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(m(2)n(1 + lg n/m)) time, while our local algorithms run in O(m(2)n(1 + lg n/m)) and O(n(2)m) time, respectively, where m

Gene proximity analysis across whole genomes via PQ trees.

Permutations on strings representing gene clusters on genomes have been studied earlier by Uno and Yagiura (2000), Heber and Stoye (2001), Bergeron et al. (2002), Eres et al. (2003), and Schmidt and Stoye (2004) and the idea of a maximal permutation pattern was introduced by Eres et al. (2003). In this paper, we present a new tool for representation and detection of gene clusters in multiple genomes, using PQ trees (Booth and Leuker, 1976): this describes the inner structure and the relations between clusters succinctly, aids in filtering meaningful from apparently meaningless clusters, and also gives a natural and meaningful way of visualizing complex clusters. We identify a minimal consensus PQ tree and prove that it is equivalent to a maximal pi pattern (Eres et al., 2003) and each subgraph of the PQ tree corresponds to a nonmaximal permutation pattern. We present a general scheme to handle multiplicity in permutations and also give a linear time algorithm to construct the minimal consensus PQ tree. Further, we demonstrate the results on whole genome datasets. In our analysis of the whole genomes of human and rat, we found about 1.5 million common gene clusters but only about 500 minimal consensus PQ trees, with E. Coli K-12 and B. Subtilis genomes, we found only about 450 minimal consensus PQ trees out of about 15,000 gene clusters, and when comparing eight different Chloroplast genomes, we found only 77 minimal consensus PQ trees out of about 6,700 gene clusters. Further, we show specific instances of functionally related genes in two of the cases.