Bennett Acceptance Ratio Method Research Articles

Human Plasma Butyrylcholinesterase Hydrolyzes Atropine: Kinetic and Molecular Modeling Studies.

The participation of butyrylcholinesterase (BChE) in the degradation of atropine has been recurrently addressed for more than 70 years. However, no conclusive answer has been provided for the human enzyme so far. In the present work, a steady-state kinetic analysis performed by spectrophotometry showed that highly purified human plasma BChE tetramer slowly hydrolyzes atropine at pH 7.0 and 25 °C. The affinity of atropine for the enzyme is weak, and the observed kinetic rates versus the atropine concentration was of the first order: the maximum atropine concentration in essays was much less than Km. Thus, the bimolecular rate constant was found to be kcat/Km = 7.7 × 104 M-1 min-1. Rough estimates of catalytic parameters provided slow kcat < 40 min-1 and high Km = 0.3-3.3 mM. Then, using a specific organophosphoryl agent, echothiophate, the time-dependent irreversible inhibition profiles of BChE for hydrolysis of atropine and the standard substrate butyrylthiocholine (BTC) were investigated. This established that both substrates are hydrolyzed at the same site, i.e., S198, as for all substrates of this enzyme. Lastly, molecular docking provided evidence that both atropine isomers bind to the active center of BChE. However, free energy perturbations yielded by the Bennett Acceptance Ratio method suggest that the L-atropine isomer is the most reactive enantiomer. In conclusion, the results provided evidence that plasma BChE slowly hydrolyzes atropine but should have no significant role in its metabolism under current conditions of medical use and even under administration of the highest possible doses of this antimuscarinic drug.

Exploring the mechanisms of diazinon adsorption onto alpha and beta cyclodextrins through molecular dynamics simulations: Insights into environmentally friendly pesticide remediation

This study investigated the adsorption of Diazinon on α and β-Cyclodextrins (CDs) through Molecular Dynamics Simulations. The entrance point variation in diazinon adsorption is analyzed, revealing distinct preferences for entry into α and β-CDs. The center of mass distance of diazinon and CDs is investigated, highlighting the dynamic behavior within β-CD. Interaction energies between diazinon, CD, and water are explored, emphasizing the significance of van der Waals interactions in diazinon adsorption. Hydrogen bonding analysis reveals preferential adsorption of diazinon on α-CD, attributed to the number and arrangement of hydrogen bonds. Free energy calculations using the Bennett acceptance ratio method indicate a stronger affinity of diazinon for α-CD, supported by molecular electrostatic potential maps. The study also examines the hydration capacity and water molecules' distribution, indicating differences between α and β-CD. Radial distribution function analysis (RDF) illustrates the adsorption process, emphasizing water molecule expulsion upon diazinon entry. Structural stability is assessed through root mean squared deviation, indicating equilibrium attainment. Gibbs free energy calculations suggest stronger hydrophobic interactions in the α-CD cavity. This comprehensive analysis contributes valuable insights into the MD of diazinon-CDs interactions, shedding light on their adsorption mechanisms and potential applications in wastewater treatment.

Bayesian Multistate Bennett Acceptance Ratio Methods.

The multistate Bennett acceptance ratio (MBAR) method is a prevalent approach for computing the free energies of thermodynamic states. In this work, we introduce BayesMBAR, a Bayesian generalization of the MBAR method. By integration of configurations sampled from thermodynamic states with a prior distribution, BayesMBAR computes a posterior distribution of free energies. Using the posterior distribution, we derive free energy estimations and compute their associated uncertainties. Notably, when a uniform prior distribution is used, BayesMBAR recovers the MBAR's result but provides more accurate uncertainty estimates. Additionally, when prior knowledge about free energies is available, BayesMBAR can incorporate this information into the estimation procedure by using nonuniform prior distributions. As an example, we show that by incorporating the prior knowledge about the smoothness of free energy surfaces, BayesMBAR provides more accurate estimates than the MBAR method. Given MBAR's widespread use in free energy calculations, we anticipate BayesMBAR to be an essential tool in various applications of free energy calculations.

