where ρ ρ ions ( r , t ) and ρ ρ perm ( r ) are the charge density of ions and permanent charges on the protein, respectively. ϵ ϵ ( r ) is the local dielectric constant or permittivity, and ϕ ϕ ( r , t ) is the local electrostatic potential. Solving this equation provides a self-consistent way to include applied bias and the effects of image charges induced at dielectric boundaries.