Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model (Communications in Computational Physics, 2011)
A multiple-image method is proposed to approximate the reaction-field potentialof a source charge inside a finite length cylinder due to the electric polarizationof the surrounding membrane and bulk water. When applied to a hybrid ion-channelmodel, this method allows a fast and accurate treatment of the electrostatic interactionsof protein with membrane and solvent. To treat the channel/membrane interfaceboundary conditions of the electric potential, an optimization approach is usedto derive image charges by fitting the reaction-field potential expressed in terms ofcylindric harmonics. Meanwhile, additional image charges are introduced to satisfythe boundary conditions at the planar membrane interfaces. In the end, we convertthe electrostatic interaction problem in a complex inhomogeneous system of ion channel/membrane/waterinto one in a homogeneous free space embedded with discretecharges (the source charge and image charges). The accuracy of this method is thenvalidated numerically in calculating the solvation self-energy of a point charge.