Impact of Combination Rules, Level of Theory, and Potential Function on the Modeling of Gas- and Condensed-Phase Properties of Noble Gases.

The systems of noble gases are particularly instructive for molecular modeling due to the elemental nature of their interactions. They do not normally form bonds nor possess a (permanent) dipole moment, and the only forces determining their bonding/clustering stems from van der Waals forces─dispersion and Pauli repulsion, which can be modeled by empirical potential functions. Combination rules, that is, formulas to derive parameters for pair potentials of heterodimers from parameters of corresponding homodimers, have been studied at length for the Lennard-Jones 12-6 potentials but not in great detail for other, more accurate, potentials. In this work, we examine the usefulness of nine empirical potentials in their ability to reproduce quantum mechanical (QM) benchmark dissociation curves of noble gas dimers (He, Ne, Ar, Kr, and Xe homo- and heterodimers), and we systematically study the efficacy of different permutations of combination relations for each parameter of the potentials. Our QM benchmark comprises dissociation curves computed by several different coupled cluster implementations as well as symmetry-adapted perturbation theory. The two-parameter Lennard-Jones potentials were decisively outperformed by more elaborate potentials that sport a 25-30 times lower root-mean-square error (RMSE) when fitted to QM dissociation curves. Very good fits to the QM dissociation curves can be achieved with relatively inexpensive four- or even three-parameter potentials, for instance, the damped 14-7 potential (Halgren, J. Am. Chem. Soc. 1992, 114, 7827-7843), a four-parameter Buckingham potential (Werhahn et al., Chem. Phys. Lett. 2015, 619, 133-138), or the three-parameter Morse potential (Morse, Phys. Rev. 1929, 34, 57-64). Potentials for heterodimers that are generated from combination rules have an RMSE that is up to 20 times higher than potentials that are directly fitted to the QM dissociation curves. This means that the RMSE, in particular, for light atoms, is comparable in magnitude to the well-depth of the potential. Based on a systematic permutation of combination rules, we present one or more combination rules for each potential tested that yield a relatively low RMSE. Two new combination rules are introduced that perform well, one for the van der Waals radius σij as (12(σi3+σj3))1/3 and one for the well-depth ϵij as (12(ϵi-2+ϵj-2))-1/2. The QM data and the fitted potentials were evaluated in the gas phase against experimental second virial coefficients for homo- and heterodimers, the latter of which allowed evaluation of the combination rules. The fitted models were used to perform condensed phase molecular dynamics simulations to verify the melting points, liquid densities at the melting point, and the enthalpies of vaporization produced by the models for pure substances. Subtle differences in the benchmark potentials, in particular, the well-depth, due to the level of theory used were found here to have a profound effect on the macroscopic properties of noble gases: second virial coefficients or the bulk properties in simulations. By explicitly including three-body dispersion in molecular simulations employing the best pair potential, we were able to obtain accurate melting points as well as satisfactory densities and enthalpies of vaporization.

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 ß-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.

Can molecular dynamics be used to simulate biomolecular recognition?

There are many problems in biochemistry that are difficult to study experimentally. Simulation methods are appealing due to direct availability of atomic coordinates as a function of time. However, direct molecular simulations are challenged by the size of systems and the time scales needed to describe relevant motions. In theory, enhanced sampling algorithms can help to overcome some of the limitations of molecular simulations. Here, we discuss a problem in biochemistry that offers a significant challenge for enhanced sampling methods and that could, therefore, serve as a benchmark for comparing approaches that use machine learning to find suitable collective variables. In particular, we study the transitions LacI undergoes upon moving between being non-specifically and specifically bound to DNA. Many degrees of freedom change during this transition and that the transition does not occur reversibly in simulations if only a subset of these degrees of freedom are biased. We also explain why this problem is so important to biologists and the transformative impact that a simulation of it would have on the understanding of DNA regulation.

Simulations of Amyloid-Forming Peptides in the Crystal State.

There still is little treatment available for amyloid diseases, despite their significant impact on individuals and the social and economic implications for society. One reason for this is that the physical nature of amyloid formation is not understood sufficiently well. Therefore, fundamental research at the molecular level remains necessary to support the development of therapeutics. A few structures of short peptides from amyloid-forming proteins have been determined. These can in principle be used as scaffolds for designing aggregation inhibitors. Attempts to this end have often used the tools of computational chemistry, in particular molecular simulation. However, few simulation studies of these peptides in the crystal state have been presented so far. Hence, to validate the capability of common force fields (AMBER19SB, CHARMM36m, and OPLS-AA/M) to yield insight into the dynamics and structural stability of amyloid peptide aggregates, we have performed molecular dynamics simulations of twelve different peptide crystals at two different temperatures. From the simulations, we evaluate the hydrogen bonding patterns, the isotropic B-factors, the change in energy, the Ramachandran plots, and the unit cell parameters and compare the results with the crystal structures. Most crystals are stable in the simulations but for all force fields there is at least one that deviates from the experimental crystal, suggesting more work is needed on these models.

