EquiSolv: O(3)-Equivariant Neural Networks for Predicting Protein Solvation 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-derived scaled enthalpy (eGIST) fields. The field is defined at any coordinate and is evaluated on the $1.0$ ŠMD grid. On peptides, EquiSolv fuses ESM-C embeddings with geometric graph features; on DUD-E proteins EquiSolv omits ESM-C, which leaves MSE essentially unchanged in ablations. We predict per-atom parametric functions constructed as linear combinations, with learnable coefficients, of products of radial basis functions and spherical harmonics. We bound the approximation error of the population-optimal network, assuming a smooth interpolant. The bound does not cover finite-sample error. Of 1100 DBAASP peptide systems we train on 880 and test on 110 peptides; of the DUD-E proteins we train on 69 and test on 10 proteins. On the held-out peptides, we achieve an RMSE of $0.176\pm 0.026$ kcal/mol/ų.