Figure 2.

TF-DNA binding free-energy difference normalized per basepair, $\Delta f=\beta \langle \Delta \mathcal{F}\rangle /\mathcal{M}$, computed using Eq. 7 as a function of the reduced design temperature, $1/{\beta }_{d}J$ (solid curves). The upper and lower branches of the graph correspond to $J<0$ (antiferromagneticlike DNA sequence correlations) and $J>0$ (ferromagneticlike correlations), respectively. The results of MC simulations of the system are in excellent agreement with the analytical results (solid circles). We used the parameters $\beta K=1$, $\mathcal{M}=18$, and $L=1000$. In Monte Carlo simulations, we used 7.5 × 10⁶ MC moves to design each DNA sequence at each value of T_d. To generate each point in the plot, we used a set of 100 sequences. To compute error bars, we divided each set of 100 sequences randomly into 10 subsets, and then calculated the SD of the subset averages for $\Delta f$. The error bars correspond to 1 SD. The numerically computed quenched average, $-\langle \ln \left(Z/Z_{\infty }\right)\rangle /\mathcal{M}$, is also shown (solid squares). In the computations, we used the same parameters and definitions as specified above. (Inset) Same data for $\Delta f$ as in the main figure, but plotted as a function of ξ.