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Haplotype Blocks

Haplotype Blocks. An Overview A. Polanski Department of Statistics Rice University. Key Papers. 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

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Haplotype Blocks

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  1. Haplotype Blocks An Overview A. Polanski Department of Statistics Rice University

  2. Key Papers • 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 • 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. • K. Zhang et al., (2002), A Dynamic Programming Algorithm for Haplotype Block Partitioning, PNAS, vol. 99, pp. 7335-7339

  3. Supplementary Papers • 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 • R. Hudson, 2002, Generating Samples under a Wright-Fisher Neutral Model of Genetic Variation, Bioinformatics, vol. 18, pp. 337-338 • D. Reich et al., (2001), Linkage Disequilibrium in the Human Genome, Nature, vol. 411, pp. 199-204

  4. What are Haplotype Blocks ? Haplotype block = a sequence of contiguous markers on DNA, homogeneous according to some criterion Markers = Single Nucleotide Polymorphisms (SNPs)

  5. 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

  6. Fig. 2 from (Patil et al. 2001)

  7. SNP no i 0100000000000000000010000000000000010000111000000000100000001001000000001001000000000000000000001000000001101000010101010 0000000010000000000010000000000100100001000000000000001011001001001010001001000000000010010001011000000001101010010101010 0000000001000100010110001010000000010100011000000000010100000000000100000100110000011101001000000110000110001000100011010 0000000000000100010010001010000000010100011000000000010100000000000100000100110000011101001000000110000110001000100011010 0000000010000000000010000100000100100000000000000000001001001001001010001001000000000010010001011000000001100100000000000 0010000000100001000010010000000000010000011000000000010100000000100100110100010000000010000001001000001001110100000000000 0000000010000000000010000100110100100000000000000000001001001001001010001001000000000010010001011000000001100100000000000 1000100000000000000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000000001000000010000000000000010000011000000000000000001001000000001001000000000000000000001000000001101000010101010 0000000010000000000010000100000100100000000000000000001001001101001010001001000000000010010001011000000001100100000000000 1000100000000000000001000001000101000000000000000001000000001001000000001001000000000000000000001000010001101010010101010 0000100000000000100001000000000101000000000000000000000000001001010000001001000000000000000000001000000001101000010101010 1000100000000000000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000100100000000010010000000000011000011010000000010100000010100100100100010010000010100001001000001001110100000000000 1000100000000010000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000000100000000010010000000000010000011000000000010100000000100100100100010000000010000001001000001001110101000000001 0000000000100000000010010000000000010000011010000000010100000010100100100100010010000010000001001001001001110100000000000 0001001000010000001000100000001010000000011001111110000000110000000000000010011101010000001010100100000000001000001011110 0000100000000000100001000000000101000000000000000000000000001001010000001001000000000000000000001000000001101000010101010 0001010000000000001000000000000010000010011101000010000000100000000000000010010001010000001000100100100000001000001011010 …… 20 i = 1, 2, …, 35989

  8. Problems

  9. How do we determine boundaries between blocks ? • Average value of standarized coefficient of linkage disequilibrium is greater thansome threshold (Wang et al. 2002, Reich et al. 2001) • Infer sites in the sample of DNA sequences where recombination events happened in the past history (Wang et al. 2002, Hudson, 2002) • Chromosome coverage – minimum number of SNPs to account for majority of haplotypes (Patil et al. 2001, Zhang et al. 2002)

  10. What evolutionary forces are responsible for haplotype blocks formation ? • Mutation • Genetic drift • Recombination • Recombination hot spots

  11. Methods

  12. Method 1 (Wang et al. 2002) Infer sites in the sample of DNA sequences where recombination events happened in the past history

  13. 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 GC SNP1 SNP2 SNP1 SNP2 AC GT A C AG CT G C G T

  14. Four gamete test (Hudson and Kaplan, 1985) If we see all four gametes at SNP1 and SNP2 SNP1 SNP2 A C 4GT G C G T A T Then there must have been a recombination event between these sites in their past history

  15. Array of pairwise 4GT test results Hudson and Kaplan, 1985 0, if there are less then 4 gametes D, dij= 1, if there are 4 gametes What is the minimal number of recombinations that could explain observed data ? Statistics FR (Hudson and Kaplan, 1985)

  16. Fig. 1 from Wang et al., 2002 D Block 1 Block 2 Block 3

  17. 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

  18. Dependence of average lengths of blocks on recombination frequency

  19. … on sample size

  20. ... on mutation intensity

  21. 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

  22. … Failed

  23. Try a mixture of two different recombination frequencies - better

  24. Method 2 (Patil, 2001) Chromosome coverage – minimum number of SNPs to account for majority of haplotypes

  25. Fig. 2 from (Patil et al. 2001)

  26. Problem formulation Define block boundaries to minimize the number of SNPs that distinguish at least  percent of the haplotypes in each block

