The AGBNP2 Implicit Solvation Model

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains

The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.

Improving the Accuracy of Physics-Based Hydration-Free Energy Predictions by Machine Learning the Remaining Error Relative to the Experiment

The accuracy of computational models of water is key to atomistic simulations of biomolecules. We propose a computationally efficient way to improve the accuracy of the prediction of hydration-free energies (HFEs) of small molecules: the remaining errors of the physics-based models relative to the experiment are predicted and mitigated by machine learning (ML) as a postprocessing step. Specifically, the trained graph convolutional neural network attempts to identify the "blind spots" in the physics-based model predictions, where the complex physics of aqueous solvation is poorly accounted for, and partially corrects for them. The strategy is explored for five classical solvent models representing various accuracy/speed trade-offs, from the fast analytical generalized Born (GB) to the popular TIP3P explicit solvent model; experimental HFEs of small neutral molecules from the FreeSolv set are used for the training and testing. For all of the models, the ML correction reduces the resulting root-mean-square error relative to the experiment for HFEs of small molecules, without significant overfitting and with negligible computational overhead. For example, on the test set, the relative accuracy improvement is 47% for the fast analytical GB, making it, after the ML correction, almost as accurate as uncorrected TIP3P. For the TIP3P model, the accuracy improvement is about 39%, bringing the ML-corrected model's accuracy below the 1 kcal/mol threshold. In general, the relative benefit of the ML corrections is smaller for more accurate physics-based models, reaching the lower limit of about 20% relative accuracy gain compared with that of the physics-based treatment alone. The proposed strategy of using ML to learn the remaining error of physics-based models offers a distinct advantage over training ML alone directly on reference HFEs: it preserves the correct overall trend, even well outside of the training set.

Tuning Potential Functions to Host-Guest Binding Data

Software to more rapidly and accurately predict protein-ligand binding affinities is of high interest for early-stage drug discovery, and physics-based methods are among the most widely used technologies for this purpose. The accuracy of these methods depends critically on the accuracy of the potential functions that they use. Potential functions are typically trained against a combination of quantum chemical and experimental data. However, although binding affinities are among the most important quantities to predict, experimental binding affinities have not to date been integrated into the experimental data set used to train potential functions. In recent years, the use of host-guest complexes as simple and tractable models of binding thermodynamics has gained popularity due to their small size and simplicity, relative to protein-ligand systems. Host-guest complexes can also avoid ambiguities that arise in protein-ligand systems such as uncertain protonation states. Thus, experimental host-guest binding data are an appealing additional data type to integrate into the experimental data set used to optimize potential functions. Here, we report the extension of the Open Force Field Evaluator framework to enable the systematic calculation of host-guest binding free energies and their gradients with respect to force field parameters, coupled with the curation of 126 host-guest complexes with available experimental binding free energies. As an initial application of this novel infrastructure, we optimized generalized Born (GB) cavity radii for the OBC2 GB implicit solvent model against experimental data for 36 host-guest systems. This refitting led to a dramatic improvement in accuracy for both the training set and a separate test set with 90 additional host-guest systems. The optimized radii also showed encouraging transferability from host-guest systems to 59 protein-ligand systems. However, the new radii are significantly smaller than the baseline radii and lead to excessively favorable hydration free energies (HFEs). Thus, users of the OBC2 GB model currently may choose between GB cavity radii that yield more accurate binding affinities and GB cavity radii that yield more accurate HFEs. We suspect that achieving good accuracy on both will require more far-reaching adjustments to the GB model. We note that binding free-energy calculations using the OBC2 model in OpenMM gain about a 10× speedup relative to corresponding explicit solvent calculations, suggesting a future role for implicit solvent absolute binding free-energy (ABFE) calculations in virtual compound screening. This study proves the principle of using host-guest systems to train potential functions that are transferrable to protein-ligand systems and provides an infrastructure that enables a range of applications.

Uncovering water effects in protein-ligand recognition: importance in the second hydration shell and binding kinetics

Developing a ligand with high affinity for a specific protein target is essential for drug design, and water molecules are well known to play a key role in protein-drug recognition. However, predicting the role of particularly ordered water molecules in drug binding remains challenging. Furthermore, hydration free energy contributed from the water network, including the second shell of water molecules, is far from being well studied. In this research we focused on these aspects to accurately and efficiently evaluate water effects in protein-ligand binding affinity. We developed a new strategy using a free-energy calculation method, VM2. We successfully predicted the stable ordered water molecules in a number of protein systems: PDE 10a, HSP90, tryptophan synthase (TRPS), CDK2 and Factor Xa. In some of these, the second shell of water molecules appeared to be critical in protein-ligand binding. We also applied the strategy to largely improve binding free energy calculation using the MM/PBSA method. When applying MM/PBSA alone for two systems, CDK2 and Factor Xa, the computed binding free energy resulted in poor to moderate R² values with experimental data. However, including water free energy correction greatly improved the free energy calculation. Furthermore, our work helped to explain how xk263 is a 1000 times faster binder to HIVp than ritonavir, a potentially useful tool for investigating binding kinetics. Our studies reveal the importance of fully considering water effects in therapeutic developments in pharmaceutical and biotechnology industries and for fundamental research in protein-ligand recognition.