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.

Binding Networks Identify Targetable Protein Pockets for Mechanism-Based Drug Design.

The human genome codes only a few thousand druggable proteins, mainly receptors and enzymes. While this pool of available drug targets is limited, there is an untapped potential for discovering new drug-binding mechanisms and modes. For example, enzymes with long binding cavities offer numerous prerequisite binding sites that may be visited by an inhibitor during migration from a bulk solution to the destination site. Drug design can use these prerequisite sites as new structural targets. However, identifying these ephemeral sites is challenging. Here, we introduce a new method called NetBinder for the systematic identification and classification of prerequisite binding sites at atomic resolution. NetBinder is based on atomistic simulations of the full inhibitor binding process and provides a networking framework on which to select the most important binding modes and uncover the entire binding mechanism, including previously undiscovered events. NetBinder was validated by a study of the binding mechanism of blebbistatin (a potent inhibitor) to myosin 2 (a promising target for cancer chemotherapy). Myosin 2 is a good test enzyme because, like other potential targets, it has a long internal binding cavity that provides blebbistatin with numerous potential prerequisite binding sites. The mechanism proposed by NetBinder of myosin 2 structural changes during blebbistatin binding shows excellent agreement with experimentally determined binding sites and structural changes. While NetBinder was tested on myosin 2, it may easily be adopted to other proteins with long internal cavities, such as G-protein-coupled receptors or ion channels, the most popular current drug targets. NetBinder provides a new paradigm for drug design by a network-based elucidation of binding mechanisms at an atomic resolution.

The structure of CO2 and CH4 at the interface of a poly(urethane urea) oligomer model from the microscopic point of view.

The world desperately needs new technologies and solutions for gas capture and separation. To make this possible, molecular modeling is applied here to investigate the structural, thermodynamic, and dynamical properties of a model for the poly(urethane urea) (PUU) oligomer model to selectively capture CO2 in the presence of CH4. In this work, we applied a well-known approach to derive atomic partial charges for atoms in a polymer chain based on self-consistent sampling using quantum chemistry and stochastic dynamics. The interactions of the gases with the PUU model were studied in a pure gas based system as well as in a gas mixture. A detailed structure characterization revealed high interaction of CO2 molecules with the hard segments of the PUU. Therefore, the structural and energy properties explain the reasons for the greater CO2 sorption than CH4. We find that the CO2 sorption is higher than the CH4 with a selectivity of 7.5 at 298 K for the gas mixture. We characterized the Gibbs dividing surface for each system, and the CO2 is confined for a long time at the gas-oligomer model interface. The simulated oligomer model showed performance above the 2008 Robeson's upper bound and may be a potential material for CO2/CH4 separation. Further computational and experimental studies are needed to evaluate the material.

Microscopic origins of conductivity in molten salts unraveled by computer simulations.

Molten salts are crucial materials in energy applications, such as batteries, thermal energy storage systems or concentrated solar power plants. Still, the determination and interpretation of basic physico-chemical properties like ionic conductivity, mobilities and transference numbers cause debate. Here, we explore a method for determination of ionic electrical mobilities based on non-equilibrium computer simulations. Partial conductivities are then determined as a function of system composition and temperature from simulations of molten LiFαClßIγ (with α + ß + γ = 1). High conductivity does not necessarily coincide with high Li+ mobility for molten LiFαClßIγ systems at a given temperature. In salt mixtures, the lighter anions on average drift along with Li+ towards the negative electrode when applying an electric field and only the heavier anions move towards the positive electrode. In conclusion, the microscopic origin of conductivity in molten salts is unraveled here based on accurate ionic electrical mobilities and an analysis of the local structure and kinetics of the materials.

Accurate absolute free energies for ligand-protein binding based on non-equilibrium approaches.

The accurate calculation of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art molecular dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equilibrium sampling of the phase space. In the current work we demonstrate that accurate absolute binding free energies (ABFE) can also be obtained via theoretically rigorous non-equilibrium approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equilibrium and non-equilibrium approaches converge to the same results. The non-equilibrium approach achieves the same level of accuracy and convergence as an equilibrium free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equilibrium approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equilibrium ABFE calculations are shown to yield reliable and well-converged estimates of protein-ligand binding affinity.

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.

A potential for molecular simulation of compounds with linear moieties.

