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.)

sess a part proximal and a part distal to the interaction zone. If both parts are charged, as is the case with DNA, complete counterion release cannot be achieved because the distal part does not interact significantly with the underlying bilayer. Therefore, although charges on the lipid membrane are fully cancelled by charges on adsorbed DNA macroions, still the portion of DNA away from the contact zone imparts a net surface charge (i.e., overcharging of the DNA-covered membrane).

Yet another interesting feature is the dependence of the DNA-DNA distance on salt concentration. As the NaCl concentration was varied between 20 and 1000 mM, this distance grew from around 45 A to almost 60 A. At first this may seem baffling: adding salt should be expected to decrease the DNA-DNA electrostatic repulsion, and hence lower the distance between neighboring interacting strands. This is indeed the general trend that has been observed in L°a complexes (101,125). However, because the DNA was primarily allowed to saturate the surface and only subsequently treated with the salt solution (which was later also washed away), adsorption here was not at equilibrium. In fact, when faced with a neat salt solution the adsorbed DNA can only detach, it will not generally readsorb onto the surface. It is therefore hard to give full theoretical reasoning for the trend.

Theoretical explanations have previously been offered to account for this salt-dependent behavior, based on a balance between membrane-mediated effective attraction (that may be the result of the DNA perturbation of the lipid bilayer) and electrostatic repulsion between DNA strands (136). The predicted DNA-DNA spacing as a function of screening length is nonmonotonic: increasing first for low screening lengths and decreasing for high values. An alternative to this approach is related to the free energy gain upon adsorption, and how it changes with the addition of salt. In the presence of added salt, the adsorption free energy can be expected to be lower because the gain in entropy upon release of counterions becomes very small when releasing an ion from an adsorbed layer into a bathing solution with a comparable concentration. Assuming that unbinding would occur when the free energy gain per persistence length is » kBT, we can estimate from a simple model that the thickness of the confined layer is leff » 5 A, rather close to the screening length in solution (3-4 A) (120-122). Thus, the lower binding free energy may cause some of the DNA strands to dissociate from the lipid surface once the system is exposed to salt. Allowing DNA to rearrange on the surface would then lead to an increase in the average DNA-DNA distance.

When multivalent salt is used, a crowding of DNA molecules is first observed as salt is added (in accordance with the observations in the Lca complexes), and then starts to grow for higher concentrations (89,137). This may be a manifestation of the 2 competing forces as salt is added: lessened repulsion between strands vs. weakened adsorption energy.

E. From Lamellar to Hexagonal Complexes

So far, we have discussed the Lca lipoplexes formed from lipid membranes that are rigid (bending rigidity much greater than

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