Dynamic Docking of Macrocycles in Bound and Unbound Protein Structures with DynaDock

Macrocycles are interesting molecules with unique features due to their conformationally constrained yet flexible ring structure. This characteristic poses a difficult challenge for computational modeling studies since they rely on accurate structural descriptions. In particular, molecular docking calculations suffer from the lack of ring flexibility during pose generation, which is often compensated by using pregenerated ligand conformer ensembles. Moreover, receptor structures are mainly treated rigidly, which limits the use of many docking tools. In this study, we optimized our previous molecular dynamics-based sampling and docking pipeline specifically designed for the accurate prediction of macrocyclic compounds. We developed a dihedral classification procedure for in-depth conformational analysis of the macrocyclic rings and extracted structural ensembles that were subsequently docked in both bound and unbound protein structures employing a fully flexible approach. Our results suggest that including a ring conformer close to the bound state in the starting ensemble increases the chance of successful docking. The bioactive conformations of a diverse set of ligands could be predicted with high and decent accuracy in bound and unbound protein structures, respectively, due to the incorporation of full molecular flexibility in our approach. The remaining unsuccessful docking calculations were mainly caused by large flexible substituents that bind to surface-exposed binding sites, rather than the macrocyclic ring per se and could be further improved by explicit molecular dynamics simulations of the docked complex.

Structure-based virtual screening workflow to identify antivirals targeting HIV-1 capsid

We have identified novel HIV-1 capsid inhibitors targeting the PF74 binding site. Acting as the building block of the HIV-1 capsid core, the HIV-1 capsid protein plays an important role in the viral life cycle and is an attractive target for antiviral development. A structure-based virtual screening workflow for hit identification was employed, which includes docking 1.6 million commercially-available drug-like compounds from the ZINC database to the capsid dimer, followed by applying two absolute binding free energy (ABFE) filters on the 500 top-ranked molecules from docking. The first employs the Binding Energy Distribution Analysis Method (BEDAM) in implicit solvent. The top-ranked compounds are then refined using the Double Decoupling method in explicit solvent. Both docking and BEDAM refinement were carried out on the IBM World Community Grid as part of the FightAIDS@Home project. Using this virtual screening workflow, we identified 24 molecules with calculated binding free energies between − 6 and − 12 kcal/mol. We performed thermal shift assays on these molecules to examine their potential effects on the stability of HIV-1 capsid hexamer and found that two compounds, ZINC520357473 and ZINC4119064 increased the melting point of the latter by 14.8 °C and 33 °C, respectively. These results support the conclusion that the two ZINC compounds are primary hits targeting the capsid dimer interface. Our simulations also suggest that the two hit molecules may bind at the capsid dimer interface by occupying a new sub-pocket that has not been exploited by existing CA inhibitors. The possible causes for why other top-scored compounds suggested by ABFE filters failed to show measurable activity are discussed.

Free Energy-Based Computational Methods for the Study of Protein-Peptide Binding Equilibria

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.

Advanced Sampling Methods for Multiscale Simulation of Disordered Proteins and Dynamic Interactions

Intrinsically disordered proteins (IDPs) are highly prevalent and play important roles in biology and human diseases. It is now also recognized that many IDPs remain dynamic even in specific complexes and functional assemblies. Computer simulations are essential for deriving a molecular description of the disordered protein ensembles and dynamic interactions for a mechanistic understanding of IDPs in biology, diseases, and therapeutics. Here, we provide an in-depth review of recent advances in the multi-scale simulation of disordered protein states, with a particular emphasis on the development and application of advanced sampling techniques for studying IDPs. These techniques are critical for adequate sampling of the manifold functionally relevant conformational spaces of IDPs. Together with dramatically improved protein force fields, these advanced simulation approaches have achieved substantial success and demonstrated significant promise towards the quantitative and predictive modeling of IDPs and their dynamic interactions. We will also discuss important challenges remaining in the atomistic simulation of larger systems and how various coarse-grained approaches may help to bridge the remaining gaps in the accessible time- and length-scales of IDP simulations.

Alchemical Transfer Approach to Absolute Binding Free Energy Estimation

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.

Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field

Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.

