The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators

Structure-Based Identification of Organoruthenium Compounds as Nanomolar Antagonists of Cannabinoid Receptors

Metal complexes exhibit a diverse range of coordination geometries, representing novel privileged scaffolds with convenient click types of preparation inaccessible for typical carbon-centered organic compounds. Herein, we explored the opportunity to identify biologically active organometallic complexes by reverse docking of a rigid, minimum-size octahedral organoruthenium scaffold against thousands of protein-binding pockets. Interestingly, cannabinoid receptor type 1 (CB1) was identified based on the docking scores and the degree of overlap between the docked organoruthenium scaffold and the hydrophobic scaffold of the cocrystallized ligand. Further structure-based optimization led to the discovery of organoruthenium complexes with nanomolar binding affinities and high selectivity toward CB2. Our work indicates that octahedral organoruthenium scaffolds may be advantageous for targeting the large and hydrophobic binding pockets and that the reverse docking approach may facilitate the discovery of novel privileged scaffolds, such as organometallic complexes, for exploring chemical space in lead discovery.

Development, Validation, and Applications of Nonbonded Interaction Parameters between Coarse-Grained Amino Acid and Water Models

Interactions between amino acids and water play an important role in determining the stability and folding/unfolding, in aqueous solution, of many biological macromolecules, which affects their function. Thus, understanding the molecular-level interactions between water and amino acids is crucial to tune their function in aqueous solutions. Herein, we have developed nonbonded interaction parameters between the coarse-grained (CG) models of 20 amino acids and the one-site CG water model. The nonbonded parameters, represented using the 12-6 Lennard Jones (LJ) potential form, have been optimized using an artificial neural network (ANN)-assisted particle swarm optimization (PSO) (ANN-assisted PSO) method. All-atom (AA) molecular dynamics (MD) simulations of dipeptides in TIP3P water molecules were performed to calculate the Gibbs hydration free energies. The nonbonded force-field (FF) parameters between CG amino acids and the one-site CG water model were developed to accurately reproduce these energies. Furthermore, to test the transferability of these newly developed parameters, we calculated the hydration free energies of the analogues of the amino acid side chains, which showed good agreement with reported experimental data. Additionally, we show the applicability of these models by performing self-assembly simulations of peptide amphiphiles. Overall, these models are transferable and can be used to study the self-assembly of various biomaterials and biomolecules to develop a mechanistic understanding of these processes.

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

In Silico Discovery of Small Molecule Modulators Targeting the Achilles' Heel of SARS-CoV-2 Spike Protein

The spike protein of SARS-CoV-2 has been a promising target for developing vaccines and therapeutics due to its crucial role in the viral entry process. Previously reported cryogenic electron microscopy (cryo-EM) structures have revealed that free fatty acids (FFA) bind with SARS-CoV-2 spike protein, stabilizing its closed conformation and reducing its interaction with the host cell target in vitro. Inspired by these, we utilized a structure-based virtual screening approach against the conserved FFA-binding pocket to identify small molecule modulators of SARS-CoV-2 spike protein, which helped us identify six hits with micromolar binding affinities. Further evaluation of their commercially available and synthesized analogs enabled us to discover a series of compounds with better binding affinities and solubilities. Notably, our identified compounds exhibited similar binding affinities against the spike proteins of the prototypic SARS-CoV-2 and a currently circulating Omicron BA.4 variant. Furthermore, the cryo-EM structure of the compound SPC-14 bound spike revealed that SPC-14 could shift the conformational equilibrium of the spike protein toward the closed conformation, which is human ACE2 (hACE2) inaccessible. Our identified small molecule modulators targeting the conserved FFA-binding pocket could serve as the starting point for the future development of broad-spectrum COVID-19 intervention treatments.

