Electroelastic Coupling Between Membrane Surface Fluctuations and Membrane-embedded Charges: Continuum Multidielectric Treatment

The coupling of electric fields and charges with membrane-water interfacial fluctuations affects membrane electroporation, ionic conductance, and voltage gating. A modified continuum model is introduced to study charge interaction with membrane-water interfacial fluctuations in multidielectric environments. By surrounding a point charge with a low dielectric sphere, the linear Poisson-Boltzmann equation is directly solved by calculating the reaction field potential via a method that eliminates singularity contributions. This allows treatment of charges located at dielectric boundaries. Two complementary mechanisms governing charge-fluctuation interactions are considered: (1) electroelastic deformation (EED), treating the membrane as an elastic slab (smectic bilayer model), and (2) electrohydrophobic solvation (EHS), accounting for water penetration into the membrane's hydrophobic core. EED often leads to large membrane thickness perturbations, far larger than those consistent with elastic model descriptions [M. B. Partenskii, G. V. Miloshevsky, and P. C. Jordan, Isr. J. Chem. 47, 385 (2007)]. We argue that a switch from EED to EHS can be energetically advantageous at intermediate perturbation amplitudes. Both perturbation mechanisms are simulated by introducing adjustable shapes optimized by the kinetic Monte Carlo reaction path following approach [G. V. Miloshevsky and P. C. Jordan, J. Chem. Phys. 122, 214901 (2005)]. The resulting energy profiles agree with those of recent atomistic molecular dynamics studies on translating a charged residue across a lipid bilayer [S. Dorairaj and T. W. Allen, Proc. Natl. Acad. Sci. U.S.A. 104, 4943 (2007)].