FIGURE 2.

Physicochemical rationale for GapmeR (GR) compaction into lamellar liquid crystal cholesteric phases composed by DC-cholesterol (DChol) under high density Coulombic condensation. (A) Molecular GR construct as a 16 base-pair oligonucleotide; LNA-flanked, single-stranded DNA with the L-PGDS gene-silencing sequence (see Materials for details). Despite electrolytic dissociation of the nucleic acid phosphates ( $p{K}_a\approx 2$ ), each GR strand appears globally with the electrostatic structure as a rigid rod polyanion; coarse-grained dimensions (16 base-pairs): $L_{GR}\approx \mathrm{5,5}nm$ length ( $l_0\approx 0.34nm$ per bp); $D_0\approx 1nm$ diameter. Topological GR parameters (per reactive anionic group (PO₄ ⁻); 1bp): specific rod area $A_0^{GR}\approx {\pi D}_0{l}_0\approx 1{nm}^2$ ; laterally exposed area per anion $a_0^{GR}\approx \pi l_0^2\approx 0.4{nm}^2\ll A_0^{GR}$ ; and nominal charge density ${\sigma }_{GR}=-e/A_0^{GR}\approx -e/{nm}^2$ . (B) Amphiphilic structure of the DC-cholesterol (DChol) molecule, as constituted by the steroidal hydrophobic moiety linked to a hydrophilic counterpart by a tail terminated in the cationic quaternary dimethylammonium head group (Me₂N⁺–), endowed of a large cross-sectional area ( $a_0\approx 1{nm}^2$ ) and a strong basic characteristic ( $p{K}_a\approx 9.3$ ). Approximated molecular dimensions (for DChol chloride; M.W. 537.3 g mol⁻¹; solid density ${\rho }_0\approx 1g/{cm}^3$ ): specific volume $v_0\approx 0.9{nm}^3$ ; Me₂N⁺–head group area $a_0^{DChol}\approx 0.5{nm}^2$ ; nominal charge density ${\sigma }_{DChol}=+e/a_0^{DChol}\approx +2e/{nm}^2$ ; head-to-tail molecular length $D_1\approx 2nm$ ; and aspect ratio $\alpha =v_0/a_0{l}_0\approx 0.9$ , predicting a cylinder-like aspect; bilayer former). (C) GR-DChol lipoplexing as promoted at high-compaction inside Bjerrum cages in a low-permittivity dielectric medium (left panel); the Bjerrum length is assumed to have a size comparable to the charged rod length ( ${\lambda }_B\approx L_{GR}$ ), much larger than the elemental charge size ( ${\lambda }_0\gg l_0$ ). A lamellar GR-DChol structure promoted by Manning condensation under steroidal mesogenicity is proposed (right panel). Expected topological lipoplex stoichiometry: $a_0^{GR}\approx a_0^{DChol}$ and ${\sigma }_{DChol}\approx -2{\sigma }_{GR}$ , suggesting a chemical formula as two DChol per GR with a bilayer organization for the DChol molecule. Because of the strong acid–base reactivity between GR and DChol, a catanionic 2:1 stoichiometry is assumed under the Coulombic assembly underlying the lamellar bilayer structure (GR: DChol₂). Lamellar lipoplex dimensions: The anionic component condensates into parallel GR-monolayers, with a thickness of $D_{GR}\approx D_0\approx 1nm$ , which are electrostatically “cemented” by intercalated bilayers made of cationic DChol, with a thickness of $D_{bil}\approx {2D}_1\approx 4nm$ . The resulting lamellar spacing expected in Manning-condensing media is expected; therefore, $D\approx D_{GR}+D_{bil}\approx D_0+{2D}_1\approx 5nm$ , in agreement with experimental ultrastructural observations (in Figure 4).