The role of spatial dispersion of the dielectric constant of spherical water cavity in the lowering of the free energy of ion transfer to the cavity

Abstract

Simple analytical expression is derived for the changes in the ion solvation energy W _NE upon its transfer to the center of water cavity with radius R _Cav, surrounded by protein substance with dielectric constant ɛ_p. In the derivation, nonlocal-electrostatic Poisson equation for the water cavity was solved by using Hildebrandt method called in literature “New Formulation of Nonlocal Electrostatics.” It was shown that for potassium channel with the most open conformation KcsA, at R _Cav = 1.6 nm and the water correlation length Λ = 0.8 nm, the energy W _NE is by 1.25 k _B T less that the resolvation energy calculated by the classical theory with the cavity’s dielectric constant ɛ_Cav = 78.5. Therefore, the nonlocal-electrostatic effects in the water cavity of the potassium channel facilitate K⁺ transfer over the potential barrier in the channel’s cavity. The lowering of the cavity radius results in the K⁺ sucking up into the channel cavity; the effect is missed in the classical electrostatics.