We develop a statistical thermodynamic model for the phase evolution of DNA-cationic lipid complexes in aqueous solution, as a function of the ratios of charged to neutral lipid and charged lipid to DNA. The complexes consist of parallel strands of DNA intercalated in the water layers of lamellar stacks of mixed lipid bilayers, as determined by recent synchrotron x-ray measurements. Elastic deformations of the DNA and the lipid bilayers are neglected, but DNA-induced spatial inhomogeneities in the bilayer charge densities are included. The relevant nonlinear Poisson-Boltzmann equation is solved numerically, including self-consistent treatment of the boundary conditions at the polarized membrane surfaces. For a wide range of lipid compositions, the phase evolution is characterized by three regions of lipid to DNA charge ratio, rho: 1) for low rho, the complexes coexist with excess DNA, and the DNA-DNA spacing in the complex, d, is constant; 2) for intermediate rho, including the isoelectric point rho = 1, all of the lipid and DNA in solution is incorporated into the complex, whose inter-DNA distance d increases linearly with rho; and 3) for high rho, the complexes coexist with excess liposomes (whose lipid composition is different from that in the complex), and their spacing d is nearly, but not completely, independent of rho. These results can be understood in terms of a simple charging model that reflects the competition between counterion entropy and inter-DNA (rho < 1) and interbilayer (rho > 1) repulsions. Finally, our approach and conclusions are compared with theoretical work by others, and with relevant experiments.
Using x-ray diffraction and NMR spectroscopy, we present structural and material properties of phosphatidylserine (PS) bilayers that may account for the well documented implications of PS headgroups in cell activity. At 30 degrees C, the 18-carbon monounsaturated DOPS in the fluid state has a cross-sectional area of 65.3 A(2) which is remarkably smaller than the area 72.5 A(2) of the DOPC analog, despite the extra electrostatic repulsion expected for charged PS headgroups. Similarly, at 20 degrees C, the 14-carbon disaturated DMPS in the gel phase has an area of 40.8 A(2) vs. 48.1 A(2) for DMPC. This condensation of area suggests an extra attractive interaction, perhaps hydrogen bonding, between PS headgroups. Unlike zwitterionic lipids, stacks of PS bilayers swell indefinitely as water is added. Data obtained for osmotic pressure versus interbilayer water spacing for fluid phase DOPS are well fit by electrostatic interactions calculated for the Gouy-Chapman regime. It is shown that the electrostatic interactions completely dominate the fluctuational pressure. Nevertheless, the x-ray data definitively exhibit the effects of fluctuations in fluid phase DOPS. From our measurements of fluctuations, we obtain the product of the bilayer bending modulus K(C) and the smectic compression modulus B. At the same interbilayer separation, the interbilayer fluctuations are smaller in DOPS than for DOPC, showing that B and/or K(C) are larger. Complementing the x-ray data, (31)P-chemical shift anisotropy measured by NMR suggest that the DOPS headgroups are less sensitive to osmotic pressure than DOPC headgroups, which is consistent with a larger K(C) in DOPS. Quadrupolar splittings for D(2)O decay less rapidly with increasing water content for DOPS than for DOPC, indicating greater perturbation of interlamellar water and suggesting a greater interlamellar hydration force in DOPS. Our comparisons between bilayers of PS and PC lipids with the same chains and the same temperature enable us to focus on the effects of these headgroups on bilayer properties.
The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is "saturated" by adsorbed proteins), the membrane charges are "overcompensated" by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.
The cooperative condensation of DNA and cationic liposomes to form ordered aggregates in aqueous solution is associated with the release of partially bound counterions. We directly determine the extent of counterion release by separating the supernatant from the precipitated condensates, measuring the conductivity of the solution before and after the phase transition. The extent of counterion release is calculated for a range of lipid/DNA concentration ratios based on the nonlinear Poisson−Boltzmann theory. Both experiment and theory show maximal, essentially complete, release of counterions at the isoelectric point, where the positive (lipid)/negative (DNA) charge ratio is 1:1. Furthermore, at this point the entropic contribution to the condensation free energy is maximal and dominant.
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