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Quite different equilibrium ordered phase morphologies were found to occur from other choices of neutral helper lipid (HL). In the case of DOPE, or lecithin, for example, inverted hexagonal (''honeycomb'' or Hcn) organization of the lipid, with stretches of double-stranded DNA lying in the aqueous solution regions, were found to form, see Fig. 19B (95,102,107). The Hcn structure may be regarded as the inverse-hexagonal (HII) lipid phase, with DNA strands wrapped within its water tubes. Here, too, the diameter of the water tubes is only slightly larger than the diameter of the DNA ''rods.'' The presence of DNA is crucial for stabilizing the hexagonal structure. Without it, strong electrostatic repulsion will generally drive the lipids to organize themselves into planar bilayers. In fact, the most abundant aggregate structure of pure CL and HL mixtures, from which hexagonal complexes are subsequently formed, is single-bilayer liposomes.

Other CL-DNA phases have also been observed. One of the earliest studies probing the structure of lipoplexes showed some evidence for an hexagonal arrangement of rodlike micelles intercalated between hexagonally packed DNA, Fig. 19C (108,109). The number of possibilities is even larger if one also considers metastable intermediates. The ''spaghetti'' structure (see Fig. 19D), observed using freeze-fracture electron microscopy, has been predicted by theory to probably be one such metastable morphology (110,111). Here, each (possibly supercoiled) DNA strand is coated by a cylindrical bilayer of the CL/HL lipid mixture (112,113). Early proposed models of the CL-DNA complexes suggested a ''beads on a string'' type complex, in which the DNA is wrapped around or in between lipid vesicles (and even spherical micelles). Although this may not turn out to be an equilibrium structure, such aggregates are sometimes found, and may also serve as unstable intermediates (114-116). Other structures, such as the bilamellar invaginated liposomes (BIV) made of DOTAP-Chol, have been proposed and demonstrated to be efficient vectors (97,117). These structures resemble to some degree the Lca phase. However, formed from extruded liposomes, the BIVs are most probably metastable.

What factors determine which of these phases (or possibly several coexisting structures) actually form in solution? To what degree can we control and predict them? Control can first be achieved through the choice of type of CL and HL, and the ratio between the 2 used in forming liposomes. This in turn will determine such basic properties as the lipid bilayer's bending rigidity, spontaneous curvature, and surface charge density of the water-lipid aggregate interface. An additional experimentally controllable parameter is the ratio between the lipid and DNA content in solution. Both these parameters, we show, have significant effects on the phases that are formed.

B. Counterion Release

From the start, it was realized that the expected condensation of DNA with oppositely charged lipids could be used to package and send DNA to transfect targeted cells. The expectation that the DNA and lipids would aggregate was intuitively based on the notion that oppositely charged bodies attract. Early experiments confirmed the aggregation of DNA and lipids. However, the mechanism by which CL and DNA were found to associate—previously termed in the context of macromo-lecular association ''counterion release'' (118)—is more intricate than the ''opposites attract'' mechanism that may be naively expected.

Prior to association, DNA and lipids are bathed in the aqueous solutions containing their respective counterions, so that the solutions are overall electrostatically neutral. The counteri-ons are attracted to the oppositely charged macromolecules, thus gaining electrostatic energy. Here, in addition to DNA, we also refer to the preformed CL liposomes as a ''macromol-ecules'' because they typically retain their integrity in solution, even upon association with other charged macromole-cules. The counterions are therefore confined to the vicinity of the oppositely charged macromolecules at the compromise of greater translational entropy in solution.

Upon association, the 2 oppositely charged macromolecules condense to form CL-DNA complexes (Fig. 20). Many (possibly all) previously confined counterions can now be expelled into the bulk solution from the lipoplex interior, thus gaining translational entropy. Although the translational entropy of the paired macromolecules is reduced by (typically) only a few kBTs (due to loss of conformational and transla-tional entropy), many released counterions can now favorably contribute to a gain in entropy, each by a comparable amount. For this reason it is sometimes stated that the DNA-lipid condensation is ''entropically driven.'' The electrostatic en-

Figure 20 Schematic illustration of the condensation of DNA and lipid bilayers (liposomes) into CL-DNA complexes. In the process, the previously confined counterions are released into the bathing solution, thereby gaining translational entropy. See the color insert for a color version of this figure.

Figure 20 Schematic illustration of the condensation of DNA and lipid bilayers (liposomes) into CL-DNA complexes. In the process, the previously confined counterions are released into the bathing solution, thereby gaining translational entropy. See the color insert for a color version of this figure.

ergy can also contribute somewhat to stabilizing the li-poplexes. However, it has been well argued, both experimentally and theoretically, that the cardinal contribution to the association free energy of CL-DNA complexes is the entropy gain associated with counterion release (119,120).

Further support was given by counting released ions, using conductivity measurements of the supernatant. It was possible to determine that a maximal number of counterions were released when the number of ''fixed'' charges on the DNA and lipid were exactly equal.

Calorimetric measurements confirm this finding and find furthermore that the association could in fact be endothermic, so that it is only favorable for entropic reasons (121,122). The special point at which the number of positive and negative fixed charges is equal has been termed the ''isoelectric point.'' At this point, the (charging) free energy of the complex is minimal: the fixed charges of opposite signs fully compensate each other, thus allowing essentially all the counterions to be released into solution. Note, that by ''counterions'' we do not refer here to added salt ions. Ions of added salt will span the entire solution, including the lipoplex interior. Thus, the salt content changes the thermodynamic phase behavior and the value of the adsorption free energy, mainly because a high ambient salt concentration lowers the entropic gain associated with releasing a counterion.

