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Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc- and stack-length restrictions. Our main result reads as follows: in the simplex of the nucleotide ratios there exists a convex region in which, in the limit of long sequences, a random structure a.a.s.~has compatible sequence with these ratios and outside of which a.a.s.~a random structure has no such compatible sequence. We localize this region for RNA secondary structures subject to various base pairing rules and minimum arc- and stack-length restrictions. In particular, for {bf GC}-sequences having a ratio of {bf G} nucleotides smaller than $1/3$, a random RNA secondary structure without any minimum arc- and stack-length restrictions has a.a.s.~no such compatible sequence. For sequences having a ratio of {bf G} nucleotides larger than $1/3$, a random RNA secondary structure has a.a.s. such compatible sequences. We discuss our results in the context of various families of RNA structures.
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological structures having
Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backb
A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological g
In this paper we analyze the length-spectrum of rainbows in RNA secondary structures. A rainbow in a secondary structure is a maximal arc with respect to the partial order induced by nesting. We show that there is a significant gap in this length-spe
We show the expected order of RNA saturated secondary structures of size $n$ is $log_4n(1+O(frac{log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures is sharply co