Molecular Modelling of Ionic Liquids: Situations When Charge Scaling Seems Insufficient

Charge scaling as an effective solution to the experiment-computation disagreement in molecular modelling of ionic liquids (ILs) could bring the computational results close to the experimental reference for various thermodynamic properties. According to the large-scale benchmark calculations of mass density, solvation, and water-ILs transfer-free energies in our series of papers, the charge-scaling factor of 0.8 serves as a near-optimal option generally applicable to most ILs, although a system-dependent parameter adjustment could be attempted for further improved performance. However, there are situations in which such a charge-scaling treatment would fail. Namely, charge scaling cannot really affect the simulation outcome, or minimally perturbs the results that are still far from the experimental value. In such situations, the vdW radius as an additional adjustable parameter is commonly tuned to minimize the experiment-calculation deviation. In the current work, considering two ILs from the quinuclidinium family, we investigate the impacts of this vdW-scaling treatment on the mass density and the solvation/partition thermodynamics in a fashion similar to our previous charge-scaling works, i.e., scanning the vdW-scaling factor and computing physical properties under these parameter sets. It is observed that the mass density exhibits a linear response to the vdW-scaling factor with slopes close to -1.8 g/mL. By further investigating a set of physiochemically relevant temperatures between 288 K and 348 K, we confirm the robustness of the vdW-scaling treatment in the estimation of bulk properties. The best vdW-scaling parameter for mass density would worsen the computation of solvation/partition thermodynamics, and a marginal decrease in the vdW-scaling factor is considered as an intermediate option balancing the reproductions of bulk properties and solvation thermodynamics. These observations could be understood in a way similar to the charge-scaling situation. i.e., overfitting some properties (e.g., mass density) would degrade the accuracy of the other properties (e.g., solvation free energies). Following this principle, the general guideline for applying this vdW-tuning protocol is by using values between the density-derived choice and the solvation/partition-derived solution. The charge and current vdW scaling treatments cover commonly encountered ILs, completing the protocol for accurate modelling of ILs with fixed-charge force fields.

Recent PELE Developments and Applications in Drug Discovery Campaigns

Computer simulation techniques are gaining a central role in molecular pharmacology. Due to several factors, including the significant improvements of traditional molecular modelling, the irruption of machine learning methods, the massive data generation, or the unlimited computational resources through cloud computing, the future of pharmacology seems to go hand in hand with in silico predictions. In this review, we summarize our recent efforts in such a direction, centered on the unconventional Monte Carlo PELE software and on its coupling with machine learning techniques. We also provide new data on combining two recent new techniques, aquaPELE capable of exhaustive water sampling and fragPELE, for fragment growing.

Prediction of Pyrolysis Kinetics of Biomass: New Insights from Artificial Intelligence-Based Modeling

The present work introduces a quantitative structure-property relationship (QSPR)-based stochastic gradient boosting (SGB) decision tree framework for simulating and capturing of the thermal decomposition kinetics of biomass considering effective parameters of the ultimate analysis (such as carbon, hydrogen, oxygen, nitrogen, and sulfur content) and process heating rate. Through a total of 149 pyrolysis kinetics, this study developed an artificial model and subjected it to training and testing phases. The proposed model was validated using error analysis, sensitivity, regression, and outlier detection. The coefficient of determination (R2) and mean relative error (%MRE) were calculated to be 0.993 and 4.354%, respectively, suggesting good performance in the estimation of the pyrolysis kinetic parameters. Also, the sensitivity results indicated the process heating rate to have the strongest effect on the model output with a relevancy factor of 0.43. Eventually, the proposed model showed superior performance compared to earlier frameworks.

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.

aquaPELE: A Monte Carlo-Based Algorithm to Sample the Effects of Buried Water Molecules in Proteins

Water is frequently found inside proteins, carrying out important roles in catalytic reactions or molecular recognition tasks. Therefore, computational models that aim to study protein-ligand interactions usually have to include water effects through explicit or implicit approaches to obtain reliable results. While full explicit models might be too computationally daunting for some applications, implicit models are normally faster but omit some of the most important contributions of water. This is the case of our in-house software, called protein energy landscape exploration (PELE), which uses implicit models to speed up conformational explorations as much as possible; the lack of explicit water sampling, however, limits its model. In this work, we confront this problem with the development of aquaPELE. It is a new algorithm that extends the exploration capabilities while keeping efficiency as it employs a mixed implicit/explicit approach to also take into account the effects of buried water molecules. With an additional Monte Carlo (MC) routine, a set of explicit water molecules is perturbed inside protein cavities and their effects are dynamically adjusted to the current state of the system. As a result, this implementation can be used to predict the principal hydration sites or the rearrangement and displacement of conserved water molecules upon the binding of a ligand. We benchmarked this new tool focusing on estimating ligand binding modes and hydration sites in cavities with important interfacial water molecules, according to crystallographic structures. Results suggest that aquaPELE sets a fast and reliable alternative for molecular recognition studies in systems with a strong water-dependency.

