Permutation Pattern Discovery in Biosequences

Abstract

Functionally related genes often appear in each others neighborhood on the genome, however the order of the genes may not be the same. These groups or clusters of genes may have an ancient evolutionary origin or may signify some other critical phenomenon and may also aid in function prediction of genes. Such gene clusters also aid toward solving the problem of local alignment of genes. Similarly, clusters of protein domains, albeit appearing in different orders in the protein sequence, suggest common functionality in spite of being nonhomologous. In the paper we address the problem of automatically discovering clusters of entities be it genes or domains: we formalize the abstract problem as a discovery problem called the πpattern problem and give an algorithm that automatically discovers the clusters of patterns in multiple data sequences. We take a model-less approach and introduce a notation for maximal patterns that drastically reduces the number of valid cluster patterns, without any loss of information, We demonstrate the automatic pattern discovery tool on motifs on E Coli protein sequences.

Improved online algorithms for jumbled matching

“…Jumbled pattern matching has numerous applications in the field of bioinformatics, such as alignments of sequences [3], SNP discovery [5], discovery of repeated patterns [21], interpretation of mass spectrometry data [4] and permutation pattern discovery in biosequences [21].…”

“…In the case of discovery of repeated patterns [21], jumbled matching algorithms can be used to solve the problem of local alignment of genes.…”

Computing abelian complexity of binary uniform morphic words

“…On the one hand, the factor complexity of a given infinite word w is a function ρ w : N → N that maps an integer n to the number of distinct factors of w of length n. On the other hand, the abelian complexity of w is a function ρ ab w : N → N that maps an integer n to the number of distinct Parikh vectors of factors of w of length n. Parikh vectors, which appear in the literature under various names such as compomers [5,6], jumbled patterns [8,7], permutation patterns [9,18,24], commutative closures [19], content vectors [19], to name a few, are vectors that record the frequency of each letter in the factors. So the abelian complexity counts the number of distinct factors of a given length up to letter permutation.…”

Statistical Significance of Large Gene Clusters

“…It turns out that the collection of sub-clusters S has an elegant form that can be captured as a nested structure (Eres et al, 2004) or a PQ tree (Landau et al, 2005), a data structure that was originally Computational Biology Center, IBM T.J. Watson Research Center, Yorktown Heights, New York.…”