Force field development phase II: Relaxation of physics-based criteria… or inclusion of more rigorous physics into the representation of molecular energetics

Fine-tuning molecular mechanics force fields to experimental free energy measurements

Alchemical free energy methods using molecular mechanics (MM) force fields are essential tools for predicting thermodynamic properties of small molecules, especially via free energy calculations that can estimate quantities relevant for drug discovery such as affinities, selectivities, the impact of target mutations, and ADMET properties. While traditional MM forcefields rely on hand-crafted, discrete atom types and parameters, modern approaches based on graph neural networks (GNNs) learn continuous embedding vectors that represent chemical environments from which MM parameters can be generated. Excitingly, GNN parameterization approaches provide a fully end-to-end differentiable model that offers the possibility of systematically improving these models using experimental data. In this study, we treat a pretrained GNN force field-here, espaloma-0.3.2-as a foundation simulation model and fine-tune its charge model using limited quantities of experimental hydration free energy data, with the goal of assessing the degree to which this can systematically improve the prediction of other related free energies. We demonstrate that a highly efficient "one-shot fine-tuning" method using an exponential (Zwanzig) reweighting free energy estimator can improve prediction accuracy without the need to resimulate molecular configurations. To achieve this "one-shot" improvement, we demonstrate the importance of using effective sample size (ESS) regularization strategies to retain good overlap between initial and fine-tuned force fields. Moreover, we show that leveraging low-rank projections of embedding vectors can achieve comparable accuracy improvements as higher-dimensional approaches in a variety of data-size regimes. Our results demonstrate that linearly-perturbative fine-tuning of foundation model electrostatic parameters to limited experimental data offers a cost-effective strategy that achieves state-of-the-art performance in predicting hydration free energies on the FreeSolv dataset.

A dual-cutoff machine-learned potential for condensed organic systems obtained via uncertainty-guided active learning

Machine-learned potentials (MLPs) trained on ab initio data combine the computational efficiency of classical interatomic potentials with the accuracy and generality of the first-principles method used in the creation of the respective training set. In this work, we implement and train a MLP to obtain an accurate description of the potential energy surface and property predictions for organic compounds, as both single molecules and in the condensed phase. We devise a dual descriptor, based on the atomic cluster expansion (ACE), that couples an information-rich short-range description with a coarser long-range description that captures weak intermolecular interactions. We employ uncertainty-guided active learning for the training set generation, creating a dataset that is comparatively small for the breadth of application and consists of alcohols, alkanes, and an adipate. Utilizing that MLP, we calculate densities of those systems of varying chain lengths as a function of temperature, obtaining a discrepancy of less than 4% compared with experiment. Vibrational frequencies calculated with the MLP have a root mean square error of less than 1 THz compared to DFT. The heat capacities of condensed systems are within 11% of experimental findings, which is strong evidence that the dual descriptor provides an accurate framework for the prediction of both short-range intramolecular and long-range intermolecular interactions.

Machine-learned molecular mechanics force fields from large-scale quantum chemical data

The development of reliable and extensible molecular mechanics (MM) force fields-fast, empirical models characterizing the potential energy surface of molecular systems-is indispensable for biomolecular simulation and computer-aided drug design. Here, we introduce a generalized and extensible machine-learned MM force field, espaloma-0.3, and an end-to-end differentiable framework using graph neural networks to overcome the limitations of traditional rule-based methods. Trained in a single GPU-day to fit a large and diverse quantum chemical dataset of over 1.1 M energy and force calculations, espaloma-0.3 reproduces quantum chemical energetic properties of chemical domains highly relevant to drug discovery, including small molecules, peptides, and nucleic acids. Moreover, this force field maintains the quantum chemical energy-minimized geometries of small molecules and preserves the condensed phase properties of peptides and folded proteins, self-consistently parametrizing proteins and ligands to produce stable simulations leading to highly accurate predictions of binding free energies. This methodology demonstrates significant promise as a path forward for systematically building more accurate force fields that are easily extensible to new chemical domains of interest.

The Open Force Field Initiative: Open Software and Open Science for Molecular Modeling

Force fields are a key component of physics-based molecular modeling, describing the energies and forces in a molecular system as a function of the positions of the atoms and molecules involved. Here, we provide a review and scientific status report on the work of the Open Force Field (OpenFF) Initiative, which focuses on the science, infrastructure and data required to build the next generation of biomolecular force fields. We introduce the OpenFF Initiative and the related OpenFF Consortium, describe its approach to force field development and software, and discuss accomplishments to date as well as future plans. OpenFF releases both software and data under open and permissive licensing agreements to enable rapid application, validation, extension, and modification of its force fields and software tools. We discuss lessons learned to date in this new approach to force field development. We also highlight ways that other force field researchers can get involved, as well as some recent successes of outside researchers taking advantage of OpenFF tools and data.