Absolute Protein Binding Free Energy Simulations for Ligands with Multiple Poses, a Thermodynamic Path That Avoids Exhaustive Enumeration of the Poses

We propose a free energy calculation method for receptor-ligand binding, which have multiple binding poses that avoids exhaustive enumeration of the poses. For systems with multiple binding poses, the standard procedure is to enumerate orientations of the binding poses, restrain the ligand to each orientation, and then, calculate the binding free energies for each binding pose. In this study, we modify a part of the thermodynamic cycle in order to sample a broader conformational space of the ligand in the binding site. This modification leads to more accurate free energy calculation without performing separate free energy simulations for each binding pose. We applied our modification to simple model host-guest systems as a test, which have only two binding poses, by using a single decoupling method (SDM) in implicit solvent. The results showed that the binding free energies obtained from our method without knowing the two binding poses were in good agreement with the benchmark results obtained by explicit enumeration of the binding poses. Our method is applicable to other alchemical binding free energy calculation methods such as the double decoupling method (DDM) in explicit solvent. We performed a calculation for a protein-ligand system with explicit solvent using our modified thermodynamic path. The results of the free energy simulation along our modified path were in good agreement with the results of conventional DDM, which requires a separate binding free energy calculation for each of the binding poses of the example of phenol binding to T4 lysozyme in explicit solvent. © 2019 Wiley Periodicals, Inc.

Accelerating the Generalized Born with Molecular Volume and Solvent Accessible Surface Area Implicit Solvent Model Using Graphics Processing Units

The generalized Born with molecular volume and solvent accessible surface area (GBMV2/SA) implicit solvent model provides an accurate description of molecular volume and has the potential to accurately describe the conformational equilibria of structured and disordered proteins. However, its broader application has been limited by the computational cost and poor scaling in parallel computing. Here, we report an efficient implementation of both the electrostatic and nonpolar components of GBMV2/SA on graphics processing unit (GPU) within the CHARMM/OpenMM module. The GPU-GBMV2/SA is numerically equivalent to the original CPU-GBMV2/SA. The GPU acceleration offers ~60- to 70-fold speedup on a single NVIDIA TITAN X (Pascal) graphics card for molecular dynamic simulations of both folded and unstructured proteins of various sizes. The current implementation can be further optimized to achieve even greater acceleration with minimal reduction on the numerical accuracy. The successful development of GPU-GBMV2/SA greatly facilitates its application to biomolecular simulations and paves the way for further development of the implicit solvent methodology. © 2019 Wiley Periodicals, Inc.

Role of Displacing Confined Solvent in the Conformational Equilibrium of β-Cyclodextrin

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.

Inclusion of enclosed hydration effects in the binding free energy estimation of dopamine D3 receptor complexes

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.

A grid-based algorithm in conjunction with a gaussian-based model of atoms for describing molecular geometry

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.

Massive-Scale Binding Free Energy Simulations of HIV Integrase Complexes Using Asynchronous Replica Exchange Framework Implemented on the IBM WCG Distributed Network

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.

The UWHAM and SWHAM Software Package

We introduce the UWHAM (binless weighted histogram analysis method) and SWHAM (stochastic UWHAM) software package that can be used to estimate the density of states and free energy differences based on the data generated by multi-state simulations. The programs used to solve the UWHAM equations are written in the C++ language and operated via the command line interface. In this paper, first we review the theoretical bases of UWHAM, its stochastic solver RE-SWHAM (replica exchange-like SWHAM)and ST-SWHAM (serial tempering-like SWHAM). Then we provide a tutorial with examples that explains how to apply the UWHAM program package to analyze the data generated by different types of multi-state simulations: umbrella sampling, replica exchange, free energy perturbation simulations, etc. The tutorial examples also show that the UWHAM equations can be solved stochastically by applying the RE-SWHAM and ST-SWHAM programs when the data ensemble is large. If the simulations at some states are far from equilibrium, the Stratified RE-SWHAM program can be applied to obtain the equilibrium distribution of the state of interest. All the source codes and the tutorial examples are available from our group's web page: https://ronlevygroup.cst.temple.edu/software/UWHAM_and_SWHAM_webpage/index.html .

Improvements to the ABSINTH Force Field for Proteins Based on Experimentally Derived Amino Acid Specific Backbone Conformational Statistics

We present an improved version of the ABSINTH implicit solvation model and force field paradigm (termed ABSINTH-C) by incorporating a grid-based term that bootstraps against experimentally derived and computationally optimized conformational statistics for blocked amino acids. These statistics provide high-resolution descriptions of the intrinsic backbone dihedral angle preferences for all 20 amino acids. The original ABSINTH model generates Ramachandran plots that are too shallow in terms of the basin structures and too permissive in terms of dihedral angle preferences. We bootstrap against the reference optimized landscapes and incorporate CMAP-like residue-specific terms that help us reproduce the intrinsic dihedral angle preferences of individual amino acids. These corrections that lead to ABSINTH-C are achieved by balancing the incorporation of the new residue-specific terms with the accuracies inherent to the original ABSINTH model. We demonstrate the robustness of ABSINTH-C through a series of examples to highlight the preservation of accuracies as well as examples that demonstrate the improvements. Our efforts show how the recent experimentally derived and computationally optimized coil-library landscapes can be used as a touchstone for quantifying errors and making improvements to molecular mechanics force fields.

