Intercalation of cationic dyes in the DNA double helix: introductory theory

The effect of salt on the intercalation of acridine dyes and DNA is rather well explained by the Gouy-Chapman double-layer theory as applied to a cylinder model of the DNA–dye complex. The free energy of transfer of a dye ion from the bulk solution to the complex is divided into several parts, one of which, ΔF₀, accounts for the short-range, nonelectrostatic interactions. The assumption that ΔF₀ should not depend on the amount of dye in the complex leads to an internal dielectric constant of the cylinder of about D_i = 7. The scatter in ΔF₀ values, as calculated from individual experimental points, is of order 0.5 kT per dye ion. This scatter is large enough to mask possible effects of heterogeneity in DNA sequences. The calculations are made for a long cylinder with radius 10 Å, with the DNA phosphate charges smeared uniformly at the surface, a uniform spacing of dye charges at the cylinder axis, and a length of b = 3.37 Å per base pair. Each intercalated dye ion also adds a length b to the total length of the cylinder. The salt-dependent part of the electric free energy of intercalation, ΔF₁, is tabulated for complexes with r = 0–0.24 dye ions per DNA phosphate in 0.002–0.2M monovalent salt and dye solutions.