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The first complete description of the solution thermodynamics of a series of linear, branched, and cyclic alkanes in water by computer simulations, including the enthalpy and entropy changes in addition to the solvation free energies is discussed. The findings obtained in this work have important implications for theories of hydrophobicity and suggest an approach to parameterize the free energies of apolar hydration and association.

The maximum entropy analytic continuation method, to determine the dynamical properties of a solvated electron from equilibrium path integral Monte Carlo data, is applied to the calculation of the optical absorption spectra, real time correlation functions, and transport coefficients of an excess electron in water, supercritical helium, and supercritical xenon. Comparisons with experiments and with analytical theories are presented. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The dipole absorption spectrum of an electron in fluid helium is calculated by the maximum entropy method (MEM) numerical inversion of quantum Monte Carlo data obtained from a path integral Monte Carlo (PIMC) simulation at 309 K at the reduced densities ρ*=0.1, 0.3, 0.5, 0.7, and 0.9. Our results agree with the RISM-polaron theory results of Nichols and Chandler [A. L. Nichols III and D. Chandler, J. Chem. Phys. 87, 6671 (1987)] and the grid wave function calculation of Coker and Berne [D. F. Coker and B. J. Berne, J. Chem. Phys. 89, 2128 (1988)]. The method generated the expected long high frequency tail and the low density zero-frequency intensity caused by high conductivity. The method has also been tested by comparing the MEM absorption spectrum to the analytical spectrum of an electron confined in a spherical cavity of fluctuating radius, a model for a solvated electron in a localized state. © 1994 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the performance of maximum entropy (ME) and singular value decomposition (SVD) analytic continuation methods to the problem of quantum mechanical vibrational relaxation processes. Application of ME and SVD to imaginary-time correlation functions; Details on the prototype model for studying vibrational relaxation in condensed phases.

Focuses on the problem of calculating the electronic absorption spectrum of a chromophore with intramolecular degrees of freedom coupled to a condensed phase environment. Use of imaginary-time path integral Monte Carlo techniques; Alternative analytic continuation methods considered; Expression for the electronic absorption spectrum.

We present receptor hopping and receptor swapping free energy estimation protocols based on the Alchemical Transfer Method (ATM) to model the binding selectivity of a set of ligands to two arbitrary receptors. The receptor hopping protocol, where a ligand is alchemically transferred from one receptor to another in one simulation, directly yields the ligand's binding selectivity free energy (BSFE) for the two receptors, which is the difference between the two individual binding free energies. In the receptor swapping protocol, the first ligand of a pair is transferred from one receptor to another while the second ligand is simultaneously transferred in the opposite direction. The receptor swapping free energy yields the differences in binding selectivity free energies of a set of ligands, which, when combined using a generalized DiffNet algorithm, yield the binding selectivity free energies of the ligands. We test these algorithms on host-guest systems and show that they yield results that agree with experimental data and are consistent with differences in absolute and relative binding free energies obtained by conventional methods. Preliminary applications to the selectivity analysis of molecular fragments binding to the trypsin and thrombin serine protease confirm the potential of the receptor swapping technology in structure-based drug discovery. The novel methodologies presented in this work are a first step toward streamlined and computationally efficient protocols for ligand selectivity optimization between mutants and homologous proteins.

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

We introduce the self-relative binding free energy (self-RBFE) approach to evaluate the intrinsic statistical variance of dual-topology alchemical binding free energy estimators. The self-RBFE is the relative binding free energy between a ligand and a copy of the same ligand, and its true value is zero. Nevertheless, because the two copies of the ligand move independently, the self-RBFE value produced by a finite-length simulation fluctuates and can be used to measure the variance of the model. The results of this validation provide evidence that a significant fraction of the errors observed in benchmark studies reflect the statistical fluctuations of unconverged estimates rather than the models' accuracy. Furthermore, we find that ligand reorganization is a significant contributing factor to the statistical variance of binding free energy estimates and that metadynamics-accelerated conformational sampling of the torsional degrees of freedom of the ligand can drastically reduce the time to convergence.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features in simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations with only a modest increase in cost.

