Three-Dimensional RISM Integral Equation Theory for Polarizable Solute Models

EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules

Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules

The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl^-, [ClO]^- (a two-site anion), and [NO₂]^- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl^-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

Implementation and Optimization of the Embedded Cluster Reference Interaction Site Model with Atomic Charges

In this work, we implemented the embedded cluster reference interaction site model (EC-RISM) originally developed by Kloss, Heil, and Kast (J. Phys. Chem. B2008, 112, 4337–4343). This method combines quantum mechanical calculations with the 3D reference interaction site model (3D-RISM). Numerous options, such as buffer, grid space, basis set, charge model, water model, closure relation, and so forth, were investigated to find the best settings. Additionally, the small point charges, which are derived from the solvent distribution from the 3D-RISM solution to represent the solvent in the QM calculation, were neglected to reduce the overhead without the loss of accuracy. On the MNSOL[a], MNSOL, and FreeSolv databases, our implemented and optimized method provides solvation free energies in water with 5.70, 6.32, and 6.44 kJ/mol root-mean-square deviations, respectively, but with different settings, 5.22, 6.08, and 6.63 kJ/mol can also be achieved. Only solvent models containing fitting parameters, like COSMO-RS and EC-RISM with universal correction and directly used electrostatic potential, perform better than our EC-RISM implementation with atomic charges.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 k_BT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

Quantum-mechanical property prediction of solvated drug molecules: what have we learned from a decade of SAMPL blind prediction challenges?

Joint academic-industrial projects supporting drug discovery are frequently pursued to deploy and benchmark cutting-edge methodical developments from academia in a real-world industrial environment at different scales. The dimensionality of tasks ranges from small molecule physicochemical property assessment over protein-ligand interaction up to statistical analyses of biological data. This way, method development and usability both benefit from insights gained at both ends, when predictiveness and readiness of novel approaches are confirmed, but the pharmaceutical drug makers get early access to novel tools for the quality of drug products and benefit of patients. Quantum-mechanical and simulation methods particularly fall into this group of methods, as they require skills and expense in their development but also significant resources in their application, thus are comparatively slowly dripping into the realm of industrial use. Nevertheless, these physics-based methods are becoming more and more useful. Starting with a general overview of these and in particular quantum-mechanical methods for drug discovery we review a decade-long and ongoing collaboration between Sanofi and the Kast group focused on the application of the embedded cluster reference interaction site model (EC-RISM), a solvation model for quantum chemistry, to study small molecule chemistry in the context of joint participation in several SAMPL (Statistical Assessment of Modeling of Proteins and Ligands) blind prediction challenges. Starting with early application to tautomer equilibria in water (SAMPL2) the methodology was further developed to allow for challenge contributions related to predictions of distribution coefficients (SAMPL5) and acidity constants (SAMPL6) over the years. Particular emphasis is put on a frequently overlooked aspect of measuring the quality of models, namely the retrospective analysis of earlier datasets and predictions in light of more recent and advanced developments. We therefore demonstrate the performance of the current methodical state of the art as developed and optimized for the SAMPL6 pKa and octanol-water log P challenges when re-applied to the earlier SAMPL5 cyclohexane-water log D and SAMPL2 tautomer equilibria datasets. Systematic improvement is not consistently found throughout despite the similarity of the problem class, i.e. protonation reactions and phase distribution. Hence, it is possible to learn about hidden bias in model assessment, as results derived from more elaborate methods do not necessarily improve quantitative agreement. This indicates the role of chance or coincidence for model development on the one hand which allows for the identification of systematic error and opportunities toward improvement and reveals possible sources of experimental uncertainty on the other. These insights are particularly useful for further academia-industry collaborations, as both partners are then enabled to optimize both the computational and experimental settings for data generation.

Towards a converged strategy for including microsolvation in reaction mechanism calculations

A major part of chemical conversions is carried out in the fluid phase, where an accurate modeling of the involved reactions requires to also take into account solvation effects. Implicit solvation models often cover these effects with sufficient accuracy but can fail drastically when specific solvent-solute interactions are important. In those cases, microsolvation, i.e., the explicit inclusion of one or more solvent molecules, is a commonly used strategy. Nevertheless, microsolvation also introduces new challenges-a consistent workflow as well as strategies how to systematically improve prediction performance are not evident. For the COSMO and COSMO-RS solvation models, this work proposes a simple protocol to decide if microsolvation is needed and how the corresponding molecular model has to look like. To demonstrate the improved accuracy of the approach, specific application examples are presented and discussed, i.e., the computation of aqueous pK_a values and a mechanistic study of the methanol mediated Morita-Baylis-Hillman reaction.

The SAMPL6 challenge on predicting octanol-water partition coefficients from EC-RISM theory

Results are reported for octanol–water partition coefficients (log P) of the neutral states of drug-like molecules provided during the SAMPL6 (Statistical Assessment of Modeling of Proteins and Ligands) blind prediction challenge from applying the “embedded cluster reference interaction site model” (EC-RISM) as a solvation model for quantum-chemical calculations. Following the strategy outlined during earlier SAMPL challenges we first train 1- and 2-parameter water-free (“dry”) and water-saturated (“wet”) models for n-octanol solvation Gibbs energies with respect to experimental values from the “Minnesota Solvation Database” (MNSOL), yielding a root mean square error (RMSE) of 1.5 kcal mol⁻¹ for the best-performing 2-parameter wet model, while the optimal water model developed for the pK_a part of the SAMPL6 challenge is kept unchanged (RMSE 1.6 kcal mol⁻¹ for neutral compounds from a model trained on both neutral and ionic species). Applying these models to the blind prediction set yields a log P RMSE of less than 0.5 for our best model (2-parameters, wet). Further analysis of our results reveals that a single compound is responsible for most of the error, SM15, without which the RMSE drops to 0.2. Since this is the only compound in the challenge dataset with a hydroxyl group we investigate other alcohols for which Gibbs energy of solvation data for both water and n-octanol are available in the MNSOL database to demonstrate a systematic cause of error and to discuss strategies for improvement.

