Hydration Free Energies in the FreeSolv Database Calculated with Polarized Iterative Hirshfeld Charges

The tale of HORTON: Lessons learned in a decade of scientific software development

HORTON is a free and open-source electronic-structure package written primarily in Python 3 with some underlying C++ components. While HORTON's development has been mainly directed by the research interests of its leading contributing groups, it is designed to be easily modified, extended, and used by other developers of quantum chemistry methods or post-processing techniques. Most importantly, HORTON adheres to modern principles of software development, including modularity, readability, flexibility, comprehensive documentation, automatic testing, version control, and quality-assurance protocols. This article explains how the principles and structure of HORTON have evolved since we started developing it more than a decade ago. We review the features and functionality of the latest HORTON release (version 2.3) and discuss how HORTON is evolving to support electronic structure theory research for the next decade.

Nonbonded Force Field Parameters from MBIS Partitioning of the Molecular Electron Density Improve Binding Affinity Predictions of the T4-Lysozyme Double Mutant

The use of computer simulation for binding affinity prediction is growing in drug discovery. However, its wider use is constrained by the accuracy of the free energy calculations. The key sources of error are the force fields used to depict molecular interactions and insufficient sampling of the configurational space. To improve the quality of the force field, we developed a Python-based computational workflow. The workflow described here uses the minimal basis iterative stockholder (MBIS) method to determine atomic charges and Lennard-Jones parameters from the polarized molecular density. This is done by performing electronic structure calculations on various configurations of the ligand when it is both bound and unbound. In addition, we validated a simulation procedure that accounts for the protein and ligand degrees of freedom to precisely calculate binding free energies. This was achieved by comparing the self-adjusted mixture sampling and nonequilibrium thermodynamic integration methods using various protein and ligand conformations. The accuracy of predicting binding affinity is improved by using MBIS-derived force field parameters and a validated simulation procedure. This improvement surpasses the chemical precision for the eight aromatic ligands, reaching a root-mean-square error of 0.7 kcal/mol.

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Assessment of Halogen Off-Center Point-Charge Models Using Explicit Solvent Simulations

Compounds containing halogens can form halogen bonds (XBs) with biological targets such as proteins and membranes due to their anisotropic electrostatic potential. To accurately describe this anisotropy, off-center point-charge (EP) models are commonly used in force field methods, allowing the description of XBs at the molecular mechanics and molecular dynamics level. Various EP implementations have been documented in the literature, and despite being efficient in reproducing protein-ligand geometries and sampling of XBs, it is unclear how well these EP models predict experimental properties such as hydration free energies (ΔGhyd), which are often used to validate force field performance. In this work, we report the first assessment of three EP models using alchemical free energy calculations to predict ΔGhyd values. We show that describing the halogen anisotropy using some EP models can lead to a slight improvement in the prediction of the ΔGhyd when compared with the models without EP, especially for the chlorinated compounds; however, this improvement is not related to the establishment of XBs but is most likely due to the improvement of the sampling of hydrogen bonds. We also highlight the importance of the choice of the EP model, especially for the iodinated molecules, since a slight tendency to improve the prediction is observed for compounds with a larger σ-hole but significantly worse results were obtained for compounds that are weaker XB donors.

Predicting absolute aqueous solubility by applying a machine learning model for an artificially liquid-state as proxy for the solid-state

In this study, we use machine learning algorithms with QM-derived COSMO-RS descriptors, along with Morgan fingerprints, to predict the absolute solubility of drug-like compounds. The QM-derived descriptors account for the molecular properties of the solute, i.e., the solute-solute interactions in an artificial-liquid-state (super-cooled liquid), and the solute-solvent interactions in solution. We employ two main approaches to predict solubility: (i) a hypothetical pathway that involves melting the solute at room temperature T = T¯ ([Formula: see text]) and mixing the artificially liquid solute into the solvent ([Formula: see text]). In this approach [Formula: see text] is predicted using machine learning models, and the [Formula: see text] is obtained from COSMO-RS calculations; (ii) direct solubility prediction using machine learning algorithms. The models were trained on a large number of Bayer in-house compounds for which water solubility data is available at physiological pH of 6.5 and ambient temperature. We also evaluated our models using external datasets from a solubility challenge. Our models present great improvements compared to the absolute solubility prediction with the QSAR model for the artificial liquid state as implemented in the COSMOtherm software, for both in-house and external datasets. We are furthermore able to demonstrate the superiority of QM-derived descriptors compared to cheminformatics descriptors. We finally present low-cost alternative models using fragment-based COSMOquick calculations with only marginal reduction in the quality of predicted solubility.

