Bennett Acceptance Ratio Method Research Articles

In silico identification and evaluation of potential interaction of Azadirachta indica phytochemicals with Plasmodium falciparum heat shock protein 90

Plasmodium falciparum heat shock protein 90 (PfHsp90) has been investigated as a potential target of antimalarial drug action using naturally occurring compounds. In this study, we performed in silico screening of 236 phytochemicals of Azadirachta indica, a plant known to possess antimalarial activity, and identified fourteen (14) potential non-carcinogenic, non-mutagenic, non-teratogenic and non-genotoxic phytochemicals. These phytochemicals were docked into the ATP-binding site of PfHsp90 using Autodock vina, and docked poses were rescored using PLANTS ChemPlp, X-Score version 1.2 and NNScore version 2.0. Consensus analysis of the scores using rank-by-rank and rank-by-number and receptor-ligand interaction assessment using LigPlot, led to the identification of margolone, margolonone, nimbinone, nimbione, nimosone and sugiol as best ranked potential interacting partners of PfHsp90. Molecular dynamic simulations of PfHsp90-ligand complexes for the six phytochemicals were performed using NAMD 2.9. The RMSD analysis of simulations trajectories, the ligand interaction analysis of receptor-ligand complex, and the free energy of binding with MMPBSA.py script and Bennett's acceptance ratio method (BAR) confirmed that these six phytochemicals may have potential to functionally interact with PfHsp90. However, though sharing several similar interacting residues with standard control binders yet the higher number of hydrogen bonds, higher level of sustained stability during molecular dynamics simulations and better free energy of binding suggest that margolonone, nimbinone and nimbione may have higher functional interaction potential with PfHsp90. Therefore, these phytochemicals may serve as potential leads in antimalarial drug design and development.

Solvation free energy of light alkanes in polar and amphiphilic environments

Computer simulations of molecular models are powerful technique that have improved the under- standing of many biochemical phenomena. The method is frequently applied to study the motions of biological macromolecules such as protein and nucleic acids, which can be useful for interpreting the results of certain biophysical experiments. In this work, we have estimated the solvation free energy for light alkane (methane, ethane, propane and n-butane) dissolved in water and methanol respectively over a broad range of temperatures, from 275 K to 375 K, using molecular dynamics simulations. The alkane (methane, ethane, propane and n-butane), and methanol molecules are described by the OPLS-AA (Optimized Potentials for Liquid Simulations-All Atom) potential, while water is modeled by TIP3P (Transferable Intermolecular Potential with 3-Points) model. We have used the free energy perturbation method (Bennett Acceptance Ratio (BAR) method) for the calculation of free energy of solvation. The estimated values of solvation free energy of alkane in the corresponding solvents agree well with the available experimental data.BIBECHANA 16 (2019) 91-104

Evaluation of the SAFT-γ Mie force field with solvation free energy calculations

Solvation free energies can be essential in the process of evaluating and developing force fields. In addition, they can be used to obtain a diversity of other thermodynamic properties such as Henry's law constants and partition coefficients, for instance. In this paper, we study the solvation of asphaltene-like molecules (polyaromatic hydrocarbons) in both aqueous and organic solvents by using a coarse-grained model known as the SAFT-γ Mie force field. This model relies on a top-down approach in which the force-field parameters are obtained using an equation of state. The use of solvation free energy calculations to evaluate this force field can help in improving the model and increasing the scale in which these simulations can be applied. The results presented here were obtained by carrying out molecular dynamics simulations, with the expanded ensemble method being applied to sample an alchemical path. For this, we employed a softcore variant of the Mie potential. From the output of these simulations, we estimated free-energy differences by means of the Multistate Bennett Acceptance Ratio method. The results with organic solvents exhibited low absolute deviations from experimental data. In turn, hydration free energy calculations required a binary interaction parameter to be estimated from molecular dynamics data, which displays a flaw in the top-down parameterization approach. Fortunately, however, a single binary parameter could be used for all pairs of polyaromatic hydrocarbons with water, proving that the SAFT-γ Mie force field exhibits a suitable transferability property that deserves further investigation.

Prediction of CB[8] host-guest binding free energies in SAMPL6 using the double-decoupling method.

This study reports the results of binding free energy calculations for CB[8] host-guest systems in the SAMPL6 blind challenge (receipt ID 3z83m). Force-field parameters were developed specific for each of host and guest molecules to improve configurational sampling. We used quantum mechanical (QM) implicit solvent calculations and QM force matching to determine non-bonded (partial atomic charges) and bonded terms, respectively. Free energy calculations were carried out using the double-decoupling method (DDM) combined with Hamiltonian replica exchange method (HREM) and Bennett acceptance ratio (BAR) method. The root mean square error (RMSE) of the predicted values using DDM with respect to the experimental results was 4.32kcal/mol. The coefficient of determination (R2) and Kendall rank coefficient (τ) were 0.49 and 0.52, respectively, highest of all submissions. In addition, these were compared to the results obtained by umbrella sampling (US) and weighted histogram analysis method (WHAM). Overall, DDM achieved a higher prediction accuracy than the US method. Results are discussed in terms of parameterization and free energy simulations.