The Alchemical Transfer Method (ATM) is herein validated against the relative binding-free energies (RBFEs) of a diverse set of protein-ligand complexes. We employed a streamlined setup workflow, a bespoke force field, and AToM-OpenMM software to compute the RBFEs of the benchmark set prepared by Schindler and collaborators at Merck KGaA. This benchmark set includes examples of standard small R-group ligand modifications as well as more challenging scenarios, such as large R-group changes, scaffold hopping, formal charge changes, and charge-shifting transformations. The novel coordinate perturbation scheme and a dual-topology approach of ATM address some of the challenges of single-topology alchemical RBFE methods. Specifically, ATM eliminates the need for splitting electrostatic and Lennard-Jones interactions, atom mapping, defining ligand regions, and postcorrections for charge-changing perturbations. Thus, ATM is simpler and more broadly applicable than conventional alchemical methods, especially for scaffold-hopping and charge-changing transformations. Here, we performed well over 500 RBFE calculations for eight protein targets and found that ATM achieves accuracy comparable to that of existing state-of-the-art methods, albeit with larger statistical fluctuations. We discuss insights into the specific strengths and weaknesses of the ATM method that will inform future deployments. This study confirms that ATM can be applied as a production tool for RBFE predictions across a wide range of perturbation types within a unified, open-source framework.

Recent studies have revealed that tropolone-amide aryl C-C(O) rotational barriers are dramatically higher than those of analogous benzamide-based systems, and as a result, they have an increased likelihood of displaying high configurational stability. Studies on other tropolone-based chiral axes are important to assess the generality of this phenomenon. Herein, we describe a series of studies on the rotational barriers of tropolone-ketone, tropolone-ester, and tropolone-aldehyde chiral axes. These studies are complemented with computational modeling of the dynamics of these and analogous benzenoid variants to illuminate the impact that tropolone may have on aryl-C(O) configurational stability.

We apply the Alchemical Transfer Method (ATM) and a bespoke fixed partial charge force field to the SAMPL9 bCD host-guest binding free energy prediction challenge that comprises a combination of complexes formed between five phenothiazine guests and two cyclodextrin hosts. Multiple chemical forms, competing binding poses, and computational modeling challenges pose significant obstacles to obtaining reliable computational predictions for these systems. The phenothiazine guests exist in solution as racemic mixtures of enantiomers related by nitrogen inversions that bind the hosts in various binding poses, each requiring an individual free energy analysis. Due to the large size of the guests and the conformational reorganization of the hosts, which prevent a direct absolute binding free energy route, binding free energies are obtained by a series of absolute and relative binding alchemical steps for each chemical species in each binding pose. Metadynamics-accelerated conformational sampling was found to be necessary to address the poor convergence of some numerical estimates affected by conformational trapping. Despite these challenges, our blinded predictions quantitatively reproduced the experimental affinities for the β-cyclodextrin host and, to a lesser extent, those with a methylated derivative. The work illustrates the challenges of obtaining reliable free energy data in in silico drug design for even seemingly simple systems and introduces some of the technologies available to tackle them.

The accurate prediction of protein-ligand binding affinities is crucial for drug discovery. Alchemical free energy calculations have become a popular tool for this purpose. However, the accuracy and reliability of these methods can vary depending on the methodology. In this study, we evaluate the performance of a relative binding free energy protocol based on the alchemical transfer method (ATM), a novel approach based on a coordinate transformation that swaps the positions of two ligands. The results show that ATM matches the performance of more complex free energy perturbation (FEP) methods in terms of Pearson correlation but with marginally higher mean absolute errors. This study shows that the ATM method is competitive compared to more traditional methods in speed and accuracy and offers the advantage of being applicable with any potential energy function.

