Information-theoretic uncertainty of SCFG-modeled folding space of the non-coding RNA

Abstract

RNA secondary structure ensembles define probability distributions for alternative equilibrium secondary structures of an RNA sequence. Shannon’s Entropy is a measure for the amount of diversity present in any ensemble. In this work, Shannon’s entropy of the SCFG ensemble on an RNA sequence is derived and implemented in polynomial time for both structurally ambiguous and unambiguous grammars. Micro RNA sequences generally have low folding entropy, as previously discovered. Surprisingly, signs of significantly high folding entropy were observed in certain ncRNA families. More effective models coupled with targeted randomization tests can lead to a better insight into folding features of these families.

Secondary structural entropy in RNA switch (Riboswitch) identification

“…This observation raised the possibility that RNAs under selective pressure to have alternative folds, may have higher (not lower) structural entropy than expected. As discussed previously in [ 55 ], this seemingly nonintuitive observation is not theoretically impossible. The above intuition lies at the center of the proposed methodology, as will be shown.…”

“…Alternative formulations and approximations of Shannon entropy exist in RNA secondary structure studies, such as [ 54 ]. Exact calculations of Shannon entropy under a given SCFG as a probabilistic secondary structural folding model, however, was done in [ 55 ] and shown to be computationally convenient achievable in polynomial time O ( n 3 ), where n is the length of the RNA sequence. In an independent work, [ 56 ] also offered an algorithm to calculate the Shannon entropy of the stochastic context-free grammar BJK [ 57 ] with parameter sets derived from a given alignment.…”

“…Other measures of structural diversity such as ensemble diversity computed by RNAfold -p in the Vienna RNA Software Package [ 58 ] also exist. In this work, structural diversity is measured by the exact RNA secondary structural information theoretic-uncertainty (or here, Shannon entropy) of the complete SCFG-modeled folding space of the RNA, as computed by [ 55 ]. From hereon, we refer to this measure as structural entropy.…”

“…It has been previously shown that both high and low structural entropy values of certain classes of ncRNAs can be potentially significant. For instance, for certain riboswitches, GC-composition was co-associated with significantly high structural entropy, regardless of model accuracy to RNA secondary structure [ 55 ]. This observation raised the possibility that RNAs under selective pressure to have alternative folds, may have higher (not lower) structural entropy than expected.…”

Fighting against uncertainty: an essential issue in bioinformatics

“…example 14 . Actually, most MEG/MEA estimators (Section 3.2) lead to posterior decoding algorithms, because the final algorithm is based on only marginal probabilities.…”