Achieving all-atom molecular dynamics accuracy from the Poisson-Boltzmann method through machine learning.

All-atom molecular dynamics (MD) simulations are a standard tool for probing the structural and dynamical properties of biomolecular systems, but their accuracy comes at the cost of high computational demands. To overcome spatial-temporal limitations, implicit models or coarse-graining are often employed, but usually at the expense of reduced accuracy. This limitation is also evident in the Poisson-Boltzmann (PB) mean-field theory, which efficiently captures long-range electrostatics but fails to account for crucial short-range interactions. In this work, we bridge this gap by introducing a graph neural network (GNN) Δ-learning approach trained on the difference between all-atom MD and PB, resulting in DIS-PB (deep implicit solvation model using the PB potential as a prior). DIS-PB, which models solutes and salt ions explicitly by MD while water is coarse-grained out, captures both short-range electrostatic correlations as well as long-range electrostatic interaction tails. Applied to a system of the DNA molecule in 1 mol l-1 salt solution, our method reproduces structural properties (NDPs, RDFs, and binding probability patterns) with high fidelity, showing that the GNN-corrected PB can reach the accuracy of all-atom MD at a lower computational cost.