Fast Pairwise Approximation of Solvent Accessible Surface Area for Implicit Solvent Simulations of Proteins on CPUs and GPUs

We propose a pairwise and readily parallelizable SASA-based nonpolar solvation approach for protein simulations, inspired by our previous pairwise GB polar solvation model development. In this work, we developed a novel function to estimate the atomic and molecular SASAs of proteins, which results in comparable accuracy as the LCPO algorithm in reproducing numerical icosahedral-based SASA values. Implemented in Amber software and tested on consumer GPUs, our pwSASA method reasonably reproduces LCPO simulation results, but accelerates MD simulations up to 30 times compared to the LCPO implementation, which is greatly desirable for protein simulations facing sampling challenges. The value of incorporating the nonpolar term in implicit solvent simulations is explored on a peptide fragment containing the hydrophobic core of HP36 and evaluating thermal stability profiles of four small proteins.

Overview of the SAMPL6 host-guest binding affinity prediction challenge

Accurately predicting the binding affinities of small organic molecules to biological macromolecules can greatly accelerate drug discovery by reducing the number of compounds that must be synthesized to realize desired potency and selectivity goals. Unfortunately, the process of assessing the accuracy of current computational approaches to affinity prediction against binding data to biological macromolecules is frustrated by several challenges, such as slow conformational dynamics, multiple titratable groups, and the lack of high-quality blinded datasets. Over the last several SAMPL blind challenge exercises, host-guest systems have emerged as a practical and effective way to circumvent these challenges in assessing the predictive performance of current-generation quantitative modeling tools, while still providing systems capable of possessing tight binding affinities. Here, we present an overview of the SAMPL6 host-guest binding affinity prediction challenge, which featured three supramolecular hosts: octa-acid (OA), the closely related tetra-endo-methyl-octa-acid (TEMOA), and cucurbit[8]uril (CB8), along with 21 small organic guest molecules. A total of 119 entries were received from ten participating groups employing a variety of methods that spanned from electronic structure and movable type calculations in implicit solvent to alchemical and potential of mean force strategies using empirical force fields with explicit solvent models. While empirical models tended to obtain better performance than first-principle methods, it was not possible to identify a single approach that consistently provided superior results across all host-guest systems and statistical metrics. Moreover, the accuracy of the methodologies generally displayed a substantial dependence on the system considered, emphasizing the need for host diversity in blind evaluations. Several entries exploited previous experimental measurements of similar host-guest systems in an effort to improve their physical-based predictions via some manner of rudimentary machine learning; while this strategy succeeded in reducing systematic errors, it did not correspond to an improvement in statistical correlation. Comparison to previous rounds of the host-guest binding free energy challenge highlights an overall improvement in the correlation obtained by the affinity predictions for OA and TEMOA systems, but a surprising lack of improvement regarding root mean square error over the past several challenge rounds. The data suggests that further refinement of force field parameters, as well as improved treatment of chemical effects (e.g., buffer salt conditions, protonation states), may be required to further enhance predictive accuracy.

Improving Prediction Accuracy of Binding Free Energies and Poses of HIV Integrase Complexes Using the Binding Energy Distribution Analysis Method with Flattening Potentials

To accelerate conformation sampling of slow dynamics from receptor or ligand, we introduced flattening potentials on selected bonded and nonbonded intramolecular interactions to the binding energy distribution analysis method (BEDAM) for calculating absolute binding free energies of protein-ligand complexes using an implicit solvent model and implemented flattening BEDAM using the asynchronous replica exchange (AsyncRE) framework for performing large scale replica exchange molecular dynamics (REMD) simulations. The advantage of using the flattening feature to reduce high energy barriers was exhibited first by the p-xylene-T4 lysozyme complex, where the intramolecular interactions of a protein side chain on the binding site were flattened to accelerate the conformational transition of the side chain from the trans to the gauche state when the p-xylene ligand is present in the binding site. Much more extensive flattening BEDAM simulations were performed for 53 experimental binders and 248 nonbinders of HIV-1 integrase which formed the SAMPL4 challenge, with the total simulation time of 24.3 μs. We demonstrated that the flattening BEDAM simulations not only substantially increase the number of true positives (and reduce false negatives) but also improve the prediction accuracy of binding poses of experimental binders. Furthermore, the values of area under the curve (AUC) of receiver operating characteristic (ROC) and the enrichment factors at 20% cutoff calculated from the flattening BEDAM simulations were improved significantly in comparison with that of simulations without flattening as we previously reported for the whole SAMPL4 database. Detailed analysis found that the improved ability to discriminate the binding free energies between the binders and nonbinders is due to the fact that the flattening simulations reduce the reorganization free energy penalties of binders and decrease the overlap of binding free energy distributions of binders relative to that of nonbinders. This happens because the conformational ensemble distributions for both the ligand and protein in solution match those at the fully coupled (complex) state more closely when the systems are more fully sampled after the flattening potentials are applied to the intermediate states.