Understanding the physical forces underlying receptor-ligand binding requires robust methods for analyzing the binding thermodynamics. In end-point binding free energy methods the binding free energy is naturally decomposable into physically intuitive contributions such as the solvation free energy and configurational entropy that can provide insights. Here we present a new end-point method called EE-BQH (Effective Energy-Boltzmann-Quasiharmonic) which combines the Boltzmann-Quasiharmonic model for configurational entropy with different solvation free energy methods, such as the continuum solvent PBSA model and the integral equation-based 3D-RISM, to estimate the absolute binding free energy. We compare EE-BQH with other treatments of configurational entropy such as Quasiharmonic models in internal coordinates (QHIC) and in Cartesian coordinates (QHCC), and Normal Mode analysis (NMA), by testing them on the octa acids host-guest complexes from the SAMPL8 blind challenge. The accuracies in the calculated absolute binding free energies strongly depend on the configurational entropy and solvation free energy methods used. QHIC and BQH yield the best agreements with the established potential of mean force (PMF) estimates, with R 2 of ∼0.7 and mean unsigned error of ∼1.7 kcal mol -1 . These results from the end-point calculations are also in similar agreement with experiments. While 3D-RISM in combination with QHIC or BQH lead to reasonable correlations with the PMF results and experiments, the calculated absolute binding free energies are underestimated by ∼5 kcal mol -1 . While the binding is accompanied by a significant reduction in the ligand translational/rotational entropy, the change in the torsional entropy in these host-guest systems is slightly positive. Compared with BQH, QHIC underestimates the reduction of configurational entropy because of the non-Gaussian probability distributions in the ligand rotation and a small number of torsions. The study highlights the crucial role of configurational entropy in determining binding and demonstrates the potential of using the new end-point method to provide insights in more complex protein-ligand systems.

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

This chapter discusses the theory and application of physics-based free energy methods to estimate protein-peptide binding free energies. It presents a statistical mechanics formulation of molecular binding, which is then specialized in three methodologies: (1) alchemical absolute binding free energy estimation with implicit solvation, (2) alchemical relative binding free energy estimation with explicit solvation, and (3) potential of mean force binding free energy estimation. Case studies of protein-peptide binding application taken from the recent literature are discussed for each method., (© 2022. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)

We report the results of our participation in the SAMPL8 GDCC Blind Challenge for host-guest binding affinity predictions. Absolute binding affinity prediction is of central importance to the biophysics of molecular association and pharmaceutical discovery. The blinded SAMPL series have provided an important forum for assessing the reliability of binding free energy methods in an objective way. In this challenge, we employed two binding free energy methods, the newly developed alchemical transfer method (ATM) and the well-established potential of mean force (PMF) physical pathway method, using the same setup and force field model. The calculated binding free energies from the two methods are in excellent quantitative agreement. Importantly, the results from the two methods were also found to agree well with the experimental binding affinities released subsequently, with R values of 0.89 (ATM) and 0.83 (PMF). These results were ranked among the best of the SAMPL8 GDCC challenge and second only to those obtained with the more accurate AMOEBA force field. Interestingly, the two host molecules included in the challenge (TEMOA and TEETOA) displayed distinct binding mechanisms, with TEMOA undergoing a dehydration transition whereas guest binding to TEETOA resulted in the opening of the binding cavity that remains essentially dry during the process. The coupled reorganization and hydration equilibria observed in these systems is a useful prototype for the study of these phenomena often observed in the formation of protein-ligand complexes. Given that the two free energy methods employed here are based on entirely different thermodynamic pathways, the close agreement between the two and their general agreement with the experimental binding free energies are a testament to the high quality and precision achieved by theory and methods. The study provides further validation of the novel ATM binding free energy estimation protocol and paves the way to further extensions of the method to more complex systems., (© 2021. The Author(s), under exclusive licence to Springer Nature Switzerland AG.)