Calculations of Absolute Solvation Free Energies with Transformato─Application to the FreeSolv Database Using the CGenFF Force Field

We recently introduced transformato, an open-source Python package for the automated setup of large-scale calculations of relative solvation and binding free energy differences. Here, we extend the capabilities of transformato to the calculation of absolute solvation free energy differences. After careful validation against the literature results and reference calculations with the PERT module of CHARMM, we used transformato to compute absolute solvation free energies for most molecules in the FreeSolv database (621 out of 642). The force field parameters were obtained with the program cgenff (v2.5.1), which derives missing parameters from the CHARMM general force field (CGenFF v4.6). A long-range correction for the Lennard-Jones interactions was added to all computed solvation free energies. The mean absolute error compared to the experimental data is 1.12 kcal/mol. Our results allow a detailed comparison between the AMBER and CHARMM general force fields and provide a more in-depth understanding of the capabilities and limitations of the CGenFF small molecule parameters.

What is the Optimal Dipole Moment for Nonpolarizable Models of Liquids?

In classical nonpolarizable models, electrostatic interactions are usually described by assigning fixed partial charges to interaction sites. Despite the multitude of methods and theories proposed over the years for partial charge assignment, a fundamental question remains─what is the correct degree of polarization that a fixed-charge model should possess to provide the best balance of interactions (including induction effects) and yield the best description of the potential energy surface of a liquid phase? We address this question by approaching it from two separate and independent viewpoints: the QUantum mechanical BEspoke (QUBE) approach, which assigns bespoke force field parameters for individual molecules from ab initio calculations with minimal empirical fitting, and the Polarization-Consistent Approach (PolCA) force field, based on empirical fitting of force field parameters with an emphasis on transferability by rigorously accounting for polarization effects in the parameterization process. We show that the two approaches yield consistent answers to the above question, namely, that the dipole moment of the model should be approximately halfway between those of the gas and the liquid phase. Crucially, however, the reference liquid-phase dipole needs to be estimated using methods that explicitly consider both mean-field and local contributions to polarization. In particular, continuum dielectric models are inadequate for this purpose because they cannot account for local effects and therefore significantly underestimate the degree of polarization of the molecule. These observations have profound consequences for the development, validation, and testing of nonpolarizable models.

Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction

Hydration free energies of small molecules are commonly used as benchmarks for solvation models. However, errors in predicting hydration free energies are partially due to the force fields used and not just the solvation model. To address this, we have used the 3D reference interaction site model (3D-RISM) of molecular solvation and existing benchmark explicit solvent calculations with a simple element count correction (ECC) to identify problems with the non-bond parameters in the general AMBER force field (GAFF). 3D-RISM was used to calculate hydration free energies of all 642 molecules in the FreeSolv database, and a partial molar volume correction (PMVC), ECC, and their combination (PMVECC) were applied to the results. The PMVECC produced a mean unsigned error of 1.01±0.04kcal/mol and root mean squared error of 1.44±0.07kcal/mol, better than the benchmark explicit solvent calculations from FreeSolv, and required less than 15 s of computing time per molecule on a single CPU core. Importantly, parameters for PMVECC showed systematic errors for molecules containing Cl, Br, I, and P. Applying ECC to the explicit solvent hydration free energies found the same systematic errors. The results strongly suggest that some small adjustments to the Lennard-Jones parameters for GAFF will lead to improved hydration free energy calculations for all solvent models.

Nonbonded Force Field Parameters from Minimal Basis Iterative Stockholder Partitioning of the Molecular Electron Density Improve CB7 Host-Guest Affinity Predictions

Binding affinity prediction by means of computer simulation has been increasingly incorporated in drug discovery projects. Its wide application, however, is limited by the prediction accuracy of the free energy calculations. The main error sources are force fields used to describe molecular interactions and incomplete sampling of the configurational space. Organic host-guest systems have been used to address force field quality because they share similar interactions found in ligands and receptors, and their rigidity facilitates configurational sampling. Here, we test the binding free energy prediction accuracy for 14 guests with an aromatic or adamantane core and the CB7 host using molecular electron density derived nonbonded force field parameters. We developed a computational workflow written in Python to derive atomic charges and Lennard-Jones parameters with the Minimal Basis Iterative Stockholder method using the polarized electron density of several configurations of each guest in the bound and unbound states. The resulting nonbonded force field parameters improve binding affinity prediction, especially for guests with an adamantane core in which repulsive exchange and dispersion interactions to the host dominate.

