Figure 22 DNA-DNA spacing as a function of p in a series of theoretical and experimental results. The theoretical results correspond to (top to bottom) ^ = 0.3, 0.4, 0.5, 0.6, and 0.8; all results are presented for a screening length of 50 A (corresponding to ca. 4 nm of bathing salt solution). The experimental results correspond to ^ = 0.3 (squares), 0.5 (circles), and 0.7 (triangles), and were performed with no added salt. (Theoretical results adapted from Refs. (125) and (145); experimental results adapted from Ref. 101.)

energy. The alternative would be to expel the excess lipid (p > 1) or excess DNA (p < 1) into solution. The charge densities on these ''free'' unneutralized macromolecules would be very large, rendering this scenario highly unfavorable. Using a simple model based on this overcharging phenomenon, it was possible to account for the considerable extent of this one phase region (125). Within this model, only the uncompensated charges on apposed (DNA-DNA or bilayer-bilayer) surfaces of an Lca unit cell (''box'') were considered in estimating the complex's free energy. Figure 22 also shows that as the membrane becomes enriched in CL (^ increases) the DNA-DNA distance is systematically reduced, reflecting the fact that smaller amounts of lipid membrane are needed to achieve isoelectricity.

Salt has a significant effect on the phase behavior. In general, added salt causes a significant decrease in d, presumably due to a screening of the repulsive DNA-DNA interaction. This effect is most pronounced when divalent salts are added in increasing amounts. A sharp decrease in the d value is observed for a certain salt molar concentration, resulting in very highly condensed DNA in each gallery (89,130). Another interesting observation is that the identity of the CL's counter-ion used changes considerably the (endothermic) association enthalpy, particularly in the excess DNA region (121). This probably reflects the nonelectrostatic interaction energies of different ions with membranes, which may influence the ther-motropic behavior of the lipid membranes (131,132).

D. DNA Adsorption on Lipid Membranes

Further insight into the in-plane DNA ordering in Lca complexes has been gained through the atomic force microscopy

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