The effect of rigidification of the n-butyl linker region of tetrahydroisoquinoline-containing D 3 R ligands via inclusion of an o-xylenyl motif was examined in this study. Generally, rigidification with an o-xylenyl linker group reduces D 3 R affinity and negatively impacts selectivity versus D 2 R for compounds possessing a 6-methoxy-1,2,3,4,-tetrahydroisoquinolin-7-ol primary pharmacophore group. However, D 3 R affinity appears to be regulated by the primary pharmacophore group and high affinity D 3 R ligands with 6,7-dihydroxy-1,2,3,4-tetrahydroisoquinoline and 6,7-dimethoxy-1,2,3,4-tetrahydroisoquinoline primary pharmacophore groups were identified. The results of this study also indicate that D 3 R selectivity versus the σ 2 R is dictated by the benzamide secondary pharmacophore group, this being facilitated with 4-substituted benzamides. Compounds 5s and 5t were identified as high affinity (K i  < 4 nM) D 3 R ligands. Docking studies revealed that the added phenyl ring moiety interacts with the Cys181 in D 3 R which partially accounts for the strong D 3 R affinity of the ligands., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

The alchemical transfer method (ATM) for the calculation of standard binding free energies of noncovalent molecular complexes is presented. The method is based on a coordinate displacement perturbation of the ligand between the receptor binding site and the explicit solvent bulk and a thermodynamic cycle connected by a symmetric intermediate in which the ligand interacts with the receptor and solvent environments with equal strength. While the approach is alchemical, the implementation of the ATM is as straightforward as that for physical pathway methods of binding. The method is applicable, in principle, with any force field, as it does not require splitting the alchemical transformations into electrostatic and nonelectrostatic steps, and it does not require soft-core pair potentials. We have implemented the ATM as a freely available and open-source plugin of the OpenMM molecular dynamics library. The method and its implementation are validated on the SAMPL6 SAMPLing host-guest benchmark set. The work paves the way to streamlined alchemical relative and absolute binding free energy implementations on many molecular simulation packages and with arbitrary energy functions including polarizable, quantum-mechanical, and artificial neural network potentials.

We present a family of alchemical perturbation potentials that enable the calculation of hydration free energies of small- to medium-sized molecules in a single concerted alchemical coupling step instead of the commonly used sequence of two distinct coupling steps for Lennard-Jones and electrostatic interactions. The perturbation potentials we employ are non-linear functions of the solute-solvent interaction energy designed to focus sampling near entropic bottlenecks along the alchemical pathway. We present a general framework to optimize the parameters of alchemical perturbation potentials of this kind. The optimization procedure is based on the λ-function formalism and the maximum-likelihood parameter estimation procedure we developed earlier to avoid the occurrence of multi-modal distributions of the coupling energy along the alchemical path. A novel soft-core function applied to the overall solute-solvent interaction energy rather than individual interatomic pair potentials critical for this result is also presented. Because it does not require modifications of core force and energy routines, the soft-core formulation can be easily deployed in molecular dynamics simulation codes. We illustrate the method by applying it to the estimation of the hydration free energy in water droplets of compounds of varying size and complexity. In each case, we show that convergence of the hydration free energy is achieved rapidly. This work paves the way for the ongoing development of more streamlined algorithms to estimate free energies of molecular binding with explicit solvation.

Initiation of protein-primed (-) strand DNA synthesis in hepatitis B virus (HBV) requires interaction of the viral reverse transcriptase with epsilon (ε), a cis -acting regulatory signal located at the 5' terminus of pre-genomic RNA (pgRNA), and several host-encoded chaperone proteins. Binding of the viral polymerase (P protein) to ε is necessary for pgRNA encapsidation and synthesis of a short primer covalently attached to its terminal domain. Although we identified small molecules that recognize HBV ε RNA, these failed to inhibit protein-primed DNA synthesis. However, since initiation of HBV (-) strand DNA synthesis occurs within a complex of viral and host components (e.g., Hsp90, DDX3 and APOBEC3G), we considered an alternative therapeutic strategy of allosteric inhibition by disrupting the initiation complex or modifying its topology. To this end, we show here that 3,7-dihydroxytropolones (3,7-dHTs) can inhibit HBV protein-primed DNA synthesis. Since DNA polymerase activity of a ribonuclease (RNase H)-deficient HBV reverse transcriptase that otherwise retains DNA polymerase function is also abrogated, this eliminates direct involvement of RNase (ribonuclease) H activity of HBV reverse transcriptase and supports the notion that the HBV initiation complex might be therapeutically targeted. Modeling studies also provide a rationale for preferential activity of 3,7-dHTs over structurally related α-hydroxytropolones (α-HTs).

