Aligning Circularly Ordered Lists. Why would anyone want to do that? Peter F. STADLER

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1 Aligning Circularly Ordered Lists Why would anyone want to do that? Peter F. STADLER Bioinformatics, Department of Computer Science University of Leipzig, Germany External Faculty: Institute f. Theoretical Chemistry & Structural Biology, University of Vienna, Austria Santa Fe Institute Bled, Villa Plemelj, Feb , 2004

2 The Footprint Sorting Problem Linearly ordered list of objects (footprints in this case).

3 No unique solution to sorting problem = different heuristic approximations. Comparison of linearly ordered lists π and π : Insertion, deletion, exact match as only edit operations: = Simple Alignment Problem D ij = min D i,j D i 1,j + 1 D i 1,j 1 whenever π (i) = π (j) MFVS OPT

4 The Circular Case: Mitochondrial Genomes Arrangement of 13 protein coding genes, 2 rrnas and 22tRNAs > NC_ cgi Branchiostoma floridae CO1 -S2 D CO2 K ATP8 ATP6 CO3 ND3 R ND4L ND4 H S L1 ND5 G -ND6 -E CYTB T -P 12S F V 16S L2 ND1 I M -Q ND2 -N W -A -C -Y Traditional approaches: Break-point distances Sorting by reversals ξ = π π 1 and compute a length function of ξ, i.e. number of reversals necessary to convert ξ to the identity permutation

5 Circular Alignments Basic Property of Alignments: A B i j Match (i, j) separates alignment into two independent parts. If (i, j) is part of the optimal alignment, then the two parts can be optimized independently.

6 A B i Computing Circular Alignments k k A B i k i Rotate sequence A such that it starts with i + 1: A Rotate sequence B such that it starts with k + 1: B Compute Alignment of A and B with the restriction that (a) inital gaps have full costs and (b) the last entries (i.e., i and k) match. Polynomial algorithm that runs in n 2 Alignment(A, B ) time with O(n 2 ) memory.

7 Resulting Alignments: NC_ <Branchiostoma_floridae > NC_ <Sus_scrofa > NC_ <Cavia_porcellus > NC_ <Chelonia_mydas > NC_ <Eumeces_egregius > NC_ <Hippopotamus_amphibius > NC_ <Mustelus_manazo > NC_ <Daphnia_pulex > NC_ <Ceratitis_capitata > NC_ <Anopheles_quadrimaculatus > (For simplicity: representing presence/absence of genes only)

8 Branchiostoma_floridae Sus_scrofa Phoca_vitulina Balaenoptera_physalus Raja_radiata Ornithorhynchus_anatinus Mustelus_manazo Hippopotamus_amphibius Eumeces_egregius Chelonia_mydas Cavia_porcellus Loxodonta_africana Strongylocentrotus_purpuratus Daphnia_pulex Ceratitis_capitata Drosophila_yakuba Anopheles_quadrimaculatus Apis_mellifera Echinococcus_multilocularis Metridium_senile Platynereis_dumerilii Terebratulina_retusa Crassostrea_gigas Ascaris_suum Caenorhabditis_elegans gap open = 10, gap extend = 10

9 Branchiostoma_floridae Sus_scrofa Phoca_vitulina Balaenoptera_physalus Raja_radiata Ornithorhynchus_anatinus Mustelus_manazo Hippopotamus_amphibius Eumeces_egregius Chelonia_mydas Cavia_porcellus Loxodonta_africana Daphnia_pulex Ceratitis_capitata Anopheles_quadrimaculatus Drosophila_yakuba Apis_mellifera Echinococcus_multilocularis Metridium_senile Crassostrea_gigas Platynereis_dumerilii Terebratulina_retusa Strongylocentrotus_purpuratus Ascaris_suum Caenorhabditis_elegans gap open = 10, gap extend = 3

10 Branchiostoma_floridae Sus_scrofa Phoca_vitulina Balaenoptera_physalus Raja_radiata Ornithorhynchus_anatinus Mustelus_manazo Hippopotamus_amphibius Eumeces_egregius Chelonia_mydas Cavia_porcellus Loxodonta_africana Daphnia_pulex Ceratitis_capitata Anopheles_quadrimaculatus Drosophila_yakuba Apis_mellifera Echinococcus_multilocularis Metridium_senile Crassostrea_gigas Platynereis_dumerilii Terebratulina_retusa Strongylocentrotus_purpuratus Ascaris_suum Caenorhabditis_elegans gap open = 10, gap extend = 1

11 Outlook trnas and proteins move with different frequencies: = more sophisticated scoring model: Gap costs depends on contents and length

12 Acknowledgements Footprint Sorting: Sonja J. Prohaska, Claudia Fried, Claus R. Stadler (Leipzig) Wim Hordijk (Canterbury, NZ) Mitochondrial Genomes: Guido Fritzsch, Martin Schlegel