Predicting Antibody Neutralization Efficacy in Hypermutated Epitopes Using Monte Carlo Simulations

Human Immunodeficiency Virus 1 (HIV-1) evades adaptive immunity by means of its extremely high mutation rate, which allows the HIV envelope glycoprotein to continuously escape from the action of antibodies. However, some broadly neutralizing antibodies (bNAbs) targeting specific viral regions show the ability to block the infectivity of a large number of viral variants. The discovery of these antibodies opens new avenues in anti-HIV therapy; however, they are still suboptimal tools as their amplitude of action ranges between 50% and 90% of viral variants. In this context, being able to discriminate between sensitive and resistant strains to an antibody would be of great interest for the design of optimal clinical antibody treatments and to engineer potent bNAbs for clinical use. Here, we describe a hierarchical procedure to predict the antibody neutralization efficacy of multiple viral isolates to three well-known anti-CD4bs bNAbs: VRC01, NIH45-46 and 3BNC117. Our method consists of simulating the three-dimensional binding process between the gp120 and the antibody by using Protein Energy Landscape Exploration (PELE), a Monte Carlo stochastic approach. Our results clearly indicate that the binding profiles of sensitive and resistant strains to a bNAb behave differently, showing the latter’s weaker binding profiles, that can be exploited for predicting antibody neutralization efficacy in hypermutated HIV-1 strains.

FragPELE: Dynamic Ligand Growing within a Binding Site. A Novel Tool for Hit-To-Lead Drug Design

The early stages of drug discovery rely on hit-to-lead programs, where initial hits undergo partial optimization to improve binding affinities for their biological target. This is an expensive and time-consuming process, requiring multiple iterations of trial and error designs, an ideal scenario for applying computer simulation. However, most state-of-the-art modeling techniques fail to provide a fast and reliable answer to the Induced-Fit protein-ligand problem. To aid in this matter, we present FragPELE, a new tool for in silico hit-to-lead drug design, capable of growing a fragment from a bound core while exploring the protein-ligand conformational space. We tested the ability of FragPELE to predict crystallographic data, even in cases where cryptic sub-pockets open because of the presence of particular R-groups. Additionally, we evaluated the potential of the software on growing and scoring five congeneric series from the 2015 FEP+ dataset, comparing them to FEP+, SP and Induced-Fit Glide, and MMGBSA simulations. Results show that FragPELE could be useful not only for finding new cavities and novel binding modes in cases where standard docking tools cannot but also to rank ligand activities in a reasonable amount of time and with acceptable precision.

Improved Poisson-Boltzmann Methods for High-Performance Computing

Implicit solvent models based on the Poisson-Boltzmann equation (PBE) have been widely used to study electrostatic interactions in biophysical processes. These models often treat the solvent and solute regions as high and low dielectric continua, leading to a large jump in dielectrics across the molecular surface which is difficult to handle. Higher order interface schemes are often needed to seek higher accuracy for PBE applications. However, these methods are usually very liberal in the use of grid points nearby the molecular surface, making them difficult to use on high-performance computing platforms. Alternatively, the harmonic average (HA) method has been used to approximate dielectric interface conditions near the molecular surface with surprisingly good convergence and is well suited for high-performance computing. By adopting a 7-point stencil, the HA method is advantageous in generating simple 7-banded coefficient matrices, which greatly facilitate linear system solution with dense data parallelism, on high-performance computing platforms such as a graphics processing unit (GPU). However, the HA method is limited due to its lower accuracy. Therefore, it would be of great interest for high-performance applications to develop more accurate methods while retaining the simplicity and effectiveness of the 7-point stencil discretization scheme. In this study, we have developed two new algorithms based on the spirit of the HA method by introducing more physical interface relations and imposing the discretized Poisson's equation to the second order, respectively. Our testing shows that, for typical biomolecules, the new methods significantly improve the numerical accuracy to that comparable to the second-order solvers and with ∼65% overall efficiency gain on widely available high-performance GPU platforms.