Polarizable Force Field for Molecular Ions Based on the Classical Drude Oscillator

Development of accurate force field parameters for molecular ions in the context of a polarizable energy function based on the classical Drude oscillator is a crucial step toward an accurate polarizable model for modeling and simulations of biological macromolecules. Toward this goal we have undertaken a hierarchical approach in which force field parameter optimization is initially performed for small molecules for which experimental data exists that serve as building blocks of macromolecular systems. Small molecules representative of the ionic moieties of biological macromolecules include the cationic ammonium and methyl substituted ammonium derivatives, imidazolium, guanidinium and methylguanidinium, and the anionic acetate, phenolate, and alkanethiolates. In the present work, parameters for molecular ions in the context of the Drude polarizable force field are optimized and compared to results from the nonpolarizable additive CHARMM general force field (CGenFF). Electrostatic and Lennard-Jones parameters for the model compounds are developed in the context of the polarizable SWM4-NDP water model, with emphasis on assuring that the hydration free energies are consistent with previously reported parameters for atomic ions. The final parameters are shown to be in good agreement with the selected quantum mechanical (QM) and experimental target data. Analysis of the structure of water around the ions reveals substantial differences between the Drude and additive force fields indicating the important role of polarization in dictating the molecular details of aqueous solvation. The presented parameters represent the foundation for the charged functionalities in future generations of the Drude polarizable force field for biological macromolecules as well as for drug-like molecules.

Assessment of a Single Decoupling Alchemical Approach for the Calculation of the Absolute Binding Free Energies of Protein-Peptide Complexes

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.

Generalized Born implicit solvent models for small molecule hydration free energies

Hydration free energy estimation of small molecules from all-atom simulations was widely investigated in recent years, as it provides an essential test of molecular force fields and our understanding of solvation effects. While explicit solvent representations result in highly accurate models, they also require extensive sampling due to the high number of solvent degrees of freedom. Implicit solvent models, such as those based on the generalized Born model for electrostatic solvation effects and a solvent accessible surface area term for nonpolar contributions (GBSA), significantly reduce the number of degrees of freedom and the computational cost to estimate hydration free energies. However, a recent survey revealed a gap in the accuracy between explicit TIP3P solvent estimates and those computed with many common GBSA models. Here we address this shortcoming by providing a thorough comparison of the performance of three implicit solvent models with different nonpolar contributions and a generalized Born term to estimate experimental hydration free energies. Starting with a minimal set of only ten atom types, we demonstrate that a nonpolar term with atom type dependent surface tension coefficients in combination with an accurate generalized Born term and fully optimized parameters performs best in estimating hydration free energies, even yielding comparable results to the explicit TIP3P water model. Analysis of our results provides evidence that the asymmetric behavior of water around oppositely charged atoms is one of the main sources of error for two of the three implicit solvent models. Explicitly accounting for this effect in the parameterization reduces the corresponding errors, suggesting this as a general strategy for improving implicit solvent models. The findings presented here will help to improve the existing generalized Born based implicit solvent models implemented in state-of-the-art molecular simulation packages.

Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database

Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.

The Roles of Water in the Protein Matrix: A Largely Untapped Resource for Drug Discovery

The value of thoroughly understanding the thermodynamics specific to a drug discovery/design study is well known. Over the past decade, the crucial roles of water molecules in protein structure, function, and dynamics have also become increasingly appreciated. This Perspective explores water in the biological environment by adopting its point of view in such phenomena. The prevailing thermodynamic models of the past, where water was seen largely in terms of an entropic gain after its displacement by a ligand, are now known to be much too simplistic. We adopt a set of terminology that describes water molecules as being "hot" and "cold", which we have defined as being easy and difficult to displace, respectively. The basis of these designations, which involve both enthalpic and entropic water contributions, are explored in several classes of biomolecules and structural motifs. The hallmarks for characterizing water molecules are examined, and computational tools for evaluating water-centric thermodynamics are reviewed. This Perspective's summary features guidelines for exploiting water molecules in drug discovery.

Efficient gaussian density formulation of volume and surface areas of macromolecules on graphical processing units

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.

Explicit consideration of spatial hydrogen bonding direction for activity coefficient prediction based on implicit solvation calculations

Directional hydrogen bonding is introduced to implicit solvation calculations for improved prediction of solvation properties and phase equilibria of associating fluids.

A combined treatment of hydration and dynamical effects for the modeling of host-guest binding thermodynamics: the SAMPL5 blinded challenge

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.