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.

Reweighting from Molecular Mechanics Force Fields to the ANI-2x Neural Network Potential

To achieve chemical accuracy in free energy calculations, it is necessary to accurately describe the system's potential energy surface and efficiently sample configurations from its Boltzmann distribution. While neural network potentials (NNPs) have shown significantly higher accuracy than classical molecular mechanics (MM) force fields, they have a limited range of applicability and are considerably slower than MM potentials, often by orders of magnitude. To address this challenge, Rufa et al. [Rufa et al. bioRxiv 2020, 10.1101/2020.07.29.227959.] suggested a two-stage approach that uses a fast and established MM alchemical energy protocol, followed by reweighting the results using NNPs, known as endstate correction or indirect free energy calculation. This study systematically investigates the accuracy and robustness of reweighting from an MM reference to a neural network target potential (ANI-2x) for an established data set in vacuum, using single-step free-energy perturbation (FEP) and nonequilibrium (NEQ) switching simulation. We assess the influence of longer switching lengths and the impact of slow degrees of freedom on outliers in the work distribution and compare the results to those of multistate equilibrium free energy simulations. Our results demonstrate that free energy calculations between NNPs and MM potentials should be preferably performed using NEQ switching simulations to obtain accurate free energy estimates. NEQ switching simulations between the MM potentials and NNPs are efficient, robust, and trivial to implement.

Enhancing Protein-Ligand Binding Affinity Predictions Using Neural Network Potentials

This letter gives results on improving protein-ligand binding affinity predictions based on molecular dynamics simulations using machine learning potentials with a hybrid neural network potential and molecular mechanics methodology (NNP/MM). We compute relative binding free energies with the Alchemical Transfer Method and validate its performance against established benchmarks and find significant enhancements compared with conventional MM force fields like GAFF2.

Martini on the Rocks: Can a Coarse-Grained Force Field Model Crystals?

Computational chemistry is an important tool in numerous scientific disciplines, including drug discovery and structural biology. Coarse-grained models offer simple representations of molecular systems that enable simulations of large-scale systems. Because there has been an increase in the adoption of such models for simulations of biomolecular systems, critical evaluation is warranted. Here, the stability of the amyloid peptide and organic crystals is evaluated using the Martini 3 coarse-grained force field. The crystals change shape drastically during the simulations. Radial distribution functions show that the distance between backbone beads in β-sheets increases by ∼1 Å, breaking the crystals. The melting points of organic compounds are much too low in the Martini force field. This suggests that Martini 3 lacks the specific interactions needed to accurately simulate peptides or organic crystals without imposing artificial restraints. The problems may be exacerbated by the use of the 12-6 potential, suggesting that a softer potential could improve this model for crystal simulations.

Combining Force Fields and Neural Networks for an Accurate Representation of Bonded Interactions

We present a formalism of a neural network encoding bonded interactions in molecules. This intramolecular encoding is consistent with the models of intermolecular interactions previously designed by this group. Variants of the encoding fed into a corresponding neural network may be used to economically improve the representation of torsional degrees of freedom in any force field. We test the accuracy of the reproduction of the ab initio potential energy surface on a set of conformations of two dipeptides, methyl-capped ALA and ASP, in several scenarios. The encoding, either alone or in conjunction with an analytical potential, improves agreement with ab initio energies that are on par with those of other neural network-based potentials. Using the encoding and neural nets in tandem with an analytical model places the agreements firmly within "chemical accuracy" of ±0.5 kcal/mol.

Density functional theory study of crown ether-magnesium complexes: from a solvated ion to an ion trap

Metal ion detection rests on host-guest recognition. We propose a theoretical protocol for designing an optimal trap for a desired metal cation. A host for magnesium ions was sought for among derivatives of crown ethers 12-crown-4, 15-crown-5, and 18-crown-6. Mg-crown complexes and their hydrated counterparts with water molecules bound to the cation were optimized using density functional theory. Based on specific geometric criteria, Interacting quantum atoms analysis and density functional theory-based molecular dynamics of Mg-crown complexes immersed in water, crown ethers for optimal accommodation of Mg2+ in aqueous solution were identified. Selectivity of the chosen crowns towards Na+, K+, and Ca2+ ions is addressed.

Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

A transferable double exponential potential for condensed phase simulations of small molecules

The Lennard-Jones potential is the most widely-used function for the description of non-bonded interactions in transferable force fields for the condensed phase. This is not because it has an optimal functional form, but rather it is a legacy resulting from when computational expense was a major consideration and this potential was particularly convenient numerically. At present, it persists because the effort that would be required to re-write molecular modelling software and train new force fields has, until now, been prohibitive. Here, we present Smirnoff-plugins as a flexible framework to extend the Open Force Field software stack to allow custom force field functional forms. We deploy Smirnoff-plugins with the automated Open Force Field infrastructure to train a transferable, small molecule force field based on the recently-proposed double exponential functional form, on over 1000 experimental condensed phase properties. Extensive testing of the resulting force field shows improvements in transfer free energies, with acceptable conformational energetics, run times and convergence properties compared to state-of-the-art Lennard-Jones based force fields.

Fitting Force Field Parameters to NMR Relaxation Data

We present an approach to optimize force field parameters using time-dependent data from NMR relaxation experiments. To do so, we scan parameters in the dihedral angle potential energy terms describing the rotation of the methyl groups in proteins and compare NMR relaxation rates calculated from molecular dynamics simulations with the modified force fields to deuterium relaxation measurements of T4 lysozyme. We find that a small modification of C^γ methyl groups improves the agreement with experiments both for the protein used to optimize the force field and when validating using simulations of CI2 and ubiquitin. We also show that these improvements enable a more effective a posteriori reweighting of the MD trajectories. The resulting force field thus enables more direct comparison between simulations and side-chain NMR relaxation data and makes it possible to construct ensembles that better represent the dynamics of proteins in solution.

Potential Energy Surfaces Sampled in Cremer-Pople Coordinates and Represented by Common Force Field Functionals for Small Cyclic Molecules

The complex conformations of the cyclic moieties impact the physical and chemical properties of molecules. In this work, we chose 22 molecules of four-, five-, and six-membered rings and performed a thorough conformational sampling using Cremer-Pople coordinates. With consideration of symmetries, we obtained a total of 1504 conformational structures for four-membered, 5576 for five-membered, and 13509 for six-membered rings. All well-known and many less well-known conformers for each molecule were identified. We represented the potential energy surfaces (PESs) by fitting the data to common analytical force field (FF) functional forms. We found that the general features of PESs can be described by the essential FF functional forms; however, the accuracy of representation can be improved remarkably by including the torsion-bond and torsion-angle coupling terms. The best fit yields R-squared (R²) values close to 1.0 and mean absolute errors in energy less than 0.3 kcal/mol.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Collaborative Assessment of Molecular Geometries and Energies from the Open Force Field

Force fields form the basis for classical molecular simulations, and their accuracy is crucial for the quality of, for instance, protein-ligand binding simulations in drug discovery. The huge diversity of small-molecule chemistry makes it a challenge to build and parameterize a suitable force field. The Open Force Field Initiative is a combined industry and academic consortium developing a state-of-the-art small-molecule force field. In this report, industry members of the consortium worked together to objectively evaluate the performance of the force fields (referred to here as OpenFF) produced by the initiative on a combined public and proprietary dataset of 19,653 relevant molecules selected from their internal research and compound collections. This evaluation was important because it was completely blind; at most partners, none of the molecules or data were used in force field development or testing prior to this work. We compare the Open Force Field "Sage" version 2.0.0 and "Parsley" version 1.3.0 with GAFF-2.11-AM1BCC, OPLS4, and SMIRNOFF99Frosst. We analyzed force-field-optimized geometries and conformer energies compared to reference quantum mechanical data. We show that OPLS4 performs best, and the latest Open Force Field release shows a clear improvement compared to its predecessors. The performance of established force fields such as GAFF-2.11 was generally worse. While OpenFF researchers were involved in building the benchmarking infrastructure used in this work, benchmarking was done entirely in-house within industrial organizations and the resulting assessment is reported here. This work assesses the force field performance using separate benchmarking steps, external datasets, and involving external research groups. This effort may also be unique in terms of the number of different industrial partners involved, with 10 different companies participating in the benchmark efforts.

Open Force Field BespokeFit: Automating Bespoke Torsion Parametrization at Scale

The development of accurate transferable force fields is key to realizing the full potential of atomistic modeling in the study of biological processes such as protein-ligand binding for drug discovery. State-of-the-art transferable force fields, such as those produced by the Open Force Field Initiative, use modern software engineering and automation techniques to yield accuracy improvements. However, force field torsion parameters, which must account for many stereoelectronic and steric effects, are considered to be less transferable than other force field parameters and are therefore often targets for bespoke parametrization. Here, we present the Open Force Field QCSubmit and BespokeFit software packages that, when combined, facilitate the fitting of torsion parameters to quantum mechanical reference data at scale. We demonstrate the use of QCSubmit for simplifying the process of creating and archiving large numbers of quantum chemical calculations, by generating a dataset of 671 torsion scans for druglike fragments. We use BespokeFit to derive individual torsion parameters for each of these molecules, thereby reducing the root-mean-square error in the potential energy surface from 1.1 kcal/mol, using the original transferable force field, to 0.4 kcal/mol using the bespoke version. Furthermore, we employ the bespoke force fields to compute the relative binding free energies of a congeneric series of inhibitors of the TYK2 protein, and demonstrate further improvements in accuracy, compared to the base force field (MUE reduced from 0.56_0.39^0.77 to 0.42_0.28^0.59 kcal/mol and R² correlation improved from 0.72_0.35^0.87 to 0.93_0.84^0.97).

