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

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

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

4. Multiple Sequence Alignment
Homologous.
Optimize the column cost.

5. 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.

6. Difficulties and solution
Computational difficulty
Unwarranted assumptions
The fallacy
The bias

7. 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

8. 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.

9. 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 .

10. The uniqueness of the consensus

11. Binary tree-based rearrangement

12. Uniqueness in tree-based rearrangement

13. 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.

14. Thank you very much for listening!