Human SNP haplotypes Statistics 246 Spring 2002 Week 15 Lecture 1 Human single nucleotide polymorphisms The majority of human sequence variation is due to substitutions that have occurred once in the history of mankind at individual base pairs SNPs Patil et al 2001 listed at the end and refs therein It has been estimated that 5 million common SNPs each with a frequency of 10 50 account for the bulk of human DNA sequence difference Such SNPs are present in the human genome about 1 in every 600 base pairs Alleles making up blocks of such SNPs in close physical proximity are often correlated and define a limited number of SNP haplotypes each of which reflects descent from a single ancient ancestral chromosome The Daly et al 2001 data set This consists of 103 common SNPs 5 minor allele frequency in a 500 kb region implicated in Crohn disease genotyped in 129 trios mom pop kid from a European derived population giving 258 transmitted and 258 untransmitted chromosomes Studies to date have revealed great variability in local haplotype structure the relative contributions of mutation recombination selection population history and stochastic events seems to vary unpredictably Some haplotypes extend only a few kb while others extend for 100 kb Here is some evidence from Figure 1 of Daly et al 2001 Linkage disequilibrium LD between an arbitrary marker 26 in a 61 in c see and every other marker in the data set is indicated using the normalized association measure D ad bc a c c d of LD Note the noisiness of the plot Daly et al 2001 Figure 1 2 tables Measures of association in 2 Given positive observed frequencies from a 2 2 table say a b c and d for the cells11 10 01 and 00 respectively how do we measure association between the two classifications Put a b c d n Geneticists like to use D p11 p1 p 1 where p11 a n p1 a b n and p1 a c n One long recognised trouble with this measure is that its values can be greater or smaller depending on the marginal proportions p1 and p1 Ideally one would like a measure of association which captured just association and was parametrically independent of the marginal frequencies One exists namely the odds ratio ad bc equivalently log log ad bc This has the nice property that for any specified marginal probabilities p 1 and p1 between 0 and 1 and any value of there is a unique 2 2 table with these marginals and log odds ratio Despite this wonderful result geneticists continue to use a normalized D namely D D Dmax where Dmax is the largest value of D with the given marginals If D 0 we can show Exercise Dmax min p1 1 p 1 1 p1 p 1 Check that this leads to the formula quoted in the previous slide but one Human SNP haplotypes cont If we identify the underlying haplotypes the LD picture becomes clearer In Figure 1b a multi allelic form of D is used to plot LD between the maximum likelihood haplotype group assignment at the location of the 26th marker and that assignment at the location of every other marker in the set Here the haplotypes have been blocked details later and each block treated as an allele Figure 1d repeats 1b but with the 61st marker Note that when haplotypes rather than single SNPs are used there is much less noise There is a r c table analogue of the result cited earlier involving r 1 c 1 log odds ratios and r s 1 marginal frequencies but what geneticists want here is a single number summarizing the association in an rxc table where max r c 2 No entirely satisfactory single number exists though many have been tried and many are in use For the multi allelic form of D used above see Hedrick Genetics 117 331 341 1987 Gametic disequilibrium measures proceed with caution The block structure of haplotypes Daly et al 2001 we able to infer offspring haplotypes largely from parents with a little help from the EM when parents and children were both heterozygous see last week They say that it became evident that the region could be largely decomposed into discrete haplotype blocks each with a striking lack of diversity Fig 2 The haplotype blocks span up to 100kb and contain 5 or more common SNPs For example one 84 kb block of 8 SNPs shows just two distinct haplotypes accounting for 95 of the observed chromosomes Table 1 A long haplotype block Construction of the haplotype blocks If I have time I ll describe Daly s method of determining haplotype blocks Basically they define an HMM rather like the one used to map markers on mouse chromosomes MapMaker and estimate what they term the historical recombination frequency between each pair of consecutive SNPs Their data is an assignment of each chromosome to one of four ancestral haplotypes Consecutive SNPs are then in the same block if 1 73 103 with 14 having 1 4 and 9 with 4 The approach is justified by the observation that the visually defined haplotype blocks have only a few 2 4 haplotypes which show no evidence of being derived from one another by recombination and which account for nearly all chromosomes 90 in the sample Further the discrete blocks are separated by intervals in which several independent recombination events seem to have occurred giving rise to greater haplotype diversity in regions spanning the blocks see Figure 2 Finally we see that the haplotypes at the various blocks can be readily assigned to one of just four ancestral long range haplotypes Daly et al 2001 Figure 2 Patil et al 2001 The data in this paper derives from a publicly available panel of 24 ethnically diverse individuals and concerns chromosome 21 SNPs The two chromosomes of each individual were separated using rodent human somatic cell hybrid technology and so were able to be typed separately leading directly to haplotypes Overall 20 independent copies of chr 21 were analyzed for SNP discovery and haplotype structure The typing was done on specially constructed high density oligonucleotide arrays Affymetrix and in total they identified 35 989 SNPs in their sample of 20 chromosomes The allele frequency distribution is depicted in Figure 1A see next page The 32 Mbp of chr 21 DNA was then divided into 200 kb segments and the observed heterozygosity was used to calculate an average nucleotide diversity for each segment and these are plotted in Figure 1B Finally Fig 1C shows the distribution of distances between consecutive SNPs Figure 1 of Patil et al 2001 SNP block structure in chromosome 21 What do we mean in this context by a haplotype block Informally a block is a set of s consecutive SNPs which although in theory could generate
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