3P model exhibit a tendency to overestimate the EIs, as evidenced by their higher MUE values of 1.761 and 1.293 kcal/mol, respectively. EEC-based molecular dynamics simulations have demonstrated that, when combined with appropriate van der Waals parameters, the EEC model can closely reproduce oxygen-oxygen radial distribution function and density of water, showing a remarkable similarity to the well-established TIP4P-like empirical water models. Our results demonstrate that the EEC model has the potential to build force fields with comparable accuracy to more sophisticated empirical TIP4P-like water models.

DMFF: An Open-Source Automatic Differentiable Platform for Molecular Force Field Development and Molecular Dynamics Simulation

In the simulation of molecular systems, the underlying force field (FF) model plays an extremely important role in determining the reliability of the simulation. However, the quality of the state-of-the-art molecular force fields is still unsatisfactory in many cases, and the FF parameterization process largely relies on human experience, which is not scalable. To address this issue, we introduce DMFF, an open-source molecular FF development platform based on an automatic differentiation technique. DMFF serves as a powerful tool for both top-down and bottom-up FF development. Using DMFF, both energies/forces and thermodynamic quantities such as ensemble averages and free energies can be evaluated in a differentiable way, realizing an automatic, yet highly flexible FF optimization workflow. DMFF also eases the evaluation of forces and virial tensors for complicated advanced FFs, helping the fast validation of new models in molecular dynamics simulation. DMFF has been released as an open-source package under the LGPL-3.0 license and is available at https://github.com/deepmodeling/DMFF.

Polarizability Plays a Decisive Role in Modulating Association between Molecular Cations and Anions

Electrostatic interactions involving proteins depend on not only the ionic charges involved but also their chemical identities. Here we examine the origins of incompletely understood differences in the strength of association of different pairs of monovalent molecular ions that are relevant to protein-protein and protein-ligand interactions. Cationic analogues of the basic amino acid side chains are simulated, along with oxyanionic analogues of cation-exchange ligands and acidic amino acids. Experimentally observed association trends with respect to the cations, but not anions, are captured by a nonpolarizable model. An effective continuum correction to account for electronic polarizability can capture both trends better but at the expense of fidelity to the underlying free energy landscape for ion-pair association. A polarizable model proves decisive in capturing experimentally suggested trends with respect to both cations and anions; critically, the free energy landscape for ion-pair association is itself altered, thus altering configurational sampling.

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

Toward a general neural network force field for protein simulations: Refining the intramolecular interaction in protein

Molecular dynamics (MD) is an extremely powerful, highly effective, and widely used approach to understanding the nature of chemical processes in atomic details for proteins. The accuracy of results from MD simulations is highly dependent on force fields. Currently, molecular mechanical (MM) force fields are mainly utilized in MD simulations because of their low computational cost. Quantum mechanical (QM) calculation has high accuracy, but it is exceedingly time consuming for protein simulations. Machine learning (ML) provides the capability for generating accurate potential at the QM level without increasing much computational effort for specific systems that can be studied at the QM level. However, the construction of general machine learned force fields, needed for broad applications and large and complex systems, is still challenging. Here, general and transferable neural network (NN) force fields based on CHARMM force fields, named CHARMM-NN, are constructed for proteins by training NN models on 27 fragments partitioned from the residue-based systematic molecular fragmentation (rSMF) method. The NN for each fragment is based on atom types and uses new input features that are similar to MM inputs, including bonds, angles, dihedrals, and non-bonded terms, which enhance the compatibility of CHARMM-NN to MM MD and enable the implementation of CHARMM-NN force fields in different MD programs. While the main part of the energy of the protein is based on rSMF and NN, the nonbonded interactions between the fragments and with water are taken from the CHARMM force field through mechanical embedding. The validations of the method for dipeptides on geometric data, relative potential energies, and structural reorganization energies demonstrate that the CHARMM-NN local minima on the potential energy surface are very accurate approximations to QM, showing the success of CHARMM-NN for bonded interactions. However, the MD simulations on peptides and proteins indicate that more accurate methods to represent protein-water interactions in fragments and non-bonded interactions between fragments should be considered in the future improvement of CHARMM-NN, which can increase the accuracy of approximation beyond the current mechanical embedding QM/MM level.

