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At least 19 records

CHARMM-GUI Free Energy Calculator for Absolute and Relative Ligand Solvation and Binding Free Energy Simulations

Alchemical free energy simulations have long been utilized to predict free energy changes for binding affinity and solubility of small molecules. However, while the theoretical foundation of these methods is well established, seamlessly handling many of the practical aspects regarding the preparation of the different thermodynamic end states of complex molecular systems and the numerous processing scripts often remains a burden for successful applications. Here, we present CHARMM-GUI Free Energy Calculator (http://www.charmm-gui.org/input/fec) that provides various alchemical free energy perturbation molecular dynamics (FEP/MD) systems with input and post-processing scripts for NAMD and GENESIS. Four submodules are available: Absolute Ligand Binder (for absolute ligand binding FEP/MD), Relative Ligand Binder (for relative ligand binding FEP/MD), Absolute Ligand Solvator (for absolute ligand solvation FEP/MD), and Relative Ligand Solvator (for relative ligand solvation FEP/MD). Each module is designed to build multiple systems of a set of selected ligands at once for high-throughput FEP/MD simulations. The capability of Free Energy Calculator is illustrated by absolute and relative solvation FEP/MD of a set of ligands and absolute and relative binding FEP/MD of a set of ligands for T4-lysozyme in solution and the adenosine A 2A receptor in a membrane. The calculated free energy values are overall consistent with the experimental and published free energy results (within ~1 kcal/mol). We hope that Free Energy Calculator is useful to carry out high-throughput FEP/MD simulations in the field of biomolecular sciences and drug discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Protein–Ligand Binding Free-Energy Calculations with ARROW–A Purely First-Principles Parameterized Polarizable Force Field

Protein–ligand binding free-energy calculations using molecular dynamics (MD) simulations have emerged as a powerful tool for in silico drug design. Here, we present results obtained with the ARROW force field (FF)–a multipolar polarizable and physics-based model with all parameters fitted entirely to high-level ab initio quantum mechanical (QM) calculations. ARROW has already proven its ability to determine solvation free energy of arbitrary neutral compounds with unprecedented accuracy. The ARROW FF parameterization is now extended to include coverage of all amino acids including charged groups, allowing molecular simulations of a series of protein–ligand systems and prediction of their relative binding free energies. We ensure adequate sampling by applying a novel technique that is based on coupling the Hamiltonian Replica exchange (HREX) with a conformation reservoir generated via potential softening and nonequilibrium MD. ARROW provides predictions with near chemical accuracy (mean absolute error of ~0.5 kcal/mol) for two of the three protein systems studied here (MCL1 and Thrombin). The third protein system (CDK2) reveals the difficulty in accurately describing dimer interaction energies involving polar and charged species. Overall, for all of the three protein systems studied here, ARROW FF predicts relative binding free energies of ligands with a similar accuracy level as leading nonpolarizable force fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of a multiphase equation of state for gallium with experiments and ab initio free-energy calculations

Here, we present a five-phase equation of state (EOS) for elemental gallium (Ga) that is developed using both experimental data and new theoretical predictions. Four experimentally observed solid phases (Ga-I, Ga-II, Ga-III, and Ga-IV) and one liquid phase are included. To improve our understanding of the thermal behavior of Ga and its phase boundaries under compression, we have performed ab initio density functional theory (DFT) free-energy calculations for the Ga-III and liquid phases, which enables us to determine the melt temperature to be 2214 ± 100 K at 110 GPa, extending significantly beyond the existing experimental melt data, which are limited to 25 GPa. In order to best describe the electron-thermal contribution, which dominates the liquid free energy at high temperatures, we have carried out averaged-atom-in-jellium DFT calculations to cover the entire temperature and density range of the EOS. The resulting multiphase Ga EOS is able to accurately reproduce a diverse variety of data, including known phase boundaries, the principal Hugoniot, low-pressure liquid isobars, and diamond-anvil-cell isotherm measurements at high pressures. It agrees more closely with key experimentally measured properties than other Ga EOS models targeted for high-pressure applications.