Theoretical predictions and estimates from calorimetry show that for a salt solution of concentration n0 = 4 mM, and a 1:1 CL/HL mole ratio, the gain in free energy upon adsorption at the isoelectric point is a bemusingly large ~7.5 kBT per fixed charge pair (DNA and CL) (120-122). This value translates to over 2000 kBT when considering the energy per persistence length of DNA (about 50 nm), carrying approximately 300 charges.

C. Lamellar DNA-lipid Complexes

Many degrees of freedom with competing contributions are expected to ultimately determine the free energy minimum for equilibrium DNA/membrane structures. Typically, these include (but are not limited to) electrostatic energy, elastic bending, solvation, van der Waals, ion mixing, and lipid mixing. Therefore, considering the lipoplex phase behavior, we begin for simplicity by discussing systems where only Lca complexes are found. This can be expected when the lipid membranes are rather rigid, such as in the case of mixtures of DOTAP/DOPC (89,102) or DMPC/DC-Chol (123). The main structural parameter for the Lca phase is the DNA-DNA distance, reflecting the DNA packing density within the complex. A series of X-ray measurements by Radler et al. revealed how the DNA-DNA spacings d vary with the ratio p of the number of lipid charges to the total number of charges on DNA. The measurements were repeated for each of several different lipid compositions defined by the ratio of charged to overall number of lipids, It was found that for a lipid mixture of a given composition the spacings are constant throughout the low p range where the complex coexists with excess DNA. In the high p range, where the complex coexists with excess lipid, the spacings are also nearly constant. In-between these limits there exists a ''single-phase'' region, where all the DNA and lipids participate in forming li-poplexes. This region is generally found to include the isoelec-tric point where, by definition, p = 1 (Fig. 21).

Several theoretical studies have been proposed to account for this phase behavior (119,124,125). It was found that it is possible to account for most of the experimental observations within the scope of the nonlinear Poisson-Boltzmann equation (125). In this theoretical model, elastic deformations of

Figure 21 Schematic illustration of the phase evolution of the complexes for a constant lipid composition (cationic to nonionic lipid ratio). As lipid is added (p increases), the systems evolve from a 2-phase (complex and excess DNA) region through a 1-phase (complex only) region, and finally to a 2-phase (complex and excess lipid) region. The isoelectric point is generally contained within the 1-phase region. See the color insert for a color version of this figure.

Figure 21 Schematic illustration of the phase evolution of the complexes for a constant lipid composition (cationic to nonionic lipid ratio). As lipid is added (p increases), the systems evolve from a 2-phase (complex and excess DNA) region through a 1-phase (complex only) region, and finally to a 2-phase (complex and excess lipid) region. The isoelectric point is generally contained within the 1-phase region. See the color insert for a color version of this figure.

the DNA and lipid bilayers were neglected, treating them as rigid macromolecules. On the other hand the lipid's lateral (in plane) mobility in the membrane layer was explicitly taken into account. This turns out to be an important degree of freedom in mixed fluid bilayers, enabling the system to greatly enhance the free energy gain upon complexation, with respect to the case where no lipid mobility is allowed. This adds to the stability of the Lca complex. Generally, it was found that lipid mobility favors optimal (local) charge matching of the apposed DNA and lipid membrane. This is the state in which a maximal number of mobile counterions are expelled from the interaction zone, implying a maximal gain in free energy upon complex formation (126). However, the tendency for charge matching (hence migration of lipid to and from the region of proximity) is opposed by an unfavorable local lipid demixing entropy loss. This entropic penalty will somewhat suppress the membrane's tendency to polarize in the vicinity of the DNA molecule. The extent to which the membrane will polarize is determined by the intricate balance between the electrostatic and lipid-mixing entropy contributions to the free energy of the complex. The contribution of lipid demixing to the stabilization of the complex is most pronounced when the membrane's average composition is far from that of the DNA, namely, for low Here, the system can gain most out of the polarization so as to come close to local charge matching.

The tendency of charged lipids to segregate in the vicinity of adsorbed rigid macromolecules has gained some experimental support from nuclear magnetic resonance (NMR) studies (127), although many systems may display a more complex behavior. Molecular dynamic simulations of Lca complexes, for a lipid mixture of DMTAP and DMPC, showed evidence for a favorable pairing of DMPC and DMTAP lipid molecules through the (partial) negative charge on DOPC, and an interaction of the (remaining) positive charge of the zwiterionic DOPC with the DNA. In contrast to the model discussed above, this implies a nonideal lipid demixing: these lipid molecules preferentially move in pairs (128). This may be anticipated because it is well known that lipids do not generally mix ideally, even in free (unassociated) membranes (129). Furthermore, there is evidence that to some extent neutral lipids also interact directly with DNA (133).

Figure 22 shows the experimental results and theoretical calculations for the dependence of d on p for several values of For a specific value of ^ (say ^ = 0.5), the 3-phase regimes can clearly be seen. As p increases, d changes from « 35 A (in the excess DNA regime, p << 1) to » 47 A (in the excess lipid regime, p >> 1). Both theory and experiment show that for a wide range of lipid composition, there exists a 1-phase, complex-only region at p values somewhat larger and smaller than the isoelectric point. This implies that complexes may become either negatively or positively ''overcharged,'' so that the total number of fixed positive and negative charges is not equal. Hence, the complex accommodates either an excess number of lipids or else an excess amount of DNA. The complex's free energy is thus not at its minimum, which occurs at isoelectricity (p = 1). The interplay between possible phases to minimize the total system's free energy dictates that the complex move away from its minimal free

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