Atomic-Resolution Experimental Structural Biology and Molecular Dynamics Simulations of Hyaluronan and Its Complexes

This review summarizes the atomic-resolution structural biology of hyaluronan and its complexes available in the Protein Data Bank, as well as published studies of atomic-resolution explicit-solvent molecular dynamics simulations on these and other hyaluronan and hyaluronan-containing systems. Advances in accurate molecular mechanics force fields, simulation methods and software, and computer hardware have supported a recent flourish in such simulations, such that the simulation publications now outnumber the structural biology publications by an order of magnitude. In addition to supplementing the experimental structural biology with computed dynamic and thermodynamic information, the molecular dynamics studies provide a wealth of atomic-resolution information on hyaluronan-containing systems for which there is no atomic-resolution structural biology either available or possible. Examples of these summarized in this review include hyaluronan pairing with other hyaluronan molecules and glycosaminoglycans, with ions, with proteins and peptides, with lipids, and with drugs and drug-like molecules. Despite limitations imposed by present-day computing resources on system size and simulation timescale, atomic-resolution explicit-solvent molecular dynamics simulations have been able to contribute significant insight into hyaluronan's flexibility and capacity for intra- and intermolecular non-covalent interactions.

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρ_liq and vaporization enthalpies ΔH_vap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κ_T, the isobaric thermal-expansion coefficient α_P, the isobaric heat capacity c_P, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔG_wat, and the free energy of solvation ΔG_che in cyclohexane. For the target properties ρ_liq and ΔH_vap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κ_T, α_P, ϵ, D, and ΔG_che; and less accurate results in terms of c_P and ΔG_wat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Is an Inductive Effect Explicit Account Required for Atomic Charges Aimed at Use within the Force Fields?

Polarization and inductive effects are the concepts that have been widely used in qualitative and even quantitative descriptions of experimentally observed properties in chemistry. The polarization effect has proven to be important in cases of biomolecular modeling though still the vast majority of molecular simulations use the classical non-polarizable force fields. In the last few decades, a lot of effort has been put into promoting the polarization effect and incorporating it into modern force fields and charge calculation methods. In contrast, the inductive effect has not attracted such attention and is effectively absent in both classic and modern force fields. Thus, a question is whether this difference corresponds to the difference in the physical significance of the effects and their explicit account, or is an artifact that should be corrected in the next generation of force fields. The significance of the electronic effects is studied in this paper through the prism of performance of specific models for atomic charge calculation that take into explicit account a nested set of effects: the formal charge, the nearest neighbors, the inductive effect, and finally the model, which takes into account all effects, which are possible to account for using atomic charges. The specific choice for the methods is the following: formal charges, MMFF94 bond charge increments, Dynamic Electronegativity Relaxation (DENR), and RESP. We propose a special scheme for the separate estimation of each particular effect contribution. By pairwise comparing the residual molecular electrostatic potential (MEP) errors of those charge models (aimed at best reproducing the quantum chemical reference MEP), we sequentially revealed how the account of each effect contributes to the better-quality MEP reproduction. The following relative importance of effects was estimated; thus, the natural hierarchy of the effects was established. First, the account of formal charges is of primordial importance. Second, the nearest neighbors account is the next in significance. Third, the explicit account of inductive effect in empirical charge calculation schemes was shown to significantly─both qualitatively and quantitatively─improve the quality of MEP reproduction. Fourth, the contribution of polarization is indirectly assessed. Surprisingly, it is of the order of magnitude of the inductive effect even for the molecular systems, for which it is anticipated to be more significant. Finally, the relative importance of anisotropic effects in neutral molecules was additionally reviewed.

Exploration and validation of force field design protocols through QM-to-MM mapping

The scale of the parameter optimisation problem in traditional molecular mechanics force field construction means that design of a new force field is a long process, and sub-optimal choices made in the early stages can persist for many generations. We hypothesise that careful use of quantum mechanics to inform molecular mechanics parameter derivation (QM-to-MM mapping) should be used to significantly reduce the number of parameters that require fitting to experiment and increase the pace of force field development. Here, we design and train a collection of 15 new protocols for small, organic molecule force field derivation, and test their accuracy against experimental liquid properties. Our best performing model has only seven fitting parameters, yet achieves mean unsigned errors of just 0.031 g cm^-3 and 0.69 kcal mol^-1 in liquid densities and heats of vaporisation, compared to experiment. The software required to derive the designed force fields is freely available at https://github.com/qubekit/QUBEKit.

