Dna

Figure 23 Atomic force microscopy images of DNA from different sources (see figure for details) condensed on DPDAP bilay-ers at room temperature in 20 mM NaCl. Striking fingerprintlike order is apparent, with a domain size of the order of the persistence length (ca. 50 nm). (Courtesy of J. Yang.)

kBT) and tend to a planar geometry. Other lipoplex structures may ensue when the lipids possess a spontaneous curvature that is nonplanar, or when the membranes are soft enough to be deformed under the influence of the apposed macroion. The lipid membrane thus responds to the presence of DNA by deforming elastically and by locally changing its composition

Membrane elasticity may be varied substantially either by changing the lipid CL/HL composition, changing the lipid species, or by adding other agents, such as alcohols, to the membrane (138,139). In contrast, double-stranded DNA generally remains rather stiff, with a typical persistence length of « 500 A. Hence, the lipoplex geometries are restricted to structures in which DNA remains linear on these large-length scales. Usually, it is the interplay between the elastic (spontaneous curvature and bending rigidity) and electrostatic (charge density) properties of the membrane that will determine the optimum lipoplex geometry at equilibrium.

Often, the membrane elasticity and electrostatic contribution to the free energy display opposing tendencies. For example, the hexagonal Hh complex, is electrostatically favored due to the cylindrical wrapping of the DNA by the lipid mono-layer. This allows better contact between the 2 macromolecu-lar charged surfaces. However, the highly curved lipid geometry may incur a substantial elastic (curvature deformation) energy fee. The price to pay will be lower when the lipid (monolayer's) spontaneous curvature matches closely the DNA intrinsic (negative) curvature or when it has low bending rigidity. Under such conditions, the Hh complex may become more stable than the Lca phase. Usually, a neutral HL is used for adjusting the spontaneous curvature to the required negative curvature because pure CLs typically tend to form un-curved or positively curved aggregates. Use of more HL in the mixed membranes may on the one hand lower the elastic penalty, while on the other hand lower the monolayer's charge density, compromising the electrostatic energy gain upon association.

These qualitative notions were elegantly demonstrated by experiments in which the elastic properties of the lipid mono-layers were controlled by changing the nature of the lipid mixture. The spontaneous curvature of the lipid bilayer was modified by changing the identity of HL. It was found that when using a mixture of DOTAP/DOPE, Hh was the preferred structure, while DOTAP/DOPC mixtures promoted the formation of the Lca phase. This is consistent with the fact that pure DOPE forms the inverted hexagonal phase, Hn, due to its high negative spontaneous curvature (140-142), while DOPC self-assembles into planar bilayer. In addition, by adding hexanol to the DOTAP/DOPC-DNA lipid mixture, the bending rigidity could be diminished by about 1 order of magnitude (138,139). This induced a clear first order Lca ^ Hcn phase transition (102).

Additional complexity can be expected when accounting for the coexistence of more than 1 phase in solution. A theoretical study of the phase equilibrium took into account the bare lipid phases La and Hn, the naked DNA and the complex Lca and Hcn phases (143). The phase diagram of the system

Figure 24 The phase diagram of a lipid-DNA mixture, for lipids that self-assemble into rigid planar membranes. The phase diagram was calculated for membranes characterized by a bending rigidity in the range of 4 < Kc < » kBT and a spontaneous curvature of c = 0 A ~1 for both helper and cationic lipid. The symbols S, B, and D denote, respectively, the Lca, La, and uncom-plexed (naked) DNA phases. (Reprinted by permission from Ref. 143, Biophysical Society.)

Figure 24 The phase diagram of a lipid-DNA mixture, for lipids that self-assemble into rigid planar membranes. The phase diagram was calculated for membranes characterized by a bending rigidity in the range of 4 < Kc < » kBT and a spontaneous curvature of c = 0 A ~1 for both helper and cationic lipid. The symbols S, B, and D denote, respectively, the Lca, La, and uncom-plexed (naked) DNA phases. (Reprinted by permission from Ref. 143, Biophysical Society.)

was evaluated by minimization of the total free energy, which included electrostatic, elastic, and lipid-demixing contributions. Several systems of different compositions were considered. Figure 24 shows the predicted phase coexistence corresponding to the simplest case already discussed of rigid planar membranes. Results are presented for lipid membranes with a bending rigidity of Kc = 10kBT per monolayer and spontaneous curvature c = 0 A "1 [typical for many bilayer-forming lipids (106)] for which only lamellar complexes are expected to form. As the overall lipid composition is enriched in CL (higher the 1 phase persists over a wider range of p. This indicates that for higher CL content, the complex may be expected to be more stable toward addition of either DNA or lipid (hence moving away from the isoelectric point).

The Gibbs phase rule allows for up to three phases to coexist concomitantly for this 3-component (DNA, HL and CL) system. Figure 25 shows the theoretical prediction for the phase diagram for a system in which the HL has a strong negative spontaneous curvature (Kc = 10kBT and c = 1/25 A_1)(143). For high ^ values, the phase behavior resembles that of the previously discussed system. However, for lower values of a multitude of regions of (up to 3) different phases coexisting together can be found. In some regions, lamellar and hexagonal complexes appear coexisting side by side. A similarly complex diagram results when the membranes are soft (bending rigidity of » kBT) as might be expected for membranes with added alcohols (143).

A more subtle demonstration of the underlying balance of forces can be found within the realm of the Lca complex. Thus far, the theoretical models considered for the lipid membranes in this lamellar phase assumed them to be perfectly planar slabs. However, this need not be so. When membranes are sufficiently soft (yet not soft enough to favor the HcII phase) or if one of the CL/HL has a propensity to form curved sur-

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