On computing the solubility of molecular systems subject to constraints using the extended Einstein crystal method (original) (raw)
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European Journal of Pharmaceutics and Biopharmaceutics, 2019
In this review we will discuss how computational methods, and in particular classical molecular dynamics simulations, can be used to calculate solubility of pharmaceutically relevant molecules and systems. To the extent possible, we focus on the non-technical details of these calculations, and try to show also the added value of a more thorough and detailed understanding of the solubilization process obtained by using computational simulations. Although the main focus is on classical molecular dynamics simulations, we also provide the reader with some insights into other computational techniques, such as the COSMO-method, and also discuss Flory-Huggins theory and solubility parameters. We hope that this review will serve as a valuable starting point for any pharmaceutical researcher, who has not yet fully explored the possibilities offered by computational approaches to solubility calculations.
Journal of Computational Chemistry, 1995
The point-chart approximation of the Miertus-Scrocco-Tomasi solvation model (MST-PC) based on a continuum representation of the solvent has been incorporated in force field calculations. Application in molecular mechanics (MM) involves conformational equilibria in solution: rotational isomers of ethylene glycol (I), 1,2-difluoroethane (10, fluoroacetic acid (110, and representative conformers of macrocyclic receptors such as 18-crown-6 (IV), cryptand 2.2.2 (V), and t-butyl-calix[4]arenetetraamide (VI). Assessment of the MST-PC results is based on the comparison with ab initio reactive field calculations (for I-111), with the continuum model of Still (W. C. Still et al., J.
Journal of Chemical Theory and Computation, 2012
An important unsolved problem in materials science is prediction of the thermodynamic stability of organic crystals and their solubility from first principles. Solubility can be defined as the saturating concentration of a molecule within a liquid solvent, where the physical picture is of solvated molecules in equilibrium with their solid phase. Despite the importance of solubility in determining the oral bioavailability of pharmaceuticals, prediction tools are currently limited to quantitative structure-property relationships that are fit to experimental solubility measurements. For the first time, we describe a consistent procedure for the prediction of the structure, thermodynamic stability and solubility of organic crystals from molecular dynamics simulations using the polarizable multipole AMOEBA force field. Our approach is based on a thermodynamic cycle that decomposes standard state solubility into the sum of solid-vapor sublimation and vaporliquid solvation free energies , which are computed via the orthogonal space random walk (OSRW) sampling strategy. Application to the n-alkylamides series from aeetamide through octanamide was selected due to the dependence of their solubility on both amide hydrogen bonding and the hydrophobic effect, which are each fundamental to protein structure and solubility. On average, the calculated absolute standard state solubility free energies are accurate to within 1.1 kcal/mol. The experimental trend of decreasing solubility as a function of n-alkylamide chain length is recapitulated by the increasing stability of the crystalline state and to a lesser degree by decreasing favorability of solvation (i.e. the hydrophobic effect). Our results suggest that coupling the polarizable AMOEBA force field with an orthogonal space based free energy algorithm, as implemented in the program Force Field X, is a consistent procedure for predicting the structure, thermodynamic stability and solubility of organic crystals.
A Novel Technique To Predict the Solubility of Planar Molecules
Energy & Fuels, 2016
We present a new computational technique to quantify the solubility of planar molecules in a solvent. Solubility is calculated as the critical concentration at which solute molecules cease to stack as columns, but rather aggregate in all directions. An explicit expression for the solubility is obtained which involves the potential of mean force between two solute molecules as a function of their centre-of-mass distance in the limit of infinite dilution. This function can be easily obtained from molecular dynamics simulations involving a pair of solute molecules in a solvent using the umbrella sampling method. As a validation of our approach, we use a generic coarse-grained molecular model to represent the molecular interactions of
We present four models of solution free-energy prediction for druglike molecules utilizing cheminformatics descriptors and theoretically calculated thermodynamic values. We make predictions of solution free energy using physics-based theory alone and using machine learning/quantitative structure−property relationship (QSPR) models. We also develop machine learning models where the theoretical energies and cheminformatics descriptors are used as combined input. These models are used to predict solvation free energy. While direct theoretical calculation does not give accurate results in this approach, machine learning is able to give predictions with a root mean squared error (RMSE) of ∼1.1 log S units in a 10-fold crossvalidation for our Drug-Like-Solubility-100 (DLS-100) dataset of 100 druglike molecules. We find that a model built using energy terms from our theoretical methodology as descriptors is marginally less predictive than one built on Chemistry Development Kit (CDK) descriptors. Combining both sets of descriptors allows a further but very modest improvement in the predictions. However, in some cases, this is a statistically significant enhancement. These results suggest that there is little complementarity between the chemical information provided by these two sets of descriptors, despite their different sources and methods of calculation. Our machine learning models are also able to predict the well-known Solubility Challenge dataset with an RMSE value of 0.9−1.0 log S units.