Wu, Christine J. [Lawrence Livermore National Labo↗

Acceleration of Solvation Free Energy Calculation via Thermodynamic Integration Coupled with Gaussian Process Regression and Improved Gelman–Rubin Convergence Diagnostics

The determination of the solvation free energy of ions and molecules holds profound importance across a spectrum of applications spanning chemistry, biology, energy storage, and the environment. Molecular dynamics simulations are powerful tools for computing this critical parameter. Nevertheless, the accurate and efficient calculation of the solvation free energy becomes a formidable endeavor when dealing with complex systems characterized by potent Coulombic interactions and sluggish ion dynamics and, consequently, slow transition across various metastable states. Here, in the present study, we expose limitations stemming from the conventional calculation of the statistical inefficiency g in the thermodynamic integration method, a factor that can hinder the determination of convergence of the solvation free energy and its associated uncertainty. Instead, we propose a robust scheme based on Gelman–Rubin convergence diagnostics. We leverage this improved estimation of uncertainties to introduce an innovative accelerated thermodynamic integration method based on the Gaussian Process regression. This methodology is applied to the calculation of the solvation free energy of trivalent rare-earth elements immersed in ionic liquids, a scenario in which the aforementioned challenges render standard approaches ineffective. The proposed method proves to be effective in computing solvation free energy in situations where traditional thermodynamic integration methods fall short.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large Scale Study of Ligand–Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols

The accurate and reliable prediction of protein–ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchemical free energy methods that furnish an estimation of relative binding free energies (RBFE) of similar molecules. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing number of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a number of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calculations. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying molecular dynamics is chaotic. These are implemented using TIES (Thermodynamic Integration with Enhanced Sampling). Results achieve chemical accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calculations which exhibit non-normal behavior. We find that the “enhanced sampling” method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous associated alchemical factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchemical region including the number of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular Dynamics and Free Energy Calculations of Dicyclohexano-18-crown-6 Diastereoisomers with Sm 2+ , Eu 2+ , Dy 2+ , Yb 2+ , Cf 2+ , and Three Halide Salts in Tetrahydrofuran and Acetonitrile Using the AMOEBA Force Field

With the continual development of lanthanides (Ln) in current technological devices, an efficient separation process is needed that can recover greater amounts of these rare elements. Dicyclohexano-18-crown-6(DCH18C6) is a crown ether that may be a promising candidate for Ln separation, but additional research is required. As such, molecular dynamics(MD) simulations have been performed on four divalent lanthanide halide salts(Sm 2+ , Eu 2+ , Dy 2+ , and Yb 2+ ) and one divalent actinide halide salt (Cf 2+ ) bound to three diastereoisomers of DCH18C6. Dy 2+ , Yb 2+ , Cf 2+ , DCH18C6, and tetrahydrofuran (THF) solvent were parameterized for the AMOEBA polarizable force field for the first time, whereas existing parameters for Sm 2+ and Eu 2+ were utilized from our previous efforts. A coordination number (CN) of six for Ln 2+ /An 2+ –O solvated in THF indicated that the cations interacted almost entirely with the oxygens of the polyether ring. A CN of one for Ln 2+ /An 2+ -N solvated in acetonitrile for systems containing iodide suggested that theN atom of acetonitrile was competitive with I – for cation interactions. Fluctuation between five and six CNs for Dy 2+ and Yb 2+ suggested that although the cations remained in the polyether ring, the size of the ring may not be an ideal fit as these cations possess comparatively smaller ionic radii. Gibbs binding free energies of Sm 2+ in all DCH18C6 diastereoisomers solvated in THF were calculated. The binding free energy of the cis-syn-cis diastereoisomer was the most favorable, followed by cis-anti-cis, and then trans-anti-trans. Lastly, two major types of conformation were observed for each diastereoisomer that were related to the electrostatic interactions and charge density of the cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-pressure phase diagram of beryllium from ab initio free-energy calculations

In this report we use first-principles molecular dynamics simulations coupled with the thermodynamic integration method to study the hexagonal close-packed (hcp) to body-centered cubic (bcc) transition and melting of beryllium up to a pressure of 1600 GPa. We derive the melting line by equating solid and liquid Gibbs free energies and represent it by a Simon-Glatzel fit T m = 1564 K [1 + P/(15.6032 GPa)] 0.383 , which is in good agreement with previous two-phase simulations <6000 K. We also derive the hcp-bcc solid-solid phase boundary and show that the quasiharmonic approximation underestimates the stability of the hcp structure, predicting lower transition pressures between hcp and bcc phases. Our results are consistent with the stability regime predicted by the phonon quasiparticle method. We also predict that the hcp-bcc-liquid triple point is located at 164.7 GPa and 4314 K. In addition, we compute the shock Hugoniot curve and show that it is in good agreement with experiments, intersecting our derived melting curve at ~235 GPa and 4900 K. Finally, we make predictions for future ramp compression experiments. Starting with an isentropic compression of the liquid, we predict the path to intersect the melting line at low pressure and temperature, then to continue along the melting line over a large temperature interval of 7000 K as the sample remains in the mixed solid-liquid state before it enters the solid phase.

