Free energy of interaction between 50 bp B-DNA double helices at 7 Å Debye screening length. (A) Effects of thermal rotation, twisting, and stretching of the helix on the pair interaction energy (θ = 0.8, f1 = 0.25, f2 = 0.5). (B) Effects of bound counterions partitioning between the middle of the minor groove (f1), middle of the major groove (f2), and random locations (1–f1–f2) on the pair interaction energy (θ = 0.8). (C and D) Interaction free energy per molecule in DNA pairs (C) and hexagonal, columnar aggregates (D) at different neutralization of DNA charge (θ) by bound counterions (f1 = 0.1, f2 = 0.9). (B–D) We accounted for thermal rotation, twisting, and stretching of the helix, using = 350 Å helical persistence length.