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Extending machine learning model for implicit solvation to free energy calculations

Rishabh Dey, Michael Brocidiacono, Kushal Koirala, Alexander Tropsha, Konstantin I. Popov

TL;DR

This work addresses the accuracy gap in implicit solvent models for free energy calculations by introducing the Lambda Solvation Neural Network (LSNN), a graph neural network that additionally learns derivatives with respect to alchemical variables to produce PMF-consistent free energies. The approach extends prior GNN implicit-solvent models to handle alchemically modified ligands, using a derivative-inclusive loss and a two-branch architecture to capture polar and nonpolar contributions, trained on ~300k molecules and benchmarked with MBAR against explicit-solvent baselines. Results show LSNN achieving substantial accuracy relative to explicit methods while delivering dramatic speedups, with R^2 ≈ 0.73 on hydration free energies and robust sampling, suggesting strong potential for scalable drug discovery workflows. The study also presents preliminary binding-affinity results indicating linear correlations with experimental data and outlines clear paths for extending LSNN to larger biomolecules, charged ligands, and protein-ligand binding energy calculations.

Abstract

The implicit solvent approach offers a computationally efficient framework to model solvation effects in molecular simulations. However, its accuracy often falls short compared to explicit solvent models, limiting its use in precise thermodynamic calculations. Recent advancements in machine learning (ML) present an opportunity to overcome these limitations by leveraging neural networks to develop more precise implicit solvent potentials for diverse applications. A major drawback of current ML-based methods is their reliance on force-matching alone, which can lead to energy predictions that differ by an arbitrary constant and are therefore unsuitable for absolute free energy comparisons. Here, we introduce a novel methodology with a graph neural network (GNN)-based implicit solvent model, dubbed Lambda Solvation Neural Network (LSNN). In addition to force-matching, this network was trained to match the derivatives of alchemical variables, ensuring that solvation free energies can be meaningfully compared across chemical species.. Trained on a dataset of approximately 300,000 small molecules, LSNN achieves free energy predictions with accuracy comparable to explicit-solvent alchemical simulations, while offering a computational speedup and establishing a foundational framework for future applications in drug discovery.

Extending machine learning model for implicit solvation to free energy calculations

TL;DR

This work addresses the accuracy gap in implicit solvent models for free energy calculations by introducing the Lambda Solvation Neural Network (LSNN), a graph neural network that additionally learns derivatives with respect to alchemical variables to produce PMF-consistent free energies. The approach extends prior GNN implicit-solvent models to handle alchemically modified ligands, using a derivative-inclusive loss and a two-branch architecture to capture polar and nonpolar contributions, trained on ~300k molecules and benchmarked with MBAR against explicit-solvent baselines. Results show LSNN achieving substantial accuracy relative to explicit methods while delivering dramatic speedups, with R^2 ≈ 0.73 on hydration free energies and robust sampling, suggesting strong potential for scalable drug discovery workflows. The study also presents preliminary binding-affinity results indicating linear correlations with experimental data and outlines clear paths for extending LSNN to larger biomolecules, charged ligands, and protein-ligand binding energy calculations.

Abstract

The implicit solvent approach offers a computationally efficient framework to model solvation effects in molecular simulations. However, its accuracy often falls short compared to explicit solvent models, limiting its use in precise thermodynamic calculations. Recent advancements in machine learning (ML) present an opportunity to overcome these limitations by leveraging neural networks to develop more precise implicit solvent potentials for diverse applications. A major drawback of current ML-based methods is their reliance on force-matching alone, which can lead to energy predictions that differ by an arbitrary constant and are therefore unsuitable for absolute free energy comparisons. Here, we introduce a novel methodology with a graph neural network (GNN)-based implicit solvent model, dubbed Lambda Solvation Neural Network (LSNN). In addition to force-matching, this network was trained to match the derivatives of alchemical variables, ensuring that solvation free energies can be meaningfully compared across chemical species.. Trained on a dataset of approximately 300,000 small molecules, LSNN achieves free energy predictions with accuracy comparable to explicit-solvent alchemical simulations, while offering a computational speedup and establishing a foundational framework for future applications in drug discovery.
Paper Structure (8 sections, 8 equations, 6 figures, 1 table)

This paper contains 8 sections, 8 equations, 6 figures, 1 table.

Table of Contents

  1. Background
  2. Methods
  3. Results
  4. Benchmarking Conditions
  5. Benchmarking Results
  6. Preliminary Binding Affinity Results
  7. Discussion
  8. Conclusion

Figures (6)

  • Figure 1: LSNN framework. This GNN model was modified from Katzberger2023 to enable modelling of alchemically-modified ligands.
  • Figure 2: Solvation Energy Accuracy Benchmark against Simulation Times for Implicit Solvent Models. GBN2 and OBC2 display similar trends while LSNN fluctuates. Result calculations were conducted with optimal speed and accuracy.
  • Figure 3: Accuracy of LSNN compared against experimentally calculated values
  • Figure 4: Accuracy of TIP3P compared against experimentally calculated values
  • Figure 5: Calculated solvation energies for conventional implicit solvent models.
  • ...and 1 more figures