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 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 K. Zhang et al., (2002), A Dynamic Programming Algorithm for Haplotype Block Partitioning, PNAS, vol. 99, pp

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

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 ( bases) Found: SNPs

Fig. 2 from (Patil et al. 2001)

…… i = 1, 2, …, 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 SNP2 SNP1SNP2 A G C C GT AGAGCTCT AC GC GT

Four gamete test (Hudson and Kaplan, 1985) If we see all four gametes at SNP1 and SNP2 SNP1SNP2 A G C C GT AT Then there must have been a recombination event between these sites in their past history 4GT

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

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

Wang et al., 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 Compute distribution of haplotype block lengths in the data from Patil et al 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 Solution 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 solution …… Optimal partition of SNPs 1,2, … i Assume that for all i=1, 2, …, j-1 we know optimal block partition, B 1 (i), B 2 (i), …, B k (i) that minimizes: i B 1 (i)B 2 (i)B 3 (i)

Bellman’s equation

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