Locality and gaps in RNA comparison

Locality is an important and well-studied notion in comparative analysis of biological sequences. Similarly, taking into account affine gap penalties when calculating biological sequence alignments is a well-accepted technique for obtaining better alignments. When dealing with RNA, one has to take into consideration not only sequential features, but also structural features of the inspected molecule. This makes the computation more challenging, and usually prohibits the comparison only to small RNAs. In this paper we introduce two local metrics for comparing RNAs that extend the Smith-Waterman metric and its normalized version used for string comparison. We also present a global RNA alignment algorithm which handles affine gap penalties. Our global algorithm runs in O(m²n(1 + lg n/m)) time, while our local algorithms run in O(m²n(1 + lg n/m)) and O(n²m) time, respectively, where m ≤ n are the lengths of the two given RNAs. These time complexities are comparable to the time complexity of any known RNA alignment algorithm. Furthermore, both our global and local algorithms are robust to selections of arbitrary scoring schemes.