Structural diversity comparison between ensemble of locally optimal structures and Boltzmann ensemble of all structures.

Given the collection of base pairing probabilities over all locally optimal structures [resp. over all structures] of a given RNA sequence , we define four measures of structural diversity. (1) The pseudo-entropy is defined by . (2) The average entropy is defined by . (3) The Morgan-Higgs structural diversity is defined by , where we define . (4) The Vienna structural diversity is defined by . In the table above, we consider these measures with respect to locally optimal structures (L) and with respect to all (M) structures. (‘L’ stands for locally optimal, and ‘M’ for McCaskill.) The table depicts the number of structures for each Rfam family considered, as well as the correlation coefficient between pseudo-entropy and average entropy. The families in the table are: RF00001 (5S-rRNA), RF00003 (U1), RF00004 (U2), RF00005 (tRNA), RF00008 (hammerhead type III ribozyme), RF00017 (eukaryotic type signal recognition particle), RF00031 (selenocysteine insertion sequence), RF00050 (FMN riboswitch aptamer), RF00059 (TPP riboswitch aptamer), RF00162 (SAM riboswitch aptamer), RF00167 (purine riboswitch aptamer), RF00168 (lysine riboswitch aptamer), RF00174 (cobalamin riboswitch aptamer), and RF00380 (ykoK leader). Although we demonstrated a markedly lower structural diversity for locally optimal structures for precursor microRNAs, the data is not shown.