The harmonic angle bending potential is used in many force fields for (bio)molecular simulation. The force associated with this potential is discontinuous at angles close to 180°, which can lead to numeric instabilities. Angle bending of linear groups, such as alkynes or nitriles, or linear molecules, such as carbon dioxide, can be treated by a simple harmonic potential if we describe the fluctuations as a deviation from a reference position of the central atom, the position of which is determined by the flanking atoms. The force constant for the linear angle potential can be derived analytically from the corresponding force constant in the traditional potential. The new potential is tested on the properties of alkynes, nitriles, and carbon dioxide. We find that the angles of the linear groups remain about 2° closer to 180° using the new potential. The bond and angle force constants for carbon dioxide were tuned to reproduce the experimentally determined frequencies. An interesting finding was that simulations of liquid carbon dioxide under pressure with the new flexible model were stable only when explicitly modeling the long-range Lennard-Jones (LJ) interactions due to the very long-range nature of the LJ interactions (>1.7 nm). In the other tested liquids, we find that a Lennard-Jones cutoff of 1.1 nm yields similar results as the particle mesh Ewald algorithm for LJ interactions. Algorithmic factors influencing the stability of liquid simulations are discussed as well. Finally, we demonstrate that the linear angle potential can be used in free energy perturbation calculations.

Toward a Computational Ecotoxicity Assay.

Thousands of anthropogenic chemicals are released into the environment each year, posing potential hazards to human and environmental health. Toxic chemicals may cause a variety of adverse health effects, triggering immediate symptoms or delayed effects over longer periods of time. It is thus crucial to develop methods that can rapidly screen and predict the toxicity of chemicals to limit the potential harmful impacts of chemical pollutants. Computational methods are being increasingly used in toxicity predictions. Here, the method of molecular docking is assessed for screening potential toxicity of a variety of xenobiotic compounds, including pesticides, pharmaceuticals, pollutants, and toxins derived from the chemical industry. The method predicts the binding energy of pollutants to a set of carefully selected receptors under the assumption that toxicity in many cases is related to interference with biochemical pathways. The strength of the applied method lies in its rapid generation of interaction maps between potential toxins and the targeted enzymes, which could quickly yield molecular-level information and insight into potential perturbation pathways, aiding in the prioritization of chemicals for further tests. Two scoring functions are compared: Autodock Vina and the machine-learning scoring function RF-Score-VS. The results are promising, although hampered by the accuracy of the scoring functions. The strengths and weaknesses of the docking protocol are discussed, as well as future directions for improving the accuracy for the purpose of toxicity predictions.

An Intuitively Understandable Quality Measure for Theoretical Vibrational Spectra.

Computational chemistry has become a central tool in spectroscopic studies in most of chemical science. The quality of a calculated vibrational spectrum is commonly expressed as the deviation of the peak position from the experimental reference. With the increasing application of vibrational spectroscopy to complex (biological) systems, this is likely not sustainable. Here we present a quality measure for theoretical vibrational spectra based on matching the spectra to a reference database with the help of correlation coefficients. This approach can easily be applied to large sets of data and complex spectra without easily identifiable peak positions. We demonstrate this on a database of infrared spectra of 670 compounds using six different theoretical (DFT and force field) methods. Most importantly, it is intuitively understandable by both theoreticians and experimentalists.

Theoretical Infrared Spectra: Quantitative Similarity Measures and Force Fields.

Infrared spectroscopy can provide significant insight into the structures and dynamics of molecules of all sizes. The information that is contained in the spectrum is, however, often not easily extracted without the aid of theoretical calculations or simulations. We present here the calculation of the infrared spectra of a database of 703 gas phase compounds with four different force fields (CGenFF, GAFF-BCC, GAFF-ESP, and OPLS) using normal-mode analysis. Modern force fields increasingly use virtual sites to describe, e.g., lone-pair electrons or the σ-holes on halogen atoms. This requires some adaptation of code to perform normal-mode analysis of such compounds, the implementation of which into the GROMACS software is briefly described as well. For the quantitative comparison of the obtained spectra with experimental reference data, we discuss the application of two different statistical correlation coefficients, Pearson and Spearman. The advantages and drawbacks of the different methods of comparison are discussed, and we find that both methods of comparison give the same overall picture, showing that present force field methods cannot match the performance of quantum chemical methods for the calculation of infrared spectra.

Making Soup: Preparing and Validating Models of the Bacterial Cytoplasm for Molecular Simulation.

Biomolecular crowding affects the biophysical and biochemical behavior of macromolecules compared with the dilute environment in experiments on isolated proteins. Computational modeling and simulation are useful tools to study how crowding affects the structural dynamics and biological properties of macromolecules. With increases in computational power, modeling and simulation of large-scale all-atom explicit-solvent models of the prokaryote cytoplasm have now become possible. In this work, we built an atomistic model of the cytoplasm of Escherichia coli composed of 1.5 million atoms and submitted it to a total of 3 µs of molecular dynamics simulations. The model consisted of eight different proteins representing about 50% of the cytoplasmic proteins and one type of t-RNA molecule. Properties of biomolecules under crowding conditions were compared with those from simulations of the individual compounds under dilute conditions. The simulation model was found to be consistent with experimental data about the diffusion coefficient and stability of macromolecules under crowded conditions. In order to stimulate further work, we provide a Python script and a set of files to enable other researchers to build their own E. coli cytoplasm models to address questions related to crowding.

