Lamellar cationic lipid‐DNA complexes from lipids with a strong preference for planar geometry: A Minimal Electrostatic Model

Abstract

We formulate and analyze a minimal model, based on condensation theory, of the lamellar cationic lipid (CL)-DNA complex of alternately charged lipid bilayers and DNA monolayers in a salt solution. Each lipid bilayer, composed by a random mixture of cationic and neutral lipids, is assumed to be a rigid uniformly charged plane. Each DNA monolayer, located between two lipid bilayers, is formed by the same number of parallel DNAs with a uniform separation distance. For the electrostatic calculation, the model lipoplex is collapsed to a single plane with charge density equal to the net lipid and DNA charge. The free energy difference between the lamellar lipoplex and a reference state of the same number of free lipid bilayers and free DNAs, is calculated as a function of the fraction of CLs, of the ratio of the number of CL charges to the number of negative charges of the DNA phosphates, and of the total number of planes. At the isoelectric point the free energy difference is minimal. The complex formation, already favoured by the decrease of the electrostatic charging free energy, is driven further by the free energy gain due to the release of counterions from the DNAs and from the lipid bilayers, if strongly charged. This minimal model compares well with experiment for lipids having a strong preference for planar geometry and with major features of more detailed models of the lipoplex.

Electrostatic theory of the assembly of PAMAM dendrimers and DNA

“…The total free energy in solution of an isolated charged sphere of radius R having on its surface N positive unit charges for a surface number charge density of is given in the condensation approach by two contributions: …”

“…To help in the determination of the equilibrium minimum, we introduce an approximation for the condensation volume, with A , a proportionality constant in the order of 1, as previously discussed . This equation is reminiscent of the result obtained for a polyelectrolyte rod at equilibrium …”

“…This will be done assuming in Eq. (9) a physical reasonable proportionality constant A , equal to 1 . In Figure the value of the equilibrium counterion condensation per sphere charge, , is reported as a function of l , for spheres of radius chosen to be correspondent to that of dendrimers of generation g = 5, 7, 11 (see Table , column 5).…”

“…Due to the importance of charged spheres in our model of dendrimers and of DNA-dendrimer complexes, we start by quantitatively calculating the free energy of a generic cationic sphere of given radius R and number of positive surface charges N, following the condensation theory approach. For a Electrostatic Theory of the PAMAM Dendrimers and DNA 277 more detailed discussion of this approach and approximations we refer to reference, 14 where we treated the formation of lamellar lipoplexes of alternatively charged planes. We assume a water solution of dielectric constant e 5 80 containing 1:1 salt in excess and characterized by a Debye screening constant j,…”

“…[10][11][12][13] We plan to face in the near future the formation of these complicate dendriplexes by a dedicated electrostatic analytic modeling following the lines of our recent analytical model for the formation of lamellar cationic lipid-DNA lipoplexes. 14 In the actual work we describe analytically the much more simple situation of a dendrimer, treated as a positively charged effective sphere, in the presence of a long DNA. The dendrimer is in a dilute solution in such a way to allow us to describe the electrostatic interactions between a single cationic dendrimer sphere and a single DNA.…”