Alchemical Free Energy and Hamiltonian Replica Exchange Molecular Dynamics to Compute Hydrofluorocarbon Isotherms in Imidazolium-Based Ionic Liquids.

Ionic liquids (ILs) have shown promise for applications that leverage differential gas solubility in an IL solvent, e.g., gas separations. Although most available literature provides Henry's law constants, the ability to efficiently estimate full isotherms is important for engineering design calculations. Molecular simulation can be used as a tool to predict full isotherms of gas in ILs. However, particle insertions or deletions in a charge-dense IL medium and the sluggish conformational dynamics of ILs present two sampling challenges for these systems. We therefore devised a method that uses Hamiltonian replica exchange (HREX) molecular dynamics (MD) combined with alchemical free energy calculations to compute full solubility isotherms of two different hydrofluorocarbons (HFCs) in imidazolium-based IL binary mixtures. This workflow is significantly faster than the Gibbs ensemble Monte Carlo (GEMC) simulations which fail to deal with the slow conformational relaxation caused by the sluggish dynamics of ILs. Multiple free energy estimators, including thermodynamic integration, free energy perturbation, and multistate Bennett acceptance ratio method, provided consistent results. Overall, the simulated Henry's law constant, isotherm curvature, and solubility trends match experimental results reasonably well. We close by calculating the full solubility isotherms of two HFCs in IL mixtures that have not been reported in the literature, demonstrating the potential of this method to be used for solubility prediction and setting the stage for future computational screening studies that search for the "best" IL to separate azeotropic HFC mixtures.

Anharmonic Correction to Free Energy Barriers from DFT-Based Molecular Dynamics Using Constrained Thermodynamic Integration.

For the calculation of anharmonic contributions to free energy barriers, constrained thermodynamic λ-path integration (λ-TI) from a harmonic reference force field to density functional theory is presented as an alternative to the established Blue Moon ensemble method (ξ-TI), in which free energy gradients along the reaction coordinate ξ are integrated. With good agreement in all cases, the λ-TI method is benchmarked against the ξ-TI method for several reactions, including the internal CH3 group rotation in ethane, a nucleophilic substitution of CH3Cl, a retro-Diels-Alder reaction, and a proton transfer in zeolite H-SSZ-13. An advantage of λ-TI is that one can use virtually any reference state to compute anharmonic contributions to reaction free energies or free energy barriers. This is particularly relevant for catalysis, where it is now possible to compute anharmonic corrections to the free energy of a transition state relative to any reference, for example, the most stable state of the active site and the reactants in the gas phase. This is in contrast to ξ-TI, where free energy barriers can only be computed relative to an initial state with all reactants coadsorbed. Finally, the Bennett acceptance ratio method combined with λ-TI is demonstrated to reduce the number of required integration grid points with tolerable accuracy, favoring thus λ-TI over ξ-TI in terms of computational efficiency.

Regularized Bennett and Zwanzig free energy estimators.

We consider the problem of free energy estimation from the general perspective of regularization and Bayes estimation theory. We try to take advantage of an assumed a priori knowledge of the free energy. We reformulate the original Bennett acceptance ratio method, in this perspective, devise a numerical algorithm to solve it, and give a closed formula to estimate the confidence in the prior. Finally, we test the derived estimators by applying them to a toy model.

The reconciliation between the experimental and calculated octanol-water partition coefficient of 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine using atomistic molecular dynamics: an open question