AMOEBA Force Field Predicts Accurate Hydrogen Bond Counts of Nitriles in SNase by Revealing Water-Protein Interaction in Vibrational Absorption Frequencies

Precisely quantifying the magnitude and direction of electric fields in proteins has long been an outstanding challenge in understanding biological functions. Nitrile vibrational Stark effect probes have been shown to be minimally disruptive to the protein structure and can be better direct reporters of local electrostatic field in the native state of a protein than other measures such as pKa shifts of titratable residues. However, interpretations of the connection between measured vibrational energy and electric field rely on the accurate molecular understanding of interactions of the nitrile group and its environment, particularly from hydrogen bonding. In this work, we compared the extent of hydrogen bonding calculated in two common force fields, the fixed charge force field Amber03 and polarizable force field AMOEBA, at 10 locations of cyanocysteine (CNC) in staphylococcal nuclease (SNase) against the experimental nitrile absorption frequency in terms of full width at half-maximum (FWHM) and frequency temperature line slope (FTLS). We observed that the number of hydrogen bonds correlated well in AMOEBA trajectories with respect to both the FWHM (r = 0.88) and the FTLS (r = -0.85), whereas the correlation of Amber03 trajectories was less reliable because the Amber03 force field predicted more hydrogen bonds in some mutants. Moreover, we demonstrated that contributions from the interactions between CNC and nearby water molecules were significant in AMOEBA trajectories but were not predicted by Amber03. We conclude that although the nitrile absorption peak shape could be qualitatively predicted by the fixed charge Amber03 force field, the detailed electrostatic environment measured by the nitrile probe in terms of the extent of hydrogen bonding could only be accurately observed in the AMOEBA trajectories, where the permanent dipole, quadrupole, and dipole-induced-dipole polarizable interactions were all taken into account. The significance of this finding to the goal of accurately predicting electric fields in complex biomolecular environments is discussed.

Unifying Charge-Flow Polarization Models

We show that several models where electric polarization in molecular systems is modeled by charge-flow between atoms can all be considered as different manifestations of a general underlying mathematical structure. The models can be classified according to whether they employ atomic or bond parameters and whether they employ atom/bond hardness or softness. We show that an ab initio calculated charge response kernel can be considered as the inverse screened Coulombic matrix projected onto the zero-charge subspace, and this may provide a method for deriving charge screening functions to be used in force fields. The analysis suggests that some models contain redundancies, and we argue that a parameterization of charge-flow models in terms of bond softness is preferable as it depends on local quantities and decay to zero upon bond dissociation, while bond hardness depends on global quantities and increases toward infinity upon bond dissociation.

Free Energy Calculations and Conformational Analysis of Dibenzo-30-crown-10 with Sm2+, Eu2+, and Three Halide Salts in THF Using the AMOEBA Force Field

