The informatics of SNPs and haplotypes

Gabor T. Marth

Department of Biology, Boston Collegemarth@bc.edu

Cold Spring Harbor LaboratoryAdvanced Bioinformatics courseOctober 17, 2005

DNA sequence variations

The Human Genome Project has determined a reference sequence of the human genome

However, every individual is unique, and is different from others at millions of nucleotide locations

sequence polymorphisms

Why do we care about variations?

underlie phenotypic differences

cause inherited diseases

allow tracking ancestral human history

How do we find sequence variations?

• look at multiple sequences from the same genome region

• use base quality values to decide if mismatches are true polymorphisms or sequencing errors

Steps of SNP discovery

Sequence clustering

Cluster refinement

Multiple alignment

SNP detection

Computational SNP mining – PolyBayes

2. Use sequence quality information (base quality values) to distinguish true mismatches from sequencing errors

sequencing errortrue polymorphism

1. Utilize the genome reference sequence as a template to organize other sequence fragments from arbitrary sources

Two innovative ideas:

SNP mining steps – PolyBayes

sequence clustering simplifies to database search with genome reference

paralog filtering by counting mismatches weighed by quality values

multiple alignment by anchoring fragments to genome reference

SNP detection by differentiating true polymorphism from sequencing error using quality values

genome reference sequence

1. Fragment recruitment

(database search)2. Anchored alignment

3. Paralog identificatio

n

4. SNP detection

SNP discovery with PolyBayes

Polymorphism discovery SW

Siablevarall

]T,G,C,A[S ]T,G,C,A[SiiiorPr

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Marth et al. Nature Genetics 1999

Genotyping by sequence

• SNP discovery usually deals with single-stranded (clonal) sequences

• It is often necessary to determine the allele state of individuals at known polymorphic locations

• Genotyping usually involves double-stranded DNA the possibility of heterozygosity exists

• there is no unique underlying nucleotide, no meaningful base quality value, hence statistical methods of SNP discovery do not apply

Het detection = Diploid base calling

Homozygous T

Homozygous C

Heterozygous C/T Automated detection of heterozygous positions in diploid individual samples

(visit Aaron Quinlan’s poster)

Large SNP mining projects

Sachidanandam et al. Nature 2001

~ 8 million

EST

WGS

BAC

genome reference

Variation structure is heterogeneous

chromosomal averages

polymorphism density along chromosomes

What explains nucleotide diversity?

5

6

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8

30 33 36 39 42 45 48 51 54

G+C Content [%]

SN

P R

ate

[per

10,

000

bp

]

5

6

7

8

0.3 1.2 2.1 3 3.9 4.8 5.7

CpG Content [%]

SN

P R

ate

[p

er

10,0

00 b

p]

G+C nucleotide content

CpG di-nucleotide content

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6

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8

9

10

0 0.5 1 1.5 2 2.5 3 3.5 4

Recombination rate [per Mb]

SN

P R

ate

[per

10,

000

bp

] recombination rate

functional constraints

3’ UTR 5.00 x 10-4

5’ UTR 4.95 x 10-4

Exon, overall 4.20 x 10-4

Exon, coding 3.77 x 10-4

synonymous 366 / 653non-synonymous 287 / 653

Variance is so high that these quantities are poor predictors of nucleotide diversity in local regions hence random processes are likely to govern the basic shape of the genome variation landscape (random) genetic drift

Where do variations come from?

• sequence variations are the result of mutation events TAAAAAT

TAACAAT

TAAAAAT TAAAAAT TAACAAT TAACAAT TAACAAT

TAAAAAT TAACAAT

TAAAAAT

MRCA• mutations are propagated down through generations

• and determine present-day variation patterns

Neutrality vs. selection

• selective mutations influence the genealogy itself; in the case of neutral mutations the processes of mutation and genealogy are decoupled

functional constraints

3’ UTR 5.00 x 10-4

5’ UTR 4.95 x 10-4

Exon, overall 4.20 x 10-4

Exon, coding 3.77 x 10-4

synonymous 366 / 653non-synonymous 287 / 653

• the genome shows signals of selection but on the genome scale, neutral effects dominate

Mutation rate

accgttatgtaga accgctatgtaga

MRCA

actgttatgtaga accgctatataga

MRCA

• higher mutation rate (µ) gives rise to more SNPS

5

6

7

8

0.3 1.2 2.1 3 3.9 4.8 5.7

CpG Content [%]

SN

P R

ate

[p

er

10,0

00 b

p]