Biosolvation Nature of Ionic Liquids: Molecular Dynamics Simulation of Methylated Nucleobases in Hydrated 1-Ethyl-3-methylimidazolium Acetate.

Solvation free energies of methylated nucleobases were calculated in pure and hydrated 1-ethyl-3-methylimidazolium acetate, [Emim][Ac], ionic liquid, and pure water using classical molecular dynamics simulations using multistate Bennett’s acceptance ratio method. The calculated solvation free energies in pure water were compared with the previous experimental and theoretical findings and found to be in agreement. We observe that the solvation free energy of methylated nucleobases is more in the pure ionic liquid compared to that in the pure water and on changing the mole fraction of water in the ionic liquid, the solvation free energy decreases gradually. Comparing the Coulombic and van der Waals contribution to the solvation free energy, electrostatic contribution is more compared to that of the latter for all nucleobases. To obtain the atomistic details and explain the solvation mechanism, we calculated radial distribution functions (RDFs), spatial distribution functions (SDFs), and stacking angle distribution of cations to the nucleobases. From RDFs and SDFs, we find that the acetate anions of the ionic liquid are forming strong hydrogen bonds with the amine hydrogen atoms of the nucleobases. These hydrogen bonds contribute to the major part of the Coulombic contribution to the solvation free energy. Stacking of cations to the nucleobases is primarily due to the van der Waals contribution to the solvation free energy.

A Novel Microemulsion Phase Transition: Toward the Elucidation of Third-Phase Formation in Spent Nuclear Fuel Reprocessing.

We present evidence that the transition between organic and third phases, which can be observed in the plutonium uranium reduction extraction (PUREX) process at high metal loading, is an unusual transition between two isotropic bicontinuous microemulsion phases. As this system contains so many components, however, we have been seeking first to investigate the properties of a simpler system, namely, the related metal-free, quaternary water/n-dodecane/nitric acid/tributyl phosphate (TBP) system. This quaternary system has been shown to exhibit, under appropriate conditions, three coexisting phases: a light organic phase, an aqueous phase, and the so-called third phase. In the current work, we focused on the coexistence of the light organic phase with the third phase. Using Gibbs ensemble Monte Carlo (GEMC) simulations, we found coexistence of a phase rich in nitric acid and dilute in n-dodecane (the third phase) with a phase more dilute in nitric acid but rich in n-dodecane (the light organic phase). The compositions and densities of these two coexisting phases determined using the simulations were in good agreement with those determined experimentally. Because such systems are generally dense and the molecules involved are not simple, the particle exchange rate in their GEMC simulations can be rather low. To test whether a system having a composition between those of the observed third and organic phases is indeed unstable with respect to phase separation, we used the Bennett acceptance ratio method to calculate the Gibbs energies of the homogeneous phase and the weighted average of the two coexisting phases, where the compositions of these phases were taken both from experimental results and from the results of the GEMC simulations. Both demixed states were determined to have statistically significant lower Gibbs energies than the uniform, mixed phase, providing confirmation that the GEMC simulations correctly predicted the phase separation. Snapshots from the simulations and a cluster analysis of the organic and third phases revealed structures akin to bicontinuous microemulsion phases, with the polar species residing within a mesh and with the surface of the mesh formed by amphiphilic TBP molecules. The nonpolar n-dodecane molecules were observed in these snapshots to be outside this mesh. The only large-scale structural differences observed between the two phases were the dimensions of the mesh. Evidence for the correctness of these structures was provided by the results of small-angle X-ray scattering (SAXS) studies, where the profiles obtained for both the organic and third phases agreed well with those calculated from simulations. Finally, we looked at the microscopic structures of the two phases. In the organic phase, the basic motif was observed to be one nitric acid molecule hydrogen-bonded to a TBP molecule. In the third phase, the most common structure was that of the hydrogen-bonded TBP-HNO3-HNO3 chain. A cluster analysis provided evidence for TBP forming an extended, connected network in both phases. Studies of the effects of metal ions on these systems will be presented elsewhere.

Nonequilibrium free-energy estimation conditioned on measurement outcomes.