Exploration and validation of force field design protocols through QM-to-MM mapping

The scale of the parameter optimisation problem in traditional molecular mechanics force field construction means that design of a new force field is a long process, and sub-optimal choices made in the early stages can persist for many generations. We hypothesise that careful use of quantum mechanics to inform molecular mechanics parameter derivation (QM-to-MM mapping) should be used to significantly reduce the number of parameters that require fitting to experiment and increase the pace of force field development. Here, we design and train a collection of 15 new protocols for small, organic molecule force field derivation, and test their accuracy against experimental liquid properties. Our best performing model has only seven fitting parameters, yet achieves mean unsigned errors of just 0.031 g cm^-3 and 0.69 kcal mol^-1 in liquid densities and heats of vaporisation, compared to experiment. The software required to derive the designed force fields is freely available at https://github.com/qubekit/QUBEKit.

In Silico Analysis of the Antagonist Effect of Enoxaparin on the ApoE4–Amyloid-Beta (Aβ) Complex at Different pH Conditions

Apolipoprotein E4 (ApoE4) is thought to increase the risk of developing Alzheimer’s disease. Several studies have shown that ApoE4-Amyloid β (Aβ) interactions can increment amyloid depositions in the brain and that this can be augmented at low pH values. On the other hand, experimental studies in transgenic mouse models have shown that treatment with enoxaparin significantly reduces cortical Aβ levels, as well as decreases the number of activated astrocytes around Aβ plaques. However, the interactions between enoxaparin and the ApoE4-Aβ proteins have been poorly explored. In this work, we combine molecular dynamics simulations, molecular docking, and binding free energy calculations to elucidate the molecular properties of the ApoE4-Aβ interactions and the competitive binding affinity of the enoxaparin on the ApoE4 binding sites. In addition, we investigated the effect of the environmental pH levels on those interactions. Our results showed that under different pH conditions, the closed form of the ApoE4 protein, in which the C-terminal domain folds into the protein, remains stabilized by a network of hydrogen bonds. This closed conformation allowed the generation of six different ApoE4-Aβ interaction sites, which were energetically favorable. Systems at pH5 and 6 showed the highest energetic affinity. The enoxaparin molecule was found to have a strong energetic affinity for ApoE4-interacting sites and thus can neutralize or disrupt ApoE4-Aβ complex formation.

Theoretical investigation complexation characteristics and UV-Vis absorption spectral properties of CdTe QDs with four capping agents

In this paper, density functional theory (DFT) and time-dependent density functional theory (TDDFT) are used to study the complexation characteristics CdTe QDs with four different capping agents, i.e. 3-mercaptopropionic acid (MPA), reduced glutathione (GSH), 1-thioglycerol (TG) and 2-mercaptoethanesulfonate (MES). The properties of these complexes are analyzed by the complexation free energies, bond lengths, LOL, ADCH charges, frontier molecular orbitals and the UV-Vis absorption spectra. The results indicate that the four capping agents could form stable complexes with CdTe QDs. Whether the four capping agents interact with (CdTe)₆ or (CdTe)₉, MES has the strongest complexation ability with CdTe QDs and the MES-complexes are the most stable. For (CdTe)_6, A2-MES is the most stable configuration. The complexation free energy and bond length of A2-MES are - 74.50 kcal/mol and 2.461 Å, respectively. When (CdTe)₉ as substrate, A4-MES is the most stable configuration and corresponding complexation free energy is - 100.97 kcal/mol, which is followed by A4-MPA (- 57.75 kcal/mol) and A3-TG (- 60.20 kcal/mol), while A4-GSH (- 44.47 kcal/mol) is the weakest. Moreover, the electron amount transferred from MES to CdTe QDs is the most, and the ADCH charge value is 1.47 e. The absorption intensity of UV-visible light after complexation is also the largest. This is consistent with the result of the complexation free energy. Thus, it can be seen that the complexation abilities of four capping agents are in order of MES > MPA≈TG > GSH.

Molecular Environment-Specific Atomic Charges Improve Binding Affinity Predictions of SAMPL5 Host-Guest Systems

Host-guest systems are widely used in benchmarks as model systems to improve computational methods for absolute binding free energy predictions. Recent advances in sampling algorithms for alchemical free energy calculations and the increase in computational power have made their binding affinity prediction primarily dependent on the quality of the force field. Here, we propose a new methodology to derive the atomic charges of host-guest systems based on quantum mechanics/molecular mechanics calculations and minimal basis iterative stockholder (MBIS) partitioning of the polarized electron density. A newly developed interface between the OpenMM and ORCA software packages provides D-MBIS charges that represent the guest's average electrostatic interactions in the hosts or the solvent. The simulation workflow also calculates the average energy required to polarize the guest in the bound and unbound state. Alchemical free energy calculations using the general Amber force field parameters with D-MBIS charges improve the binding affinity prediction of six guests bound to two octa acid hosts compared to the AM1-BCC charge set after correction with the average energetic polarization cost. This correction originates from the difference in potential energy that is required to polarize the guest in the bound and unbound state and contributes significantly to the binding affinity of anionic guests.

Automation of some macromolecular properties using a machine learning approach

In this study, we employed a newly developed method to predict macromolecular properties using a swarm artificial neural network (ANN) method as a machine learning approach. In this method, the molecular structures are represented by the feature description vectors used as training input data for a neural network. This study aims to develop an efficient approach for training an ANN using either experimental or quantum mechanics data. We aim to introduce an error model controlling the reliability of the prediction confidence interval using a bootstrapping swarm approach. We created different datasets of selected experimental or quantum mechanics results. Using this optimized ANN, we hope to predict properties and their statistical errors for new molecules. There are four datasets used in this study. That includes the dataset of 642 small organic molecules with known experimental hydration free energies, the dataset of 1475 experimental pKa values of ionizable groups in 192 proteins, the dataset of 2693 mutants in 14 proteins with given experimental values of changes in the Gibbs free energy, and a dataset of 7101 quantum mechanics heat of formation calculations. All the data are prepared and optimized using the AMBER force field in the CHARMM macromolecular computer simulation program. The bootstrapping swarm ANN code for performing the optimization and prediction is written in Python computer programming language. The descriptor vectors of the small molecules are based on the Coulomb matrix and sum over bond properties. For the macromolecular systems, they consider the chemical-physical fingerprints of the region in the vicinity of each amino acid.

Optimized Halogen Atomic Radii for PBSA Calculations Using Off-Center Point Charges

In force-field methods, the usage of off-center point charges, also called extra points (EPs), is a common strategy to tackle the anisotropy of the electrostatic potential of covalently bonded halogens (X), thus allowing the description of halogen bonds (XBs) at the molecular mechanics/molecular dynamics (MM/MD) level. Diverse EP implementations exist in the literature differing on the charge sets and/or the X-EP distances. Poisson-Boltzmann and surface area (PBSA) calculations can be used to obtain solvation free energies (ΔG_solv) of small molecules, often to compute binding free energies (ΔG_bind) at the MM-PBSA level. This method depends, among other parameters, on the empirical assignment of atomic radii (PB radii). Given the multiplicity of off-center point-charge models and the lack of specific PB radii for halogens compatible with such implementations, in this work, we assessed the performance of PBSA calculations for the estimation of ΔG_solv values in water (ΔG_hyd), also conducting an optimization of the halogen PB radii (Cl, Br, and I) for each EP model. We not only expand the usage of EP models in the scope of the general AMBER force field (GAFF) but also provide the first optimized halogen PB radii in the context of the CHARMM general force field (CGenFF), thus contributing to improving the description of halogenated compounds in PBSA calculations.

Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state

We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This allows for a coarse-grained description of the solvent based on an inhomogeneous density of PC-SAFT segments. The solute, on the other hand, is described in full detail by atomistic Lennard-Jones interaction sites. The approach is entirely predictive as it only takes the PC-SAFT parameters of the solvent and the force-field parameters of the solute as input. No adjustable parameters or empirical corrections are involved. The framework is applied to study self-solvation of n-alkanes and to the calculation of residual chemical potentials in binary solvent mixtures. Our DFT approach accurately predicts solvation free energies of small molecular solutes in three different non-polar solvents, namely n-hexane, cyclohexane, and benzene. Additionally, we show that the calculated solvation free energies agree well with those obtained by molecular dynamics simulations and with the residual chemical potential calculated by the bulk PC-SAFT equation of state. We observe higher deviations for the solvation free energy of systems with significant solute-solvent Coulomb interactions.

Structural and Energetic Affinity of Annocatacin B with ND1 Subunit of the Human Mitochondrial Respiratory Complex I as a Potential Inhibitor: An In Silico Comparison Study with the Known Inhibitor Rotenone

ND1 subunit possesses the majority of the inhibitor binding domain of the human mitochondrial respiratory complex I. This is an attractive target for the search for new inhibitors that seek mitochondrial dysfunction. It is known, from in vitro experiments, that some metabolites from Annona muricata called acetogenins have important biological activities, such as anticancer, antiparasitic, and insecticide. Previous studies propose an inhibitory activity of bovine mitochondrial respiratory complex I by bis-tetrahydrofurans acetogenins such as annocatacin B, however, there are few studies on its inhibitory effect on human mitochondrial respiratory complex I. In this work, we evaluate the in silico molecular and energetic affinity of the annocatacin B molecule with the human ND1 subunit in order to elucidate its potential capacity to be a good inhibitor of this subunit. For this purpose, quantum mechanical optimizations, molecular dynamics simulations and the molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) analysis were performed. As a control to compare our outcomes, the molecule rotenone, which is a known mitochondrial respiratory complex I inhibitor, was chosen. Our results show that annocatacin B has a greater affinity for the ND1 structure, its size and folding were probably the main characteristics that contributed to stabilize the molecular complex. Furthermore, the MM/PBSA calculations showed a 35% stronger binding free energy compared to the rotenone complex. Detailed analysis of the binding free energy shows that the aliphatic chains of annocatacin B play a key role in molecular coupling by distributing favorable interactions throughout the major part of the ND1 structure. These results are consistent with experimental studies that mention that acetogenins may be good inhibitors of the mitochondrial respiratory complex I.

A Simple Method for Including Polarization Effects in Solvation Free Energy Calculations When Using Fixed-Charge Force Fields: Alchemically Polarized Charges

The incorporation of polarizability in classical force-field molecular simulations is an ongoing area of research. We focus here on its application to hydration free energy simulations of organic molecules. In contrast to computationally complex approaches involving the development of explicitly polarizable force fields, we present herein a simple methodology for incorporating polarization into such simulations using standard fixed-charge force fields, which we call the alchemically polarized charges (APolQ) method. APolQ employs a standard classical alchemical free energy change simulation to calculate the free energy difference between a fully polarized solute particle in a condensed phase and its unpolarized state in a vacuum. APolQ can in principle be applied to any microscopically homogeneous system (e.g., pure or mixed solvents). We applied APolQ to hydration free energy data for a test set of 45 neutral solute molecules in the FreeSolv database and compared results obtained using three different water models (SPC/E, TIP3P, and OPC3) and using minimal basis iterative Stockholder (MBIS) and restrained electrostatic potential (RESP) partial charge methodologies. In comparison with AM1-BCC, we found that APolQ outperforms it for the test set. Despite our method using default GAFF parameters, the MBIS partial charges yield absolute average deviations 1.5-1.9 kJ mol-1 lower than using AM1 bond charge correction (AM1-BCC). We conjecture that this method can be further improved by fitting the Lennard-Jones and torsional parameters to partial charges derived using MBIS or RESP methodologies.

Simulating protein-ligand binding with neural network potentials

Drug molecules adopt a range of conformations both in solution and in their protein-bound state. The strain and reduced flexibility of bound drugs can partially counter the intermolecular interactions that drive protein-ligand binding. To make accurate computational predictions of drug binding affinities, computational chemists have attempted to develop efficient empirical models of these interactions, although these methods are not always reliable. Machine learning has allowed the development of highly-accurate neural-network potentials (NNPs), which are capable of predicting the stability of molecular conformations with accuracy comparable to state-of-the-art quantum chemical calculations but at a billionth of the computational cost. Here, we demonstrate that these methods can be used to represent the intramolecular forces of protein-bound drugs within molecular dynamics simulations. These simulations are shown to be capable of predicting the protein-ligand binding pose and conformational component of the absolute Gibbs energy of binding for a set of drug molecules. Notably, the conformational energy for anti-cancer drug erlotinib binding to its target was found to be considerably overestimated by a molecular mechanical model, while the NNP predicts a more moderate value. Although the ANI-1ccX NNP was not trained to describe ionic molecules, reasonable binding poses are predicted for charged ligands, but this method is not suitable for modeling charged ligands in solution.