We report the free-energy landscape and thermodynamics of the protein-protein association responsible for the drug-induced multimerization of HIV-1 integrase (IN). Allosteric HIV-1 integrase inhibitors promote aberrant IN multimerization by bridging IN-IN intermolecular interactions. However, the thermodynamic driving forces and kinetics of the multimerization remain largely unknown. Here, we explore the early steps in the IN multimerization by using umbrella sampling and unbiased molecular dynamics simulations in explicit solvent. In direct simulations, the two initially separated dimers spontaneously associate to form near-native complexes that resemble the crystal structure of the aberrant tetramer. Most strikingly, the effective interaction of the protein-protein association is very short-ranged: the two dimers associate rapidly within tens of nanoseconds when their binding surfaces are separated by d ≤ 4.3 Å (less than two water diameters). Beyond this distance, the oligomerization kinetics appears to be diffusion controlled with a much longer association time. The free-energy profile also captured the crucial role of allosteric IN inhibitors in promoting multimerization and explained why several C-terminal domain mutations are remarkably resistant to the drug-induced multimerization. The results also show that at small separation, the protein-protein binding process contains two consecutive phases with distinct thermodynamic signatures. First, interprotein water molecules are expelled to the bulk, resulting in a small increase in entropy, as the solvent entropy gain from the water release is nearly cancelled by the loss of side-chain entropies as the two proteins approach each other. At shorter distances, the two dry binding surfaces adapt to each other to optimize their interaction energy at the expense of further protein configurational entropy loss. Although the binding interfaces feature clusters of hydrophobic residues, overall, the protein-protein association in this system is driven by enthalpy and opposed by entropy., (Copyright © 2020 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The Hepatitis B Virus (HBV) ribonuclease H (RNaseH) is a promising but unexploited drug target. Here, we synthesized and analyzed a library of 57 amide-containing α-hydroxytropolones (αHTs) as potential leads for HBV drug development. Fifty percent effective concentrations ranged from 0.31 to 54 μM, with selectivity indexes in cell culture of up to 80. Activity against the HBV RNaseH was confirmed in semi-quantitative enzymatic assays with recombinant HBV RNaseH. The compounds were overall poorly active against human ribonuclease H1, with 50% inhibitory concentrations of 5.1 to >1,000 μM. The αHTs had modest activity against growth of the fungal pathogen Cryptococcus neoformans, but had very limited activity against growth of the Gram - bacterium Escherichia coli and the Gram + bacterium Staphylococcus aureus, indicating substantial selectivity for HBV. A molecular model of the HBV RNaseH templated against the Ty3 RNaseH was generated. Docking the compounds to the RNaseH revealed the anticipated binding pose with the divalent cation coordinating motif on the compounds chelating the two Mn ++ ions modeled into the active site. These studies reveal that that amide αHTs can be strong, specific HBV inhibitors that merit further assessment toward becoming anti-HBV drugs., (Copyright © 2020 Elsevier B.V. All rights reserved.)