The Jarzynski equality is one of the most influential results in the field of nonequilibrium statistical mechanics. This celebrated equality allow the calculation of equilibrium free-energy differences from work distributions of nonequilibrium processes. In practice, such calculations often suffer from poor convergence due to the need to sample rare events. Here we examine if the inclusion of measurement and feedback can improve the convergence of nonequilibrium free-energy calculations. A modified version of the Jarzynski equality in which realizations with a given outcome are kept, while others are discarded, is used. We find that discarding realizations with unwanted outcomes can result in improved convergence compared to calculations based on the Jarzynski equality. We argue that the observed improved convergence is closely related to Bennett's acceptance ratio method, which was developed without any reference to measurements or feedback.

A Coarse-Grained Force Field Parameterized for MgCl2 and CaCl2 Aqueous Solutions.

Calcium and magnesium ions play important roles in many physicochemical processes. To facilitate the investigation of phenomena related to these ions that occur over large length and time scales, a coarse-grained force field (CGFF) is developed for MgCl2 and CaCl2 aqueous solutions. The ions are modeled by CG beads with characteristics of hydration shells. To accurately describe the nonideal behavior of the solutions, osmotic coefficients in a wide range of concentrations were used as guidance for parametrization. The osmotic coefficients were obtained from the chemical potential increments of water calculated using the Bennett acceptance ratio (BAR) method. The result CGFF accurately reproduces experimental osmotic coefficients, densities, surface tensions, and cation-anion separations of calcium chloride and magnesium chloride solutions at molalities up to 3.0 mol/kg. As a preliminary application, the force field is applied to simulate aggregations of sodium dodecyl sulfate (SDS) in calcium chloride solution, and the simulation results are consistent with experimental observations.

Theoretical and experimental study of polycyclic aromatic compounds as β-tubulin inhibitors.

In this work, through a docking analysis of compounds from the ZINC chemical library on human β-tubulin using high performance computer cluster, we report new polycyclic aromatic compounds that bind with high energy on the colchicine binding site of β-tubulin, suggesting three new key amino acids. However, molecular dynamic analysis showed low stability in the interaction between ligand and receptor. Results were confirmed experimentally in in vitro and in vivo models that suggest that molecular dynamics simulation is the best option to find new potential β-tubulin inhibitors. Graphical abstract Bennett's acceptance ratio (BAR) method.

The free energy of locking a ring: Changing a deoxyribonucleoside to a locked nucleic acid

Locked nucleic acid (LNA), a modified nucleoside which contains a bridging group across the ribose ring, improves the stability of DNA/RNA duplexes significantly, and therefore is of interest in biotechnology and gene therapy applications. In this study, we investigate the free energy change between LNA and DNA nucleosides. The transformation requires the breaking of the bridging group across the ribose ring, a problematic transformation in free energy calculations. To address this, we have developed a 3‐step (easy to implement) and a 1‐step protocol (more efficient, but more complicated to setup), for single and dual topologies in classical molecular dynamics simulations, using the Bennett Acceptance Ratio method to calculate the free energy. We validate the approach on the solvation free energy difference for the nucleosides thymidine, cytosine, and 5‐methyl‐cytosine. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Solvation free energies of nucleic acid bases in ionic liquids

The solvation free energies of five nucleic acid bases in [Cnbim]Br (where n = 2, 4, 6) ionic liquids (ILs) were computed using the Bennett acceptance ratio (BAR) method employing molecular dynamics simulations. The computed free energies using BAR were in agreement with other methods. The large and negative predicted free energies of the bases in ILs indicated that the bases were better solvated in the ILs rather than in water. Hydrogen bonding interactions between polar sites of the bases and ILs’ ions significantly contributed to the solvation mechanism.

Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM, and the closely-related multiple Bennett acceptance ratio method can be improved using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

Alchemical Free Energy Calculations and Isothermal Titration Calorimetry Measurements of Aminoadamantanes Bound to the Closed State of Influenza A/M2TM.

Adamantane derivatives, such as amantadine and rimantadine, have been reported to block the transmembrane domain (TM) of the M2 protein of influenza A virus (A/M2) but their clinical use has been discontinued due to evolved resistance in humans. Although experiments and simulations have provided adequate information about the binding interaction of amantadine or rimantadine to the M2 protein, methods for predicting binding affinities of whole series of M2 inhibitors have so far been scarcely applied. Such methods could assist in the development of novel potent inhibitors that overcome A/M2 resistance. Here we show that alchemical free energy calculations of ligand binding using the Bennett acceptance ratio (BAR) method are valuable for determining the relative binding potency of A/M2 inhibitors of the aminoadamantane type covering a binding affinity range of only ∼2 kcal mol(-1). Their binding affinities measured by isothermal titration calorimetry (ITC) against the A/M2TM tetramer from the Udorn strain in its closed form at pH 8 were used as experimental probes. The binding constants of rimantadine enantiomers against M2TMUdorn were measured for the first time and found to be equal. Two series of alchemical free energy calculations were performed using 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipids to mimic the membrane environment. A fair correlation was found for DPPC that was significantly improved using DMPC, which resembles more closely the DPC lipids used in the ITC experiments. This demonstrates that binding free energy calculations by the BAR approach can be used to predict relative binding affinities of aminoadamantane derivatives toward M2TM with good accuracy.

Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level.

In this article, the convergence of quantum mechanical (QM) free‐energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa‐acid deep‐cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158–224 atoms). We use single‐step exponential averaging (ssEA) and the non‐Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi‐empirical PM6‐DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free‐energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis.

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

Calculating binding free energies of host-guest systems using the AMOEBA polarizable force field.

Molecular recognition is of paramount interest in many applications. Here we investigate a series of host-guest systems previously used in the SAMPL4 blind challenge by using molecular simulations and the AMOEBA polarizable force field. The free energy results computed by Bennett's acceptance ratio (BAR) method using the AMOEBA polarizable force field ranked favorably among the entries submitted to the SAMPL4 host-guest competition [Muddana, et al., J. Comput.-Aided Mol. Des., 2014, 28, 305-317]. In this work we conduct an in-depth analysis of the AMOEBA force field host-guest binding thermodynamics by using both BAR and the orthogonal space random walk (OSRW) methods. The binding entropy-enthalpy contributions are analyzed for each host-guest system. For systems of inordinate binding entropy-enthalpy values, we further examine the hydrogen bonding patterns and configurational entropy contribution. The binding mechanism of this series of host-guest systems varies from ligand to ligand, driven by enthalpy and/or entropy changes. Convergence of BAR and OSRW binding free energy methods is discussed. Ultimately, this work illustrates the value of molecular modelling and advanced force fields for the exploration and interpretation of binding thermodynamics.

A classical force field for tetrahedral oxyanions developed using hydration properties: The examples of pertechnetate (TcO4−) and sulfate (SO42−)

Radioactive pertechnetate, (99)TcO4(-), is one of the most problematic ionic species in the context of the clean up and storage of nuclear waste. Molecular simulations can be used to understand the behavior of TcO4(-) in dilute aqueous solutions, providing reliable potentials are available. This work outlines the development of a new potential model for TcO4(-) and competing SO4(2-), optimized using their hydration properties, such as the Gibbs hydration free energy (calculated using Bennett's acceptance ratio method). The findings show that the TcO4(-) oxyanion has a very low hydration free energy (-202 kJ mol(-1)) compared to other anions (Cl(-), I(-), SO4(2-)) leading to fast water exchange dynamics and explaining its observed high mobility in the aqueous environment. Its hydrated structure, investigated using ion-water radial distribution functions, shows that it is unique amongst the other anions in that it does not possess well-defined hydration shells. Since contaminants and ubiquitous species in the aqueous environment are often present as tetrahedral oxyanions, it is proposed that the approach could easily be extended to a whole host of other species.

Free energy of solvation and Henry's law solubility constants for mono-, di- and tri-ethylene glycol in water and methane

Free energy of solvation (i.e. residual chemical potential) and Henry's law solubility constants were estimated for mono ethylene glycol (MEG), diethylene glycol (DEG) and triethylene glycol (TEG) with water and methane as solvents at both 298 K and 1 atm and at 283 K and 80 atm using molecular dynamics simulations. Three methods of calculating free energies of solvation were compared: free energy perturbation (FEP), thermodynamic integration (TI) and Bennett acceptance ratio (BAR) method. The solubility constants were estimated based on the obtained free energies and were compared to the previously reported values. We found that free energy differences obtained using the three applied methods agreed very well. For both MEG and DEG the estimated solubility constants were within the same order of magnitude as previously reported solubility constants and therefore in good agreement. The estimated solubility constants of TEG were found to be about an order of magnitude smaller than the lowest reported value, and would still yield a reasonable estimate of residual chemical potential due to the logarithmic dependence.

Computational scheme for pH-dependent binding free energy calculation with explicit solvent.

We present a computational scheme to compute the pH-dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant-pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi-grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host-guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pKa shift upon complex formation. The pH-dependent binding free energy profiles of the benchmark system are obtained with three different long-range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH-dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol(-1) . We also discuss the characteristics of three long-range interaction calculation methods for constant-pH simulations.

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model.

The most general way to improve the accuracy of binding-affinity calculations for protein-ligand systems is to use quantum-mechanical (QM) methods together with rigorous alchemical-perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin-3 at a reasonably high QM level (dispersion-corrected density functional theory with a triple-zeta basis set) and with a sufficiently large QM system to include all short-range interactions with the ligand (744-748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non-Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ∼3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations.