FIG. 8.

(Color online) (a) Equilibrium energy of a hairpin with sequence A-TTTT-T. This hairpin has an internal loop comprising four T’s and a stem with a single base pair A-T. Differently from Fig. 3, we consider that the stacking energy of the T’s is zero. Under these conditions, a hairpin configuration can only take four energy values, ε=-3, when the hairpin is closed (A-T hydrogen bond is formed) and A is stacked with its neighboring T; ε=-2, when the A is stacked with its neighboring T and the hairpin is open; ε=-1, when the hairpin is closed but there is no stacking between the A and its neighboring T; ε=0, for all other cases. Under these conditions, the exact number of configurations for each energy level, g_i, can be computed. (b) Occupation number 〈n_i(T)〉 of each energy level, i=0 to -3, as a function of temperature. Colored dots indicate the numerical results obtained from averages over 5 000 000 Monte Carlo steps (MCS) using the parallel tempering MC method [80]. Purple solid lines correspond to the theoretical expressions for the energy $e={\Sigma }_i{∊}_i{g}_i{e}^{-{∊}_i∕T}∕\mathcal{Z}$ in (a), and the occupation number $\langle n_i\left(T\right)\rangle =g_i{e}^{-{∊}_i∕T}∕\mathcal{Z}$ in (b), where $\mathcal{Z}={\Sigma }_i{g}_i{e}^{-{∊}_i∕T}$ is the partition function. Note the excellent agreement between theoretical predictions and simulation results.