We present a new approach to more accurately and efficiently compute the absolute binding free energy for receptor-ligand complexes. Currently, the double decoupling method (DDM) and the potential of mean force method (PMF) are widely used to compute the absolute binding free energy of biomolecular complexes. DDM relies on alchemically decoupling the ligand from its environments, which can be computationally challenging for large ligands and charged ligands because of the large magnitude of the decoupling free energies involved. In contrast, the PMF method uses a physical pathway to directly transfer the ligand from solution to the receptor binding pocket and thus avoids some of the aforementioned problems in DDM. However, the PMF method has its own drawbacks: because of its reliance on a ligand binding/unbinding pathway that is free of steric obstructions from the receptor atoms, the method has difficulty treating ligands with buried atoms. To overcome the limitation in the standard PMF approach and enable buried ligands to be treated, here we develop a new method called AlchemPMF in which steric obstructions along the physical pathway for binding are alchemically removed. We have tested the new approach on two important drug targets involving charged ligands. One is HIV-1 integrase bound to an allosteric inhibitor; the other is the human telomeric DNA G-quadruplex in complex with a natural product protoberberine buried in the binding pocket. For both systems, the new approach leads to more reliable estimates of absolute binding free energies with smaller error bars and closer agreements with experiments compared with those obtained from the existing methods, demonstrating the effectiveness of the new method in overcoming the hysteresis often encountered in PMF binding free energy calculations of such systems. The new approach could also be used to improve the sampling of water equilibration and resolvation of the binding pocket as the ligand is extracted.

This study investigates the role of hydration and its relationship to the conformational equilibrium of the host molecule β-cyclodextrin. Molecular dynamics simulations indicate that the unbound β-cyclodextrin exhibits two state behavior in explicit solvent due to the opening and closing of its cavity. In implicit solvent, these transitions are not observed, and there is one dominant conformation of β-cyclodextrin with an open cavity. Based on these observations, we investigate the hypothesis that the expulsion of thermodynamically unfavorable water molecules into the bulk plays an important role in controlling the accessibility of the closed macrostate at room temperature. We compare the results of the molecular mechanics analytical generalized Born plus nonpolar solvation approach to those obtained through grid inhomogeneous solvation theory analysis with explicit solvation to elucidate the thermodynamic forces at play. The work illustrates the use of continuum solvent models to tease out solvation effects related to the inhomogeneity and the molecular nature of water and demonstrates the key role of the thermodynamics of enclosed hydration in driving the conformational equilibrium of molecules in solution.

Confined hydration and conformational flexibility are some of the challenges encountered for the rational design of selective antagonists of G-protein coupled receptors. We present a set of C3-substituted (-)-stepholidine derivatives as potent binders of the dopamine D3 receptor. The compounds are characterized biochemically, as well as by computer modeling using a novel molecular dynamics-based alchemical binding free energy approach which incorporates the effect of the displacement of enclosed water molecules from the binding site. The free energy of displacement of specific hydration sites is obtained using the Hydration Site Analysis method with explicit solvation. This work underscores the critical role of confined hydration and conformational reorganization in the molecular recognition mechanism of dopamine receptors and illustrates the potential of binding free energy models to represent these key phenomena., Competing Interests: The authors have declared that no competing interests exist.

We investigate the role of order/disorder transitions in alchemical simulations of protein-ligand absolute binding free energies. We show, in the context of a potential of mean force description, that for a benchmarking system (the complex of the L99A mutant of T4 lysozyme with 3-iodotoluene) and for a more challenging system relevant for medicinal applications (the complex of the farnesoid X receptor with inhibitor 26 from a recent D3R challenge) that order/disorder transitions can significantly hamper Hamiltonian replica exchange sampling efficiency and slow down the rate of equilibration of binding free energy estimates. We further show that our analytical model of alchemical binding combined with the formalism developed by Straub et al. for the treatment of order/disorder transitions of molecular systems can be successfully employed to analyze the transitions and help design alchemical schedules and soft-core functions that avoid or reduce the adverse effects of rare binding/unbinding transitions. The results of this work pave the way for the application of these techniques to the alchemical estimation with explicit solvation of hydration free energies and absolute binding free energies of systems undergoing order/disorder transitions.

