Title: Evaluation of the Haplotype Motif Model using the Principle of Minimum Description
1Evaluation 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.
2Motivation
- 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
3Single Nucleotide Polymorphism (SNP)
- Rows Individual samples Columns Nucleotides
- ACCTGTATACGTA 0000000000000
- ACATGTAGACGGA 0010000100010
- ACCTGTAGACGGA 0000000100010
- ACATGTATACGTA 0010000000000
- ACATGTATACGTA 0010000000000
- ACCTGTAGACGGA 0000000100010
4Related Article
5Evolution
- 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
6Recombination
- Ancestral Sequences
-
- Current Population
7Comparison of blocks and motifs
Blocks Daly et al, 2000
Motifs Schwartz 2003
Blocks Daly et al. 2000
Motifs Schwartz, 2003
8Minimum 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
9Dynamic 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
10Expectation-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
11Example
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15Example
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Example - Re-normalize
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16Heuristics
- 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
17Experimental 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
18Experimental Results
19Experimental Results
Motifs High recombination
Motifs Low Recombination
Blocks High recombination
Blocks Low Recombination
20Conclusion
- 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
21Discussion 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/?
22Encoding 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
23Explanation
- 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
-
24Human 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
25Single 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
26Encoding 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
27Encoding 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
-
-
28DNA
- Building blocks (nucleotides) Adenine(A),
Cytosine(C), Guanine(G) and Thymine(T) - Adenine(A) pairs with Thymine(T)Cytosine(C)
pairs with Guanine(G)
29Haplotypes
- 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
30Comparison of Blocks and Motifs
Two models Haplotype blocksDaly et al. 2000
and haplotype motifs Schwartz 2003
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