Electrical energy required to form large conducting pores

This study computes the contribution of the externally induced transmembrane potential to the energy of large, highly conductive pores. This work was undertaken because the pore energy formulas existing in the literature predict qualitatively different behavior of large pores: the original formula proposed by Abidor et al. in 1979 implies that the electrical force expanding the pore increases linearly with pore radius, while later extensions of this formula imply that this force decreases to zero for large pores. Starting from the Maxwell stress tensors, our study derives the formula for the mechanical work required to deform a dielectric body in an ionic solution with steady-state electric current. This formula is related to a boundary value problem (BVP) governing electric potentials and fields in a proximity of a pore. Computer simulations yield estimates of the electrical energy for pores of two different shapes: cylindrical and toroidal. In both cases, the energy increases linearly for pore radii above approximately 20 nm, implying that the electrical force expanding the pore asymptotes to a constant value for large pores. This result is different from either of the two energy formulas mentioned above. Our study traces the source of this disagreement to approximations made by previous studies, which are suitable only for small pores. Therefore, this study provides a better understanding of the energy of large pores, which is needed for designing pulsing protocols for DNA delivery.