The octanol-water partition coefficient of 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC) was investigated using atomistic molecular dynamics simulations via thermodynamic integration and multistate Bennett acceptance ratio methods. The GAFF and CHARMM36 force fields were used with six water models widely used in molecular dynamics simulations. The OPC4 water model provided the best agreement with the experimental octanol-water partition coefficient of DPPC using the two force fields. However, there is still plenty of room for improvement in water models with correct estimation of surface tension that uses better and suitable non-bonded interaction parameters between water-water and water-DPPC. The Gibbs free energy of transferring DPPC from octanol to water phase was calculated to be 19.8 ± 0.3 and 20.2 ± 0.3 kcal mol−1, giving a partition coefficient of 14.5 ± 0.4 and 14.8 ± 0.3 for the GAFF and CHARMM36 force fields, respectively. This study reinforces the importance of developing new water models that reproduce experimental surface tensions to reconcile the water-water and water-DPPC non-bonded interactions and the existing discrepancy between experimental measurements of amphiphilic molecules that are important in many areas of scientific applications and industry such as biophysics, surfactant, colloids, membranes, medicine, nanotechnology, and food and pharmaceutical industries, and so on. It raises two important open questions: Is the experimental octanol-water partition coefficient of DPPC reliable? Or is its calculation accurate using the OPC4 water model? With respect to the experimental measurements, there may be non-treated aspects such as the formation of aggregates in aqueous phase and limit of detection of the applied method. And, in the calculation, some effects are not possible to be considered in a correct way or viable time such as calculating quantum effects, sampling all conformations, considering phase transitions, and correctly evaluating the intermolecular forces to estimate an accurate surface tension. Communicated by Ramaswamy H. Sarma

Iterative Landmark-Based Umbrella Sampling (ILBUS) Protocol for Sampling of Conformational Space of Biomolecules.

Computer simulations of biomolecules such as molecular dynamics often suffer from insufficient sampling. Due to limited computational resources, insufficient sampling prevents obtaining proper equilibrium distributions of observed properties. To deal with this problem, we proposed a simulation protocol for efficient resampling of collected off-equilibrium trajectories. These trajectories are utilized for the initial mapping of the conformational space, which is later properly resampled by the introduced Iterative Landmark-Based Umbrella Sampling (ILBUS) method. Reconstruction of static equilibrium properties is achieved by the multistate Bennett acceptance ratio (MBAR) method, which enables efficient use of simulated data. The ILBUS protocol is geometry-based and does not demand any additional collective variable or a dimensional-reduction technique. The only requirement is a set of suitably spaced reference conformations, which serve as landmarks in the mapped conformational space. Additionally, the ILBUS protocol encompasses an iterative process that optimizes the force constant used in the umbrella sampling simulation. Such tuning is an inherent feature of the protocol and does not need to be performed by the user in advance. Furthermore, even the simulations with suboptimal force constants can be used in estimates by MBAR. We demonstrate the feasibility and the performance of this approach in the study of the conformational landscape of the alanine dipeptide, met-enkephalin, and adenylate kinase.

Absolute binding free energies of mucroporin and its analog mucroporin-M1 with the heptad repeat 1 domain and RNA-dependent RNA polymerase of SARS-CoV-2

The peptide Mucroporin and its analog Mucroporin-M1 were studied using the molecular docking and molecular dynamics simulation of their complexation with two protein targets, the Heptad Repeat 1 (HR1) domain and RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2. The molecular docking of the peptide-protein complexes was performed using the glowworm swarm optimization algorithm. The lowest energy poses were submitted to molecular dynamics simulation. Then, the binding free energies of Mucroporin and its analog Mucroporin-M1 with these two protein targets were calculated using the Multistate Bennett Acceptance Ratio (MBAR) method. It was verified that the peptides/HR1 domain complex showed stability in the interaction site determined by molecular docking. It was also found that Mucroporin-M1 has a much higher affinity than Mucroporin to the HR1 protein target. The peptides showed similar stability and affinity at the NTP binding site in the RdRp protein. Additional experimental studies are needed to confirm the antiviral activity of Mucroporin-M1 and a possible mechanism of action against SARS-CoV-2. However, here we indicate that Mucroporin-M1 may have potential antiviral activity against the HR1 domain with the possibility for further peptide optimization. Communicated by Ramaswamy H. Sarma

Computational analysis of the tryptophan cation radical energetics in peroxidase Compound I

