Roadmap

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Roadmap

• Discovering Patterns
• Structure-preserving patterns
• Strings, Networks
• Permuting patterns
• Combinatorics
• Algorithmics
• Statistics
• Analyzing Patterns
• Genographic Project
• LD Patterns
• Then
• Now (IRIS)

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• Who ? National Geographic and IBM on a five year
  study, launched in April 2005
• What ? Although fossil records fix human origins
  in Africa, little is known about the great
  journey that took Homo sapiens to the far reaches
  of the earth.
  How did we,
  each of us, end up where we are?
• How ? Using genetics as a tool samples all
  around the world are being collected and the
  mtDNA and NRY chr are being analyzed

• phylogeographic question

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www.nationalgeographic.com/genographic
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www.ibm.com/genographic
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Public Participation

• Over 250,000 public participants to date (April,
  2008)
• www.nationalgeographic.com/genographic
• www.ibm.com/genographic
• www.ibm.com/dna

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Map of Migration
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How?

• Each of us carries ancestral material
• marked by signatures due to imperfections in DNA
  replication
• SNPs (Single Nucleotide Polymorphisms)
• STR numbers (Short Tandem Repeats)
• Inversions
• ..etc
• Uni-parental Model (topologytree)
• Non-recombining segments of genome

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mtDNA Micro-Phylogeny Tree
22 (coding-region) SNPs
The Genographic Project Public Participation
MtDNA Database, Behar et al, PLoS Genetics. 2007
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mtDNA Haplogroup Distribution
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Migration Map based on mtDNA
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Locus
16000 bp
58 mill bp 0.38
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Missing information in unilinear transmissions
past
present
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Population over generations (flow of ancestral
material)
past
MRCA
present
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Bi-parental Model
past
GMRCA MRCA
present
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What is recombination?

• Genetic recombination is the process by which a
  strand of DNA is broken then joined to the end
  of a different DNA molecule.
• It occurs during meiosis and between paired
  chromosomes. This process leads to offspring
  having different combinations of genes from their
  parents

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Recombnations CaptureRequirements Specification

• Enumerate the (multiple) recombinations
• Statistical averages not adequate..
• Identify the participating lineages
• Detect ancient recombinations as well as recent
  ones

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Then our task is to

• Estimate the phylogenetic network, called the
• Ancestral Recombinations Graph (ARG)

ARG coined by Griffiths Marjoram, 1996
Joint work with Marta Mele, Jaume Bertranpetit,
Francesc Callafel
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An Inconvenient Truth

• Theorem Given data D, the problem of computing
  the ARG G with minimum number of recombinations
  is NP-complete.

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An Inconvenient Truth

• Theorem Given data D, the problem of computing
  the ARG G with minimum number of recombinations
  is NP-complete.

Recall other inconvenient truths.
Theorem The problem of computing the most
parsimonious tree T is NP-complete.
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Flavors of hardness.

• (Uni-parental)
• In a NON infinite-sites model, TREE construction
  hard
• No back mutations No parallel mutations
• But reality is infinite-sites
• Yet, problem is tractable, in practice
• (Bi-parental)
• In a pure recombinations model, problem is hard
• Generally a statistical average has been
  pursued thru LD
• Combining potentially misleading mutations with
  recombinations makes the general problem
  intractable in practice

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Tractability Model(Balance between reality and
simplicity)

• Use characteristics of the observed haplotypes
• Use a compatible network model
  (not a generic phylogenetic model)

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IRIS(Identifying Recombinations In Sequences)
Stage Haplotypes use SNP block patterns

• biological insights

Segment along the length infer trees
computational insights
Infer network (ARG)
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Input Haplotypes
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Stage 1 Staging the Input

• 0 1 2 3 4 5 6 7 8 910 1 2 3 4 5 6 7
  8 910 1 2 3 4 5 6 7 8 0) 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1) 1 3
  4 2 3 2 2 2 2 3 4 3 3 3 3 2 2 3 3 4 4 3 2 2 2 2 2
  2 1 2 1 2) 1 3 4 2 3 2 2 2 2 3 4 3 3 3 3 2 2 3
  3 4 4 3 2 4 1 1 4 3 2 6 1 3) 1 3 5 2 3 2 2 2 2
  4 5 1 1 1 1 1 3 1 4 1 5 4 3 5 3 4 5 3 1 3 1 4)
  2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 3
  0 3 3 1 2 1 5) 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 115 1 6) 2 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 3 1
  7) 2 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 1 1 1 1 1
  3 2 3 3 3 1 3 1 8) 2 1 2 2 2 2 2 2 2 2 2 1 1 1
  2 2 2 2 1 2 2 2 2 2 2 2 2 2 111 1 9) 2 3 4 2 3
  2 2 2 2 3 4 3 3 3 3 2 2 3 3 4 4 3 2 4 1 1 4 3 2 8
  1 10) 2 3 5 2 3 2 2 2 2 4 5 1 1 1 1 1 3 1 4 1 5
  4 3 5 3 4 5 3 1 5 1 11) 3 2 3 2 2 3 2 3 2 2 3 2
  2 2 3 2 2 2 2 3 1 1 1 3 2 3 3 3 1 6 1 12) 3 2 3
  2 2 3 2 3 2 2 3 2 2 2 3 2 2 2 2 3 1 1 1 0 1 1 4 3
  2 2 1 13) 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 2 1 14) 5 1 6 2 2 2 2 2 2 5
  3 4 2 2 3 3 2 3 1 1 1 1 1 1 1 1 1 1 1 2 1 15) 7
  2 3 2 2 3 2 3 2 2 3 2 2 2 3 2 2 2 2 3 1 1 1 3 2 3
  3 3 1 2 1 16) 7 2 3 2 2 3 2 3 2 2 3 2 2 2 3 2 2
  2 2 3 1 1 1 6 1 1 1 1 1 2 1 17) 3 2 3 2 2 3 2 3
  2 2 3 2 2 2 3 2 2 2 2 3 0 2 2 2 2 2 2 2 1 1 1
  18) 2 1 1 1 1 1 1 1 1 1 4 3 3 3 3 2 2 3 3 4 4 3
  2 4 1 1 4 3 2 1 1 19) 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 20) 3 2 3 2
  2 3 2 3 2 2 3 2 2 2 3 2 2 3 3 4 4 3 2 4 1 1 4 3 2
  1 1 21) 2 3 5 2 3 2 2 2 2 4 5 1 1 1 1 1 3 1 4 1
  5 4 3 5 2 2 2 2 1 1 1 22) 5 1 2 2 2 2 2 2 2 2 2
  1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1 1