Comprehensive Benchmark of Association (Free) Energies of Realistic Host-Guest Complexes

The S12L test set for supramolecular Gibbs free energies of association ΔGa (Grimme, S. Chem. Eur. J. 2012, 18, 9955-9964) is extended to 30 complexes (S30L), featuring more diverse interaction motifs, anions, and higher charges (-1 up to +4) as well as larger systems with up to 200 atoms. Various typical noncovalent interactions like hydrogen and halogen bonding, π-π stacking, nonpolar dispersion, and CH-π and cation-dipolar interactions are represented by "real" complexes. The experimental Gibbs free energies of association (ΔGa exp) cover a wide range from -0.7 to -24.7 kcal mol-1. In order to obtain a theoretical best estimate for ΔGa, we test various dispersion corrected density functionals in combination with quadruple-ζ basis sets for calculating the association energies in the gas phase. Further, modern semiempirical methods are employed to obtain the thermostatistical corrections from energy to Gibbs free energy, and the COSMO-RS model with several parametrizations as well as the SMD model are used to include solvation contributions. We investigate the effect of including counterions for the charged systems (S30L-CI), which is found to overall improve the results. Our best method combination consists of PW6B95-D3 (for neutral and charged systems) or ωB97X-D3 (for systems with counterions) energies, HF-3c thermostatistical corrections, and Gibbs free energies of solvation obtained with the COSMO-RS 2012 parameters for nonpolar solvents and 2013-fine for water. This combination gives a mean absolute deviation for ΔGa of only 2.4 kcal mol-1 (S30L) and 2.1 kcal mol-1 (S30L-CI), with a mean deviation of almost zero compared to experiment. Regarding the relative Gibbs free energies of association for the 13 pairs of complexes which share the same host, the correct trend in binding affinities could be reproduced except for two cases. The MAD compared to experiment amounts to 1.2 kcal mol-1, and the MD is almost zero. The best-estimate theoretical corrections are used to back-correct the experimental ΔGa values in order to get an empirical estimate for the "experimental", zero-point vibrational energy exclusive, gas phase binding energies. These are then utilized to benchmark the performance of various "lowcost" quantum chemical methods for noncovalent interactions in large systems. The performance of other common DFT methods as well as the use of semiempirical methods for structure optimizations is discussed.

The SAMPL5 challenge for embedded-cluster integral equation theory: solvation free energies, aqueous pK a, and cyclohexane-water log D

We predict cyclohexane-water distribution coefficients (log D _7.4) for drug-like molecules taken from the SAMPL5 blind prediction challenge by the "embedded cluster reference interaction site model" (EC-RISM) integral equation theory. This task involves the coupled problem of predicting both partition coefficients (log P) of neutral species between the solvents and aqueous acidity constants (pK _a) in order to account for a change of protonation states. The first issue is addressed by calibrating an EC-RISM-based model for solvation free energies derived from the "Minnesota Solvation Database" (MNSOL) for both water and cyclohexane utilizing a correction based on the partial molar volume, yielding a root mean square error (RMSE) of 2.4 kcal mol^-1 for water and 0.8-0.9 kcal mol^-1 for cyclohexane depending on the parametrization. The second one is treated by employing on one hand an empirical pK _a model (MoKa) and, on the other hand, an EC-RISM-derived regression of published acidity constants (RMSE of 1.5 for a single model covering acids and bases). In total, at most 8 adjustable parameters are necessary (2-3 for each solvent and two for the pK _a) for training solvation and acidity models. Applying the final models to the log D _7.4 dataset corresponds to evaluating an independent test set comprising other, composite observables, yielding, for different cyclohexane parametrizations, 2.0-2.1 for the RMSE with the first and 2.2-2.8 with the combined first and second SAMPL5 data set batches. Notably, a pure log P model (assuming neutral species only) performs statistically similarly for these particular compounds. The nature of the approximations and possible perspectives for future developments are discussed.

Using dispersion-corrected density functional theory to understand supramolecular binding thermodynamics

A recently published theoretical approach employing a nondynamic structure model using dispersion-corrected density functional theory (DFT-D3) to calculate equilibrium free energies of association (Chem. – Eur. J., 2012, 18, 9955–9964) is illustrated by its application to eight supramolecular complexes.

Acidity in DMSO from the embedded cluster integral equation quantum solvation model

The embedded cluster reference interaction site model (EC-RISM) is applied to the prediction of acidity constants of organic molecules in dimethyl sulfoxide (DMSO) solution. EC-RISM is based on a self-consistent treatment of the solute's electronic structure and the solvent's structure by coupling quantum-chemical calculations with three-dimensional (3D) RISM integral equation theory. We compare available DMSO force fields with reference calculations obtained using the polarizable continuum model (PCM). The results are evaluated statistically using two different approaches to eliminating the proton contribution: a linear regression model and an analysis of pK(a) shifts for compound pairs. Suitable levels of theory for the integral equation methodology are benchmarked. The results are further analyzed and illustrated by visualizing solvent site distribution functions and comparing them with an aqueous environment.