Improving Force Field Accuracy by Training against Condensed-Phase Mixture Properties

Developing a sufficiently accurate classical force field representation of molecules is key to realizing the full potential of molecular simulations as a route to gaining a fundamental insight into a broad spectrum of chemical and biological phenomena. This is only possible, however, if the many complex interactions between molecules of different species in the system are accurately captured by the model. Historically, the intermolecular van der Waals (vdW) interactions have primarily been trained against densities and enthalpies of vaporization of pure (single-component) systems, with occasional usage of hydration free energies. In this study, we demonstrate how including physical property data of binary mixtures can better inform these parameters, encoding more information about the underlying physics of the system in complex chemical mixtures. To demonstrate this, we retrain a select number of Lennard-Jones parameters describing the vdW interactions of the OpenFF 1.0.0 (Parsley) fixed charge force field against training sets composed of densities and enthalpies of mixing for binary liquid mixtures as well as densities and enthalpies of vaporization of pure liquid systems and assess the performance of each of these combinations. We show that retraining against the mixture data improves the force field's ability to reproduce mixture properties, including solvation free energies, correcting some systematic errors that exist when training vdW interactions against properties of pure systems only.

High Order Ab Initio Valence Force Field with Chemical Pattern Based Parameter Assignment

Bonded (or valence) interactions, which directly determine the local structures of the molecules, are fundamental parts of molecular mechanics force fields (FFs). Most popular classical FFs adopt the simple harmonic models for bond stretching and angle bending and ignore cross-coupling effects among the valence terms. This may lead to less accurate vibrational properties and configurations in molecular dynamics (MD) simulations. AMOEBA models utilize an MM3(MM4)-style bonded interaction model, in which the vibrational anharmonicity, the coupling effects among different energy terms, and the out-of-plane bending for sp2-hybridized atoms are considered. In this work, we report the development of bonded interaction parameters for a wide range of chemistry based on quantum mechanics (QM). About 270 atomic types defined by SMARTS strings were used to model the valence interactions. Our results indicate that the resulting valence parameters produce accurate vibrational frequencies (RMSD from QM is less than ~36.6 cm^-1) over a large set of molecules with diverse functional groups (445 molecules). By contrast, the harmonic models usually give an RMS error greater than 60 cm^-1. Meanwhile, this model accurately reflects the potential energy surface of the out-of-plane bending. Our model can generally be applied to the AMOEBA family and any MM3(MM4)-based molecular mechanics FFs.

Automated fitting of transition state force fields for biomolecular simulations

The generation of surrogate potential energy functions (PEF) that are orders of magnitude faster to compute but as accurate as the underlying training data from high-level electronic structure methods is one of the most promising applications of fitting procedures in chemistry. In previous work, we have shown that transition state force fields (TSFFs), fitted to the functional form of MM3* force fields using the quantum guided molecular mechanics (Q2MM) method, provide an accurate description of transition states that can be used for stereoselectivity predictions of small molecule reactions. Here, we demonstrate the applicability of the method for fit TSFFs to the well-established Amber force field, which could be used for molecular dynamics studies of enzyme reaction. As a case study, the fitting of a TSFF to the second hydride transfer in Pseudomonas mevalonii 3-hydroxy-3-methylglutaryl coenzyme A reductase (PmHMGR) is used. The differences and similarities to fitting of small molecule TSFFs are discussed.

Unavoidable failure of point charge descriptions of electronic density changes for out-of-plane distortions

Population analyses based on point charge approximations accurately estimating the equilibrium dipole moment will systematically fail when predicting infrared intensities of out-of-plane vibrations of planar molecules, whereas models based on both charges and dipoles will always succeed. It is not a matter of how the model is devised but rather how many degrees of freedom are available for the calculation. Population analyses based on point charges are very limited in terms of the amount of meaningful chemical information they provide, whereas models employing both atomic charges and atomic dipoles should be preferred for molecular distortions. A good model should be able to correctly describe not only static, equilibrium structures but also distorted geometries in order to correctly assess information from vibrating molecules. The limitations of point charge models also hold for distortions much larger than those encountered vibrationally.

