  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.

Combinatorics;Biomolecules;Quantitative Methods