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.

An efficient second-order poisson-boltzmann method

Immersed interface method (IIM) is a promising high-accuracy numerical scheme for the Poisson-Boltzmann model that has been widely used to study electrostatic interactions in biomolecules. However, the IIM suffers from instability and slow convergence for typical applications. In this study, we introduced both analytical interface and surface regulation into IIM to address these issues. The analytical interface setup leads to better accuracy and its convergence closely follows a quadratic manner as predicted by theory. The surface regulation further speeds up the convergence for nontrivial biomolecules. In addition, uncertainties of the numerical energies for tested systems are also reduced by about half. More interestingly, the analytical setup significantly improves the linear solver efficiency and stability by generating more precise and better-conditioned linear systems. Finally, we implemented the bottleneck linear system solver on GPUs to further improve the efficiency of the method, so it can be widely used for practical biomolecular applications. © 2019 Wiley Periodicals, Inc.

Hydration Thermodynamics of Non-Polar Aromatic Hydrocarbons: Comparison of Implicit and Explicit Solvation Models

The precise description of solute-water interactions is essential to understand the chemo-physical nature in hydration processes. Such a hydration thermodynamics for various solutes has been explored by means of explicit or implicit solvation methods. Using the Poisson-Boltzmann solvation model, the implicit models are well designed to reasonably predict the hydration free energies of polar solutes. The implicit model, however, is known to have shortcomings in estimating those for non-polar aromatic compounds. To investigate a cause of error, we employed a novel systematic framework of quantum-mechanical/molecular-mechanical (QM/MM) coupling protocol in explicit solvation manner, termed DFT-CES, based on the grid-based mean-field treatment. With the aid of DFT-CES, we delved into multiple energy parts, thereby comparing DFT-CES and PB models component-by-component. By applying the modified PB model to estimate the hydration free energies of non-polar solutes, we find a possibility to improve the predictability of PB models. We expect that this study could shed light on providing an accurate route to study the hydration thermodynamics for various solute compounds.

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.

Recent Developments and Applications of the MMPBSA Method

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensions to membrane proteins and high-speed screening, and new automation toolkits. Recent applications in various important biomedical and chemical fields are also reviewed. We conclude with a few future directions aimed at making MMPBSA a more robust and efficient method.

Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling

Solvent-mediated electrostatic interactions were well recognized to be important in the structure and function of molecular systems. Ionic interaction is an important component in electrostatic interactions, especially in highly charged molecules, such as nucleic acids. Here, we focus on the quality of the widely used Poisson-Boltzmann surface area (PBSA) continuum models in modeling ionic interactions by comparing with both explicit solvent simulations and the experiment. In this work, the molality-dependent chemical potentials for sodium chloride (NaCl) electrolyte were first simulated in the SPC/E explicit solvent. Our high-quality simulation agrees well with both the previous study and the experiment. Given the free-energy simulations in SPC/E as the benchmark, we used the same sets of snapshots collected in the SPC/E solvent model for PBSA free-energy calculations in the hope to achieve the maximum consistency between the two solvent models. Our comparative analysis shows that the molality-dependent chemical potentials of NaCl were reproduced well with both linear PB and nonlinear PB methods, although nonlinear PB agrees better with SPC/E and the experiment. Our free-energy simulations also show that the presence of salt increases the hydrophobic effect in a nonlinear fashion, in qualitative agreement with previous theoretical studies of Onsager and Samaras. However, the lack of molality-dependency in the nonelectrostatics continuum models dramatically reduces the overall quality of PBSA methods in modeling salt-dependent energetics. These analyses point to further improvements needed for more robust modeling of solvent-mediated interactions by the continuum solvation frameworks.

