Incorporating headgroup structure into the Poisson-Boltzmann model of charged lipid membranes.

Charged lipids often possess a complex headgroup structure with several spatially separated charges and internal conformational degrees of freedom. We propose a headgroup model consisting of two rod-like segments of the same length that form a flexible joint, with three charges of arbitrary sign and valence located at the joint and the two terminal positions. One terminal charge is firmly anchored at the polar-apolar interface of the lipid layer whereas the other two benefit from the orientational degrees of freedom of the two headgroup segments. This headgroup model is incorporated into the mean-field continuum Poisson-Boltzmann formalism of the electric double layer. For sufficiently small lengths of the two rod-like segments a closed-form expression of the charging free energy is calculated. For three specific examples--a zwitterionic headgroup with conformational freedom and two headgroups that carry an excess charge--we analyze and discuss conformational properties and electrostatic free energies.