EquiSolv: O(3)-Equivariant Neural Networks for Predicting Protein Solvation Free Energy Fields

Drug design is an arduous process that depends on the discovery of functional protein-molecule interactions, whose energetic favourability depends on displacing solvent from the binding pocket. In practice, Grid Inhomogeneous Solvation Theory (GIST) is a commonly used method that provides accurate, computationally costly solvation thermodynamics through molecular dynamics (MD) simulations, rendering it infeasible for large-scale drug screenings. We propose an O(3)-equivariant graph neural network architecture, named EquiSolv, built on Euclidean neural network (e3nn) primitives that predicts GIST free-energy (eGIST) fields at arbitrary coordinates in 3D space. EquiSolv integrates sequence-level information from ESM-C embeddings with structure-level geometric graph features. We predict per-atom parametric functions constructed as linear combinations, with learnable coefficients, of products of radial basis functions and spherical harmonics. We theoretically prove that the approximation error of EquiSolv is upper-bounded by a sum of terms that decay algebraically fast as functions of the network depth and width. We train and evaluate EquiSolv on 1100 anti-microbial peptides from DBAASP and 96 proteins from DUD-E, demonstrating that EquiSolv approaches MD accuracy while enabling rapid prediction of continuous solvation fields for large-scale protein analysis.