Large deviation principles and evolutionary multiple structure alignment of non-coding RNA

Non-coding RNA are functional molecules that are not translated into proteins. Their function comes as important regulators of biological function. Because they are not translated, they need not be as stable as other types of RNA. The TKF91 Structure Tree from Holmes 2004 is a probability model that effectively describes correlated substitution, insertion, and deletion of base pairs, and found to have some worth in understanding dynamic folding patterns. In this paper, we provide a new probabilistic analysis of the TKF91 Structure Tree. Large deviation principles on stem lengths, helix lengths, and tree size are proved. Additionally, we give a new alignment procedure that constructs accurate sequence and structural alignments for sequences with low identity for a dense enough phylogeny.