Binary Encoding and Gene Rearrangement Analysis

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Binary Encoding and Gene Rearrangement Analysis

• Jijun Tang
• Tianjin University
• University of South Carolina
• jtang_at_cse.sc.edu
• [phone]

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Outline

• Backgrounds
• Maximum Likelihood Methods for Phylogenetic
  Reconstruction
• Maximum Likelihood Methods for Ancestral Genome
  Inferrence
• Conclusions

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Phylogenetic Reconstruction
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Data Type

• Sequence Data
• DNA/RNA/Protein Sequences
• String on an alphabet of 4 or 20 characters
• Gene-Order Data

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Simple Rearrangements
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Rearrangement Phylogeny
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Median Problem
Goal find M so that DAMDBMDCM is minimized NP
hard for most metric distances
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Binary Encoding
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Biased Model

• Model of evolution
• Duplications, insertions and deletions of
  syntenic blocks
• Rearrangements inversions, translocations,
  fusions, fissions
• Binary sequences 1(presence) vs. 0(absence)
• Adjacency Pr (1 -gt0) vs. Pr (0 -gt 1)
• Gene content Pr (1 -gt 0) vs. Pr (0 -gt 1)
• Strong bias
• Pr (1 -gt0) gtgt Pr (0 -gt1) for adjacency
• Lose an existing adjacency Pr (1-gt0) ? 1/O(n)
• Gain a new adjacency Pr (0 -gt 1) ? 1/O(n2)

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ML Phylogenetic Reconstruction
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Simulated Results
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Ancestral Inference

• Step 1. Encoding gene orders into binary
  sequences.
• Step 2. Setup the biased transition model.
• Step 3. Arrange target ancestor to the root, and
  calculate the probabilities of character states
  for each character in the root.
• Step 4. Building the adjacency graph and use a
  greedy heuristic to assemble adjacencies into
  valid gene order for the target ancestor.

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Step 3 Root Tree

• Probabilities are calculated with a bottom-up
  recursive manner, so the target ancestor is
  placed to the root to prevent information loss.

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Step 3 Probabilities of Adjacencies

• Likelihood of a tree given sequence data at
  leaves can be computed (Felsenstein1981)

0
1
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0
W
X
Y
Z
W
X
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Pick one tree
Pick one site
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Step 3 Probabilities of Adjacencies

• Posterior probabilities of character states (0
  and 1) can be calculated according to Yang
  (Yang1995).
• This is calculated by summing over all other
  ancestral states except root

 
 
 
8 histories
4 histories
4 histories
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Step 4 Assemble Adjacencies

• Independent adjacencies are assembled into valid
  gene order permutations by a greedy heuristic
  proposed by Jian Ma (Ma2007).
• Sort the edges by weight.
• Add the current heaviest edge to the path until a
  cycle is formed, then repeat the process until
  all vertices are traversed.
• Remove the lightest edge in each cycle.

(1 -4 -3 5 2)
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Simulation Result

• Transition model and reroot procedure are
  necessary

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Results-2

• PMAG was compared with InferCarsPro (Ma2011) and
  GRAPPA_DCJ(Xu2008)

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Tests on Large Scale Dataset
Genome Gene Tree Diameter Tree Diameter Tree Diameter Tree Diameter
Genome Gene 1n 2n 3n 4n
PMAG 20 10000
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Conclusions

• ML on Binary Encoding is more accurate and
  thousands of times faster than other methods
• Binary encoding reduces the complexity and allows
  us to using existing methods for sequence data
• Biased transition model and rerooting procedure
  are very useful
• Future work
• Extend PMAG to handle a more general model of
  evolution, including gene indel and duplication
• Missing Adjacencies?

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Thank You!