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Stage 2 Segmentation (Marginal
Compatible--Trees)
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Ancestral Recombination Graph (ARG) (our
characterization)

• ARG is a fortified compatible graph
• Defined on k segments G(k)
• A node can have at most 2 incoming edges (2
  parents)
• When 2 parents denotes recombination of two
  segments incoming edge is labeled by one segment
  each

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ARG
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Stage 3 Trees to ForestDSR Algorithm
Input Two graphs G1 and G2 Output
Consensus ARG G
Optimization
Topology
DSR
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DSR Algorithm Overview
initialization

• Let G1 and G2 be defined on leaf labels L
• Let universe U ? L
• P1 and P2 are partitions on U at leaf level
• DO-WHILE
• A network structure with nodes in G and the
  labels derived from P1 and P2
• Universe U ? this nodes in G
• Increment layer and update P1 and P2 as sets on U
  of this layer
• P1 has labels from G1
• P2 has labels from G2
• WHILE (P1 is nonempty) OR (P2 is nonempty)

iterative loop
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Walk-through of DSR Algorithm

• (0 2 5 9 12-14 16 18-20 23-24 28-30 33 35-36)
  2 7241 7251
• (1 6 8 17 21-22 26 31) 1 7252
• (7 11 15 34 37) 1 7253
• (25) 1 7707
• (3 10 27) 1 7254
• (4) 1 7009
• (32) 1 7000

(0 5 13-14 16 23-24 29-30) 1 8271 (1 6 8
17 21-22 26) 1 8272 (19 36) 1 8275
(2 9 12 18 20 31) 1 8282 (3-4 7 10-11
15 25 27-28 32 34-35 37) 1 8806 (33)
1 8000
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DSR Dominant Subdominant Recombinant

1. Dominant labels of G1 AND G2
2. Subdominant label of G1 OR G2
3. Recombinant no labels (NEITHER G1 NOR G2)

• Rules
• 1. Each row and each column
• has at most one dominant
• ELSE has at most one subdominant
• ELSE all recombinants
• 2. A non-recombinant can have non-recombinants
  either in its row or its column but NOT both

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DSR Algorithm X-matrix
P2







P1 labels
P1
P2 labels
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DSR Algorithm Assign DSR colors (optimization)
P2







P1 labels
P1
P2 labels
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DSR Algorithm rows cols DSR
P2







P1 labels
P1
P2 labels
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DSR Algorithm rows cols DSR
P2







P1 labels
P1
P2 labels
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DSR Algorithm rows cols DSR
P2







P1 labels
P1
P2 labels
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DSR ? Feasible Topology
Next layer
Last layer
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DSR Continuity Across Layers (iterations)
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chr2114505500 -14602168

• Chinese (2 subpops CBx, HNx) Japanese (JTx)
  data
• Around 200 SNPs
• Around 100 haplotypes

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Network
Median-joining networks for inferring
intraspecific phylogenies, Bandelt, Forster
Rohl, Molecular Biology and Evolution, Vol 16,
37-48, 1999
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IRIS(Identifying Recombinations In Sequences)
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
1234567890123456789012345 111111111111111111111111
11111111111111112222222222222222222222222222222222
233333333344444444455555555555555----
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IRIS Non-recombining Cluster Ids
11 12 13 14 15 16 0 17 1 18 4 19 6
5 20 8 21 9 10 7 22 23 3 2 24
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Chr 21 locus Preliminary Results

• Not distinguishable
• share recent ancient recombinations
• No pop-specific mutation/recombination

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Mazumdar et al, Journal of Genetics, 2008.
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The Big Picture
Ecosystem
Population Genomics
Species
Organism
Physiology
Metabolism
Network
Function
Structure
Sequence
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Thank You!
success stories in bioinformatics will depend
on algorithmic and statistical ingenuity.
Pavel
Pevzner