Predicting solvation free energies with an implicit solvent machine learning potential

TL;DR

This paper introduces ReSolv, a two-stage Solvation Free Energy Path Reweighting framework to train an implicit-solvent ML potential. By first fitting a vacuum ML potential to DFT data and then refining it against experimental hydration free energies via differentiable trajectory reweighting (DiffTRe) and BAR/FEP-based free-energy accumulation, ReSolv achieves hydration free energy predictions near experimental uncertainty while delivering substantial speedups over explicit-solvent ML potentials. The approach demonstrates strong performance on the FreeSolv dataset, robust generalization to unseen functional groups, and insightful error-analysis correlations that inform data curation. Overall, ReSolv offers a scalable, accurate, and efficient path toward implicit-solvent ML models that can accelerate drug design and related solvation studies.

Abstract

Machine learning (ML) potentials are a powerful tool in molecular modeling, enabling ab initio accuracy for comparably small computational costs. Nevertheless, all-atom simulations employing best-performing graph neural network architectures are still too expensive for applications requiring extensive sampling, such as free energy computations. Implicit solvent models could provide the necessary speed-up due to reduced degrees of freedom and faster dynamics. Here, we introduce a Solvation Free Energy Path Reweighting (ReSolv) framework to parametrize an implicit solvent ML potential for small organic molecules that accurately predicts the hydration free energy, an essential parameter in drug design and pollutant modeling. With a combination of top-down (experimental hydration free energy data) and bottom-up (ab initio data of molecules in a vacuum) learning, ReSolv bypasses the need for intractable ab initio data of molecules in explicit bulk solvent and does not have to resort to less accurate data-generating models. On the FreeSolv dataset, ReSolv achieves a mean absolute error close to average experimental uncertainty, significantly outperforming standard explicit solvent force fields. Compared to the explicit solvent ML potential, ReSolv offers a computational speedup of four orders of magnitude and attains closer agreement with experiments. The presented framework paves the way toward deep molecular models that are more accurate yet computationally cheaper than classical atomistic models.

Figures (6)

• Figure 1: Solvation Free Energy Path Reweighting (ReSolv). The green color indicates ReSolv's stage one, where we train an ML potential $U_{\mathrm{vac}}$ for molecules in a vacuum based on the ab initio dataset containing configurations $S$ and the corresponding energies $U_\mathrm{DFT}$ and forces $F_\mathrm{DFT}$. The blue color represents ReSolv's stage two, where we train an ML potential $U_{\mathrm{sol}}$ for molecules in an implicit solvent by initializing the parameters with $\theta_{\mathrm{vac}}$ and perturbing them towards $\theta_{\mathrm{sol}}$ where the free energy difference between $U_\mathrm{vac}$ and $U_{\mathrm{sol}}$ equals experimental solvation free energy $\Delta A_{\mathrm{exp}}$. The red color depicts the parameter update procedure involving trajectory reweighting, Free Energy Perturbation (FEP), and Bennett acceptance ratio (BAR) methods. See main text for more details.
• Figure 2: Prediction performance. The implicit solvent ReSolv model (blue) is referenced against the explicit solvent classical atomistic models Amber (GAFF; red) and CHARMM (CGenFF; green). The results are shown for the test dataset. (a) Parity plot with the error bars denoting the experimental uncertainty and the gray dash-dotted line indicating the perfect prediction. (b) Error probability distribution relative to the experimental values. The distributions are fitted with the Gaussian kernel density estimator. (c) The number of predictions with errors lower than the experimental uncertainty. The gray background histogram depicts the distribution of experimental uncertainty. The total percentage of predictions within the experimental uncertainty is 57%, 31%, and 46% for the ReSolv, Amber, and CHARMM models, respectively. (d) Mean absolute error (MAE) increase with decreasing experimental hydration free energy. The red solid line denotes the median, red dashed line mean, the box ranges are from the first to the third quartile, and the whiskers correspond to the 1.5x interquartile range.
• Figure 3: Error analysis. The box plots of the mean absolute error (MAE) with respect to (a) chemical functional groups, (b) number of heavy atoms, and (c) number of heavy atom types are shown for the test set molecules. The red line denotes the median, red dashed line mean, the box ranges are from the first to the third quartile, and the whiskers correspond to the 1.5x interquartile range. The gray bar plots depict the number of corresponding samples in the training set. We compare three different models: ReSolv (blue), Amber (GAFF; red), and CHARMM (CGenFF; green). In subplot (a), the 'other' group corresponds to the remaining functional groups with less than three samples in the test set.
• Figure 4: Extrapolation to unseen functional groups. Box plots of the mean absolute error (MAE) with respect to chemical functional groups, comparing four different models: ReSolv with primary amines unseen during training (dark blue); ReSolv with primary alcohols unseen during training (light blue); Amber (GAFF; red); and CHARMM (CGenFF; green). The 'other' group corresponds to the remaining functional groups with less than three samples in the test set. The red line denotes the median, red dashed line mean, the box ranges are from the first to the third quartile, and the whiskers correspond to the 1.5x interquartile range.
• Figure 5: Correlation of errors in kcal/mol between the ReSolv, Amber (GAFF), and CHARMM (CGenFF) models for the test dataset. The gray dash-dotted line indicates the perfect correlation. Eight molecules with absolute errors greater than 1.7 kcal/mol simultaneously for x- and y-axes are marked with distinct symbols as shown in the legend. In supplementary material Table 1 we list the mean errors across all models and experimental uncertainties for these eight molecules.