Three well-characterized heme peroxidases (cytochrome c peroxidase = CCP, ascorbate peroxidase = APX, and Leishmania major peroxidase = LMP) all have a Trp residue tucked under the heme stacked against the proximal His heme ligand. The reaction of peroxidases with H2O2 to give Compound I results in the oxidation of this Trp to a cationic radical in CCP and LMP but not in APX. Considerable experimental data indicate that the local electrostatic environment controls whether this Trp or the porphyrin is oxidized in Compound I. Attempts have been made to place the differences between these peroxidases on a quantitative basis using computational methods. These efforts have been somewhat limited by the approximations required owing to the computational cost of using fully solvated atomistic models with well-developed forcefields. This now has changed with available GPU computing power and the associated development of software. Here we employ thermodynamic integration and multistate Bennett acceptance ratio methods to help fine-tune our understanding on the energetic differences in Trp radical stabilization in all three peroxidases. These results indicate that the local solvent structure near the redox active Trp plays a significant role in stabilization of the cationic Trp radical.Graphical abstract

Phenol release from pNIPAM hydrogels: scaling molecular dynamics simulations with dynamical density functional theory.

We employed molecular dynamic simulations (MD) and the Bennett's acceptance ratio method to compute the free energy of transfer, ΔGtrans, of phenol, methane, and 5-fluorouracil (5-FU), between bulk water and water-pNIPAM mixtures of different polymer volume fractions, ϕp. For this purpose, we first calculate the solvation free energies in both media to obtain ΔGtrans. Phenol and 5-FU (a medication used to treat cancer) attach to the pNIPAM surface so that they show negative values of ΔGtrans irrespective of temperature (above or below the lower critical solution temperature of pNIPAM, Tc). Conversely, methane switches the ΔGtrans sign when considering temperatures below (positive) and above (negative) Tc. In all cases, and contrasting with some theoretical predictions, ΔGtrans maintains a linear behavior with the pNIPAM concentration up to large polymer densities. We have also employed MD to compute the diffusion coefficient, D, of phenol in water-pNIPAM mixtures as a function of ϕp in the diluted limit. Both ΔGtrans and D as a function of ϕp are required inputs to obtain the release halftime of hollow pNIPAM microgels through Dynamic Density Functional Theory (DDFT). Our scaling strategy captures the experimental value of 2200 s for 50 μm radius microgels with no cavity, for ϕp ≃ 0.83 at 315 K.

Small-sample limit of the Bennett acceptance ratio method and the variationally derived intermediates.

Free energy calculations based on atomistic Hamiltonians provide microscopic insight into the thermodynamic driving forces of biophysical or condensed matter systems. Many approaches use intermediate Hamiltonians interpolating between the two states for which the free energy difference is calculated. The Bennett acceptance ratio (BAR) and variationally derived intermediates (VI) methods are optimal estimator and intermediate states in that the mean-squared error of free energy calculations based on independent sampling is minimized. However, BAR and VI have been derived based on several approximations that do not hold for very few sample points. Analyzing one-dimensional test systems, we show that in such cases BAR and VI are suboptimal and that established uncertainty estimates are inaccurate. Whereas for VI to become optimal, less than seven samples per state suffice in all cases; for BAR the required number increases unboundedly with decreasing configuration space densities overlap of the end states. We show that for BAR, the required number of samples is related to the overlap through an inverse power law. Because this relation seems to hold universally and almost independent of other system properties, these findings can guide the proper choice of estimators for free energy calculations.

Thermodynamic and structural description of relative solubility of the flavonoid rutin by DFT calculations and molecular dynamics simulations