Rotational and Translational Diffusion of Proteins as a Function of Concentration.

Atomistic simulations of three different proteins at different concentrations are performed to obtain insight into protein mobility as a function of protein concentration. We report on simulations of proteins from diluted to the physiological water concentration (about 70% of the mass). First, the viscosity was computed and found to increase by a factor of 7-9 going from pure water to the highest protein concentration, in excellent agreement with in vivo nuclear magnetic resonance results. At a physiological concentration of proteins, the translational diffusion is found to be slowed down to about 30% of the in vitro values. The slow-down of diffusion found here using atomistic models is slightly more than that of a hard sphere model that neglects the electrostatic interactions. Interestingly, rotational diffusion of proteins is slowed down somewhat more (by about 80-95% compared to in vitro values) than translational diffusion, in line with experimental findings and consistent with the increased viscosity. The finding that rotation is retarded more than translation is attributed to solvent-separated clustering. No direct interactions between the proteins are found, and the clustering can likely be attributed to dispersion interactions that are stronger between proteins than between protein and water. Based on these simulations, we can also conclude that the internal dynamics of the proteins in our study are affected only marginally under crowding conditions, and the proteins become somewhat more stable at higher concentrations. Simulations were performed using a force field that was tuned for dealing with crowding conditions by strengthening the protein-water interactions. This force field seems to lead to a reproducible partial unfolding of an α-helix in one of the proteins, an effect that was not observed in the unmodified force field.

Prediction of Partition Coefficients of Environmental Toxins Using Computational Chemistry Methods.

The partitioning of compounds between aqueous and other phases is important for predicting toxicity. Although thousands of octanol-water partition coefficients have been measured, these represent only a small fraction of the anthropogenic compounds present in the environment. The octanol phase is often taken to be a mimic of the inner parts of phospholipid membranes. However, the core of such membranes is typically more hydrophobic than octanol, and other partition coefficients with other compounds may give complementary information. Although a number of (cheap) empirical methods exist to compute octanol-water (log k OW) and hexadecane-water (log k HW) partition coefficients, it would be interesting to know whether physics-based models can predict these crucial values more accurately. Here, we have computed log k OW and log k HW for 133 compounds from seven different pollutant categories as well as a control group using the solvation model based on electronic density (SMD) protocol based on Hartree-Fock (HF) or density functional theory (DFT) and the COSMO-RS method. For comparison, XlogP3 (log k OW) values were retrieved from the PubChem database, and KowWin log k OW values were determined as well. For 24 of these compounds, log k OW was computed using potential of mean force (PMF) calculations based on classical molecular dynamics simulations. A comparison of the accuracy of the methods shows that COSMO-RS, KowWin, and XlogP3 all have a root-mean-square deviation (rmsd) from the experimental data of ≈0.4 log units, whereas the SMD protocol has an rmsd of 1.0 log units using HF and 0.9 using DFT. PMF calculations yield the poorest accuracy (rmsd = 1.1 log units). Thirty-six out of 133 calculations are for compounds without known log k OW, and for these, we provide what we consider a robust prediction, in the sense that there are few outliers, by averaging over the methods. The results supplied may be instrumental when developing new methods in computational ecotoxicity. The log k HW values are found to be strongly correlated to log k OW for most compounds.

Systematically improved melting point prediction: a detailed physical simulation model is required.

Accurate prediction of fundamental properties such as melting points using direct physical simulation is challenging. Here, we investigate the melting point (Tm) of alkali halides that are often considered to be the simplest category of salts. Popular force fields that have been examined for this task leave considerable room for improvement. Recently we introduced a new force field for alkali halides (WBK) as part of the Alexandria project, featuring explicit polarisation and distributed charges. This new force field significantly improves the prediction of a large set of physicochemical properties and in this contribution we show that the same is valid for the prediction of Tm. For reference, we calculated Tm using a non-polarisable force field by Joung and Cheatham (JC), and compare our results to existing literature data on the widely used Tosi-Fumi (TF) parameters. In contrast to the predictions of the WBK model, the JC force field consistently overestimates the experimental Tm, while the accuracy of the TF model strongly depends on the investigated salt. Our results show that the inclusion of more realistic physics into a force field opens up the possibility to accurately describe many physicochemical properties over a large range of temperatures, even including phase transitions.