Sylvio May and Avinoam Ben-Shaul,
The Phase Behavior of Cationic Lipid-DNA Complexes,
Biophys J., submitted
We present a theoretical analysis of the phase behaviour of solutions containing DNA, cationic lipids and nonionic (helper) lipids. Our model allows for five possible structures, treated as incompressible macroscopic phases: two lipid-DNA composite (``lipoplex'') phases, namely, the lamellar (L_alpha^C) and hexagonal (H_II^C) complexes; two binary (cationic/neutral) lipid phases, that is, the bilayer (L_alpha) and inverse-hexagonal (H_II) structures, and uncomplexed DNA. The free energy of the four lipid-containing phases is expressed as a sum of composition-dependent electrostatic, elastic and mixing terms. The electrostatic free energies of all phases are calculated based on Poisson-Boltzmann theory. The phase diagram of the system is evaluated by minimizing the total free energy of the three component mixture with respect to all the compositional degrees of freedom. We show that the phase behavior, in particular the preferred lipid-DNA complex geometry, is governed by a subtle interplay between the electrostatic, elastic and mixing terms which depend, in turn, on the lipid composition and lipid/DNA ratio. Detailed calculations are presented for three prototypical systems, exhibiting markedly different phase behaviors. The simplest mixture corresponds to a rigid planar membrane as the lipid source, in which case only lamellar complexes appear in solution. When the membranes are ``soft'' (i.e., low bending modulus) the system exhibits the formation of both lamellar and hexagonal complexes, sometimes coexisting with each other, as well as with pure lipid or DNA phases. The last system corresponds to a lipid mixture involving helper lipids with strong propensity towards the inverse-hexagonal phase. Here, again, the phase diagram is rather complex, revealing a multitude of phase transitions and coexistences. Lamellar and hexagonal complexes appear, sometimes together, in different regions of the phase diagram.