Charging Free Energy Calculations Using the Generalized Solvent Boundary Potential (GSBP) and Periodic Boundary Condition: A Comparative Analysis Using Ion Solvation and Oxidation Free Energy in Proteins

Abstract

Free energy simulations using a finite sphere boundary condition rather than a periodic boundary condition (PBC) are attractive in the study of very large biomolecular systems. To understand the quantitative impact of various approximations in such simulations, we compare charging free energies in both solution and protein systems calculated in a linear response framework with the Generalized Solvent Boundary Potential (GSBP) and PBC simulations. For simple ions in solution, we find good agreements between GSBP and PBC charging free energies, once the relevant correction terms are taken into consideration. For PBC simulations with the particle-mesh-Ewald for long-range electrostatics, the contribution (ΔG(P-M)) due to the use of a particle rather than molecule based summation scheme in real space is found to be significant, as pointed out by Hünenberger and co-workers. For GSBP, when the inner region is close to be charge neutral, the key correction is the overpolarization of water molecules at the inner/outer dielectric boundary; the magnitude of the correction (ΔG(s-pol)), however, is relatively small. For charging (oxidation) free energy in proteins, the situation is more complex, although good agreement between GSBP and PBC can still be obtained when care is exercised. The smooth dielectric boundary approximation inherent to GSBP tends to make significant errors when the inner region is featured with a high net charge. However, the error can be corrected with Poisson-Boltzmann calculations using snapshots from GSBP simulations in a straightforward and robust manner. Because of the more complex charge and solvent distributions, the magnitudes of ΔG(P-M) and ΔG(s-pol) in protein simulations appear to be different from those derived for solution simulations, leading to uncertainty in directly comparing absolute charging free energies from PBC and GSBP simulations for protein systems. The relative charging/oxidation free energies, however, are robust. With the linear response approximation, for the specific protein system (CueR) studied, the effect of freezing the protein structure in the outer region is found to be small, unless a very small (8 Å) inner region is used; even in the latter case, the result is substantially improved when the nearby metal binding loop is allowed to respond to metal oxidation. The implications of these results to the applicability of GSBP to complex biomolecules and in ab initio QM/MM simulations are discussed.