Diminazene Is a Slow Pore Blocker of Acid-Sensing Ion Channel 1a (ASIC1a)

Acid-sensing ion channels (ASICs) are neuronal receptors for extracellular protons. They contribute to the excitatory postsynaptic current and to the detection of painful acidosis. Moreover, they are activated during peripheral inflammation and acidosis associated with various neuronal disorders, such as stroke and neuroinflammation, rendering them interesting drug targets. Diminazene aceturate is a small-molecule inhibitor of ASICs with a reported apparent affinity in the low micromolar range, making it an interesting lead compound. It was reported that diminazene accelerates desensitization of ASICs, which was, however, not explained mechanistically. Furthermore, a binding site in a groove of the extracellular domain was proposed but not experimentally verified. In this study, we revisited the mechanism of inhibition by diminazene and its binding site on ASIC1a, the ASIC subunit with the greatest importance in the central nervous system. We show that diminazene slowly blocks ASIC1a, leading to the apparent acceleration of desensitization and underestimating its potency; we show that diminazene indeed has a submicromolar potency at ASIC1a (IC₅₀ 0.3 μM). Moreover, we show that the inhibition is voltage-dependent and competes with that by amiloride, a pore blocker of ASICs. Finally, we identify by molecular docking a binding site in the ion pore that we confirm by site-directed mutagenesis. In summary, our results show that diminazene blocks ASIC1a by a slow open-channel block and suggest that diminazene is an interesting lead compound for high-affinity blockers of ASICs.

Solvation Thermodynamics of Oligoglycine with Respect to Chain Length and Flexibility

Oligoglycine is a backbone mimic for all proteins and is prevalent in the sequences of intrinsically disordered proteins. We have computed the absolute chemical potential of glycine oligomers at infinite dilution by simulation with the CHARMM36 and Amber ff12SB force fields. We performed a thermodynamic decomposition of the solvation free energy (ΔG(sol)) of Gly2-5 into enthalpic (ΔH(sol)) and entropic (ΔS(sol)) components as well as their van der Waals and electrostatic contributions. Gly2-5 was either constrained to a rigid/extended conformation or allowed to be completely flexible during simulations to assess the effects of flexibility on these thermodynamic quantities. For both rigid and flexible oligoglycine models, the decrease in ΔG(sol) with chain length is enthalpically driven with only weak entropic compensation. However, the apparent rates of decrease of ΔG(sol), ΔH(sol), ΔS(sol), and their elec and vdw components differ for the rigid and flexible models. Thus, we find solvation entropy does not drive aggregation for this system and may not explain the collapse of long oligoglycines. Additionally, both force fields yield very similar thermodynamic scaling relationships with respect to chain length despite both force fields generating different conformational ensembles of various oligoglycine chains.

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.

Heterogeneous dielectric generalized Born model with a van der Waals term provides improved association energetics of membrane-embedded transmembrane helices

The heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is extended by the addition of a van der Waals dispersion term to better describe the nonpolar components of the free energy of solvation. The new model, termed HDGBvdW, improves the energy estimates in the hydrophobic interior of the membrane, where polar and charged species are rarely found and nonpolar interactions become significant. The implicit van der Waals term for the membrane environment extends the model from Gallicchio et al. (J. Comput. Chem. 2004, 25, 479) by combining separate contributions from each of the membrane components. The HDGBvdW model is validated with a series of test cases ranging from membrane insertion and pair association profiles of amino acid side chain analogs and transmembrane helices. Overall, the HDGBvdW model leads to increased agreement with explicit membrane simulation results and experimental data. © 2016 Wiley Periodicals, Inc.

Using polarizable POSSIM force field and fuzzy-border continuum solvent model to calculate pK(a) shifts of protein residues

Our Fuzzy-Border (FB) continuum solvent model has been extended and modified to produce hydration parameters for small molecules using POlarizable Simulations Second-order Interaction Model (POSSIM) framework with an average error of 0.136 kcal/mol. It was then used to compute pKa shifts for carboxylic and basic residues of the turkey ovomucoid third domain (OMTKY3) protein. The average unsigned errors in the acid and base pKa values were 0.37 and 0.4 pH units, respectively, versus 0.58 and 0.7 pH units as calculated with a previous version of polarizable protein force field and Poisson Boltzmann continuum solvent. This POSSIM/FB result is produced with explicit refitting of the hydration parameters to the pKa values of the carboxylic and basic residues of the OMTKY3 protein; thus, the values of the acidity constants can be viewed as additional fitting target data. In addition to calculating pKa shifts for the OMTKY3 residues, we have studied aspartic acid residues of Rnase Sa. This was done without any further refitting of the parameters and agreement with the experimental pKa values is within an average unsigned error of 0.65 pH units. This result included the Asp79 residue that is buried and thus has a high experimental pKa value of 7.37 units. Thus, the presented model is capable or reproducing pKa results for residues in an environment that is significantly different from the solvated protein surface used in the fitting. Therefore, the POSSIM force field and the FB continuum solvent parameters have been demonstrated to be sufficiently robust and transferable. © 2016 Wiley Periodicals, Inc.