36 MATERIALS SCIENCE↗

Understanding Pore Filling Processes and Adsorption/Desorption Hysteresis in Nanoporous Metal–Organic Frameworks: Insights from Grand Canonical Monte Carlo Simulations and Free Energy Calculations

Grand canonical Monte Carlo (GCMC) simulations were used to investigate pore filling and hysteresis in nanoporous metal-organic frameworks (MOFs). Adsorption and desorption isotherms were calculated for argon at 87 K in 1866 MOFs from the CoRE MOF database and for short n-alkanes in selected MOFs, keeping the adsorbent structure rigid. Analysis of the molecular configurations showed two different mechanisms and origins of hysteresis: one involving a transition of the adsorbate arrangement in the pores similar to a gas-to-liquid transition associated with a large change in the loading and one more similar to a liquid-to-solid transition associated with a relatively small change in the loading. Our GCMC simulations in MOFs with diverse pore topologies indicate exceptions to an empirical relationship for the minimum diameter of a cylindical pore required for hysteresis as a function of the adsorbate diameter and reduced temperature. The simulations reveal some structures where isotherms exhibit two steps in the adsorption branch and only one step in the desorption branch. Hysteresis loops with a different number of adsorption and desorption steps are not common. Here, to better understand why hysteresis is observed in the GCMC simulations, the concept of the transition probability for observing a step in the adsorption isotherm at a given pressure in a GCMC simulation is introduced. We used two different methods to calculate the transition probabilities and find that these yield comparable results. Furthermore, the transition probability provides a measure for the length of GCMC simulations to yield reliable results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solvent effects on extractant conformational energetics in liquid–liquid extraction: a simulation study of molecular solvents and ionic liquids

Extractant design in liquid–liquid extraction (LLE) is a research frontier of metal ion separations that typically focuses on the direct extractant–metal interactions. However, a more detailed understanding of energetic drivers of separations beyond primary metal coordination is often lacking, including the role of solvent in the extractant phase. In this work, we propose a new mechanism for enhancing metal-complexant energetics with nanostructured solvents. Using molecular dynamics simulations with umbrella sampling, we find that the organic solvent can reshape the energetics of the extractant's intramolecular conformational landscape. Here, we calculate free energy profiles of different conformations of a representative bidentate extractant, n-octyl(phenyl)-N,N-diisobutyl carbamoyl methyl phosphinoxide (CMPO), in four different solvents: dodecane, tributyl phosphate (TBP), and dry and wet ionic liquid (IL) 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM][Tf 2 N]). By promoting reorganization of the extractant molecule into its binding conformation, our findings reveal how particular solvents can ameliorate this unfavorable step of the metal separation process. In particular, the charge alternating nanodomains formed in ILs substantially reduce the free energy penalty associated with extractant reorganization. Importantly, using alchemical free energy calculations, we find that this stabilization persists even when we explicitly include the extracted cation. These findings provide insight into the energetic drivers of metal ion separations and potentially suggest a new approach to designing effective separations using a molecular-level understanding of solvent effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large-scale application of free energy perturbation calculations for antibody design

Abstract Alchemical free energy perturbation (FEP) is a rigorous and powerful technique to calculate the free energy difference between distinct chemical systems. Here we report our implementation of automated large-scale FEP calculations, using the Amber software package, to facilitate antibody design and evaluation. In combination with Hamiltonian replica exchange, our FEP simulations aim to predict the effect of mutations on both the binding affinity and the structural stability. Importantly, we incorporate multiple strategies to faithfully estimate the statistical uncertainties in the FEP results. As a case study, we apply our protocols to systematically evaluate variants of the m396 antibody for their conformational stability and their binding affinity to the spike proteins of SARS-CoV-1 and SARS-CoV-2. By properly adjusting relevant parameters, the particle collapse problems in the FEP simulations are avoided. Furthermore, large statistical errors in a small fraction of the FEP calculations are effectively reduced by extending the sampling, such that acceptable statistical uncertainties are achieved for the vast majority of the cases with a modest total computational cost. Finally, our predicted conformational stability for the m396 variants is qualitatively consistent with the experimentally measured melting temperatures. Our work thus demonstrates the applicability of FEP in computational antibody design.

