Adapting the semi-explicit assembly solvation model for estimating water-cyclohexane partitioning with the SAMPL5 molecules

Abstract

We describe here some tests we made in the SAMPL5 communal event of 'Semi-Explicit Assembly' (SEA), a recent method for computing solvation free energies. We combined the prospective tests of SAMPL5 with followup retrospective calculations, to improve two technical aspects of the field variant of SEA. First, SEA uses an approximate analytical surface around the solute on which a water potential is computed. We have improved and simplified the mathematical model of that surface. Second, some of the solutes in SAMPL5 were large enough to need a way to treat solvating waters interacting with 'buried atoms', i.e. interior atoms of the solute. We improved SEA with a buried-atom correction. We also compare SEA to Thermodynamic Integration molecular dynamics simulations, so that we can sort out force field errors.

Keywords: Distribution coefficient; Partitioning; SAMPL; SEA; Solvation free energy.

Fig. 1. SEA can predict the partition coefficient of a molecule in two solvents

SEA accurately estimates the solvation free energy of a molecule combining pre-computed free energy terms. Each one describes how the solvent interacts with a small region of the solute. The pre-computation is computationally expensive, but it needs to be done only once for a given solute at a given state point. At run-time SEA is fast since it only needs to assemble pre-computed data. Different solvent react differently to the presence of the solute: different look-up tables need to be built for different solvent. With SEA it is in principle possible to compute the solvation free energy of any molecule in any solvent. From these it is possible to evaluate the partition coefficient of a molecule in any pair of solvents.

Fig. 2. The `buried-atom problem'

Some solute molecules are big enough to require more than just treating in the nonpolar term: (A) how solvent waters interact with surface atoms (gray). (B) The red sphere shows a buried atom, with which solvating waters will also interact. Here, we give a buried-atom correction.

Fig. 3. Comparing Field SEA predictions to its underlying model (TI MD simulations) and experimental results

for the 53 SAMPL5 logD values. The deviation of points from the 45° line indicate where the SEA method differs from its underlying force field model. Shaded areas in the graphs represent an uncertainty of 0.61 log P units. This value comes from propagating a solvation free energy error of k_BT in Eq.5. We compared two force fields for the solute: GAFF (blue), and GAFF-scaled (orange) with experimental data (purple line). Force field-wise GAFF-scaled is better than GAFF, which favors the cyclohexane phase too strongly.

Fig. 4. Comparing polar and nonpolar terms in water and cyclohexane, for SEA vs. the TI simulations

The calculations are reported for two different solute force fields: GAFF (blue dots) and GAFF-scaled (orange dots). Shaded areas represent an uncertainty of k_BT = 0.6 kcal mol⁻¹ in the determination of the solvation free energy. We note that our average statistical error is about 0.3 kcal mol⁻¹, but physically an error of k_BT is more sensible. The errors (deviations from the diagonal line) are independent of the force field, and SEA shows reasonable agreement with TI. Note the differences in scales for the NP and P terms in the different solvents.

Fig. 5. What's the best cyclohexane solvation shell?

(Right) The gray object is an arbitrary solute. For NP solvation, the position of a solvating cyclohexane molecule can be determined either as cyclohexane's closest small atom (green circle at the top, predicting a tight solvation shell), or as cyclohexane's center of mass (COM) (orange circle at the bottom, predicting a loose solvation shell). (Left) Comparing SEA with the TI simulations shows that the COM is a better model of the solvation shell.

Fig. 6. Improvement from the buried-atom correction for NP solvation

When the effect of buried atoms is ignored (oragane points) the NP solvation free energy calculated using SEA tends to be underestimated (i.e. the solute is less soluble) compared to TI calculations. This effect is more evident in CYH-DC solvent. When the effect of buried atom is considered the points shifts in the right direction (blue and light blue points; see text for details). The applied correction (highlighted in eq.2) is quite approximate and this causes to be overestimated for CYH-AA.

Fig. 7

Polar solvation free energy calculated using SEA and TI for two different solvents for 106 comparison point for the SAMPL5 solutes. SEA value are reported on the vertical axes and TI values are reported on the horizontal ones. Each SEA calculation was performed using a uniform single function fit (orange) or a piece-wise multiple function fit (blue) polar table. It is clear that the more complicated piece-wise fit is not necessary to accurately describe the P solvation free energy of a solute in water or CYH.

Fig. 8. Comparing SEA, TI, and experiments

On the left we show a comparison of log P SEA prediction against TI calculations. Yellow dots represent SAMPL submission and red ones represent the improved version of SEA. We can note how the predictions have been shifted upward. On the right we show the comparison of the same data with respect to experimental values. We also show in blue the results of the TI calculations. With the latest version of SEA tables and volume correction we see improvements of 1.4 log P units in RMSE, 2.1 log P unit in AUE and 1.1 log P unit in MSE.