ESES: Software for Eulerian solvent excluded surface

Solvent excluded surface (SES) is one of the most popular surface definitions in biophysics and molecular biology. In addition to its usage in biomolecular visualization, it has been widely used in implicit solvent models, in which SES is usually immersed in a Cartesian mesh. Therefore, it is important to construct SESs in the Eulerian representation for biophysical modeling and computation. This work describes a software package called Eulerian solvent excluded surface (ESES) for the generation of accurate SESs in Cartesian grids. ESES offers the description of the solvent and solute domains by specifying all the intersection points between the SES and the Cartesian grid lines. Additionally, the interface normal at each intersection point is evaluated. Furthermore, for a given biomolecule, the ESES software not only provides the whole surface area, but also partitions the surface area according to atomic types. Homology theory is utilized to detect topological features, such as loops and cavities, on the complex formed by the SES. The sizes of loops and cavities are measured based on persistent homology with an evolutionary partial differential equation-based filtration. ESES is extensively validated by surface visualization, electrostatic solvation free energy computation, surface area and volume calculations, and loop and cavity detection and their size estimation. We used the Amber PBSA test set in our electrostatic solvation energy, area, and volume validations. Our results are either calibrated by analytical values or compared with those from the MSMS software. © 2017 Wiley Periodicals, Inc.

Bayesian Model Averaging for Ensemble-Based Estimates of Solvation-Free Energies

This paper applies the Bayesian Model Averaging statistical ensemble technique to estimate small molecule solvation free energies. There is a wide range of methods available for predicting solvation free energies, ranging from empirical statistical models to ab initio quantum mechanical approaches. Each of these methods is based on a set of conceptual assumptions that can affect predictive accuracy and transferability. Using an iterative statistical process, we have selected and combined solvation energy estimates using an ensemble of 17 diverse methods from the fourth Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) blind prediction study to form a single, aggregated solvation energy estimate. Methods that possess minimal or redundant information are pruned from the ensemble and the evaluation process repeats until aggregate predictive performance can no longer be improved. We show that this process results in a final aggregate estimate that outperforms all individual methods by reducing estimate errors by as much as 91% to 1.2 kcal mol^-1 accuracy. This work provides a new approach for accurate solvation free energy prediction and lays the foundation for future work on aggregate models that can balance computational cost with prediction accuracy.

Minimization and Eulerian Formulation of Differential Geormetry Based Nonpolar Multiscale Solvation Models

In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.

Calculating protein-ligand binding affinities with MMPBSA: Method and error analysis

Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) methods have become widely adopted in estimating protein-ligand binding affinities due to their efficiency and high correlation with experiment. Here different computational alternatives were investigated to assess their impact to the agreement of MMPBSA calculations with experiment. Seven receptor families with both high-quality crystal structures and binding affinities were selected. First the performance of nonpolar solvation models was studied and it was found that the modern approach that separately models hydrophobic and dispersion interactions dramatically reduces RMSD's of computed relative binding affinities. The numerical setup of the Poisson-Boltzmann methods was analyzed next. The data shows that the impact of grid spacing to the quality of MMPBSA calculations is small: the numerical error at the grid spacing of 0.5 Å is already small enough to be negligible. The impact of different atomic radius sets and different molecular surface definitions was further analyzed and weak influences were found on the agreement with experiment. The influence of solute dielectric constant was also analyzed: a higher dielectric constant generally improves the overall agreement with experiment, especially for highly charged binding pockets. The data also showed that the converged simulations caused slight reduction in the agreement with experiment. Finally the direction of estimating absolute binding free energies was briefly explored. Upon correction of the binding-induced rearrangement free energy and the binding entropy lost, the errors in absolute binding affinities were also reduced dramatically when the modern nonpolar solvent model was used, although further developments were apparently necessary to further improve the MMPBSA methods. © 2016 Wiley Periodicals, Inc.

