Evaluation of the Haplotype Motif Model using the Principle of Minimum Description

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Evaluation of the Haplotype Motif Model using the
Principle of Minimum Description

• Srinath Sridhar, Kedar Dhamdhere,
• Guy E. Blelloch, R. Ravi and Russell Schwartz
• Computer Science Dept, Tepper School of Business
  and Dept of Biological Sciences.Carnegie Mellon
  University.

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Motivation

• Individual characteristics genetic
  factors
• Model the structure of correlated genetic
  variation (haplotypes) in the DNA
• Extract haplotype patterns (motifs) from the
  model
• Perform association studies comparing motifs to
  susceptibility to diseases

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Single Nucleotide Polymorphism (SNP)

• Rows Individual samples Columns Nucleotides
• ACCTGTATACGTA 0000000000000
• ACATGTAGACGGA 0010000100010
• ACCTGTAGACGGA 0000000100010
• ACATGTATACGTA 0010000000000
• ACATGTATACGTA 0010000000000
• ACCTGTAGACGGA 0000000100010

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Related Article
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Evolution

• Two types of events mutation and recombination
• Mutation (one strand of one chromosome shown)
• ACGTACCGTATATA
• ACGTACTGTATATA
• Recombination (one strand of two homologous
  chromosomes shown)
• ACGTACCGTATATA ACGTACCGTACGTA
• GTACTACGTACGTA GTACTACGTATATA

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Recombination

• Ancestral Sequences
• 
  
  
• Current Population

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Comparison of blocks and motifs
Blocks Daly et al, 2000
Motifs Schwartz 2003
Blocks Daly et al. 2000
Motifs Schwartz, 2003
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Minimum Description Length (MDL)

• Let
• M represent the parameters of the model
• I represent the input matrix
• E be the explanation of I using M
• L be the length of encoding
• Objective
• Minimize L(M) L(E(I)M)
• Complicated models are penalized
• Prevents over-fitting

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Dynamic Program - Blocks

• Dynamic Program Koivisto et al. 2003
• where C ( j1, i ) is the cost of creating a
  single block from j1 to i.
• Running time O(n2)
• Work space O(n)

best
i

single block
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Expectation-Maximization Algorithm - Motifs

• Create a DAG of all possible motifs with a
  start vertex
• Initialize probabilities
• For each EM iteration
• For each row r in R
• In sub-graph corresponding to r find ML path from
  start
• Re-normalize probabilities based on the number of
  times the vertices were used in ML path

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Example
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Example
Example
Example - Re-normalize
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Heuristics

• EM finds P1 and P2 but cost(P1) cost(P2)
  cost(P1 U P2)
• Use knowledge from previous EM iteration
• Multiple shortest paths with weight
  (1e)-cost(P)
• Addition of small constants to prevent zero
  probability in first few iterations
• Initialize the probabilities to favor smaller
  motifs
• Restrict maximum length of motifs

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Experimental Results
Simulated data using the ms program Hudson, 2002
Num Seqs/ Recomb Rt Num SNPs Desc Length Motifs (in bits) Desc Length- Blocks (in bits)
100/low 229.00 4528.26 5029.53
200/low 241.00 6600.21 8528.48
300/low 248.33 9944.45 13341.84
400/low 219.00 12735.52 18270.20
100/high 202.33 5787.31 6025.29
200/high 250.33 8852.31 10511.31
300/high 209.67 11921.38 15418.65
400/high 211.00 19626.85 26233.36
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Experimental Results
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Experimental Results
Motifs High recombination
Motifs Low Recombination
Blocks High recombination
Blocks Low Recombination
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Conclusion

• Characterized the problem of inferring haplotype
  structure as an optimization problem that is
  robust against over-fitting
• Haplotype motif model better captures the
  structure than haplotype blocks
• Furthermore, motif method performs progressively
  better with larger input size

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Discussion Future Work

• Extensions
• Polynomial time algorithm/NP-hardness
• Clustering and error models
• Real data recombination hot-spots
• Future directions

direct optimization
phasing
htSNP, association tests, ?
current work
Disease Analysis/ Drug design
Genotype data
Haplotype Data
Motifs/ Blocks/?
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Encoding Motifs

• Let si be the start locations of motifs
• Let ti,j be the number of motifs that start at i
  and end at j
• Let Ei ei, 1, , ei,k be the ordered set of
  end locations for motifs that start at i
• Cost for encoding model
• Additional cost for encoding motif probabilities

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Explanation

• Explanation of a row specify the ordered set of
  block haplotypes that produce the bits of the row
• Cost for explanation of row r
• Cost for explanation

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Human Genetic Structure

• Chromosomes in the nucleus of cells
• 23 pairs of chromosomes
• Double helix structure of chromosomes
• Chromosomes Genes and inter-genic regions
• Genes Encode for proteins

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Single Nucleotide Polymorphism (SNP)

• Human genomes are very similar
• SNP Single base with high probability of
  variation
• Bi-allelic Two out of four possible nucleotides
• In humans reduction in size 300

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Encoding Blocks

• Let
• si represent the start columns of blocks
• ti represent the number of blocks starting at ti
• Cost of encoding Model
• Additionally, encoding for probabilities for
  block haplotypes

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Encoding Blocks

• Explanation of a row specify the ordered set of
  block haplotypes that produce the bits of the row
• Cost for explanation of row r
• Cost for explanation

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DNA

• Building blocks (nucleotides) Adenine(A),
  Cytosine(C), Guanine(G) and Thymine(T)
• Adenine(A) pairs with Thymine(T)Cytosine(C)
  pairs with Guanine(G)

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Haplotypes

• Contiguous regions of correlated genetic
  variation
• Two models Blocks and Motifs
• Blocks
• Popular and widely assumed Daly et al. 2000
• Boundary aligned block haplotypes
• Motifs
• Recently introduced Schwartz 2003
• Overlapping haplotype motifs

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Comparison of Blocks and Motifs
Two models Haplotype blocksDaly et al. 2000
and haplotype motifs Schwartz 2003
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