Abstract
Partition coefficients quantify a molecule’s distribution between two immiscible liquid phases. While there are many methods to compute them, there is not yet a method based on the free energy of each system in terms of energy and entropy, where entropy depends on the probability distribution of all quantum states of the system. Here we test a method in this class called Energy Entropy Multiscale Cell Correlation (EE-MCC) for the calculation of octanol–water logP values for 22 N-acyl sulfonamides in the SAMPL7 Physical Properties Challenge (Statistical Assessment of the Modelling of Proteins and Ligands). EE-MCC logP values have a mean error of 1.8 logP units versus experiment and a standard error of the mean of 1.0 logP units for three separate calculations. These errors are primarily due to getting sufficiently converged energies to give accurate differences of large numbers, particularly for the large-molecule solvent octanol. However, this is also an issue for entropy, and approximations in the force field and MCC theory also contribute to the error. Unique to MCC is that it explains the entropy contributions over all the degrees of freedom of all molecules in the system. A gain in orientational entropy of water is the main favourable entropic contribution, supported by small gains in solute vibrational and orientational entropy but offset by unfavourable changes in the orientational entropy of octanol, the vibrational entropy of both solvents, and the positional and conformational entropy of the solute.
Highlights
The partition coefficient P is a widely-used quantity to understand the transport and distribution of chemicals in biological, industrial and environmental systems [1, 2]
We have developed a general method to evaluate free energy directly from an molecular dynamics (MD) simulation for all molecules in the system, both solvent and solute alike, and over a large range of length scales [26,27,28]
The octanol–water logP values computed by Energy Entropy Multiscale Cell Correlation (EE-Multiscale cell correlation (MCC)) using Equations 1, 2 and 3 are presented in Fig. 2 versus experiment for all 22 SAMPL7 compounds, together with error metrics of mean absolute error (MAE), rootmean-square error (RMSE) and Standard Error of the Mean (SEM) given by Equations 11–13
Summary
The partition coefficient P is a widely-used quantity to understand the transport and distribution of chemicals in biological, industrial and environmental systems [1, 2]. Values of logP are relatively straightforward to measure by the “Shake-Flask” method, followed by slow-stirring and reverse phase High Performance Liquid Chromatography [3, 4], and recently, by more accurate methods such as potentiometric titration [5]. They take time and material to measure, often give highly variable results [6] and provide little insight into values obtained. There is a valuable role to play for predictive methods of logP which can save time, lower costs, and facilitate the more rational development of new chemicals,
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