Locally weighted histogram analysis and stochastic solution for large-scale multi-state free energy estimation

The weighted histogram analysis method (WHAM) including its binless extension has been developed independently in several different contexts, and widely used in chemistry, physics, and statistics, for computing free energies and expectations from multiple ensembles. However, this method, while statistically efficient, is computationally costly or even infeasible when a large number, hundreds or more, of distributions are studied. We develop a locally WHAM (local WHAM) from the perspective of simulations of simulations (SOS), using generalized serial tempering (GST) to resample simulated data from multiple ensembles. The local WHAM equations based on one jump attempt per GST cycle can be solved by optimization algorithms orders of magnitude faster than standard implementations of global WHAM, but yield similarly accurate estimates of free energies to global WHAM estimates. Moreover, we propose an adaptive SOS procedure for solving local WHAM equations stochastically when multiple jump attempts are performed per GST cycle. Such a stochastic procedure can lead to more accurate estimates of equilibrium distributions than local WHAM with one jump attempt per cycle. The proposed methods are broadly applicable when the original data to be "WHAMMED" are obtained properly by any sampling algorithm including serial tempering and parallel tempering (replica exchange). To illustrate the methods, we estimated absolute binding free energies and binding energy distributions using the binding energy distribution analysis method from one and two dimensional replica exchange molecular dynamics simulations for the beta-cyclodextrin-heptanoate host-guest system. In addition to the computational advantage of handling large datasets, our two dimensional WHAM analysis also demonstrates that accurate results similar to those from well-converged data can be obtained from simulations for which sampling is limited and not fully equilibrated.

Free Energy-Based Virtual Screening and Optimization of RNase H Inhibitors of HIV-1 Reverse Transcriptase

We report the results of a binding free energy-based virtual screening campaign of a library of 77 α-hydroxytropolone derivatives against the challenging RNase H active site of the reverse transcriptase (RT) enzyme of human immunodeficiency virus-1. Multiple protonation states, rotamer states, and binding modalities of each compound were individually evaluated. The work involved more than 300 individual absolute alchemical binding free energy parallel molecular dynamics calculations and over 1 million CPU hours on national computing clusters and a local campus computational grid. The thermodynamic and structural measures obtained in this work rationalize a series of characteristics of this system useful for guiding future synthetic and biochemical efforts. The free energy model identified key ligand-dependent entropic and conformational reorganization processes difficult to capture using standard docking and scoring approaches. Binding free energy-based optimization of the lead compounds emerging from the virtual screen has yielded four compounds with very favorable binding properties, which will be the subject of further experimental investigations. This work is one of the few reported applications of advanced-binding free energy models to large-scale virtual screening and optimization projects. It further demonstrates that, with suitable algorithms and automation, advanced-binding free energy models can have a useful role in early-stage drug-discovery programs.

Overview of the SAMPL5 host-guest challenge: Are we doing better?

The ability to computationally predict protein-small molecule binding affinities with high accuracy would accelerate drug discovery and reduce its cost by eliminating rounds of trial-and-error synthesis and experimental evaluation of candidate ligands. As academic and industrial groups work toward this capability, there is an ongoing need for datasets that can be used to rigorously test new computational methods. Although protein-ligand data are clearly important for this purpose, their size and complexity make it difficult to obtain well-converged results and to troubleshoot computational methods. Host-guest systems offer a valuable alternative class of test cases, as they exemplify noncovalent molecular recognition but are far smaller and simpler. As a consequence, host-guest systems have been part of the prior two rounds of SAMPL prediction exercises, and they also figure in the present SAMPL5 round. In addition to being blinded, and thus avoiding biases that may arise in retrospective studies, the SAMPL challenges have the merit of focusing multiple researchers on a common set of molecular systems, so that methods may be compared and ideas exchanged. The present paper provides an overview of the host-guest component of SAMPL5, which centers on three different hosts, two octa-acids and a glycoluril-based molecular clip, and two different sets of guest molecules, in aqueous solution. A range of methods were applied, including electronic structure calculations with implicit solvent models; methods that combine empirical force fields with implicit solvent models; and explicit solvent free energy simulations. The most reliable methods tend to fall in the latter class, consistent with results in prior SAMPL rounds, but the level of accuracy is still below that sought for reliable computer-aided drug design. Advances in force field accuracy, modeling of protonation equilibria, electronic structure methods, and solvent models, hold promise for future improvements.

Large scale free energy calculations for blind predictions of protein-ligand binding: the D3R Grand Challenge 2015

We describe binding free energy calculations in the D3R Grand Challenge 2015 for blind prediction of the binding affinities of 180 ligands to Hsp90. The present D3R challenge was built around experimental datasets involving Heat shock protein (Hsp) 90, an ATP-dependent molecular chaperone which is an important anticancer drug target. The Hsp90 ATP binding site is known to be a challenging target for accurate calculations of ligand binding affinities because of the ligand-dependent conformational changes in the binding site, the presence of ordered waters and the broad chemical diversity of ligands that can bind at this site. Our primary focus here is to distinguish binders from nonbinders. Large scale absolute binding free energy calculations that cover over 3000 protein-ligand complexes were performed using the BEDAM method starting from docked structures generated by Glide docking. Although the ligand dataset in this study resembles an intermediate to late stage lead optimization project while the BEDAM method is mainly developed for early stage virtual screening of hit molecules, the BEDAM binding free energy scoring has resulted in a moderate enrichment of ligand screening against this challenging drug target. Results show that, using a statistical mechanics based free energy method like BEDAM starting from docked poses offers better enrichment than classical docking scoring functions and rescoring methods like Prime MM-GBSA for the Hsp90 data set in this blind challenge. Importantly, among the three methods tested here, only the mean value of the BEDAM binding free energy scores is able to separate the large group of binders from the small group of nonbinders with a gap of 2.4 kcal/mol. None of the three methods that we have tested provided accurate ranking of the affinities of the 147 active compounds. We discuss the possible sources of errors in the binding free energy calculations. The study suggests that BEDAM can be used strategically to discriminate binders from nonbinders in virtual screening and to more accurately predict the ligand binding modes prior to the more computationally expensive FEP calculations of binding affinity.