SAMPL6 Octanol-water partition coefficients from alchemical free energy calculations with MBIS atomic charges

In molecular modeling the description of the interactions between molecules forms the basis for a correct prediction of macroscopic observables. Here, we derive atomic charges from the implicitly polarized electron density of 11 molecules in the SAMPL6 challenge using the Hirshfeld-I and Minimal Basis Set Iterative Stockholder (MBIS) partitioning method. These atomic charges combined with other parameters in the GAFF force field and different water/octanol models were then used in alchemical free energy calculations to obtain hydration and solvation free energies, which after correction for the polarization cost, result in the blind prediction of the partition coefficient. From the tested partitioning methods and water models the S-MBIS atomic charges with the TIP3P water model presented the smallest deviation from the experiment. Conformational dependence of the free energies and the energetic cost associated with the polarization of the electron density are discussed.

Tackling Halogenated Species with PBSA: Effect of Emulating the σ-Hole

To model halogen-bond phenomena using classical force fields, an extra point (EP) of charge is frequently introduced at a given distance from the halogen (X) to emulate the σ-hole. The resulting molecular dynamics (MD) trajectories can be used in subsequent molecular mechanics (MM) combined with Poisson-Boltzmann and surface area calculations (PBSA) to estimate protein-ligand binding free energies (Δ G_bind). While EP addition improves the MM/MD description of halogen-containing systems, its effect on the calculation of solvation free energies (Δ G_solv) using the PBSA approach is yet to be assessed. As the PBSA calculations depend, among other parameters, on the empirical assignment of radii (PB radii), a problematic issue arises, since standard halogen radii are smaller than the typical X···EP distances, thus placing the EP within the solvent dielectric. Herein, we took a common literature EP parametrization scheme, which uses X···EP = R_min and RESP charges in the context of GAFF, and performed a comprehensive study on the performance of PBSA (using three different setups) in the calculation of Δ G_solv values for 142 halogenated compounds (bearing Cl, Br, or I) for which the experimental values are known. By conducting an optimization (minimizing the error against experimental values), we provide a new optimized set of halogen PB radii, for each PBSA setup, that should be used in the context of the aforementioned scenario. A simultaneous optimization of PB radii and X···EP distances shows that a wide range of distance/radius pairs can be used without significant loss of accuracy, therefore laying the basis for expanding this halogen radii optimization strategy to other force fields and EP implementations. As ligand Δ G_solv estimation is an important term in the determination of protein-ligand Δ G_bind, this work is particularly relevant in the framework of structure-based virtual screening and related computer-aided drug design routines.

Conformational sampling and polarization of Asp26 in pKa calculations of thioredoxin

Thioredoxin is a protein that has been used as model system by various computational methods to predict the pK_a of aspartate residue Asp26 which is 3.5 units higher than a solvent exposed one (eg, Asp20). Here, we use extensive atomistic molecular dynamics simulations of two different protonation states of Asp26 in combination with conformational analysis based on RMSD clustering and principle component analysis to identify representative conformations of the protein in solution. For each conformation, the Gibbs free energy of proton transfer between Asp26 and Asp20, which is fully solvated in a loop region of the protein, is calculated with the Amber99sb force field in alchemical transformations. The varying polarization of the two residues in different molecular environments and protonation states is described by Hirshfeld-I (HI) atomic charges obtained from the averaged polarized electron density. Our results show that the Gibbs free energy of proton transfer is dependent on the protein conformation, the proper sampling of the neighboring Lys57 residue orientations and on water molecules entering the hydrophobic cavity upon deprotonating Asp26. The inclusion of the polarization of both aspartate residues in the free energy cycle by HI atomic charges corrects the results from the non-polarizable force field and reproduces the experimental ΔpK_a value of Asp26.