Exploring Phylogenetic Relationships in Drosophila with Ciliate Operations Anna Nelson Department of Mathematics, Boise State University AAAS Pacific Division, 93rd Annual Meeting 25 June 2012 A. Nelson () Phylogenetic Relationships 25 June 2012 1 / 19
Background Acknowledgements The research resulted from the 2011 Boise State University REU in Mathematics with Jacob Herlin from University of Northern Colorado under the mentorship of Dr. Marion Scheepers from Boise State University. We gratefully acknowledge Boise State University for hosting and the National Science Foundation for funding the project under grant number DMS 1062857 A. Nelson () Phylogenetic Relationships 25 June 2012 2 / 19
Background What is a phylogenetic relationship? Phylogenetics is the study of evolutionary relationships between groups of organisms. A. Nelson () Phylogenetic Relationships 25 June 2012 3 / 19
Background What is a phylogenetic relationship? Phylogenetics is the study of evolutionary relationships between groups of organisms. Described by using phylogenetic trees A. Nelson () Phylogenetic Relationships 25 June 2012 3 / 19
Background What is a phylogenetic relationship? Phylogenetics is the study of evolutionary relationships between groups of organisms. Described by using phylogenetic trees Image courtesy of DroSpeGe: Drosophila Species Genomes. http://insects.eugenes.org/DroSpeGe A. Nelson () Phylogenetic Relationships 25 June 2012 3 / 19
Background Genetic Operations Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila Pseudoobscura and their use in the study of the history of the species . Proceedings of the National Academy of Science 22(1936), 448 - 350. A. Nelson () Phylogenetic Relationships 25 June 2012 4 / 19
Background Genetic Operations Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome Reversals have been the main genetic operation used to decrypt 1 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila Pseudoobscura and their use in the study of the history of the species . Proceedings of the National Academy of Science 22(1936), 448 - 350. A. Nelson () Phylogenetic Relationships 25 June 2012 4 / 19
Background Genetic Operations Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome Reversals have been the main genetic operation used to decrypt 1 Using a canonical reference species, use number of reversals as a measure of evolutionary distance from other species. 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila Pseudoobscura and their use in the study of the history of the species . Proceedings of the National Academy of Science 22(1936), 448 - 350. A. Nelson () Phylogenetic Relationships 25 June 2012 4 / 19
Background Genetic Operations Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome Reversals have been the main genetic operation used to decrypt 1 Using a canonical reference species, use number of reversals as a measure of evolutionary distance from other species. 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila Pseudoobscura and their use in the study of the history of the species . Proceedings of the National Academy of Science 22(1936), 448 - 350. A. Nelson () Phylogenetic Relationships 25 June 2012 4 / 19
Background Micronucleus and macronucleus of ciliates Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments. A. Nelson () Phylogenetic Relationships 25 June 2012 5 / 19
Background Micronucleus and macronucleus of ciliates Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments. Micronucleus: Long strands of DNA, encrypted version of macronucleus. Contain nonsense DNA that will be eliminated. A. Nelson () Phylogenetic Relationships 25 June 2012 5 / 19
Background Micronucleus and macronucleus of ciliates Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments. Micronucleus: Long strands of DNA, encrypted version of macronucleus. Contain nonsense DNA that will be eliminated. Macronucleus: Larger than the micronucleus and contains many short strands of DNA. Contain expressed DNA. A. Nelson () Phylogenetic Relationships 25 June 2012 5 / 19
