Improving the Accuracy of Physics-Based Hydration-Free Energy Predictions by Machine Learning the Remaining Error Relative to the Experiment

Abstract

The accuracy of computational models of water is key to atomistic simulations of biomolecules. We propose a computationally efficient way to improve the accuracy of the prediction of hydration-free energies (HFEs) of small molecules: the remaining errors of the physics-based models relative to the experiment are predicted and mitigated by machine learning (ML) as a postprocessing step. Specifically, the trained graph convolutional neural network attempts to identify the "blind spots" in the physics-based model predictions, where the complex physics of aqueous solvation is poorly accounted for, and partially corrects for them. The strategy is explored for five classical solvent models representing various accuracy/speed trade-offs, from the fast analytical generalized Born (GB) to the popular TIP3P explicit solvent model; experimental HFEs of small neutral molecules from the FreeSolv set are used for the training and testing. For all of the models, the ML correction reduces the resulting root-mean-square error relative to the experiment for HFEs of small molecules, without significant overfitting and with negligible computational overhead. For example, on the test set, the relative accuracy improvement is 47% for the fast analytical GB, making it, after the ML correction, almost as accurate as uncorrected TIP3P. For the TIP3P model, the accuracy improvement is about 39%, bringing the ML-corrected model's accuracy below the 1 kcal/mol threshold. In general, the relative benefit of the ML corrections is smaller for more accurate physics-based models, reaching the lower limit of about 20% relative accuracy gain compared with that of the physics-based treatment alone. The proposed strategy of using ML to learn the remaining error of physics-based models offers a distinct advantage over training ML alone directly on reference HFEs: it preserves the correct overall trend, even well outside of the training set.

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains

“…In particular, the accuracy of the IWM-GB models in the critically important case of amino acids (AA), which utilize a slightly different set of atomic partial charges (RESP 184 ) and FF, 185 is not guaranteed to be as good as seen for the subset of small molecules in Tables 4 and 5 . While experimental HFEs for the 20 essential AA are unavailable, and it is unclear how these could even be measured for the charged ones, one can use 150 TIP3P polar solvation energies, Δ G el , as a reasonable proxy to assess the overall performance of the new IWM-GB models for this critically important class of small molecules. A test of the two optimized IWM-GB models, presented in Table 4 , against TIP3P polar hydration energies of 22 blocked AA 109 , 174 (including neutral forms of Glu and Asp 174 ) yields fairly large RMSEs: 5.39 kcal/mol for the IWM-GB WC model and 6.34 kcal/mol for the IWM-GB NC model.…”

“…Approaches based directly on the fundamental variational principles ,,,,− are arguably among the most conceptually advanced, physics-based implicit solvent models. Recently, approaches based on deep neural networks (DNNs) began to show promise in improving the accuracy of description of complex solvation effects, − including a strategy in which the initial prediction by a physics-based implicit solvent model is further refined by a DNN correction …”

“…Recently, approaches based on deep neural networks (DNNs) began to show promise in improving the accuracy of description of complex solvation effects, 142 − 149 including a strategy in which the initial prediction by a physics-based implicit solvent model is further refined by a DNN correction. 150 …”