Connecting free energy surfaces in implicit and explicit solvent: an efficient method to compute conformational and solvation free energies

The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.

A unique binding mode of the eukaryotic translation initiation factor 4E for guiding the design of novel peptide inhibitors

The interaction between the eukaryotic translation initiation factor 4E (eIF4E) and eIF4E binding proteins (4E-BP) is a promising template for the inhibition of eIF4E and the treatment of diseases such as cancer and a spectrum of autism disorders, including the Fragile X syndrome (FXS). Here, we report an atomically detailed model of the complex between eIF4E and a peptide fragment of a 4E-BP, the cytoplasmic Fragile X interacting protein (CYFIP1). This model was generated using computer simulations with enhanced sampling from an alchemical replica exchange approach and validated using long molecular dynamics simulations. 4E-BP proteins act as post-transcriptional regulators by binding to eIF4E and preventing mRNA translation. Dysregulation of eIF4E activity has been linked to cancer, FXS, and autism spectrum disorders. Therefore, the study of the mechanism of inhibition of eIF4E by 4E-BPs is key to the development of drug therapies targeting this regulatory pathways. The results obtained in this work indicate that CYFIP1 interacts with eIF4E by an unique mode not shared by other 4E-BP proteins and elucidate the mechanism by which CYFIP1 interacts with eIF4E despite having a sequence binding motif significantly different from most 4E-BPs. Our study suggests an alternative strategy for the design of eIF4E inhibitor peptides with superior potency and specificity than currently available.

Hydration of proteins and nucleic acids: Advances in experiment and theory. A review

BACKGROUND

Most biological processes involve water, and the interactions of biomolecules with water affect their structure, function and dynamics.

SCOPE OF REVIEW

This review summarizes the current knowledge of protein and nucleic acid interactions with water, with a special focus on the biomolecular hydration layer. Recent developments in both experimental and computational methods that can be applied to the study of hydration structure and dynamics are reviewed, including software tools for the prediction and characterization of hydration layer properties.

MAJOR CONCLUSIONS

In the last decade, important advances have been made in our understanding of the factors that determine how biomolecules and their aqueous environment influence each other. Both experimental and computational methods contributed to the gradually emerging consensus picture of biomolecular hydration.

GENERAL SIGNIFICANCE

An improved knowledge of the structural and thermodynamic properties of the hydration layer will enable a detailed understanding of the various biological processes in which it is involved, with implications for a wide range of applications, including protein-structure prediction and structure-based drug design.

Binding Energy Distribution Analysis Method: Hamiltonian Replica Exchange with Torsional Flattening for Binding Mode Prediction and Binding Free Energy Estimation

Molecular dynamics modeling of complex biological systems is limited by finite simulation time. The simulations are often trapped close to local energy minima separated by high energy barriers. Here, we introduce Hamiltonian replica exchange (H-REMD) with torsional flattening in the Binding Energy Distribution Analysis Method (BEDAM), to reduce energy barriers along torsional degrees of freedom and accelerate sampling of intramolecular degrees of freedom relevant to protein-ligand binding. The method is tested on a standard benchmark (T4 Lysozyme/L99A/p-xylene complex) and on a library of HIV-1 integrase complexes derived from the SAMPL4 blind challenge. We applied the torsional flattening strategy to 26 of the 53 known binders to the HIV Integrase LEDGF site found to have a binding energy landscape funneled toward the crystal structure. We show that our approach samples the conformational space more efficiently than the original method without flattening when starting from a poorly docked pose with incorrect ligand dihedral angle conformations. In these unfavorable cases convergence to a binding pose within 2-3 Å from the crystallographic pose is obtained within a few nanoseconds of the Hamiltonian replica exchange simulation. We found that torsional flattening is insufficient in cases where trapping is due to factors other than torsional energy, such as the formation of incorrect intramolecular hydrogen bonds and stacking. Work is in progress to generalize the approach to handle these cases and thereby make it more widely applicable.

