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Fig. 5 | BMC Bioinformatics

Fig. 5

From: RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory

Fig. 5

Analysis of expected free energy 〈E〉 for structures in Rfam 12.0 [24]. Given a secondary structure s, the expected free energy of all sequences a with respect to s is defined by \(\langle E(s) \rangle = \sum _{\mathbf {a}} E(\mathbf {a},s) \cdot \frac {\exp (-E(\mathbf {a},s)/RT)}{Z^{*}(\mathbf {a},s)}\), where Z is the dual partition function defined in equation (7). For each Rfam family, we took the family consensus structure s c , and computed 〈E(s c )〉. Additionally, for each Rfam family, we selected that sequence a 0, whose minimum free energy (MFE) structure s 0 has smallest base pair distance to the consensus structure s c . The expected energy 〈E(s 0)〉 was computed, as well as the free energies E(a,s c ) and E(a,s 0). The fold change \(\frac {\langle E(s_{c}) \rangle }{E(\mathbf {a}_{0},s_{c})}\) for the consensus structure and the fold change \(\frac {\langle E(s_{0}) \rangle }{E(\mathbf {a}_{0},s_{0})}\) for the minimum free energy structure were computed. The box-and-whiskers plots show the mean, 25th and 75th percentile, minimum and maximum values. As indicated in the legend, these computations were performed either with respect to all sequences or with respect to all sequences having the same (exact) GC-content. These data clearly indicate that natural RNA sequences, whose MFE structures most closely resemble the Rfam consensus structures, have higher free energy than expected

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