Journal of Physical Chemistry B, 2001
The expanded ensemble method, developed to calculate solvation free energies, is applied to calculate octanol/ water partition coefficients P for some organic drug-related molecules and compared with experimental results. The experimental log P results were obtained by a miniaturized vial procedure using liquid chromatography with UV for quantification. The expanded ensemble technique, implemented within molecular dynamics scheme, is adapted to treat molecules of arbitrary size and type. For octanol, both all-atom and united atom models are evaluated. The solvation free energy of the organic solute molecules is found to be sensitive to the used sets of partial charges on the atoms in polar groups, particularly in water but also in the saturated octanol phase. Although this effect partially cancels out in the calculated partition coefficients, the charges obtained from ab initio Mulliken population analysis give consistently larger log P values than those obtained in simulations with the larger empirical atomic charges included in the CHARMM force field. In general, calculated log P turned out to be systematically higher than those measured experimentally. The possibility of improving potential models for the solutes in water and oil phase, respectively, is discussed.
Molecular Thermodynamic Modeling of Mixed Solvent Solubility
Industrial & Engineering Chemistry Research, 2010
A method based on statistical mechanical fluctuation solution theory for composition derivatives of activity coefficients is employed for estimating dilute solubilities of 11 solid pharmaceutical solutes in nearly 70 mixed aqueous and nonaqueous solvent systems. The solvent mixtures range from nearly ideal to strongly nonideal. The database covers a temperature range from 293 to 323 K. Comparisons with available data and other existing solubility methods show that the method successfully describes a variety of observed mixed solvent solubility behaviors using solute-solvent parameters from global regression of ternary data as well as predictions based on pure solvent solubilities with an average error of about 10% on mole fractions.
Journal of Chemical Theory and Computation, 2009
The 1-octanol/water partition coefficient is an important thermodynamic variable usually employed to understand and quantify the partitioning of solutes between aqueous and organic phases. It finds widespread use in many empirical correlations to evaluate the environmental fate of pollutants as well as in the design of pharmaceuticals. The experimental evaluation of 1-octanol/water partition coefficients is an expensive and time-consuming procedure, and thus, theoretical estimation methods are needed, particularly when a physical sample of the solute may not yet be available, such as in pharmaceutical screening. 1-Octanol/water partition coefficients can be obtained from Gibbs free energies of solvation of the solute in both the aqueous and the octanol phases. The accurate evaluation of free energy differences remains today a challenging problem in computational chemistry. In order to study the absolute solvation Gibbs free energies in 1-octanol, a solvent that can mimic many properties of important biological systems, free energy calculations for n-alkanes in the range C 1 -C 8 were performed using molecular simulation techniques, following the thermodynamic integration approach. In the first part of this paper, we test different force fields by evaluating their performance in reproducing pure 1-octanol properties. It is concluded that all-atom force fields can provide good accuracy but at the cost of a higher computational time compared to that of the united-atom force fields. Recent versions of united-atom force fields, such as Gromos and TraPPE, provide satisfactory results and are, thus, useful alternatives to the more expensive all-atom models. In the second part of the paper, the Gibbs free energy of solvation in 1-octanol is calculated for several n-alkanes using three force fields to describe the solutes, namely Gromos, TraPPE, and OPLS-AA. Generally, the results obtained are in excellent agreement with the available experimental data and are of similar accuracy to commonly used QSPR models. Moreover, we have estimated the Gibbs free energy of hydration for the different compounds with the three force fields, reaching average deviations from experimental data of less than 0.2 kcal/mol for the case of the Gromos force field. Finally, we systematically compare different strategies to obtain the 1-octanol/water partition coefficient from the simulations. It is shown that a fully predictive method combining the Gromos force field in the aqueous phase and the OPLS-AA/TraPPE force field for the organic phase can give excellent predictions for n-alkanes up to C 8 with an absolute average deviation of 0.1 log P units to the experimental data.
Journal of Chemical Information and Modeling, 2005
A molecular modeling procedure, based on internal coordinates and strictly analytical even in the most intricated cases, is described. Internal coordinates, always nonredundant, become mutually independent and can be varied without constraints. Structural refinement from diffraction data (Least-square method, LS) can be done using the classical Gauss-Newton approach and avoiding Lagrange multipliers. A comparative test done using published data has shown that while the new method gives rise to a structural refinement in perfect agreement with the known structure, the traditional methods (z-matrix and constraints based) does not work.
Explicitly Representing the Solvation Shell in Continuum Solvent Calculations
The Journal of Physical Chemistry A, 2009
A method is presented to explicitly represent the first solvation shell in continuum solvation calculations. Initial solvation shell geometries were generated with classical molecular dynamics simulations. Clusters consisting of solute and 5 solvent molecules were fully relaxed in quantum mechanical calculations. The free energy of solvation of the solute was calculated from the free energy of formation of the cluster and the solvation free energy of the cluster calculated with continuum solvation models. The method has been implemented with two continuum solvation models, a Poisson-Boltzmann model and the IEF-PCM model. Calculations were carried out for a set of 60 ionic species. Implemented with the Poisson-Boltzmann model the method gave an unsigned average error of 2.1 kcal/mol and a RMSD of 2.6 kcal/mol for anions, for cations the unsigned average error was 2.8 kcal/mol and the RMSD 3.9 kcal/mol. Similar results were obtained with the IEF-PCM model.