  27. Common haplotypes Those represented more than one in the block

  28. Condition Common haplotypes must constitute at least =80 percent of all haplotypes in the block Blocks that do not satisfy this are not allowed

  29. Fragment of Fig. 2 from Patil et al., 2001

  30. 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

  31. Greedy Solution 0100000000000000000010000000000000010000111000000000100000001001000000001001000000000000000000001000000001101000010101010 0000000010000000000010000000000100100001000000000000001011001001001010001001000000000010010001011000000001101010010101010 0000000001000100010110001010000000010100011000000000010100000000000100000100110000011101001000000110000110001000100011010 0000000000000100010010001010000000010100011000000000010100000000000100000100110000011101001000000110000110001000100011010 0000000010000000000010000100000100100000000000000000001001001001001010001001000000000010010001011000000001100100000000000 0010000000100001000010010000000000010000011000000000010100000000100100110100010000000010000001001000001001110100000000000 0000000010000000000010000100110100100000000000000000001001001001001010001001000000000010010001011000000001100100000000000 1000100000000000000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000000001000000010000000000000010000011000000000000000001001000000001001000000000000000000001000000001101000010101010 0000000010000000000010000100000100100000000000000000001001001101001010001001000000000010010001011000000001100100000000000 1000100000000000000001000001000101000000000000000001000000001001000000001001000000000000000000001000010001101010010101010 0000100000000000100001000000000101000000000000000000000000001001010000001001000000000000000000001000000001101000010101010 1000100000000000000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000100100000000010010000000000011000011010000000010100000010100100100100010010000010100001001000001001110100000000000 1000100000000010000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000000100000000010010000000000010000011000000000010100000000100100100100010000000010000001001000001001110101000000001 0000000000100000000010010000000000010000011010000000010100000010100100100100010010000010000001001001001001110100000000000 0001001000010000001000100000001010000000011001111110000000110000000000000010011101010000001010100100000000001000001011110 0000100000000000100001000000000101000000000000000000000000001001010000001001000000000000000000001000000001101000010101010 0001010000000000001000000000000010000010011101000010000000100000000000000010010001010000001000100100100000001000001011010 ……. Start End 0. Fix Start =End 1. Increment end 2. Compute ratio L(B)/f(B) 3. Stop at max 4. Go to 0

  32. Results • 4563 representative SNPs (13%) • 4135 blocks

  33. Method 3 (Zhang et al. 2002) Solves the same problem of 80% chromosome coverage, but using the better method of dynamic programming

  34. Dynamic programming solution i B1(i) B2(i) B3(i) 0100000000000000000010000000000000010000111000000000100000001001000000001001000000000000000000001000000001101000010101010 0000000010000000000010000000000100100001000000000000001011001001001010001001000000000010010001011000000001101010010101010 0000000001000100010110001010000000010100011000000000010100000000000100000100110000011101001000000110000110001000100011010 0000000000000100010010001010000000010100011000000000010100000000000100000100110000011101001000000110000110001000100011010 0000000010000000000010000100000100100000000000000000001001001001001010001001000000000010010001011000000001100100000000000 0010000000100001000010010000000000010000011000000000010100000000100100110100010000000010000001001000001001110100000000000 0000000010000000000010000100110100100000000000000000001001001001001010001001000000000010010001011000000001100100000000000 1000100000000000000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000000001000000010000000000000010000011000000000000000001001000000001001000000000000000000001000000001101000010101010 0000000010000000000010000100000100100000000000000000001001001101001010001001000000000010010001011000000001100100000000000 1000100000000000000001000001000101000000000000000001000000001001000000001001000000000000000000001000010001101010010101010 0000100000000000100001000000000101000000000000000000000000001001010000001001000000000000000000001000000001101000010101010 1000100000000000000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000100100000000010010000000000011000011010000000010100000010100100100100010010000010100001001000001001110100000000000 1000100000000010000001000001000101000000000000000001000000001001000001001001000000100000000100001000000001101010010101010 0000000000100000000010010000000000010000011000000000010100000000100100100100010000000010000001001000001001110101000000001 0000000000100000000010010000000000010000011010000000010100000010100100100100010010000010000001001001001001110100000000000 0001001000010000001000100000001010000000011001111110000000110000000000000010011101010000001010100100000000001000001011110 0000100000000000100001000000000101000000000000000000000000001001010000001001000000000000000000001000000001101000010101010 0001010000000000001000000000000010000010011101000010000000100000000000000010010001010000001000100100100000001000001011010 …… 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:

  35. Bellman’s equation

  36. Results • 3582 representative SNPs (compared to 4563 from greedy algorithm) • 2575 blocks (compared to 4135 blocks from greedy algorithm)

  37. Conclusions • Studying haplotype block partitions is very important to 1. Constructing haplotype maps for genetic traits 2. Understanding recombination in human genome

  38. To expect • A lot of papers in this area appearing in scientific journals

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