Figure 3.

Phase states of DNA aggregates. (a) Potts state: The molecules have the same set of three different helical phases Φ̄⁽¹⁾, Φ̄⁽²⁾ and Φ̄⁽³⁾ (Φ̄⁽¹⁾ -Φ̄⁽²⁾ = Φ̄⁽³⁾ -Φ̄⁽¹⁾ = Ψ_p) within each triangle of the hexagonal lattice (top picture). (b) Ferro state: All molecules have the same helical phase (Ψ_p =0). (c) Random state: The helical phases are random. Color contour plots illustrate the dependence of the free energy F_DNA (in log scale) on Ψ_p and normalized structural adaptation length ( ${\lambda }_h^{\ast }/2{\lambda }_c$, Eq. (34)). Bottom graphs show the dependence of F_DNA on ${\lambda }_h^{\ast }/2{\lambda }_c$ at Ψ_p =0; the insets enlarge the boxed, shaded regions. F_DNA may have up to three distinct minima: ${\lambda }_h^{\ast }/2{\lambda }_c\sim 0.1$ and Ψ_p ~ ± π/4 is the Potts state [global minimum in (a)]; ${\lambda }_h^{\ast }/2{\lambda }_c\sim 1$ and Ψ_p = 0 is the ferro state [global minimum in (b), local minimum in (a) and (c)]; ${\lambda }_h^{\ast }/2{\lambda }_c\to \infty$ and arbitrary Ψ_p is the random state [global minimum in (c), local minimum in (a) and (b)]. The calculations were performed at θ = 0.7 and f₁=f₂=0 with the same values of other parameters as in Fig. 2.