Understanding the solubility of flavonoids is of relevance in view of the broad application such as antioxidant and antitumor agents. The solubility of flavonoid rutin has been experimentally investigated in a homologous series of alcohols, acetone, n-heptane and water solvents. In this work theoretical evaluation of Gibbs free energy of solvation was performed at the Density Functional Theory (DFT) and Molecular Dynamics (MD) levels, with the ωB97x-D functional and multistate Bennett acceptance ratio (MBAR) method, respectively. The degree of solubility of a given solute among various solvents is dictated by solute-solvent interactions, which may be represented by the solvation energy. Our calculated relative energy values due to solvent effects, using quantum chemical methods (PCM and SMD solvent models) do not follow strictly the observed solubility trend. However, the PCM model including solute-solvent dispersion interaction, solute-solvent repulsion interaction and solute cavitation energy contribution to the total energy (named DIS,REP,CAV) yielded an overall agreement with experimental solubility profile, with exception of ethanol solvent. A similar satisfactory accordance with experiment was found for MBresults, with a discrepancy also found for 1-butanol, which deserve further investigation. Analysis of spatial and radial distribution functions (SDF and RDF) for pure solvents and the analysis of the contributions of vdW and electrostatic terms for the total free energy reveal that a balance between dispersive and electrostatic interactions between the rutin and the solvent is necessary to solubilize the flavonoid, which corroborates with the values of these energy contributions to the solvation-free energy calculated by the MBAR method. The use of explicit solvent molecules in DFT calculations is precluded due to the size, flexibility, and many sites for solvent interactions of rutin molecule. Our results indicate that in general DFT-PCM (DIS,REP,CAV) and MBAR levels of calculations can satisfactorily predict the solvation free energy and solubility trend for flavonoid rutin along a series of solvents, and also provide a reasonable estimate of relative solubilities of other flavonoids, information that can be relevant for further molecular modeling studies.

Solvation Free Energy of Protonated Lysine: Molecular Dynamics Study

In the present work, we have used an alchemical approach for calculating solvation free energy of protonated lysine in water from molecular dynamics simulations. These approaches use a non-physical pathway between two end states in order to compute free energy difference from the set of simulations. The solute is modeled using bonded and non-bonded interactions described by OPLS-AA potential, while four different water models: TIP3P, SPC, SPC/E and TIP4P are used. The free energy of solvation of protonated lysine in water has been estimated using thermodynamic integration, free energy perturbation, and Bennett acceptance ratio methods at 310 K temperature. The contributions to the free energy due to van der Waals and electrostatics parameters are also separately computed. The estimated values of free energy of solvation using different methods are in well agreement with previously reported experimental value within 14 %.

Molecular Dynamics Simulations Reveal Interactions of an IgG1 Antibody With Selected Fc Receptors.

In a survey of novel interactions between an IgG1 antibody and different Fcγ receptors (FcγR), molecular dynamics simulations were performed of interactions of monoclonal antibody involved complexes with FcγRs. Free energy simulations were also performed of isolated wild-type and substituted Fc regions bound to FcγRs with the aim of assessing their relative binding affinities. Two different free energy calculation methods, Molecular Mechanical/Generalized Born Molecular Volume (MM/GBMV) and Bennett Acceptance Ratio (BAR), were used to evaluate the known effector substitution G236A that is known to selectively increase antibody dependent cellular phagocytosis. The obtained results for the MM/GBMV binding affinity between different FcγRs are in good agreement with previous experiments, and those obtained using the BAR method for the complete antibody and the Fc-FcγR simulations show increased affinity across all FcγRs when binding to the substituted antibody. The FcγRIIa, a key determinant of antibody agonistic efficacy, shows a 10-fold increase in binding affinity, which is also consistent with the published experimental results. Novel interactions between the Fab region of the antibody and the FcγRs were discovered with this in silico approach, and provide insights into the antibody-FcγR binding mechanism and show promise for future improvements of therapeutic antibodies for preclinical studies of biological drugs.

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins.

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

Extension of the Variational Free Energy Profile and Multistate Bennett Acceptance Ratio Methods for High-Dimensional Potential of Mean Force Profile Analysis.

