Calculated Hydration Free Energies of Small Organic Molecules Using a Nonlinear Dielectric Continuum Model

Fast calculation of hydrogen-bond strengths and free energy of hydration of small molecules

Hydrogen bonding is an interaction of great importance in drug discovery and development as it may significantly affect chemical and biological processes including the interaction of small molecules with other molecules, proteins, and membranes. In particular, hydrogen bonding can impact drug-like properties such as target affinity and oral availability which are critical to developing effective pharmaceuticals, and therefore, numerous methods for the calculation of properties such as hydrogen-bond strengths, free energy of hydration, or water solubility have been proposed over time. However, the accessibility to efficient methods for the predictions of such properties is still limited. Here, we present the development of Jazzy, an open-source tool for the prediction of hydrogen-bond strengths and free energies of hydration of small molecules. Jazzy also allows the visualisation of hydrogen-bond strengths with atomistic resolution to support the design of compounds with desired properties and the interpretation of existing data. The tool is described in its implementation, parameter fitting, and validation against two data sets of experimental hydration free energies. Jazzy is also applied against two chemical series of bioactive compounds to show that hydrogen-bond strengths can be used to understand their structure-activity relationships. Results from the validations highlight the strengths and limitations of Jazzy, and suggest its suitability for interactive design, screening, and machine-learning featurisation.

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model

Molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. In this work, we develop and assess two multiscale solvation models for computing solvation thermodynamic properties. The new SLIC/CDC model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with new statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). Given the structures of 500 solutes, the SLIC/CDC model predicts Gibbs energies of solvation in water with an average accuracy better than 1 kcal/mol, when compared to experimental measurements, and better than 0.8 kcal/mol, when compared to explicit-solvent molecular dynamics simulations. The individual SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The previously published SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent-accessible surface area (SASA) nonpolar energy mode. With our new, improved parametrization method, the SLIC/SASA model now predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems, compared to experimental and explicit-solvent molecular dynamics, and better than 1.6 kcal/mol average accuracy in ionic liquids, compared to explicit-solvent molecular dynamics. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.

Predicting hydration free energies with chemical accuracy: the SAMPL4 challenge

An implicit solvent model described by a non-simple dielectric medium is used for the prediction of hydration free energies on the dataset of 47 molecules in the SAMPL4 challenge. The solute is represented by a minimal parameter set model based on a new all atom force-field, named the liquid simulation force-field. The importance of a first solvation shell correction to the hydration free energy prediction is discussed and two different approaches are introduced to address it: either with an empirical correction to a few functional groups (alcohol, ether, ester, amines and aromatic nitrogen), or an ab initio correction based on the formation of a solute/explicit water complex. Both approaches give equally good predictions with an average unsigned error <1 kcal/mol. Chemical accuracy is obtained.

Molecular screening of alcohol and polyol adsorption onto MFI-type zeolites

Configurational-bias grand canonical Monte Carlo (CB-GCMC) simulations and expanded ensemble (EE)-CB-GCMC simulations were performed to obtain adsorption isotherms of alcohols and polyols onto MFI-type zeolites from the gas phase and aqueous solution. In adsorption from both phases, Henry's constants and heats of adsorption at infinite dilution for straight-chain alcohols, diols, and triols in silicalite-1 are found to increase, and the saturation loadings decrease with increasing carbon number. Adsorption of straight-chain alcohols is more favorable than that of branched-chain alcohols. Henry's constants increase with increasing number of hydroxyl groups for gas-phase adsorption but decrease for adsorption from aqueous solution due to the strong hydrophilic solvent effect of water. The location of the hydroxyls does not affect significantly the adsorption from aqueous solution but does so in gas-phase adsorption. The saturation pressures for gas-phase adsorption decrease by orders of magnitude from the alcohols to the triols. Nonframework cations increase the adsorption of the small alcohols by an order magnitude at low concentrations (<1 mg/mL), but result in only a factor of 2 increase for larger alcohols like butanol at low concentrations (<0.03 mg/mL), and then decrease the adsorption at higher concentrations. Overall, the simulated results are in reasonable agreement with available experimental data.

Langevin-Debye model for nonlinear electrostatic screening of solvated ions

Ion-ion interactions are central to numerous phenomena in geology, biology, and material science, but current understanding is based on linear theories of limited physical applicability. Using the Langevin-Debye model, we investigate how nonlinear dielectric saturation alters screening of electrostatic interactions between solvated charges and show that charge screening in liquids strongly depends on the charge magnitudes but negligibly on the ion radii. Qualitatively different universal screening functions are predicted for ions with charges of the same or opposite signs.

