Electrostatic model for mixed cationic-zwitterionic lipid bilayers

The current interest in mixed cationic-zwitterionic lipid membranes derives from their potential use as transfer vectors in nonviral gene therapy. Mixed cationic-zwitterionic lipid membranes have a number of structural properties that are distinct from the corresponding anionic-zwitterionic lipid membranes. As known from experiment and reproduced by computer simulations, the average cross-sectional area per lipid changes nonmonotonically with the mole fraction of the charged lipid, passing through a minimum at a roughly equimolar mixture. At the same time, the average orientation of the zwitterionic headgroup dipoles changes from more parallel to the membrane plane to more perpendicular. We suggest a simple mean-field model that reveals the physical mechanisms underlying the observed structural properties. To backup the mean-field calculations, we have also performed Monte Carlo simulations. Our model extends Poisson-Boltzmann theory to include (besides the cationic headgroup charges) the individual charges of the zwitterionic lipid headgroups. We model these charges to be arranged as dipoles of fixed length with rotational degrees of freedom. Our model includes, in a phenomenological manner, the changes in steric headgroup interactions upon reorientation of the zwitterionic headgroups. Our numerical results suggest that two different mechanisms contribute to the observed structural properties: one involves the lateral electrostatic pressure and the other the zwitterionic headgroup orientation, the latter modifying steric headgroup interactions. The two mechanisms operate in parallel as they both originate in the electrostatic properties of the involved lipids. We have also applied our model to a mixed anionic-zwitterionic lipid membrane for which neither a significant headgroup reorientation nor a nonmonotonic change in the average lateral cross- sectional area is predicted.