On generalizing the induced surface charge method to heterogeneous Poisson-Boltzmann models for electrostatic free energy calculation.

The induced surface charges (ISC) method, which computes the induced charges on the molecular surface of macromolecules and uses them via Coulomb's law to calculate the polar solvation energy, was shown to be a robust and almost grid independent approach for electrostatic analysis based on the sharp-interface Poisson-Boltzmann (PB) model. Besides being physically intuitive, the ISC method avoids using the potential near the point charges, which is singular at each atom center. However, the ISC method cannot be physically generalized to heterogeneous dielectric PB models, due to the non-existence of a dielectric boundary. In this work, a novel far-field (FF) method is proposed to calculate the polar solvation free energy, which is derived through reformulating the energy functionals of nonlinear PB potential in solvent and vacuum states. Built upon a rigorous mathematical analysis, the FF method reconstructs the free energies by using far-field solutions outside the solute so that the self-energy terms generated by the singular charges are avoided, just as in the ISC method. Being valid for both sharp-interface and heterogeneous PB models, the performance of the proposed FF method has been validated by considering diffuse interface, Gaussian and super-Gaussian PB models for Kirkwood spheres and various protein systems. Comparison with grid-energy cancellation and regularization methods is also considered. The robustness of the FF method in treating a non-rigid biomolecule with different molecular structures in solvent and vacuum states has been explored, taking advantage of the fact that the far-field potential is insensitive to perturbations of singular charge locations.