We show that the generalized Boltzmann distribution is the only distribution for which the Gibbs-Shannon entropy equals the thermodynamic entropy. This result means that the thermodynamic entropy and the Gibbs-Shannon entropy are not generally equal, but rather the equality holds only in the special case where a system is in equilibrium with a reservoir.

A novel grid-based method is presented, which in conjunction with a smooth Gaussian-based model of atoms, is used to compute molecular volume (MV) and surface area (MSA). The MV and MSA are essential for computing nonpolar component of free energies. The objective of our grid-based approach is to identify solute atom pairs that share overlapping volumes in space. Once completed, this information is used to construct a rooted tree using depth-first method to yield the final volume and SA by using the formulations of the Gaussian model described by Grant and Pickup (J. Phys Chem, 1995, 99, 3503). The method is designed to function uninterruptedly with the grid-based finite-difference method implemented in Delphi, a popular and open-source package used for solving the Poisson-Boltzmann equation (PBE). We demonstrate the time efficacy of the method while also validating its performance in terms of the effect of grid-resolution, positioning of the solute within the grid-map and accuracy in identification of overlapping atom pairs. We also explore and discuss different aspects of the Gaussian model with key emphasis on its physical meaningfulness. This development and its future release with the Delphi package are intended to provide a physically meaningful, fast, robust and comprehensive tool for MM/PBSA based free energy calculations. © 2019 Wiley Periodicals, Inc., (© 2019 Wiley Periodicals, Inc.)

To perform massive-scale replica exchange molecular dynamics (REMD) simulations for calculating binding free energies of protein-ligand complexes, we implemented the asynchronous replica exchange (AsyncRE) framework of the binding energy distribution analysis method (BEDAM) in implicit solvent on the IBM World Community Grid (WCG) and optimized the simulation parameters to reduce the overhead and improve the prediction power of the WCG AsyncRE simulations. We also performed the first massive-scale binding free energy calculations using the WCG distributed computing grid and 301 ligands from the SAMPL4 challenge for large-scale binding free energy predictions of HIV-1 integrase complexes. In total there are ∼10000 simulated complexes, ∼1 million replicas, and ∼2000 μs of aggregated MD simulations. Running AsyncRE MD simulations on the WCG requires accepting a trade-off between the number of replicas that can be run (breadth) and the number of full RE cycles that can be completed per replica (depth). As compared with synchronous Replica Exchange (SyncRE) running on tightly coupled clusters like XSEDE, on the WCG many more replicas can be launched simultaneously on heterogeneous distributed hardware, but each full RE cycle requires more overhead. We compared the WCG results with that from AutoDock and more advanced RE simulations including the use of flattening potentials to accelerate sampling of selected degrees of freedom of ligands and/or receptors related to slow dynamics due to high energy barriers. We propose a suitable strategy of RE simulations to refine high throughput docking results which can be matched to corresponding computing resources: from HPC clusters, to small or medium-size distributed campus grids, and finally to massive-scale computing networks including millions of CPUs like the resources available on the WCG.

We present a parametrized analytic statistical model of the thermodynamics of alchemical molecular binding within the solvent potential of mean force formalism. The model describes the free energy profiles of linear single-decoupling alchemical binding free energy calculations accurately. The parameters of the model, which are physically motivated, are derived by maximum likelihood inference from data obtained from alchemical molecular simulations. The validity of the model has been assessed on a set of host-guest complexes. The model faithfully reproduces both the binding free energy profiles and the probability densities of the perturbation energy as a function of the alchemical progress parameter. The model offers a rationalization for the characteristic shape of binding free energy profiles. The parameters obtained from the model are potentially useful descriptors of the association equilibrium of molecular complexes. Potential applications of the model for the classification of molecular complexes and the design of alchemical molecular simulations are envisioned.