Solvation effect on conformations of 1,2:dimethoxyethane: charge-dependent nonlinear response in implicit solvent models

The physical content of and, in particular, the nonlinear contributions from the Langevin-Debye model are illustrated using two applications. First, we provide an improvement in the Langevin-Debye model currently used in some implicit solvent models for computer simulations of solvation free energies of small organic molecules, as well as of biomolecular folding and binding. The analysis is based on the implementation of a charge-dependent Langevin-Debye (qLD) model that is modified by subsequent corrections due to Onsager and Kirkwood. Second, the physical content of the model is elucidated by discussing the general treatment within the LD model of the self-energy of a charge submerged in a dielectric medium for three different limiting conditions and by considering the nonlinear response of the medium. The modified qLD model is used to refine an implicit solvent model (previously applied to protein dynamics). The predictions of the modified implicit solvent model are compared with those from explicit solvent molecular dynamics simulations for the equilibrium conformational populations of 1,2-dimethoxyethane (DME), which is the shortest ether molecule to reproduce the local conformational properties of polyethylene oxide, a polymer with tremendous technological importance and a wide variety of applications. Because the conformational population preferences of DME change dramatically upon solvation, DME is a good test case to validate our modified qLD model. The present analysis of the modified qLD model provides the motivation and tools for studying a wide variety of other interesting systems with heterogeneous dielectric properties and spatial anisotropy.

A Linear Scaling Study of Solvent−Solute Interaction Energy of Drug Molecules in Aqua Solution

Solvent-solute interaction energies for three well-known drug molecules in water solution are computed at the Hartree-Fock and B3LYP density functional theory levels using a linear scaling technique, which allows one to explicitly include in the model water molecules up to 14 A away from the solute molecule. The dependence of calculated interaction energies on the amount of included solvent has been examined. It is found that it is necessary to account for water molecules within an 8 A radius around the drug molecule to reach the saturated solvent interaction level. Effects of electron correlation and basis set on solvent-solute interaction energies are discussed.

A Kirkwood-Buff derived force field for amides

A force field for the computer simulation of aqueous solutions of amides is presented. The force field is designed to reproduce the experimentally observed density and Kirkwood-Buff integrals for N-methylacetamide (NMA), allowing for an accurate description of the NMA activity. Other properties such as the translational diffusion constant and heat of mixing are also well reproduced. The force field is then extended to include N,N'-dimethylacetamide and acetamide with good success. Analysis of the simulations of low concentrations of NMA in water indicates a high degree of solvation with only 15% of the NMA molecules involved in solute-solute hydrogen bonding. There is only a weak angular dependence of the solute-solute hydrogen bonding interaction with a minimum at an angle of 65 degrees for the N-H and C=O dipole vectors. The models presented here provide a basis for an accurate force field for peptides and proteins.

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: Application to solvatochromic shift calculations

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.

In Silico Prediction of Drug Solubility: 1. Free Energy of Hydration

As a first step in the computational prediction of drug solubility the free energy of hydration, DeltaG*(vw) in TIP4P water has been computed for a data set of 48 drug molecules using the free energy of perturbation method and the optimized potential for liquid simulations all-atom force field. The simulations were performed in two steps, where first the Coulomb and then the Lennard-Jones interactions between the solute and the water molecules were scaled down from full to zero strength to provide physical understanding and simpler predictive models. The results have been interpreted using a theory assuming DeltaG*(vw) = A(MS)gamma + E(LJ) + E(C)/2 where A(MS) is the molecular surface area, gamma is the water-vapor surface tension, and E(LJ) and E(C) are the solute-water Lennard-Jones and Coulomb interaction energies, respectively. It was found that by a proper definition of the molecular surface area our results as well as several results from the literature were found to be in quantitative agreement using the macroscopic surface tension of TIP4P water. This is in contrast to the surface tension for water around a spherical cavity that previously has been shown to be dependent on the size of the cavity up to a radius of approximately 1 nm. The step of scaling down the electrostatic interaction can be represented by linear response theory.

Coupling Quantum Monte Carlo to a Nonlinear Polarizable Continuum Model for Spherical Solutes

Starting from the nonlinear dielectric response model of Sandberg and Edholm, we derive an analytical expression of the polarization contribution to the solvation free energy in terms of the electronic density of the solute and the dielectric properties of the solvent. The solvent inhomogeneity is taken into account with the use of a smooth switching function whose spacial variation is established on the basis of how the solvent is arranged around the solute. An explicit form of a local potential representing the solvent effect on the solute is thus obtained by functional analysis. This effective potential can be combined with density functional or quantum chemical methods for the quantum mechanical treatment of the solute. Here, we use quantum Monte Carlo techniques for the solute and apply the method to the hydration of atomic ions finding very good agreement with experimental data.

Computation of hydration free energies of organic solutes with an implicit water model

A new approach for computing hydration free energies DeltaG(solv) of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component DeltaG(el) of DeltaG(solv) and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (DeltaG(nel)). The novel features include the following: (a) two different cavities are used for treating DeltaG(el) and DeltaG(nel). For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of DeltaG(nel) is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H-bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed.

A simple simulation methodology for estimation of dehydration energies and surface potentials of concentrated NaCl solutions

A novel simulation procedure for estimating the dehydration energies of NaCl solutions spanning a wide range of concentrations, which incorporates ionic and molecular sizes, ion-pair formation, etc., is proposed on geometric and phenomenological considerations. The extent of dehydration during each movement of the hydrated molecule is evaluated using the expected and actual displacement of the species and mean nearest-neighbor distances. The interdependence between the size of the simulation box, number of molecules, and electrolyte concentration is pointed out.