Lamellar cationic lipid-DNA complexes from lipids with a strong preference for planar geometry: A Minimal...

We formulate and analyze a minimal model, based on condensation theory, of the lamellar cationic lipid (CL)-DNA complex of alternately charged lipid bilayers and DNA monolayers in a salt solution. Each lipid bilayer, composed by a random mixture of cationic and neutral lipids, is assumed to be a rigid uniformly charged plane. Each DNA monolayer, located between two lipid bilayers, is formed by the same number of parallel DNAs with a uniform separation distance. For the electrostatic calculation, the model lipoplex is collapsed to a single plane with charge density equal to the net lipid and DNA charge. The free energy difference between the lamellar lipoplex and a reference state of the same number of free lipid bilayers and free DNAs, is calculated as a function of the fraction of CLs, of the ratio of the number of CL charges to the number of negative charges of the DNA phosphates, and of the total number of planes. At the isoelectric point the free energy difference is minimal. The complex formation, already favoured by the decrease of the electrostatic charging free energy, is driven further by the free energy gain due to the release of counterions from the DNAs and from the lipid bilayers, if strongly charged. This minimal model compares well with experiment for lipids having a strong preference for planar geometry and with major features of more detailed models of the lipoplex.