We redevelop the variational free energy profile (vFEP) method using a cardinal B-spline basis to extend the method for analyzing free energy surfaces (FESs) involving three or more reaction coordinates. We also implemented software for evaluating high-dimensional profiles based on the multistate Bennett acceptance ratio (MBAR) method which constructs an unbiased probability density from global reweighting of the observed samples. The MBAR method takes advantage of a fast algorithm for solving the unbinned weighted histogram (UWHAM)/MBAR equations which replaces the solution of simultaneous equations with a nonlinear optimization of a convex function. We make use of cardinal B-splines and multiquadric radial basis functions to obtain smooth, differentiable MBAR profiles in arbitrary high dimensions. The cardinal B-spline vFEP and MBAR methods are compared using three example systems that examine 1D, 2D, and 3D profiles. Both methods are found to be useful and produce nearly indistinguishable results. The vFEP method is found to be 150 times faster than MBAR when applied to periodic 2D profiles, but the MBAR method is 4.5 times faster than vFEP when evaluating unbounded 3D profiles. In agreement with previous comparisons, we find the vFEP method produces superior FESs when the overlap between umbrella window simulations decreases. Finally, the associative reaction mechanism of hammerhead ribozyme is characterized using 3D, 4D, and 6D profiles, and the higher-dimensional profiles are found to have smaller reaction barriers by as much as 1.5 kcal/mol. The methods presented here have been implemented into the FE-ToolKit software package along with new methods for network-wide free energy analysis in drug discovery.

DeepBAR: A Fast and Exact Method for Binding Free Energy Computation.

The fast and accurate calculation of standard binding free energy has many important applications. Existing methodologies struggle at balancing accuracy and efficiency. We introduce a new method to compute binding free energy using deep generative models and the Bennett acceptance ratio method (DeepBAR). Compared to the rigorous potential of mean force (PMF) approach that requires sampling from intermediate states, DeepBAR is an order-of-magnitude more efficient as demonstrated in a series of host-guest systems. Notably, DeepBAR is exact and does not suffer from approximations for entropic contributions used in methods such as the molecular mechanics energy combined with the generalized Born and surface area continuum solvation (MM/GBSA). We anticipate DeepBAR to be a valuable tool for computing standard binding free energy used in drug design.

Evaluating the Multifunctionality of a New Modulator of Zinc-Induced Aβ Aggregation Using a Novel Computational Approach.

The high concentration of zinc metal ions in Aβ aggregations is one of the most cited hallmarks of Alzheimer's disease (AD), and several substantial pieces of evidence emphasize the key role of zinc metal ions in the pathogenesis of AD. In this study, while designing a multifunctional peptide for simultaneous targeting Aβ aggregation and chelating the zinc metal ion, a novel and comprehensive approach is introduced for evaluating the multifunctionality of a multifunctional drugs based on computational methods. The multifunctional peptide consists of inhibitor and chelator domains, which are included in the C-terminal hydrophobic region of Aβ, and the first four amino acids of human albumin. The ability of the multifunctional peptide in zinc ion chelation has been investigated using molecular dynamics (MD) simulations of the peptide-zinc interaction for 300 ns, and Bennett's acceptance ratio (BAR) method has been used to accurately calculate the chelation free energy. Data analysis demonstrates that the peptide chelating domain can be stably linked to the zinc ion. Besides, the introduced method used for evaluating chelation and calculating the free energy of peptide binding to zinc ions was successfully validated by comparison with previous experimental and theoretical published data. The results indicate that the multifunctional peptide, coordinating with the zinc metal ion, can be effective in Aβ inhibition by preserving the native helical structure of the Aβ42 monomer as well as disrupting the β-sheet structure of Aβ42 aggregates. Detailed assessments of the Aβ42-peptide interactions elucidate that the inhibition of Aβ is achieved by considerable hydrophobic interactions and hydrogen bonding between the multifunctional peptide and the hydrophobic Aβ regions, along with interfering in stable bridges formed inside the Aβ aggregate.

Computing Absolute Free Energy with Deep Generative Models

Fast and accurate evaluation of free energy has broad applications from drug design to material engineering. Computing the absolute free energy is of particular interest since it allows the assessment of the relative stability between states without the use of intermediates. In this letter, we introduce a general framework for calculating the absolute free energy of a state. A key step of the calculation is the definition of a reference state with tractable deep generative models using locally sampled configurations. The absolute free energy of this reference state is zero by design. The free energy for the state of interest can then be determined as the difference from the reference. We applied this approach to both discrete and continuous systems and demonstrated its effectiveness. It was found that the Bennett acceptance ratio method provides more accurate and efficient free energy estimations than approximate expressions based on work. We anticipate the method presented here to be a valuable strategy for computing free energy differences.