1. Rearrangement Phylogeny of Genomes in Contig form
Adriana Muñoz and David Sankoff
Presented by Jessica Saigle

2. Goal
Is there any way to use genome rearrangement algorithms to compare genomes available in contig form?

3. Phylogeny

4. Background
Inversions, transposition, translocation, chromosome fission and fusion
Algorithm to determine genomic distance
Equations relating actual number of rearrangements and the genomic distance
What are Contigs

5. Operations
Inversions, transposition, translocation, chromosome fission and fusion
Successive genes are called an adjacency
Important note fusion does not disrupt adjacencies

6. Genomic Distance
Minimum number of operations required to transform one genome into another
Algorithms are available for deriving the distance given that the given genomes are composed of ordered chromosomes represented by the same genes

7. Relationship between actual vs. inferred
The genomic distance is the inferred number of rearrangements (d)
Actual number of rearrangements (τ)
There is no simple probability relationship in reference to time
However they modeled the proportion of adjacencies that will be disrupted versus the proportion that will remain intact after τ times

8. Equations E(d) ≈ n(1 − e−λτ /n)
This equation is derived from the probability that each adjacencies will remain undisrupted after τ rearrangements
With
n is the number of genes
λ-depends on the various kinds of rearrangements of the model
E(d) ≈ n(1 − e−λτ /n)

9. Equations The previous equation does not accurately represent E(d)
So a two parameter model was created

11. Contigs
Contigs are overlapping's of short genomic sequences created when using bottom up sequencing

12. Case 1: assembled genome and contig form
We treat each contig as a chromosome
XA - # number of contigs in A
XB - # number of chromosomes in B
Fusion can be separated out as without changing the number of rearrangements
We also know how many fusions are required

13. Proposed Correction d=d’-|XA-XB|
But this correction only works for small values of τ
This correction to the apparent rearrangement distance is too large when compared to correctly assembled genomes
This is caused by creating more economical rearrangements
To correct this we should only remove a portion of |XA-XB|

14. Simulation
Through simulation it was determined that α(t) is a decreasing function and this decrease is not linear

16. Case 2: both genomes in Contig form
New problems
No longer comparing a fragmented genome to a complete one
There is no obvious way to combine the number of contigs of one genome to the other
We can still attempt to find the appropriate correction using simulations

18. Phylogeny

20. Conclusion Created a model for t – d relationship
Subtracted artificial fusion and fissions
Improved a phylogenetic tree for a data set on 14 insect genomes
Main short coming
Model is not analytically derived