The impact of surface area, volume, curvature, and Lennard-Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.

Why is Benzene Soluble in Water? Role of OH/π Interaction in Solvation

The XH/π interaction (X = C, N, or O) plays an essential role in a variety of fundamental processes in condensed phase, and it attracts broad interests in the fields of chemistry and biochemistry in recent years. This issue has a direct relevance to an intriguing phenomenon that a benzene molecule exhibits a negative solvation free energy of -0.87 kcal/mol in ambient water though it is a typical nonpolar organic solute. In this work, we developed a novel method to analyze the free energy δμ due to the electron density fluctuation of a solute in solution to clarify the mechanism responsible for the affinity of benzene to bulk water. Explicitly, the free energy δμ is decomposed into contributions from σ and π electrons in π-conjugated systems on the basis of the QM/MM method combined with a theory of solutions. With our analyses, the free energy δμ(π) arising from the fluctuation of π electrons in benzene was obtained as -0.94 kcal/mol and found to be the major source of the affinity of benzene to water. Thus, the role of π electrons in hydration is quantified for the first time with our analyses. Our method was applied to phenyl methyl ether (PME) in water solution to examine the substituent effects of the electron donating group (EDG) on the hydration of a π-conjugated system. The delocalization effect of the π electrons on hydration was also investigated performing the decomposition analyses for ethene and 1,3-butadiene molecules in water solutions. It was revealed that the stabilization due to δμ(π) for butadiene (-0.76 kcal/mol) is about three times as large as that for ethene (-0.26 kcal/mol), which suggests the importance of the delocalization effect of the π electrons in mediating the affinity to polar solvent.

Simple Predictive Models of Passive Membrane Permeability Incorporating Size-Dependent Membrane-Water Partition

We investigate the relationship between passive permeability and molecular size, in the context of solubility-diffusion theory, using a diverse compound set with molecular weights ranging from 151 to 828, which have all been characterized in a consistent manner using the RRCK cell monolayer assay. Computationally, each compound was subjected to extensive conformational search and physics-based permeability prediction, and multiple linear regression analyses were subsequently performed to determine, empirically, the relative contributions of hydrophobicity and molecular size to passive permeation in the RRCK assay. Additional analyses of Log D and PAMPA data suggest that these measurements are not size selective, a possible reason for their sometimes weak correlation with cell-based permeability.

Modeling of babesipain-1 and identification of natural and synthetic leads for bovine babesiosis drug development

Babesiosis is a tick-borne, zoonotic disease caused by species of the intraerythrocytic protozoan Babesia. It is distributed all around the world and affects various domestic and wild animals, mainly cattle. Recently, the cysteine protease enzyme, babesipain-1 from Babesia bigemina has been identified as a potential target for designing new anti-babesiosis drugs. In the present study, a three-dimensional structural model of babesipain-1 was developed. An active site with three pockets (S1, S2, and S3), which is congruent with its homolog, falcipain-3, was also identified. Moreover, the conservation of active site residues was consistent with the cysteine protease family. In order to identify potential inhibitors, a virtual screening workflow was employed with a chemical library containing natural and synthetic compounds. Potential inhibitors interacting with all the three subsites were identified. Further, molecular dynamic simulations were carried out to assess the interactions and stability of the inhibitors. The informatics approach, and the findings presented in this study will assist researchers in further development of potential anti-babesiosis molecules.

Prediction of Solvation Free Energies with Thermodynamic Integration Using the General Amber Force Field

Computer-aided drug design (CADD) techniques can be very effective in reducing costs and speeding up drug discovery. The determination of binding and solvation free energies is pivotal for this process and is, therefore, the subject of many studies. In this work, the solvation free energy change (ΔΔGsolv) for a total of 92 transformations in small molecules was predicted using Thermodynamic Integration (TI). It was our aim to compare experimental and calculated solvation free energies for typical and prime additions considered in drug optimizations, analyzing trends, and optimizing a TI protocol. The results showed a good agreement between experimental and predicted values, with an overestimation of the predicted values for CH3, halogens, and NH2, as well as an underestimation for CONH2, but all fall within ±1 kcal/mol. NO2 addition showed a larger and systematic underestimation of the predicted ΔΔGsolv, indicating the need for special attention in these cases. For small molecules, if no experimental data is available, using TI as a theoretical strategy thus appears to be a suitable choice in CADD. It provides a good compromise between time and accuracy.

