Haplotype Blocks
An Overview
A. Polanski
Department of Statistics
Rice University
Key Papers
1. N. Patil et al., (2001), Blocks of Limited Haplotype Diversity Revealed by High-Resolution Scanning of Human Chromosome 21, Science, vol. 294, pp. 1719-1723
2. N. Wang et al., (2002), Distribution of Recombination Crossovers and the Origin of Haplotype Blocks: The Interplay of Population History, Recombination and Mutation, Am. J. Hum. Genet., vol. 71, pp. 1227-1234.
3. K. Zhang et al., (2002), A Dynamic Programming Algorithm for Haplotype Block Partitioning, PNAS, vol. 99, pp. 7335-7339
Supplementary Papers
1. R. Hudson, N. Kaplan, (1985), Statistical Properties of the Number of Recombination Events in The History of a Sample of DNA sequences, Genetics, vol. 111, pp. 147-164
2. R. Hudson, 2002, Generating Samples under a Wright-Fisher Neutral Model of Genetic Variation, Bioinformatics, vol. 18, pp. 337-338
3. D. Reich et al., (2001), Linkage Disequilibrium in the Human Genome, Nature, vol. 411, pp. 199-204
What are Haplotype Blocks ?
Haplotype block = a sequence of contiguous markers on DNA, homogeneous according to some criterion
Markers = Single Nucleotide Polymorphisms (SNPs)
Data (Patil et al. 2001)
Chromosome 21
Physically separated the two copies of chromosome 21 using a rodent-human somatic cell hybrid technique
Sample of 20 copies of chromosome 21 (32397439 bases)
Found: 35989 SNPs
Fig. 2 from (Patil et al. 2001)
01000000000000000000100000000000000100001110000000001000000010010000000010010000000000000000000010000000011010000101010100000000010000000000010000000000100100001000000000000001011001001001010001001000000000010010001011000000001101010010101010000000000100010001011000101000000001010001100000000001010000000000010000010011000001110100100000011000011000100010001101000000000000001000100100010100000000101000110000000000101000000000001000001001100000111010010000001100001100010001000110100000000010000000000010000100000100100000000000000000001001001001001010001001000000000010010001011000000001100100000000000001000000010000100001001000000000001000001100000000001010000000010010011010001000000001000000100100000100111010000000000000000000100000000000100001001101001000000000000000000010010010010010100010010000000000100100010110000000011001000000000001000100000000000000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010000000000000100000001000000000000001000001100000000000000000100100000000100100000000000000000000100000000110100001010101000000000100000000000100001000001001000000000000000000010010011010010100010010000000000100100010110000000011001000000000001000100000000000000001000001000101000000000000000001000000001001000000001001000000000000000000001000010001101010010101010000010000000000010000100000000010100000000000000000000000000100101000000100100000000000000000000100000000110100001010101010001000000000000000010000010001010000000000000000010000000010010000010010010000001000000001000010000000011010100101010100000000100100000000010010000000000011000011010000000010100000010100100100100010010000010100001001000001001110100000000000100010000000001000000100000100010100000000000000000100000000100100000100100100000010000000010000100000000110101001010101000000000001000000000100100000000000100000110000000000101000000001001001001000100000000100000010010000010011101010000000010000000000100000000010010000000000010000011010000000010100000010100100100100010010000010000001001001001001110100000000000000100100001000000100010000000101000000001100111111000000011000000000000001001110101000000101010010000000000100000101111000001000000000001000010000000001010000000000000000000000000010010100000010010000000000000000000010000000011010000101010100001010000000000001000000000000010000010011101000010000000100000000000000010010001010000001000100100100000001000001011010
20 ……
i = 1, 2, …, 35989
SNP no i
Problems
How do we determine boundaries between blocks ?
1. Average value of standarized coefficient of linkage disequilibrium is greater than some threshold (Wang et al. 2002, Reich et al. 2001)
2. Infer sites in the sample of DNA sequences where recombination events happened in the past history (Wang et al. 2002, Hudson, 2002)
3. Chromosome coverage – minimum number of SNPs to account for majority of haplotypes (Patil et al. 2001, Zhang et al. 2002)
What evolutionary forces are responsible for haplotype blocks
formation ?
• Mutation
• Genetic drift
• Recombination
• Recombination hot spots
Methods
Method 1 (Wang et al. 2002)
Infer sites in the sample of DNA sequences where recombination events happened in the past history
Three gamete condition
Consider a pair of SNPs, SNP1 and SNP2. If there was no recombination between SNP1 and SNP2, they must satisfy three gamete condition
SNP1 SNP2SNP1 SNP2
AG
CC
G T
AG CTAC
GC
GT
Four gamete test (Hudson and Kaplan, 1985)
If we see all four gametes at SNP1 and SNP2
SNP1 SNP2
AG
CC
G T
A T
Then there must have been a recombination event between these sites in their past history
4GT
Array of pairwise 4GT test resultsHudson and Kaplan, 1985
D, dij=
0, if there are less then 4 gametes
1, if there are 4 gametes
What is the minimal number of recombinations that couldexplain observed data ?Statistics FR (Hudson and Kaplan, 1985)
Fig. 1 from Wang et al., 2002
D
Block 1 Block 2 Block 3
Wang et al., 2002 - Study
• R. Hudson’s program for simulating genealogies with mutation, drift and recombination under various demographic scenarios
• Study of dependence of average lengths of blocks on different factors
• Comparison of simulation results to data from Patil et al., 2002
Dependence of average lengths of blocks on recombination frequency
… on sample size
... on mutation intensity
Comparison to data from Patil et al. 2001
• Compute distribution of haplotype block lengths in the data from Patil et al. 2001
• Try to tune parameters and R to obtain similar distribution in the simulations
… Failed
Try a mixture of two different recombination frequencies - better
Method 2 (Patil, 2001)
Chromosome coverage – minimum number of SNPs to account for majority of haplotypes
Fig. 2 from (Patil et al. 2001)
Problem formulation
Define block boundaries to minimize the number of SNPs that distinguish at least percent of the haplotypes in each block
Common haplotypes
Those represented more than one in the block
Condition
Common haplotypes must constitute at least =80 percent of all haplotypes in the block
Blocks that do not satisfy this are not allowed
Fragment of Fig. 2 from Patil et al., 2001
Notation
• B – block defined as numbers of SNPs,
e.g., B = 45, 46,….50, or B = i, i+1,…, j
• L(B) length of the block (number of SNPs)
• f(B) – minimum number of SNP’s required to distinguish common haplotypes
Greedy 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
Start End
1. Increment end0. Fix Start =End
2. Compute ratio L(B)/f(B)
…….
3. Stop at max
4. Go to 0
Results
• 4563 representative SNPs (13%)
• 4135 blocks
Method 3 (Zhang et al. 2002)
Solves the same problem of 80% chromosome coverage, but using the better method of dynamic programming
Dynamic programming 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
……
Optimal partition of SNPs 1,2, … i
Assume that for all i=1, 2, …, j-1 we know optimal block partition,B1(i), B2(i), …, Bk(i) that minimizes:
i
K
kki iBfS
1
)]([
B1(i) B2(i) B3(i)
Bellman’s equation
)},...,1,({ 11,..1
min jiifSS iji
j
Results
• 3582 representative SNPs (compared to 4563 from greedy algorithm)
• 2575 blocks (compared to 4135 blocks from greedy algorithm)
Conclusions
• Studying haplotype block partitions is very important to
1. Constructing haplotype maps for genetic
traits
2. Understanding recombination in human
genome
To expect
• A lot of papers in this area appearing in scientific journals
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