Abstract
Various international efforts are underway to catalog the genomic similarities and variations in the human population. Some key discoveries such as inversions and transpositions within the members of the species have also been made over the years. The task of constructing a phylogeny tree of the members of the same species, given this knowledge and data, is an important problem. In this context, a key observation is that the “distance” between two members, or member and ancestor, within the species is small. In this paper, we pose the tree reconstruction problem exploiting some of these peculiarities. The central idea of the paper is based on the notion of minimal consensus PQ tree T of sequences introduced in [29]. We use a modified PQ structure (termed oPQ) and show that both the number and size of each T is \(\mathcal{O}(1)\). We further show that the tree reconstruction problem is statistically well-defined (Theorem [7]) and give a simple scheme to construct the phylogeny tree and the common ancestors. Our preliminary experiments with simulated data look very promising.
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References
Bergeron, A.: A very elementary presentation of the hannenhalli-pevzner theory. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 106–117. Springer, Heidelberg (2001)
Bergeron, A., Stoye, J.: On the similarity of sets of permutations and its applications to genome comparison. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 68–79. Springer, Heidelberg (2003)
Bloom, S.: Using genetics to unearth our path on earth. J. of Clinical Investigation 115, 1395 (2005)
Bourque, G., Pevzner, P.A.: Genome-scale evolution: Reconstructing gene orders in the ancestral species. In: Genome Research, pp. 26–36. Cold Spring Harbor Laboratory Press (2002)
Cann, R.L., Stoneking, M., Wilson, A.C.: Mitochondrial DNA and human evolution. Nature 356, 389–390 (1992)
Caprara, A.: Formulations and complexity of multiple sorting by reversals. In: Proceedings of the Annual Conference on Computational Molecular Biology (RECOMB 1999), pp. 84–93. ACM Press, New York (1999)
The International HapMap Consortium. The International HapMap Project. Nature, 426, 789–796 (2003)
Eres, R., Landau, G., Parida, L.: A combinatorial approach to automatic discovery of cluster-patterns. In: Benson, G., Page, R.D.M. (eds.) WABI 2003. LNCS (LNBI), vol. 2812, pp. 139–150. Springer, Heidelberg (2003)
Kakizuka, A., et al.: Chromosomal translocation t(15;17) in human acute promyelocytic leukemia fuses rar alpha with a novel putative transcription factor, PML. Cell 66(4), 663–674 (1991)
Kakizuka, A., et al.: Identification of novel genes, SYT and SSX, involved in the t(X;18)(p11.2;q11.2) translocation found in human synovial sarcoma. Nature Genetics 7, 502–508 (1994)
Tilford, C.A., et al.: A physical map of the human Y chromosome. Nature 409, 943–945 (2001)
Lakich, D., et al.: Inversions disrupting the factor VIII gene are a common casue of severe haemophilia. Nature Genetics 5, 236–241 (1993)
Kehrer-Sawatzki, H., et al.: Molecular characterizations of the pericentric inversion that causes difference between chimpanzee chromosome 19 and human chromosome 17. Am J. of Hum. Genetics 71, 375–388 (2002)
Stefansson, H., et al.: A common inversion under selection in europeans. Nat. genetics 37(2), 129–137 (2005)
Cosner, M.E., et al.: An empirical comparison of phylogenetic methods on chloroplast gene order data in campanulaceae. Comparative Genomics: Empirical and Analytical Approaches to Gene Order Dynamics, Map Alignment, and the Evolution of Gene Families (2000)
Pettenati, M.J., et al.: Paracentric inversions in humans: a review of 446 paracentric inversions with presentations of 120 new cases. Am J. of Med. Genetics 55, 171–187 (1995)
Bondeson, M.L., et al.: Inversion of the IDS gene resulting from recombination with IDS-related sequences is a common cause of the Hunter syndrome. Molecular Genetics 4, 615–621 (1995)
Pletcher, M.T., et al.: Use of comparative physical and sequence mapping to annotate mouse chromosome 16 and human chromosome 21. Genomics 74, 45–54 (2001)
Giglio, S., et al.: Olfactory receptor-gene clusters, genomic inversion polymorphisms and common chromosome rearrangements. Am J. of Hum. Genetics 68, 874–883 (2001)
Felsenstein, J.: Inferring phylogenies. Sinauer Associates (2004)
Gersen, S.L., Keagle, M.B.: Principles of Clinical Cytogenetics. Humana Press (2004)
Gusfield, D.: Algorithms on strings, trees and sequencess: computer science and computational biology. Cambridge University Press, New York (1997)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. J. of ACM 46, 1–27 (1999)
Huynen, M.A., Snel, B., Bork, P.: Inversions and the dynamics of eukaryotic gene order. Trends in Genetics 17, 304–306 (2001)
Booth, K., Leukar, G.: Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms. Journal of Computer and System Sciences 13, 335–379 (1976)
Kaplan, H., Shamir, R., Tarjan, R.E.: A faster and simpler algorithm for sorting signed permutations by reversals. SIAM J. of Computing 29, 880–892 (1999)
Karim, M.E., Parida, L., Lakhotia, A.: Using permutation patterns for content-based phylogeny. Lecture Notes in Bioinformatics (to appear, 2006)
Feuk, L., Macdonald, J.R., Tang, T., Carson, A.R., Li, A.M., Rao, M.G., Khaja, R., Scherer, S.W.: Discovery of human inversion polymorphisms by comparative analysis of human and chimpanzee DNA sequence assemblies. PLoS Genetics 1(4) (2005)
Landau, G., Parida, L., Weimann, O.: Using PQ trees for comparative genomics. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 128–143. Springer, Heidelberg (2005)
Sankoff, D.: Edit distance for genome comparison based on non-local operations. In: Proc. of the Third Symp. on Comp. Pattern Matching, pp. 121–135. Springer, Heidelberg (1992)
Sankoff, D., Blanchette, M.: Multiple genome rearrangement and breakpoint phylogeny. Journal of Computational Biology 5(3), 555–570 (1998)
Sankoff, D., Leduc, G., Antoine, N., Paquin, B., Lang, B., Cedergren, R.: Gene order comparisons for phylogenetic inference: Evolution of the mitochondrial genome. Proc. Nat. Acad. Sci. 89, 6575–6579 (1992)
Small, K., Iber, J., Warren, S.T.: Emerin deletion reveals a common X-chromosome inversion mediated by inverted repeats. Nature Genetics 16, 96–99 (1997)
Sturtevant, A.H.: Genetic studies on Drosophila melanogaster. Genetics 5, 488–500 (1920)
Waterman, M.S.: An Introduction to Computational Biology: Maps, Sequences and Genomes. Chapman Hall, Boca Raton (1995)
Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21(16), 3340–3346 (2005)
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Parida, L. (2006). A PQ Framework for Reconstructions of Common Ancestors and Phylogeny. In: Bourque, G., El-Mabrouk, N. (eds) Comparative Genomics. RCG 2006. Lecture Notes in Computer Science(), vol 4205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864127_12
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DOI: https://doi.org/10.1007/11864127_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44529-6
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