Analytical model study of dendrimer/DNA complexes

The interaction between positively charged poly(amido amine) (PAMAM) dendrimers of generation 4 and DNA has been investigated for two DNA lengths; 2000 basepairs (bp; L = 680 nm) and 4331 bp (L = 1472.5 nm) using a theoretical model by Schiessel for a semiflexible polyelectrolyte and hard spheres. The model was modified to take into account that the dendrimers are to be regarded as soft spheres, that is, the radius is not constant when the DNA interact with the dendrimer. For the shorter and longer DNA, the estimated optimal wrapping length, l(opt) is ≈15.69 and ≈12.25 nm, respectively, for dendrimers that retain their original size (R(o) = 2.25 nm) upon DNA interaction. However, the values of l(opt) for the dendrimers that were considered to have a radius of (R = 0.4R(o)) 0.9 nm were 9.3 and 9.4 nm for the short and long DNA, respectively, and the effect due to the DNA length is no longer observed. For l(opt) = 10.88 nm, which is the length needed to neutralize the 64 positive charges of the G4 dendrimer, the maximum number of dendrimers per DNA (N(max)) was ≈76 for the shorter DNA, which is larger than the corresponding experimental value of 35 for 2000 bp DNA. For the longer DNA, N(max) ≈ 160, which is close to the experimental value of 140 for the 4331 bp DNA. Charge inversion of the dendrimer is only observed when they retain their size or only slightly contract upon DNA interaction.