Background Micronucleus and macronucleus of ciliates Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments. Micronucleus: Long strands of DNA, encrypted version of macronucleus. Contain nonsense DNA that will be eliminated. Macronucleus: Larger than the micronucleus and contains many short strands of DNA. Contain expressed DNA. Micronuclear DNA is decrypted to form macronuclear DNA using three ciliate operations: reversal, block interchange, excisionoperations: reversal, block interchange, excision A. Nelson () Phylogenetic Relationships 25 June 2012 5 / 19
Background Macronuclear vs. Micronuclear DNA Micronuclear DNA has three elements: 1. Macronuclear destined sequences (MDSs) A. Nelson () Phylogenetic Relationships 25 June 2012 6 / 19
Background Macronuclear vs. Micronuclear DNA Micronuclear DNA has three elements: 1. Macronuclear destined sequences (MDSs) 2. Internal eliminated sequences (IESs) A. Nelson () Phylogenetic Relationships 25 June 2012 6 / 19
Background Macronuclear vs. Micronuclear DNA Micronuclear DNA has three elements: 1. Macronuclear destined sequences (MDSs) 2. Internal eliminated sequences (IESs) 3. Pointers occur on the flanks of the MDSs A. Nelson () Phylogenetic Relationships 25 June 2012 6 / 19
Methodology Pointer Lists An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. A. Nelson () Phylogenetic Relationships 25 June 2012 7 / 19
Methodology Pointer Lists An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers: A. Nelson () Phylogenetic Relationships 25 June 2012 7 / 19
Methodology Pointer Lists An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers: [1 , 4 , − 3 , − 2 , 6 , − 5] A. Nelson () Phylogenetic Relationships 25 June 2012 7 / 19
Methodology Pointer Lists An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers: [1 , 4 , − 3 , − 2 , 6 , − 5] [(1 , 2) , (4 , 5) , (4 , 3) , (3 , 2) , (6 , 7) , (6 , 5)] Each pair ( a , b ) represents a section of genome spanning from a pointer a to a pointer b . A. Nelson () Phylogenetic Relationships 25 June 2012 7 / 19
Methodology Pointer Lists An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers: [1 , 4 , − 3 , − 2 , 6 , − 5] [(1 , 2) , (4 , 5) , (4 , 3) , (3 , 2) , (6 , 7) , (6 , 5)] Each pair ( a , b ) represents a section of genome spanning from a pointer a to a pointer b . [1 , 2 , 4 , 5 , − 4 , − 3 , − 3 , − 2 , 6 , 7 , − 6 , − 5] We call this representation a pointer list . A. Nelson () Phylogenetic Relationships 25 June 2012 7 / 19
Methodology Pointer Lists We define a pointer list formally as a list L = [ x 1 , x 2 , . . . x n ] that satisfies the following six conditions: Example: [1 , 2 , 4 , 5 , − 4 , − 3 , − 3 , − 2 , 6 , 7 , − 6 , − 5] A. Nelson () Phylogenetic Relationships 25 June 2012 8 / 19
Methodology Pointer Lists We define a pointer list formally as a list L = [ x 1 , x 2 , . . . x n ] that satisfies the following six conditions: 1 n is even. Example: [1 , 2 , 4 , 5 , − 4 , − 3 , − 3 , − 2 , 6 , 7 , − 6 , − 5] A. Nelson () Phylogenetic Relationships 25 June 2012 8 / 19
Methodology Pointer Lists We define a pointer list formally as a list L = [ x 1 , x 2 , . . . x n ] that satisfies the following six conditions: 1 n is even. 2 There is a unique i with µ = | x i | = min {| x j | : i ≤ j ≤ n } . (There is a minimum element) Example: [1 , 2 , 4 , 5 , − 4 , − 3 , − 3 , − 2 , 6 , 7 , − 6 , − 5] A. Nelson () Phylogenetic Relationships 25 June 2012 8 / 19
Methodology Pointer Lists We define a pointer list formally as a list L = [ x 1 , x 2 , . . . x n ] that satisfies the following six conditions: 1 n is even. 2 There is a unique i with µ = | x i | = min {| x j | : i ≤ j ≤ n } . (There is a minimum element) 3 There is a unique j with λ = | x i | = max {| x j | : i ≤ j ≤ n } . (There is a maximum element) Example: [1 , 2 , 4 , 5 , − 4 , − 3 , − 3 , − 2 , 6 , 7 , − 6 , − 5] A. Nelson () Phylogenetic Relationships 25 June 2012 8 / 19
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