Crown ether complexes have been tailored for use in industrial separations of lanthanides (Ln) as a part of rare earth mining and refining. Dibenzo-30-crown-10 (DB30C10) is one of the most efficient complexants for the separation of rare earth mixtures based on the cation size. To understand the origin of this complexation, molecular dynamics (MD) simulations of DB30C10 have been performed using different combinations of divalent Sm and Eu and three halide salts Cl^-, Br^-, and I^- in tetrahydrofuran (THF) solvent. DB30C10 was parameterized here for the polarizable atomic multipole optimized energetics for biomolecular simulation (AMOEBA) force field, and the existing parameters of THF, Sm²⁺, and Eu²⁺ were employed from our previous efforts. The large conformational fluctuations present in the DB30C10 systems were found to be dependent both on the identity of the lanthanide and halide complexes. For Cl^- and Br^- systems, there were no observed conformational changes at 200 ns, while in I^- systems, there were two conformational changes with Sm²⁺ and one with Eu²⁺ within that same timeframe. In SmI₂-DB30C10, there were three stages of conformational changes. In the first stage, the molecule is unfolded, in the second stage, the molecule is partly folded, and finally, in the third stage, the molecule is completely folded. Lastly, the Gibbs binding free energies of DB30C10 with SmBr₂ and EuBr₂ have been computed, which resulted in nearly identical ΔG_comp values for each lanthanide with Sm²⁺ being slightly more favorable. Considering the folding mechanism of the SmI₂ system with DB30C10, the Gibbs binding free energies of DB30C10 and dicyclohexano-18-crown-6 (DCH18C6) with SmI₂ were calculated separately and compared to probe their complexation affinities, in which the former was found to be more favorable.

Assessing variants of uncertain significance implicated in hearing loss using a comprehensive deafness proteome

Hearing loss is the leading sensory deficit, affecting ~ 5% of the population. It exhibits remarkable heterogeneity across 223 genes with 6328 pathogenic missense variants, making deafness-specific expertise a prerequisite for ascribing phenotypic consequences to genetic variants. Deafness-implicated variants are curated in the Deafness Variation Database (DVD) after classification by a genetic hearing loss expert panel and thorough informatics pipeline. However, seventy percent of the 128,167 missense variants in the DVD are "variants of uncertain significance" (VUS) due to insufficient evidence for classification. Here, we use the deep learning protein prediction algorithm, AlphaFold2, to curate structures for all DVD genes. We refine these structures with global optimization and the AMOEBA force field and use DDGun3D to predict folding free energy differences (∆∆GFold) for all DVD missense variants. We find that 5772 VUSs have a large, destabilizing ∆∆GFold that is consistent with pathogenic variants. When also filtered for CADD scores (> 25.7), we determine 3456 VUSs are likely pathogenic at a probability of 99.0%. Of the 224 genes in the DVD, 166 genes (74%) exhibit one or more missense variants predicted to cause a pathogenic change in protein folding stability. The VUSs prioritized here affect 119 patients (~ 3% of cases) sequenced by the OtoSCOPE targeted panel. Approximately half of these patients previously received an inconclusive report, and reclassification of these VUSs as pathogenic provides a new genetic diagnosis for six patients.

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.

Evaluating the Transition State Stabilization/Destabilization Effects of the Electric Fields from Scaffold Residues by a QM/MM Approach

The protein scaffolds of enzymes not only provide structural support for the catalytic center but also exert preorganized electric fields for electrostatic catalysis. In recent years, uniform oriented external electric fields (OEEFs) have been widely applied to enzymatic reactions to mimic the electrostatic effects of the environment. However, the electric fields exerted by individual residues in proteins may be quite heterogeneous across the active site, with varying directions and strengths at different positions of the active site. Here, we propose a QM/MM-based approach to evaluate the effects of the electric fields exerted by individual residues in the protein scaffold. In particular, the heterogeneity of the residue electric fields and the effect of the native protein environment can be properly accounted for by this QM/MM approach. A case study of the O-O heterolysis reaction in the catalytic cycle of TyrH shows that (1) for scaffold residues that are relatively far from the active site, the heterogeneity of the residue electric field in the active site is not very significant and the electrostatic stabilization/destabilization due to each residue can be well approximated with the interaction energy between a uniform electric field and the QM region dipole; (2) for scaffold residues near the active site, the residue electric fields can be highly heterogeneous along the breaking O-O bond. In such a case, approximating the residue electric fields as uniform fields may misrepresent the overall electrostatic effect of the residue. The present QM/MM approach can be applied to evaluate the residues' electrostatic impact on enzymatic reactions, which also can be useful in computational optimization of electric fields to boost the enzyme catalysis.