Bayesian-Inference-Driven Model Parametrization and Model Selection for 2CLJQ Fluid Models

A high level of physical detail in a molecular model improves its ability to perform high accuracy simulations but can also significantly affect its complexity and computational cost. In some situations, it is worthwhile to add complexity to a model to capture properties of interest; in others, additional complexity is unnecessary and can make simulations computationally infeasible. In this work, we demonstrate the use of Bayesian inference for molecular model selection, using Monte Carlo sampling techniques accelerated with surrogate modeling to evaluate the Bayes factor evidence for different levels of complexity in the two-centered Lennard-Jones + quadrupole (2CLJQ) fluid model. Examining three nested levels of model complexity, we demonstrate that the use of variable quadrupole and bond length parameters in this model framework is justified only for some chemistries. Through this process, we also get detailed information about the distributions and correlation of parameter values, enabling improved parametrization and parameter analysis. We also show how the choice of parameter priors, which encode previous model knowledge, can have substantial effects on the selection of models, penalizing careless introduction of additional complexity. We detail the computational techniques used in this analysis, providing a roadmap for future applications of molecular model selection via Bayesian inference and surrogate modeling.

Linear Atomic Cluster Expansion Force Fields for Organic Molecules: Beyond RMSE

We demonstrate that fast and accurate linear force fields can be built for molecules using the atomic cluster expansion (ACE) framework. The ACE models parametrize the potential energy surface in terms of body-ordered symmetric polynomials making the functional form reminiscent of traditional molecular mechanics force fields. We show that the four- or five-body ACE force fields improve on the accuracy of the empirical force fields by up to a factor of 10, reaching the accuracy typical of recently proposed machine-learning-based approaches. We not only show state of the art accuracy and speed on the widely used MD17 and ISO17 benchmark data sets, but we also go beyond RMSE by comparing a number of ML and empirical force fields to ACE on more important tasks such as normal-mode prediction, high-temperature molecular dynamics, dihedral torsional profile prediction, and even bond breaking. We also demonstrate the smoothness, transferability, and extrapolation capabilities of ACE on a new challenging benchmark data set comprised of a potential energy surface of a flexible druglike molecule.

The future of biomolecular simulation in the pharmaceutical industry: what we can learn from aerodynamics modelling and weather prediction. Part 1. understanding the physical and computational complexity of in silico drug design

The predictive power of simulation has become embedded in the infrastructure of modern economies. Computer-aided design is ubiquitous throughout industry. In aeronautical engineering, built infrastructure and materials manufacturing, simulations are routinely used to compute the performance of potential designs before construction. The ability to predict the behaviour of products is a driver of innovation by reducing the cost barrier to new designs, but also because radically novel ideas can be piloted with relatively little risk. Accurate weather forecasting is essential to guide domestic and military flight paths, and therefore the underpinning simulations are critical enough to have implications for national security. However, in the pharmaceutical and biotechnological industries, the application of computer simulations remains limited by the capabilities of the technology with respect to the complexity of molecular biology and human physiology. Over the last 30 years, molecular-modelling tools have gradually gained a degree of acceptance in the pharmaceutical industry. Drug discovery has begun to benefit from physics-based simulations. While such simulations have great potential for improved molecular design, much scepticism remains about their value. The motivations for such reservations in industry and areas where simulations show promise for efficiency gains in preclinical research are discussed. In this, the first of two complementary papers, the scientific and technical progress that needs to be made to improve the predictive power of biomolecular simulations, and how this might be achieved, is firstly discussed (Part 1). In Part 2, the status of computer simulations in pharma is contrasted with aerodynamics modelling and weather forecasting, and comments are made on the cultural changes needed for equivalent computational technologies to become integrated into life-science industries.

Additive CHARMM36 Force Field for Nonstandard Amino Acids

Nonstandard amino acids are both abundant in nature, where they play a key role in various cellular processes, and can be synthesized in laboratories, for example, for the manufacture of a range of pharmaceutical agents. In this work, we have extended the additive all-atom CHARMM36 and CHARMM General force field (CGenFF) to a large set of 333 nonstandard amino acids. These include both amino acids with nonstandard side chains, such as post-translationally modified and artificial amino acids, as well as amino acids with modified backbone groups, such as chromophores composed of several amino acids. Model compounds representative of the nonstandard amino acids were parametrized for protonation states that are likely at the physiological pH of 7 and, for some more common residues, in both d- and l-stereoisomers. Considering all protonation, tautomeric, and stereoisomeric forms, a total of 406 nonstandard amino acids were parametrized. Emphasis was placed on the quality of both intra- and intermolecular parameters. Partial charges were derived using quantum mechanical (QM) data on model compound dipole moments, electrostatic potentials, and interactions with water. Optimization of all intramolecular parameters, including torsion angle parameters, was performed against information from QM adiabatic potential energy surface (PES) scans. Special emphasis was put on the quality of terms corresponding to PES around rotatable dihedral angles. Validation of the force field was based on molecular dynamics simulations of 20 protein complexes containing different nonstandard amino acids. Overall, the presented parameters will allow for computational studies of a wide range of proteins containing nonstandard amino acids, including natural and artificial residues.

