A coalescent computational platform for tagging marker selection for clinical studies Gabor T. Marth Department of Biology, Boston College [email protected].

A coalescent computational platform for tagging marker selection for clinical studies

Gabor T. Marth

Department of Biology, Boston [email protected]

How to use markers to find disease?

Allelic association

• allelic association is the non-random assortment between alleles i.e. it measures how well knowledge of the allele state at one site permits prediction at another marker site functional site

• by necessity, the strength of allelic association is measured between markers

• significant allelic association between a marker and a functional site permits localization (mapping) even without having the functional site in our collection

• there are pair-wise and multi-locus measures of association

Linkage disequilibrium

• LD measures the deviation from random assortment of the alleles at a pair of polymorphic sites

D=f( ) – f( ) x f( )

• other measures of LD are derived from D, by e.g. normalizing according to allele frequencies (r2)

strong association: most chromosomes carry one of a few common haplotypes – reduced haplotype diversity

Haplotype diversity

• the most useful multi-marker measures of associations are related to haplotype diversity

2n possible haplotypesn

markers

random assortment of alleles at different sites

Haplotype blocks

Daly et al. Nature Genetics 2001

• experimental evidence for reduced haplotype diversity (mainly in European samples)

The promise for medical genetics

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• within blocks a small number of SNPs are sufficient to distinguish the few common haplotypes significant marker reduction is possible

• if the block structure is a general feature of human variation structure, whole-genome association studies will be possible at a reduced genotyping cost

• this motivated the HapMap project

Gibbs et al. Nature 2003

The HapMap initiative

• goal: to map out human allele and association structure of at the kilobase scale

• deliverables: a set of physical and informational reagents

HapMap physical reagents

• reference samples: 4 world populations, ~100 independent chromosomes from each

• SNPs: computational candidates where both alleles were seen in multiple chromosomes

• genotypes: high-accuracy assays from various platforms; fast public data release

Haplotype annotations – LD based

• Pair-wise LD-plots

Wall & Pritchard Nature Rev Gen 2003

• LD-based multi-marker block definitions requiring strong pair-wise LD between all pairs in block

Annotations – haplotype blocks

• Dynamic programming approachZhang et al.

AJHG 2001

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1. meet block definition based on common haplotype requirements

2. within each block, determine the number of SNPs that distinguishes common haplotypes (htSNPs)

3. minimize the total number of htSNPs over complete region including all blocks

Haplotype tagging SNPs (htSNPs)

Find groups of SNPs such that each possible pair is in strong LD (above threshold).

CarlsonAJHG 2005

Focal questions about the HapMap

CEPH European samples

1. Required marker density

Yoruban samples

4. How general the answers are to these questions among different human populations

2. How to quantify the strength of allelic association in genome region

3. How to choose tagging SNPs

Samples from a single population?

(random 60-chromosome subsets of 120 CEPH chromosomes from 60 independent individuals)

Consequence for marker performance

Markers selected based on the allele structure of the HapMap reference samples…

… may not work well in another set of samples such as those used for a clinical study.

Sample-to-sample variability?1. Understanding intrinsic properties of a given genome region, e.g. estimating local recombination rate from the HapMap data

3. It would be a desirable alternative to generate such additional sets with computational means

McVean et al. Science 2004

2. Experimentally genotype additional sets of samples, and compare association structure across consecutive sets directly

Towards a marker selection tool

2. generate computational samples for this genome region

3. test the performance of markers across consecutive sets of computational samples

1. select markers (tag SNPs) with standard methods

Generating data-relevant haplotypes

1. Generate a pair of haplotype sets with Coalescent genealogies. This “models” that the two sets are “related” to each other by being drawn from a single population.

3. Use the second haplotype set induced by the same mutations as our computational samples.

2. Only accept the pair if the first set reproduces the observed haplotype structure of the HapMap reference samples. This enforces relevance to the observed genotype data in the specific region.

Generating computational samples

Problem: The efficiency of generating data-relevant genealogies (and therefore additional sample sets) with standard Coalescent tools is very low even for modest sample size (N) and number of markers (M). Despite serious efforts with various approaches (e.g. importance sampling) efficient generation of such genealogies is an unsolved problem.

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We are developing a method to generate “approximative” M-marker haplotypes by composing consecutive, overlapping sets of data-relevant K-site haplotypes (for small K)Motivation from composite likelihood approaches to recombination rate estimation by Hudson, Clark, Wall, and others.

M-site haplotypes as composites of overlapping K-site haplotypes

1. generate K-site sets

2. build M-site composites

M

Piecing together K-site sets

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the constraint at overlapping markers preserves long-range marker association

Building composite haplotypes

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A composite haplotype is built from a complete path through the (M-K+1) K-sites.

3-site composite haplotypes

a typical 3-site composite

30 CEPH HapMap reference individuals (60 chr)

Hinds et al. Science, 2005

3-site composite vs. data

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3-site composites: the “best case”

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1. generate K-site sets

Variability across setsThe purpose of the composite haplotypes sets …

… is to model sample variance across consecutive data sets.

But the variability across the composite haplotype sets is compounded by the inherent loss of long-range association when 3-sites are used.

4-site composite haplotypes

4-site composite

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“Best-case” 4 site composites

Composite of exact 4-site sub-haplotypes

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Variability across 4-site composites

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… is comparable to the variability across data sets.

Towards a marker selection tool

2. generate computational samples for this genome region

3. test the performance of markers across consecutive sets of computational samples

1. select markers (tag SNPs) with standard methods