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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 pKa 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., J Comput Aided Mol Des;34

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.

The bridge function of a simple liquid is calculated for the repulsive part of the Weeks–Chandler–Andersen (WCA) separation of the Lennard–Jones potential. We employ explicit molecular dynamics simulations of the potential of mean force between constrained dimers in order to extract bridge data near zero separation and illustrate the difference to full Lennard–Jones results. We compare direct, reciprocal space and iterative, real space inversions of the Ornstein–Zernike equation. Bridge functions for various thermodynamic states are analyzed as to their parametric dependence on the renormalized indirect correlation function, which has consequences for the analytic representation of the free energy functional.

We predict cyclohexane-water distribution coefficients (log D

Pressure perturbation calorimetry (PPC) is an efficient technique to study the volumetric properties of biomolecules in solution. In PPC, the coefficient of thermal expansion of the partial volume of the biomolecule is deduced from the heat consumed or produced after small isothermal pressure-jumps. The expansion coefficient strongly depends on the interaction of the biomolecule with the solvent or cosolvent as well as on its packing and internal dynamic properties. This technique, complemented with molecular acoustics and densimetry, provides valuable insights into the basic thermodynamic properties of solvation and volume effects accompanying interactions, reactions and phase transitions of biomolecular systems. After outlining the principles of the technique, we present representative examples on protein folding, including effects of cosolvents and crowding, together with a discussion of the interpretation, and further applications.

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.

We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.