Figure 2

Boltzmann density plot for RNAbor , along with approximating relative frequency plots for RNAborMEA and RNAlocopt for the 101 nt RNA sequence UACUUAUCAA GAGAGGUGGA GGGACUGGCC CGCUGAAACC UCAGCAACAG AACGCAUCUG UCUGUGCUAA AUCCUGCAAG CAAUAGCUUG AAAGAUAAGU U for the SAM riboswitch aptamter with GenBank accession code AP004597.1/118941-119041. The program RNAbor computes the Boltzmann probability $p_k=\frac{Z_k}{Z}$, where $Z_k={\sum }_{\left\{S:d_{BP}\left(S,S_0\right)=k\right\}}\text{exp}\left(-E\left(S\right)/RT\right)$, where S₀ is the initial structure (taken as the minimum free energy here). The script RNAbor-Sample calls Sfold on 1000 structures, in order to compute a relative frequence f _k ≈ p _k of all k-neighbors of S₀. Finally, we compute relative frequency of RNAlocopt[34], a program that samples only locally optimal secondary structures, having the property that one cannot obtain a lower energy structure by adding or removing a single base pair.