### abstract ###
RNA molecules will tend to adopt a folded conformation through the pairing of bases on a single strand; the resulting so-called secondary structure is critical to the function of many types of RNA.
The secondary structure of a particular substring of functional RNA may depend on its surrounding sequence.
Yet, some RNAs such as microRNAs retain their specific structures during biogenesis, which involves extraction of the substructure from a larger structural context, while other functional RNAs may be composed of a fusion of independent substructures.
Such observations raise the question of whether particular functional RNA substructures may be selected for invariance of secondary structure to their surrounding nucleotide context.
We define the property of self containment to be the tendency for an RNA sequence to robustly adopt the same optimal secondary structure regardless of whether it exists in isolation or is a substring of a longer sequence of arbitrary nucleotide content.
We measured degree of self containment using a scoring method we call the self-containment index and found that miRNA stem loops exhibit high self containment, consistent with the requirement for structural invariance imposed by the miRNA biogenesis pathway, while most other structured RNAs do not.
Further analysis revealed a trend toward higher self containment among clustered and conserved miRNAs, suggesting that high self containment may be a characteristic of novel miRNAs acquiring new genomic contexts.
We found that miRNAs display significantly enhanced self containment compared to other functional RNAs, but we also found a trend toward natural selection for self containment in most functional RNA classes.
We suggest that self containment arises out of selection for robustness against perturbations, invariance during biogenesis, and modular composition of structural function.
Analysis of self containment will be important for both annotation and design of functional RNAs.
A Python implementation and Web interface to calculate the self-containment index are available at LINK.
### introduction ###
Our understanding of the significance of noncoding RNAs has increased dramatically over the last decade, notably marked by the discovery of the endogenously coded microRNAs CITATION CITATION.
Along with the increased awareness of the diversity of ncRNAs has come a corresponding heightened attention to RNA sequence and structural measures with which to characterize known and novel RNAs.
The secondary structure of an RNA, consisting of the energy-minimizing base interactions along the length of the molecule, has a direct effect on its function CITATION, a fact that has been well-characterized for a variety of RNA classes.
Ribosomal RNAs are among the largest examples that illustrate the functional importance of RNA structure several rRNAs along with associated proteins assemble into the large and small subunits of the ribosome, with the structural specificity to direct protein translation CITATION.
The cloverleaf transfer RNA structure allows it to associate with the ribosome and properly orient its bound amino acid during aminoacylation CITATION.
Various small nuclear RNAs and small nucleolar RNAs are involved in RNA editing and splicing on the basis of their shape specificity CITATION, CITATION, while the stem-loop structure of precursor miRNAs allows them to be recognized by the ribonuclease Dicer during the miRNA maturation process CITATION.
Structure-derived functionality is not limited to nonprotein coding RNAs; however, some messenger RNAs contain structural regulatory motifs, such as the hairpin selenocysteine insertion sequence that occurs predominantly in the 3 untranslated regions of mRNAs coding for selenoproteins CITATION and the internal ribosome entry site in viral 5 UTRs that promotes translation initiation in the middle of the mRNA CITATION.
Additionally, recognition of specific mRNAs by RNA binding proteins as well as pre-mRNA splicing all involve molecular interactions of the folded RNA structure CITATION, CITATION .
The importance of structural specificity is not limited to the end product sequence and structural specificity during various stages of RNA biogenesis are also critical.
Eukaryotic tRNAs, for example, are transcribed as longer precursor transcripts, which are recognized and cleaved on both the 5 and 3 ends by RNaseP and an uncharacterized endonuclease, respectively CITATION, CITATION ; some tRNAs also contain introns, which disrupt the canonical cloverleaf structure and are spliced out before the mature tRNA is exported out of the nucleus CITATION, CITATION.
The eukaryotic 18S, 5.8S, and 28S rRNAs are transcribed as a single unit and subsequently cleaved apart CITATION, CITATION.
The hammerhead ribozyme is an example of a self-splicing RNA, such that its three helices mediate cleavage of a motif that occurs on the same RNA molecule CITATION .
In the case of miRNAs, biogenesis begins with the transcription of long primary transcripts, which fold into large structures that serve as substrates for the endonuclease Drosha CITATION.
Drosha, in complex with Pasha to form the Microprocessor complex, recognizes specific hairpin substructures in the pri-miRNA and cleaves them at the base of the helical stem region, yielding the pre-miRNA hairpins CITATION, CITATION.
These range in size from 60 120 nucleotides and are subsequently processed by Dicer, which targets the pre-miRNAs on the basis of their hairpin shape CITATION, CITATION.
miRNAs are notable in that the sequence of the pre-miRNA hairpin remains a robust structure through these biogenesis steps, regardless of the sequence context: when embedded in the larger primary sequence, the pre-miRNA subsequence folds into a hairpin, and when it is cleaved off to form an independent unit, the sequence folds into the same hairpin CITATION .
The need for context-independent structural conservation, as exemplified by the miRNA biogenesis pathway, is a hallmark of a broader phenomenon of modular composability i.e., the generation of biopolymers through combinatorial composition of structural motifs.
It is now well recognized that novel proteins can arise from shuffling of structural domains, the most vivid example being circularly permuted proteins CITATION, CITATION.
Given the critical role of structural features in RNA function and the already recognized motifs as compiled in databases such as RFAM CITATION, it is conceivable that many RNAs might also have arisen from evolutionary steps of domain shuffling and domain fusions.
Such a process would require that the novel molecule reach a folded state that is a composition of the structural features of its parts i.e., the structural features of the combinatorial pieces need to be invariant to composition with other sequences.
On the one hand, structural context robustness may be a product of the specific relationship between each sequence and its genomic context, a property that has been exploited in computational miRNA finders such as in CITATION.
On the other hand, certain subsequences may have some intrinsic tendency to be structurally indifferent to their surrounding sequence, irrespective of the particular identity of that surrounding sequence e.g., a pre-miRNA would still be structurally robust if it were inserted into a different context.
We call this property of intrinsic structural invariance self containment.
A self-contained structural RNA has the potential to be a modular building block in a larger structure, carry out consistent function through biochemical modifications of surrounding sequences, and potentially maintain function when inserted into novel contexts, as might occur with viral elements.
Previously, while studying the general mutational robustness of 170 structural elements of RNA viral genomes, Wagner and Stadler found that there was a trend toward higher structural robustness in conserved elements than in nonconserved elements when placed in short nongenomic contexts CITATION.
Using a similar approach, Ancel and Fontana studied the intrinsic context insensitivity of a set of canalized artificial RNAs, selected to have reduced environmental plasticity, and found a positive relationship between environmental canalization and modularity CITATION.
Other work in RNA and proteins suggests that there is an intimate relationship between mutational robustness and domain modularity with folding kinetics, thermodynamic stability, as well as other biogenerative processes.
In this work, we analyze self containment over a broad range of biological RNAs using an intuitive scoring method to quantify different degrees of context robustness.
We show that in fact pre-miRNAs do exhibit a high degree of intrinsic self containment, while most other biologically relevant RNAs tend not to show such self containment.
We relate self containment to other sequence and structural features of RNA and find that no simple combination of features can completely explain self containment.
Finally, we show that variation among miRNAs in degree of self containment is correlated with genomic location and miRNA-family membership, as well as their biogenerative process, as illustrated by miRNAs produced by the alternate mirtron pathway.
We propose that high self containment is an intrinsic property of particular RNA sequences and may be an evolutionarily selected characteristic in molecules that need to maintain structural robustness for some aspect of their function in the face of genetic perturbations, generative perturbations, and modular composition in combinatorial contexts.
