A generalized G-SFED continuum solvation free energy calculation model

Abstract

An empirical continuum solvation model, solvation free energy density (SFED), has been developed to calculate solvation free energies of a molecule in the most frequently used solvents. A generalized version of the SFED model, generalized-SFED (G-SFED), is proposed here to calculate molecular solvation free energies in virtually any solvent. G-SFED provides an accurate and fast generalized framework without a complicated description of a solution. In the model, the solvation free energy of a solute is represented as a linear combination of empirical functions of the solute properties representing the effects of solute on various solute-solvent interactions, and the complementary solvent effects on these interactions were reflected in the linear expansion coefficients with a few solvent properties. G-SFED works well for a wide range of sizes and polarities of solute molecules in various solvents as shown by a set of 5,753 solvation free energies of diverse combinations of 103 solvents and 890 solutes. Octanol-water partition coefficients of small organic compounds and peptides were calculated with G-SFED with accuracy within 0.4 log unit for each group. The G-SFED computation time depends linearly on the number of nonhydrogen atoms (n) in a molecule, O(n).

Fig. 1.

The solute and solvent of a solution are described as an assemblage of interacting compartments. r_ik is the distance between the ith atom and the kth surface fragment on the SAS of the solute, and γ^m is the macroscopic surface tension of the solvent. A dielectric constant, ε^m, and a refractive index, η^m, of the solvent are placed at the grid points on the SAS. Hydrogen-bond acidity and basicity of the solvent, A^m and B^m, and of the solute, A^s and B^s, represent the contribution of a hydrogen bond.

Fig. 2.

Comparison of the training and external validation sets based on molecular weight (A) and number of hydrogen-bond acceptors (B). The training set consists mainly of small non- or uni-polar molecules, and the external validation set includes a large number of multipolar large molecules. The rightmost bars represent the number of molecules that are larger than 400 Da (A) and have more than seven hydrogen-bond acceptors (B), respectively.

Fig. 3.

Performance, MAE and R², of G-SFED (filled black symbols) and SM5.42R (filled gray symbols) for the external validation set. MAE (left y-axis, bars) and R² (right y-axis, circles) are plotted for each solvent. The MAE and R² values are given in Table S4.

Fig. 4.

Scatter plots of ΔG_solv calculated with G-SFED (A) and SM5.42 (B) against experimental . Red and black dots represent the solvation free energies in the training and external validation sets, respectively. The MAEs and R²s were 0.73 kcal/cal and 0.95, respectively, for G-SFED, and 0.90 kcal/mol and 0.89, respectively, for SM.42R.

Fig. 5.

The calculated octanol-water partition coefficients from G-SFED vs. experimental values for 601 organic molecules (A) and 193 neutral peptides (B). The MAEs and R²s were 0.33 log units and 0.94, respectively, for A, and 0.41 log units and 0.91, respectively, for B. If the single largest outlier [(Me)Arg-Lys-Pro-Trp-tLeu-LeuOEt] in B is removed, the MAE and R² are 0.40 log unit and 0.92, respectively.

Fig. 6.

Computation time vs. alkane chain length. G-SFED and SM5.42R are written in C++ and FORTRAN 77, respectively. Because the G-SFED model is based on simple empirical functions, the runtime of the model is linearly proportional to the number of nonhydrogen atoms of a molecule.