Parallelization and improvements of the generalized born model with a simple sWitching function for modern graphics processors

Two fundamental challenges of simulating biologically relevant systems are the rapid calculation of the energy of solvation and the trajectory length of a given simulation. The Generalized Born model with a Simple sWitching function (GBSW) addresses these issues by using an efficient approximation of Poisson-Boltzmann (PB) theory to calculate each solute atom's free energy of solvation, the gradient of this potential, and the subsequent forces of solvation without the need for explicit solvent molecules. This study presents a parallel refactoring of the original GBSW algorithm and its implementation on newly available, low cost graphics chips with thousands of processing cores. Depending on the system size and nonbonded force cutoffs, the new GBSW algorithm offers speed increases of between one and two orders of magnitude over previous implementations while maintaining similar levels of accuracy. We find that much of the algorithm scales linearly with an increase of system size, which makes this water model cost effective for solvating large systems. Additionally, we utilize our GPU-accelerated GBSW model to fold the model system chignolin, and in doing so we demonstrate that these speed enhancements now make accessible folding studies of peptides and potentially small proteins.

Evaluating the dynamics and electrostatic interactions of folded proteins in implicit solvents

Three implicit solvent models, namely GBMVII, FACTS, and SCPISM, were evaluated for their abilities to emulate an explicit solvent environment by comparing the simulated conformational ensembles, dynamics, and electrostatic interactions of the Src SH2 domain and the Lyn kinase domain. This assessment in terms of structural features in folded proteins expands upon the use of hydration energy as a metric for comparison. All-against-all rms coordinate deviation, average positional fluctuations, and ion-pair distance distribution were used to compare the implicit solvent models with the TIP3P explicit solvent model. Our study shows that the Src SH2 domains solvated with TIP3P, GBMVII, and FACTS sample similar global conformations. Additionally, the Src SH2 ion-pair distance distributions of solvent-exposed side chains corresponding to TIP3P, GBMVII, and FACTS do not differ substantially, indicating that GBMVII and FACTS are capable of modeling these electrostatic interactions. The ion-pair distance distributions of SCPISM are distinct from others, demonstrating that these electrostatic interactions are not adequately reproduced with the SCPISM model. On the other hand, for the Lyn kinase domain, a non-globular protein with bilobal structure and a large concavity on the surface, implicit solvent does not accurately model solvation to faithfully reproduce partially buried electrostatic interactions and lobe-lobe conformations. Our work reveals that local structure and dynamics of small, globular proteins are modeled well using FACTS and GBMVII. Nonetheless, global conformations and electrostatic interactions in concavities of multi-lobal proteins resulting from simulations with implicit solvent models do not match those obtained from explicit water simulations.

Spatial Decomposition of Translational Water-Water Correlation Entropy in Binding Pockets

A number of computational tools available today compute the thermodynamic properties of water at surfaces and in binding pockets by using inhomogeneous solvation theory (IST) to analyze explicit-solvent simulations. Such methods enable qualitative spatial mappings of both energy and entropy around a solute of interest and can also be applied quantitatively. However, the entropy estimates of existing methods have, to date, been almost entirely limited to the first-order terms in the IST’s entropy expansion. These first-order terms account for localization and orientation of water molecules in the field of the solute but not for the modification of water–water correlations by the solute. Here, we present an extension of the Grid Inhomogeneous Solvation Theory (GIST) approach which accounts for water–water translational correlations. The method involves rewriting the two-point density of water in terms of a conditional density and utilizes the efficient nearest-neighbor entropy estimation approach. Spatial maps of this second order term, for water in and around the synthetic host cucurbit[7]uril and in the binding pocket of the enzyme Factor Xa, reveal mainly negative contributions, indicating solute-induced water–water correlations relative to bulk water; particularly strong signals are obtained for sites at the entrances of cavities or pockets. This second-order term thus enters with the same, negative, sign as the first order translational and orientational terms. Numerical and convergence properties of the methodology are examined.

Effective Approximation of Molecular Volume Using Atom-Centered Dielectric Functions in Generalized Born Models

The generalized Born (GB) theory is a prime choice for implicit treatment of solvent that provides a favorable balance between efficiency and accuracy for reliable simulation of protein conformational equilibria. In GB, the dielectric boundary is a key physical property that needs to be properly described. While it is widely accepted that the molecular surface (MS) should provide the most physical description, most existing GB models are based on van der Waals (vdW)-like surfaces for computational simplicity and efficiency. A simple and effective approximation to molecular volume is explored here using atom-centered dielectric functions within the context of a generalized Born model with simple switching (GBSW). The new model, termed GBSW/MS2, is as efficient as the original vdW-like-surface-based GBSW model, but is able to reproduce the Born radii calculated from the "exact" Poisson-Boltzmann theory with a correlation of 0.95. More importantly, examination of the potentials of mean force of hydrogen-bonding and charge-charge interactions demonstrates that GBSW/MS2 correctly captures the first desolvation peaks, a key signature of true MS. Physical parameters including atomic input radii and peptide backbone torsion were subsequently optimized on the basis of solvation free energies of model compounds, potentials of mean force of their interactions, and conformational equilibria of a set of helical and β-hairpin model peptides. The resulting GBSW/MS2 protein force field reasonably recapitulates the structures and stabilities of these model peptides. Several remaining limitations and possible future developments are also discussed.