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Multiple Genome Rearrangement
David Sankoff and Mathieu Blanchette, 1998 Presented by Nuray Kabasakal
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Introduction Breakpoint analysis Consensus-based rearrangement The uniqueness of the consensus Binary tree-based rearrangement Uniqueness in tree-based rearrangement Conclusion
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Introduction Multiple alignment of macromolecular sequences.
Insertion, deletion, substitution.
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Multiple Sequence Alignment
Homologous. Optimize the column cost.
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Phylogenetic tree- based
Column cost Complete comparison Phylogenetic tree- based comparison Consensus comparison Gene order comparison: Alignment is given and number of divergence step must be calculated.
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Difficulties and solution
Computational difficulty Unwarranted assumptions The fallacy The bias
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Breakpoint analysis Two genomes and on the same set of genes
Circular genome: ai is adjacent to ai+1 and an Breakpoints: If genes g and h are adjacent in A but not in B, they determine the breakpoints, , for both A and B Oriented Genomes: Assuming that we know the direction of transcription. If gene order is gh in a genome; Breakpoint: hg, -g-h, g-h, -gh, h-g or -hg Not breakpoint: gh or –h-g
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Tree-based multiple genome rearrangement
T=(V,E) is unrooted tree with N≥3 leaves and ∑={g1,…,gn} Assumptions; leaves of the tree, where are internal vertices of the tree. For each leaf the data contains a circular permutation of the genes in ∑. Goal: Finding permutations associated with the internal vertices, so that is minimized. Binary tree vs consensus-based multiple genome rearrangement 1-Binary, L=2N-2, internal nodes have degree of 3. 2-Stars, L=N+l, internal node has degree N.
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Consensus-based rearrangement
:complete graph whose vertices are the element of ∑ . For each edge gh in E( ), let u(gh)=number of times g and h adjacent in N data genome and w(gh)=N-u(gh) Then, solution to Travelling Salesman Problem(TSP) on ( ,w) traces out an optimal genome S on ∑. is the solution of the TSP on( ,w), then the median is given by .
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The uniqueness of the consensus
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Binary tree-based rearrangement
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Uniqueness in tree-based rearrangement
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Conclusion This work establishes the computational feasibility of exact breakpoint analysis as a method of multiple genome rearrangement, in contrast to the difficulties with edit distance-based approaches. Non-uniqueness remains a major consideration in genomic reconstruction, but we see that it is less problematic in breakpoint analysis than the other approaches.
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