Local Exact Pattern Matching for Non-Fixed RNA Structures

Detecting local common sequence-structure regions of RNAs is a biologically important problem. Detecting such regions allows biologists to identify functionally relevant similarities between the inspected molecules. We developed dynamic programming algorithms for finding common structure-sequence patterns between two RNAs. The RNAs are given by their sequence and a set of potential base pairs with associated probabilities. In contrast to prior work on local pattern matching of RNAs, we support the breaking of arcs. This allows us to add flexibility over matching only fixed structures; potentially matching only a similar subset of specified base pairs. We present an
$O(n^3)$
algorithm for local exact pattern matching between two nested RNAs, and an
$O(n^3\ \log\ n)$
algorithm for one nested RNA and one bounded-unlimited RNA. In addition, an algorithm for approximate pattern matching is introduced that for two given nested RNAs and a number
$k$
, finds the maximal local pattern matching score between the two RNAs with at most
$k$
mismatches in
$O(n^3k^2)$
time. Finally, we present an
$O(n^3)$
algorithm for finding the most similar subforest between two nested RNAs.