Stereoselectivity Predictions for the Pd-Catalyzed 1,4-Conjugate Addition Using Quantum-Guided Molecular Mechanics

The conjugate addition of aryl boronic acids to enones is a powerful synthetic tool to introduce quaternary chiral centers, but the experimentally observed stereoselectivities vary widely, and the identification of suitable substrate-ligand combinations requires significant effort. We describe the development and application of a transition-state force field (TSFF) by the quantum-guided molecular mechanics (Q2MM) method that is validated using an automated screen of 9 ligands, 38 aryl boronic acids, and 22 enones, leading to a MUE of 1.8 kJ/mol and a R² value of 0.877 over 82 examples. A detailed error analysis identified the structural origin for the deviations in the small group of outliers. The TSFF was then used to predict the stereoselectivity for 27 ligands and 59 enones. The vast majority of the virtual screening results are in line with the expected results. Selected results for 6-substituted pyrox ligands, which were not part of the training set, were followed up by density functional theory and experimental studies.

AC/DC Analysis: Broad and Comprehensive Approach to Analyze Infrared Intensities at the Atomic Level

We present a complete theoretical protocol to partition infrared intensities into terms owing to individual atoms by two different but related approaches: the atomic contributions (ACs) show how the entire molecular vibrational motion affects the electronic structure of a single atom and the total infrared intensity. On the other hand, the dynamic contributions (DCs) show how the displacement of a single atom alters the electronic structure of the entire molecule and the total intensity. The two analyses are complementary ways of partitioning the same total intensity and conserve most of the features of the total intensity itself. Combined, they are called the AC/DC analysis. These can be further partitioned following the CCTDP (or CCT) models according to the population analysis chosen by the researcher. The main conceptual features of the equations are highlighted, and representative numerical results are shown to support the interpretation of the equations. The results are invariant to rotation and translation and can readily be extended to molecules of any size, shape, or symmetry. Although the AC/DC analysis requires the choice of a charge model, all charge models that correctly reproduce the total molecular dipole moment can be used. A fully automated protocol managed by the Placzek program is made available, free of charge and with input examples.

Improving small molecule force fields by identifying and characterizing small molecules with inconsistent parameters

Many molecular simulation methods use force fields to help model and simulate molecules and their behavior in various environments. Force fields are sets of functions and parameters used to calculate the potential energy of a chemical system as a function of the atomic coordinates. Despite the widespread use of force fields, their inadequacies are often thought to contribute to systematic errors in molecular simulations. Furthermore, different force fields tend to give varying results on the same systems with the same simulation settings. Here, we present a pipeline for comparing the geometries of small molecule conformers. We aimed to identify molecules or chemistries that are particularly informative for future force field development because they display inconsistencies between force fields. We applied our pipeline to a subset of the eMolecules database, and highlighted molecules that appear to be parameterized inconsistently across different force fields. We then identified over-represented functional groups in these molecule sets. The molecules and moieties identified by this pipeline may be particularly helpful for future force field parameterization.

Benchmark assessment of molecular geometries and energies from small molecule force fields

Background: Force fields are used in a wide variety of contexts for classical molecular simulation, including studies on protein-ligand binding, membrane permeation, and thermophysical property prediction. The quality of these studies relies on the quality of the force fields used to represent the systems. Methods: Focusing on small molecules of fewer than 50 heavy atoms, our aim in this work is to compare nine force fields: GAFF, GAFF2, MMFF94, MMFF94S, OPLS3e, SMIRNOFF99Frosst, and the Open Force Field Parsley, versions 1.0, 1.1, and 1.2. On a dataset comprising 22,675 molecular structures of 3,271 molecules, we analyzed force field-optimized geometries and conformer energies compared to reference quantum mechanical (QM) data. Results: We show that while OPLS3e performs best, the latest Open Force Field Parsley release is approaching a comparable level of accuracy in reproducing QM geometries and energetics for this set of molecules. Meanwhile, the performance of established force fields such as MMFF94S and GAFF2 is generally somewhat worse. We also find that the series of recent Open Force Field versions provide significant increases in accuracy. Conclusions: This study provides an extensive test of the performance of different molecular mechanics force fields on a diverse molecule set, and highlights two (OPLS3e and OpenFF 1.2) that perform better than the others tested on the present comparison. Our molecule set and results are available for other researchers to use in testing.

On the many-body nature of intramolecular forces in FFLUX and its implications

FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modeled as 3N_atoms -6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to N_atoms . This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9%) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.

