The phase behavior of cationic lipid-DNA complexes

Sylvio May, Daniel Harries, Avinoam Ben-Shaul*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


We present a theoretical analysis of the phase behavior 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(α)(C) and hexagonal (H(II)(C) complexes; two binary (cationic/neutral) lipid phases, that is, the bilayer (L(α)) 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, and with pure lipid or DNA phases. The last system corresponds to a lipid mixture involving helper lipids with strong propensity toward 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.

Original languageAmerican English
Pages (from-to)1681-1697
Number of pages17
JournalBiophysical Journal
Issue number4
StatePublished - Apr 2000

Bibliographical note

Funding Information:
S.M. thanks the Minerva foundation for a post-doctoral Fellowship and D.H. the Clore Foundation for a doctoral Fellowship. The Fritz Haber Center is supported by the Minerva Foundation, Munich, Germany.

Funding Information:
We thank Cyrus Safinya, Joachim Rädler, and Bill Gelbart for helpful discussions. We also thank the Israel Science Foundation (grant 8003/97) and the US–Israel Binational Science Foundation (grant 97-205) for financial support.


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