A series of analogues featuring a 6-methoxy-1,2,3,4-tetrahydroisoquinolin-7-ol unit as the arylamine "head" group of a classical D3 antagonist core structure were synthesized and evaluated for affinity at dopamine D1, D2, and D3 receptors (D1R, D2R, D3R). The compounds generally displayed strong affinity for D3R with very good D3R selectivity. Docking studies at D2R and D3R crystal structures revealed that the molecules are oriented such that their arylamine units are positioned in the orthosteric binding pocket of D3R, with the arylamide "tail" units residing in the secondary binding pocket. Hydrogen bonding between Ser 182 and Tyr 365 at D3R stabilize extracellular loop 2 (ECL2), which in turn contributes to ligand binding by interacting with the "tail" units of the ligands in the secondary binding pocket. Similar interactions between ECL2 and the "tail" units were absent at D2R due to different positioning of the D2R loop region. The presence of multiple H-bonds with the phenol moiety of the headgroup of 7 and Ser192 accounts for its stronger D3R affinity as compared to the 6,7-dimethoxy-1,2,3,4-tetrahydroisoquinoline-containing analogue 8 ., Competing Interests: The authors declare no competing financial interest.

The computational modeling of peptide inhibitors to target protein-protein binding interfaces is growing in interest as these are often too large, too shallow, and too feature-less for conventional small molecule compounds. Here, we present a rare successful application of an alchemical binding free energy method for the calculation of converged absolute binding free energies of a series of protein-peptide complexes. Specifically, we report the binding free energies of a series of cyclic peptides derived from the LEDGF/p75 protein to the integrase receptor of the HIV1 virus. The simulations recapitulate the effect of mutations relative to the wild-type binding motif of LEDGF/p75, providing structural, energetic and dynamical interpretations of the observed trends. The equilibration and convergence of the calculations are carefully analyzed. Convergence is aided by the adoption of a single-decoupling alchemical approach with implicit solvation, which circumvents the convergence difficulties of conventional double-decoupling protocols. We hereby present the single-decoupling methodology and critically evaluate its advantages and limitations. We also discuss some of the challenges and potential pitfalls of binding free energy calculations for complex molecular systems which have generally limited their applicability to the quantitative study of protein-peptide binding equilibria.

3,7-Dihydroxytropolones (3,7-dHTs) are highly oxygenated troponoids that have been identified as lead compounds for several human diseases. To date, structure-function studies on these molecules have been limited due to a scarcity of synthetic methods for their preparation. New synthetic strategies towards structurally novel 3,7-dHTs would be valuable in further studying their therapeutic potential. Here we describe the successful adaptation of a [5 + 2] oxidopyrilium cycloaddition/ring-opening for 3,7-dHT synthesis, which we apply in the synthesis of a plausible biosynthetic intermediate to the natural products puberulic and puberulonic acid. We have also tested these new compounds in several biological assays related to human immunodeficiency virus (HIV), hepatitis B virus (HBV) and herpes simplex virus (HSV) in order to gain insight into structure-functional analysis related to antiviral troponoid development.

We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc., (© 2017 Wiley Periodicals, Inc.)

As part of the SAMPL5 blinded experiment, we computed the absolute binding free energies of 22 host-guest complexes employing a novel approach based on the BEDAM single-decoupling alchemical free energy protocol with parallel replica exchange conformational sampling and the AGBNP2 implicit solvation model specifically customized to treat the effect of water displacement as modeled by the Hydration Site Analysis method with explicit solvation. Initial predictions were affected by the lack of treatment of ionic charge screening, which is very significant for these highly charged hosts, and resulted in poor relative ranking of negatively versus positively charged guests. Binding free energies obtained with Debye-Hückel treatment of salt effects were in good agreement with experimental measurements. Water displacement effects contributed favorably and very significantly to the observed binding affinities; without it, the modeling predictions would have grossly underestimated binding. The work validates the implicit/explicit solvation approach employed here and it shows that comprehensive physical models can be effective at predicting binding affinities of molecular complexes requiring accurate treatment of conformational dynamics and hydration.