Systematic design of biomolecular force fields

Force fields for the study of biomolecules have been developed in a predominantly organic manner by regular updates over half a century. Together with better algorithms and advances in computer technology, force fields have improved to yield more robust predictions. However, there are also indications to suggest that intramolecular energy functions have not become better and that there still is room for improvement. In this review, systematic efforts toward development of novel force fields from scratch are described. This includes an estimate of the complexity of the problem and the prerequisites in the form of data and algorithms. It is suggested that in order to make progress, an effort is needed to standardize reference data and force field validation benchmarks.

Parameterization of Unnatural Amino Acids with Azido and Alkynyl R-Groups for Use in Molecular Simulations

Recent new methods to functionalize proteins at specific amino acid locations use unnatural amino acids that contain azido and alkynyl groups. This capability is unprecedented and enables the creation of site-specific protein devices. Because of the high specificity of these devices, many protein configurations are possible and in silico screens have shown promise in predicting optimal attachment site locations. Therefore, there is significant interest in improving current molecular dynamics (MD) models to include the unique chemistries of these linear moieties. This work uses the force field tool kit to obtain the bonded and nonbonded CHARMM parameters for small molecules that contain azido and alkynyl groups. Next, the reliability of these parameters is tested by running simulated MD analysis to prove that the modeled structures match those found in the literature and quantum theory. Finally, the protein MD simulation compares this parameter set with crystallographic data to give a greater understanding of unnatural amino acid influence on the protein structure.

Rigorous Free Energy Simulations in Virtual Screening

Virtual high throughput screening (vHTS) in drug discovery is a powerful approach to identify hits: when applied successfully, it can be much faster and cheaper than experimental high-throughput screening approaches. However, mainstream vHTS tools have significant limitations: ligand-based methods depend on knowledge of existing chemical matter, while structure-based tools such as docking involve significant approximations that limit their accuracy. Recent advances in scientific methods coupled with dramatic speedups in computational processing with GPUs make this an opportune time to consider the role of more rigorous methods that could improve the predictive power of vHTS workflows. In this Perspective, we assert that alchemical binding free energy methods using all-atom molecular dynamics simulations have matured to the point where they can be applied in virtual screening campaigns as a final scoring stage to prioritize the top molecules for experimental testing. Specifically, we propose that alchemical absolute binding free energy (ABFE) calculations offer the most direct and computationally efficient approach within a rigorous statistical thermodynamic framework for computing binding energies of diverse molecules, as is required for virtual screening. ABFE calculations are particularly attractive for drug discovery at this point in time, where the confluence of large-scale genomics data and insights from chemical biology have unveiled a large number of promising disease targets for which no small molecule binders are known, precluding ligand-based approaches, and where traditional docking approaches have foundered to find progressible chemical matter.

Transition State Force Field for the Asymmetric Redox-Relay Heck Reaction

A transition state force field (TSFF) was developed using the quantum-guided molecular mechanics (Q2MM) method to describe the stereodetermining migratory insertion step of the enantioselective redox-relay Heck reaction for a range of multisubstituted alkenes. We show that the TSFF is highly predictive through an external validation of the TSFF against 151 experimentally determined stereoselectivities resulting in an R² of 0.89 and MUE of 1.8 kJ/mol. In addition, limitations in the underlying force field were identified by comparison of the TSFF results to DFT level calculations. A novel application of the TSFF was demonstrated for 31 cases where the enantiomer predicted by the TSFF differed from the originally published values. Experimental determination of the absolute configuration demonstrated that the computational predictions were accurate, suggesting that TSFFs can be used for the rapid prediction of the absolute stereochemistry for a class of reactions. Finally, a virtual ligand screen was conducted utilizing both the TSFF and a simple molecular correlation method. Both methods were similarly predictive, but the TSFF was able to show greater utility through transferability, speed, and interpretability.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

Implementation of Geometry-Dependent Charge Flux into the Polarizable AMOEBA+ Potential

Molecular dynamics (MD) simulations employing classical force fields (FFs) have been widely used to model molecular systems. The important ingredient of the current FFs, atomic charge, remains fixed during MD simulations despite the atomic environment or local geometry changes. This approximation hinders the transferability of the potential being used in multiple phases. Here we implement a geometry-dependent charge flux (GDCF) model into the multipole-based AMOEBA+ polarizable potential. The CF in the current work explicitly depends on the local geometry (bond and angle) of the molecule. To our knowledge, this is the first study that derives energy and force expressions due to GDCF in a multipole-based polarizable FF framework. Due to the inclusion of GDCF, the AMOEBA+ water model is noticeably improved in terms of describing the monomer properties, cluster binding/interaction energy, and a variety of liquid properties, including the infrared spectra that previous flexible water models were not able to capture.