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.

Defense against genome invaders universally relies on RNA-guided immunity. Prokaryotic CRISPR-Cas and eukaryotic RNA interference pathways recognize targets by complementary base-pairing, which places the sequences of their guide RNAs at the center of self/nonself discrimination. Here, we explore the sequence space of PIWI-interacting RNAs (piRNAs), the genome defense of animals, and establish functional priority among individual sequences. Our results reveal that only the topmost abundant piRNAs are commonly present in every cell, whereas rare sequences generate cell-to-cell diversity in flies and mice. We identify a skewed distribution of sequence abundance as a hallmark of piRNA populations and show that quantitative differences of more than a 1000-fold are established by conserved mechanisms of biogenesis. Finally, our genomics analyses and direct reporter assays reveal that abundance determines function in piRNA-guided genome defense. Taken together, we identify an effective sequence space and untangle two classes of piRNAs that differ in complexity and function. The first class represents the topmost abundant sequences and drives silencing of genomic parasites. The second class sparsely covers an enormous sequence space. These rare piRNAs cannot function in every cell, every individual, or every generation but create diversity with potential for adaptation in the ongoing arms race with genome invaders.

BackgroundRNA regulatory elements play a significant role in gene regulation. Riboswitches, a widespread group of regulatory RNAs, are vital components of many bacterial genomes. These regulatory elements generally function by forming a ligand-induced alternative fold that controls access to ribosome binding sites or other regulatory sites in RNA. Riboswitch-mediated mechanisms are ubiquitous across bacterial genomes. A typical class of riboswitch has its own unique structural and biological complexity, making de novo riboswitch identification a formidable task. Traditionally, riboswitches have been identified through comparative genomics based on sequence and structural homology. The limitations of structural-homology-based approaches, coupled with the assumption that there is a great diversity of undiscovered riboswitches, suggests the need for alternative methods for riboswitch identification, possibly based on features intrinsic to their structure. As of yet, no such reliable method has been proposed.ResultsWe used structural entropy of riboswitch sequences as a measure of their secondary structural dynamics. Entropy values of a diverse set of riboswitches were compared to that of their mutants, their dinucleotide shuffles, and their reverse complement sequences under different stochastic context-free grammar folding models. Significance of our results was evaluated by comparison to other approaches, such as the base-pairing entropy and energy landscapes dynamics. Classifiers based on structural entropy optimized via sequence and structural features were devised as riboswitch identifiers and tested on Bacillus subtilis, Escherichia coli, and Synechococcus elongatus as an exploration of structural entropy based approaches. The unusually long untranslated region of the cotH in Bacillus subtilis, as well as upstream regions of certain genes, such as the sucC genes were associated with significant structural entropy values in genome-wide examinations.ConclusionsVarious tests show that there is in fact a relationship between higher structural entropy and the potential for the RNA sequence to have alternative structures, within the limitations of our methodology. This relationship, though modest, is consistent across various tests. Understanding the behavior of structural entropy as a fairly new feature for RNA conformational dynamics, however, may require extensive exploratory investigation both across RNA sequences and folding models.