An ensemble-averaged Poisson-Boltzmann model for modeling solute conformational flexibility

The Poisson-Boltzmann (PB) model is one of the most widely used implicit solvent frameworks for computing the polar component of solvation free energy, the energetic cost of transferring a solute molecule from a vacuum into an ionic solvent environment. However, the classical PB formulation treats solute atomic charges as fixed point singularities and therefore cannot efficiently accommodate the conformational changes that arise during solvation. Moreover, obtaining physically meaningful ensemble-averaged solvation energies typically requires explicit solvent model, e.g. molecular dynamics (MD) or Monte Carlo (MC) simulations, to generate conformational ensemble, followed by solving a rigid conformation PB equation for each snapshot, an approach that is computationally very expensive. To address these limitations, we introduce an ensemble-averaged Poisson-Boltzmann (EAPB) model that directly approximates the ensemble-averaged polar solvation energy near equilibrium of the solute-solvent system. In this formulation, each point charge is replaced by a smooth Gaussian-like density, enabling the PB calculation to naturally incorporate conformational variations that occur during solvation. The resulting ensemble-averaged energy is obtained by solving a single PB-type equation, rather than averaging over hundreds or even thousands of explicit solvent snapshots, yielding substantial computational savings. We conduct extensive numerical studies to identify suitable modeling parameter ranges and to assess the robustness, stability, efficiency, and accuracy of the proposed model. Additional tests, including solute structural perturbation analysis and total solvation free energy evaluation, demonstrate that the EAPB model produces physically consistent, numerically stable, and highly accurate predictions, highlighting its potential as an efficient alternative to traditional PB and explicit-solvent approaches.