Improving the Accuracy of the Linear Interaction Energy Method for Solvation Free Energies

A linear response method for estimating the free energy of solvation is presented and validated using explicit solvent molecular dynamics, thermodynamic perturbation calculations, and experimental data. The electrostatic contribution to the solvation free energy is calculated using a linear response estimate, which is obtained by comparison to the free energy calculated using thermodynamic perturbation. Systematic deviations from the value of (1)/2 in the potential energy scaling factor are observed for some types of compounds, and these are taken into account by introducing specific coefficients for different chemical groups. The derived model reduces the rms error of the linear response estimate significantly from 1.6 to 0.3 kcal/mol on a training set of 221 molecules used to parametrize the model and from 3.7 to 1.3 kcal/mol on a test set of 355 molecules that were not used in the derivation of the model. The total solvation free energy is estimated by combining the derived model with an empirical size dependent term for predicting the nonpolar contribution. Using this model, the experimental hydration free energies for 192 molecules are reproduced with an rms error of 1.1 kcal/mol. The use of LIE in simplified binding free energy calculations to predict protein-ligand binding free energies is also discussed.

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.

PELE: Protein Energy Landscape Exploration. A Novel Monte Carlo Based Technique

Combining protein structure prediction algorithms and Metropolis Monte Carlo techniques, we provide a novel method to explore all-atom energy landscapes. The core of the technique is based on a steered localized perturbation followed by side-chain sampling as well as minimization cycles. The algorithm and its application to ligand diffusion are presented here. Ligand exit pathways are successfully modeled for different systems containing ligands of various sizes:  carbon monoxide in myoglobin, camphor in cytochrome P450cam, and palmitic acid in the intestinal fatty-acid-binding protein. These initial applications reveal the potential of this new technique in mapping millisecond-time-scale processes. The computational cost associated with the exploration is significantly less than that of conventional MD simulations.

Monte Carlo Sampling with Hierarchical Move Sets: POSH Monte Carlo

We present a new Monte Carlo method for sampling rugged energy landscapes that allows for efficient transitions across sparsely distributed local basins. The trial move consists of two steps. The first step is a large initial trial move, and the second step is a Monte Carlo trajectory generated using smaller trial moves. To maintain detailed balance, a reverse transition probability is estimated along a path that differs from the forward path. Since the forward and reverse transitions are different, we name the algorithm POSH (port out, starboard home) Monte Carlo. The process obeys detailed balance to the extent that the transition probabilities are correctly estimated. There is an optimal range of performance for a given energy landscape, which depends on how sparsely the low energy states of the system are distributed. For simple model systems, adequate precision is obtained over a large range of inner steps settings. Side chain sampling of residues in the binding region of progesterone antibody 1dba are studied, and show that significant improvement over a comparable standard protocol can be obtained using POSH sampling. To compare with experimental data, the phosphopeptide Ace-Gly-Ser-pSer-Ser-Nma is also studied, and the resulting NMR observables compare well with experiment. For the biomolecular systems studied, we show that POSH sampling generates precise distributions using the number of inner steps set up to 20.

New Monte Carlo Based Technique To Study DNA-Ligand Interactions

We present a new all-atom Monte Carlo technique capable of performing quick and accurate DNA-ligand conformational sampling. In particular, and using the PELE software as a frame, we have introduced an additional force field, an implicit solvent, and an anisotropic network model to effectively map the DNA energy landscape. With these additions, we successfully generated DNA conformations for a test set composed of six DNA fragments of A-DNA and B-DNA. Moreover, trajectories generated for cisplatin and its hydrolysis products identified the best interacting compound and binding site, producing analogous results to microsecond molecular dynamics simulations. Furthermore, a combination of the Monte Carlo trajectories with Markov State Models produced noncovalent binding free energies in good agreement with the published molecular dynamics results, at a significantly lower computational cost. Overall our approach will allow a quick but accurate sampling of DNA-ligand interactions.