Fig. 13.

a$M{S}_1$- and $M{S}_2$-degree distribution for the 65 nt fourU RNA from Klebsiella pneumoniae subsp. pneumoniae with sequence GGACAAGCAA UGCUUGCCUU UAUGUUGAGC UUUUGAAUGA AUAUUCAGGA GGUUAAUUAU GGCAC and EMBL accession code CP000647.1/1773227-1773291. FourU RNA is a class of thermometers found in bacteria such as E. coli, Salmonella, V. cholerae, etc. that regulate protein expression by undergoing a conformation change triggered by temperature—for instance, the conformational change of the V. cholerae fourU thermometer at ${37}^{\circ }$C permits the transcription of a virulence factor. All 1,079,102 secondary structures having free energy within 13 kcal/mol of the minimum free energy (MFE) of this RNA were generated using RNAsubopt from the Vienna RNA Package (Lorenz et al. 2011). The $M{S}_1$ and $M{S}_2$ degree of each secondary structure were determined in order to produce the degree relative frequency histogram. Although the collection of structures having free energy within ${13}^{\circ }$C of the MFE contains over one million structures (computation required 1–2 days), there are 1995457849526533 ($\approx 1.99546\times {10}^{15}$) many secondary structures altogether. The average $M{S}_1$ degree is 38.0, while the average $M{S}_2$ degree is 64.2. FourU$M{S}_1$analysis: Using RNApowerlaw, $x_{\min }=93$, $\alpha =6.02$, and p value is 0 (to 10 decimal places). Using powerlaw, $x_{\min }=96$, $\alpha =6.02$, and the log ratio of power-law fit to log-normal fit is $R=-23.6283$ with corresponding p value of $1.77\times {10}^{-4}$—in other words, a log-normal distribution provides a significantly better fit than a power-law distribution for the $M{S}_1$ degree data of this fourU RNA. FourU$M{S}_2$analysis: Using RNApowerlaw, $x_{\min }=85$, $\alpha =6.159$, and p value is 0 (to 10 decimal places). Using powerlaw, $x_{\min }=85$, $\alpha =6.159$, and the log ratio of power-law fit to log-normal fit is $R=-122.1518$ with corresponding p value of $5.9389\times {10}^{-20}$—in other words, a log-normal distribution provides a significantly better fit than a power-law distribution for the $M{S}_2$ degree data of this fourU RNA. b$M{S}_1$- and $M{S}_2$-degree distribution for the 76 nt alanine transfer RNA from Mycoplasma mycoides with accession code tdbR00000006 from tRNAdb (Juhling et al. 2009) (accession code RA1180 from the Sprinzl tRNA database) with sequence GGGCCCUUAG CUCAGCUGGG AGAGCACCUG CCUUGCACGC AGGGGGUCGA CGGUUCGAUC CCGUUAGGGU CCACCA. All 408414 secondary structures having free energy within 13 kcal/mol of the minimum free energy of this RNA were generated using RNAsubopt from the Vienna RNA Package (Lorenz et al. 2011). The MS1 and MS2 degree of each secondary structure were determined in order to produce the degree relative frequency histogram. Although the collection of secondary structures having free energy within ${13}^{\circ }$C of the MFE contains about one-half million structures (computation required 1-2 days), there are 877346780605139050 ($\approx 8.77347\times {10}^{17}$) many secondary structures altogether. The average $M{S}_1$ degree is 38.1, while the average $M{S}_2$ degree is 68.3. tRNA$M{S}_1$analysis: Using RNApowerlaw, $x_{\min }=36$, $\alpha =5.1419$, and p value is 0 (to 10 decimal places). Using powerlaw, $x_{\min }=36$, $\alpha =5.1419$, and the log ratio of power-law fit to log-normal fit is $R=-95.3556$, with corresponding p value of $1.6193\times {10}^{-16}$—in other words, a log-normal distribution provides a significantly better fit than a power-law distribution for the $M{S}_1$ degree data of this fourU RNA. tRNA$M{S}_2$analysis: Using RNApowerlaw, $x_{\min }=114$, $\alpha =7.0845$ and p value is 0 (to 10 decimal places). Using powerlaw, $x_{\min }=122$, $\alpha =7.1352$, and the log ratio of power-law fit to log-normal fit is $R=-41.1935$ with corresponding p value of $5.0374\times {10}^{-6}$—in other words, a log-normal distribution provides a better fit than power-law for the $M{S}_{2}2$ degree data of this tRNA (color figure online)