2010/06/21 by Thomas J. X. Li, Li, Thomas J. X., Christian M. Reidys +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Genomics and Chromatin Dynamics #RNA Research and Splicing #RNA and protein synthesis mechanisms #math.CO #msc:05A16 #msc:92E10 #q-bio.BM #q-bio.QM
paper · pdf · doi:10.48550/arxiv.1006.4089
22 pages, 15 figures
arxiv created 2010/06/21 · arxiv updated 2010/06/22
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.