An ionic concentration and size dependent dielectric permittivity Poisson-Boltzmann model for biomolecular solvation studies.

By considering the influence of volume exclusion on the solvent dielectric, a variable dielectric Poisson-Boltzmann (VDPB) model is explored for molecular solvation studies by using a dielectric as an explicit function of ionic sizes and concentrations. A finite element method is adopted and an iterative strategy is introduced to numerically solve the VDPB equation. According to our computations, the current dielectric model can result in considerable differences compared with the traditional Poisson-Boltzmann (PB) solutions, especially for those systems with highly charged biomolecule and/or under high salt concentration condition. The model to certain extent captures the fact of dielectric decrement of electrolyte solutions, which is especially remarkable in the vicinity of molecules. Counter-ion concentration very near the molecular surface in VDPB calculation is found higher than that in PB. The new dielectric model may also influence the charge compensation behavior near biomolecular surface. For a spherical cavity solvated in a concentrated ionic solution, charge inversion is observed in VDPB, which does not occur with the traditional PB model. Besides, the solvation energy predicted by VDPB will always be greater than that by PB. Moreover, differing from PB, the VDPB also allows non-monotonous dependencies of solvation energy on ionic strength.