59 BASIC BIOLOGICAL SCIENCES↗

Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility

The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat a myriad of diseases. In this work, we examine the computation of alchemical relative binding free energies with an eye for assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2, and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2, and NAMD3 alpha. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between them of 0.50 kcal/mol. The correlation between packages is very good, with the lowest Spearman’s, Pearson’s and Kendall’s tau correlation coefficients being 0.92, 0.91, and 0.76, respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-Precision Calculation of Nanoparticle (Nanocrystal) Potentials of Mean Force and Internal Energies

Thermodynamic stability assessment of nanocrystal systems requires precise free energy calculations. This study highlights the importance of meticulous control over various factors, including the thermostat, time step, potential cutoff, initial configuration, sampling method, and overall simulation duration. Free energy computations in dry (solvent-free) systems are on the order of several hundred $k_BT$ but can be obtained with consistent accuracy. However, calculation of internal energies becomes challenging, as they are typically much larger in magnitude than free energies and exhibit significant noise and reduced reliability. To address this limitation, we propose a new internal energy estimate that drastically reduces the noise. Here, we also present formulas that enable the optimization of the parameters of the harmonic bias potential for optimal convergence. Finally, we discuss the implications of these findings for the computation of free energies in nanocrystal clusters and superlattices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Potent Noncovalent Inhibitors of the Main Protease of SARS-CoV-2 from Molecular Sculpting of the Drug Perampanel Guided by Free Energy Perturbation Calculations

Starting from our previous finding of 14 known drugs as inhibitors of the main protease (M pro ) of SARS-CoV-2, the virus responsible for COVID-19, we have redesigned the weak hit perampanel to yield multiple noncovalent, nonpeptidic inhibitors with ca. 20 nM IC 50 values in a kinetic assay. Free-energy perturbation (FEP) calculations for M pro -ligand complexes provided valuable guidance on beneficial modifications that rapidly delivered the potent analogues. The design efforts were confirmed and augmented by determination of high-resolution X-ray crystal structures for five analogues bound to M pro . Results of cell-based antiviral assays further demonstrated the potential of the compounds for treatment of COVID-19. In addition to the possible therapeutic significance, the work clearly demonstrates the power of computational chemistry for drug discovery, especially FEP-guided lead optimization.

99 GENERAL AND MISCELLANEOUS↗

Revisiting the pseudo-supercritical path method: An improved formulation for the alchemical calculation of solid–liquid coexistence

Alchemical free energy calculations via molecular dynamics have been applied to obtain thermodynamic properties related to solid–liquid equilibrium conditions, such as melting points. In recent years, the pseudo-supercritical path (PSCP) method has proved to be an important approach to melting point prediction due to its flexibility and applicability. In the present work, we propose improvements to the PSCP alchemical cycle to make it more compact and efficient through a concerted evaluation of different potential energies. The multistate Bennett acceptance ratio (MBAR) estimator was applied at all stages of the new cycle to provide greater accuracy and uniformity, which is essential concerning uncertainty calculations. In particular, for the multistate expansion stage from solid to liquid, we employed the MBAR estimator with a reduced energy function that allows affine transformations of coordinates. Free energy and mean derivative profiles were calculated at different cycle stages for argon, triazole, propenal, and the ionic liquid 1-ethyl-3-methyl-imidazolium hexafluorophosphate. Comparisons showed a better performance of the proposed method than the original PSCP cycle for systems with higher complexity, especially the ionic liquid. Furthermore, a detailed study of the expansion stage revealed that remapping the centers of mass of the molecules or ions is preferable to remapping the coordinates of each atom, yielding better overlap between adjacent states and improving the accuracy of the methodology.

25 ENERGY STORAGE↗

Binding Free Energy Analysis of Colicin D, E3 and E8 to Their Respective Cognate Immunity Proteins Using Computational Simulations

Colicins are antimicrobial proteins produced by bacteria for the purpose of destroying neighboring bacteria. Colicin activity is neutralized by a specific cognate immunity protein in order to protect the host. This study investigates the structural and binding mechanisms underlying the interaction of colicin-D, -E3 and -E8 to their respective immunity proteins (ImD, Im3 and Im8) using structure prediction, molecular dynamics (MD) simulations and MM-PBSA approach of free energy calculations. High-confidence colicin-immunity (Col-Im) complex structures predicted using AlphaFold2 were subjected to MD simulations of 150 ns with GROMACS and were analyzed for the binding free energy calculation using gmx_MMPBSA. Results showed that the complex of Col_E3-Im3 exhibited the most favorable binding free energy, driven by strong van der Waals and electrostatic interactions. Col_D-ImD and Col_E8-Im8 also showed the favorable binding. Electrostatics and hydrogen bonding emerged as a key factor driving binding and stability, while polar solvation acted as a destabilizing factor across all systems. These outcomes provide an understanding of the molecular mechanisms of Col-Im systems, with potential applications for developing natural antimicrobials for food safety.

Biochemistry & Molecular Biology↗