Multiple Genome Rearrangement David Sankoff and Mathieu Blanchette, 1998 Presented by Nuray Kabasakal

Introduction Breakpoint analysis Consensus-based rearrangement The uniqueness of the consensus Binary tree-based rearrangement Uniqueness in tree-based rearrangement Conclusion

Introduction Multiple alignment of macromolecular sequences. Insertion, deletion, substitution.

Multiple Sequence Alignment Homologous. Optimize the column cost.

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.

Difficulties and solution Computational difficulty Unwarranted assumptions The fallacy The bias

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

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.

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 .

The uniqueness of the consensus

Binary tree-based rearrangement

Uniqueness in tree-based rearrangement

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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