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Combinatorial analysis of interacting RNA molecules
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 backbones drawn horizontally on top of each other such that (1)
intramolecular and intermolecular bonds are noncrossing and (2) there is no
"zig-zag" configuration. This paper studies joint structures with arc-length at
least four in which both, interior and exterior stack-lengths are at least two
(no isolated arcs). The key idea in this paper is to consider a new type of
shape, based on which joint structures can be derived via symbolic enumeration.
Our results imply simple asymptotic formulas for the number of joint structures
with surprisingly small exponential growth rates. They are of interest in the
context of designing prediction algorithms for RNA-RNA interactions.Comment: 22 pages, 15 figure
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