• there is evidence for regional differences in observed mutation rates in the genomeCpG content

SN

P d

en

sity

Long-term demography

small (effective) population size N

large (effective)

population size N

• different world populations have varying long-term effective population sizes (e.g. African N is larger than European)

Population subdivision

unique unique

shared

• geographically subdivided populations will have differences between their respective variation structures

Recombination

acggttatgtaga accgttatgtaga

accgttatgtaga

acggttatgtaga

acggttatgtaga

acggttatgtaga

accgttatgtaga

accgttatgtaga

accgttatgtaga

acggttatgtaga

Recombination

acggttatgtaga accgttatgtaga

accgttatgtaga

acggttatgtaga

acggttatgtaga

acggttatgtaga

acggttatgtaga

acggttatgtaga

acggttatgtaga

acggttatgtaga

accgttatgtaga

accgttatgtaga

accgttatgtaga

• recombination has a crucial effect on the association between different alleles

Modeling genetic drift: Genealogy

present generation

randomly mating population, genealogy evolves in a non-deterministic fashion

Modeling genetic drift: Mutation

mutation randomly “drift”: die out, go to higher frequency or get fixed

Modulators: Natural selection

negative (purifying) selection

positive selection

the genealogy is no longer independent of (and hence cannot be decoupled from) the mutation process

Modeling ancestral processes

“forward simulations” the “Coalescent” process

By focusing on a small sample, complexity of the relevant part of the ancestral process is greatly reduced. There are,

however, limitations.

Models of demographic history

past

present

stationary expansioncollapse

MD(simulation)

AFS(direct form)

histo

ry

0

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bottleneck

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1. marker density (MD): distribution of number of SNPs in pairs of sequences

Data: polymorphism distributions

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“rare” “common”

2. allele frequency spectrum (AFS): distribution of SNPs according to allele frequency in a set of samples

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Clone 1 Clone 2 # SNPs

AL00675 AL00982 8

AS81034 AK43001 0

CB00341 AL43234 2

SNP Minor allele Allele count

A/G A 1

C/T T 9

A/G G 3

Model: processes that generate SNPs

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computable formulations

simulation procedures

3/5 1/5 2/5

Models of demographic history

past

present

stationary expansioncollapse

MD(simulation)

AFS(direct form)

histo

ry

0

0.05

0.1

1 2 3 4 5 6 7 8 9 10

0

0.05

0.1

1 2 3 4 5 6 7 8 9 100

0.05

0.1

1 2 3 4 5 6 7 8 9 10

0

0.05

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1 2 3 4 5 6 7 8 9 10

bottleneck

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0.005.00

10.0015.00

20.0025.00

30.0035.00

40.00

4 kb4 kb

8 kb8kb

12 kb12 kb

16 kb16kb0

0.1

0.2

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0.4

• best model is a bottleneck shaped population size history

presentN1=6,000T1=1,200 gen.

N2=5,000T2=400 gen.

N3=11,000

Data fitting: marker density

Marth et al. PNAS 2003

• our conclusions from the marker density data are confounded by the unknown ethnicity of the public genome sequence we looked at allele frequency data from ethnically defined samples

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presentN1=20,000T1=3,000 gen.

N2=2,000T2=400 gen.

N3=10,000

model consensus: bottleneck

Data fitting: allele frequency

• Data from other populations?

Population specific demographic history

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minor allele count

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minor allele count

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minor allele count

European data

African data

bottleneck

modest but uninterrupted

expansionMarth et al.

Genetics 2004

Model-based prediction

computational model encapsulating what we know about the processgenealogy + mutationsallele structure

arbitrary number of additional replicates

African dataEuropean data

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00

0.01

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Pro

port

ion

of A

FS

Mutational Size (i)1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.00

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Pro

port

ion

of A

FS

Mutational size (i)

contribution of the past to

alleles in various

frequency classes

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

20,000

40,000

60,000

80,000

Mut

atio

nal A

ge (

gene

ratio

ns)

Mutational Size (i)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

20,000

40,000

60,000

80,000

Mut

atio

nal A

ge (

gener

atio

ns)

Mutational Size (i)

average age of

polymorphism

Prediction – allele frequency and age

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

CACTACCGACACGACTATTTGGCGTAT

• 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

Informational: haplotypes

• the problem: the substrate for genotyping is diploid, genomic DNA; phasing of alleles at multiple loci is in general not possible with certainty

• experimental methods of haplotype determination (single-chromosome isolation followed by whole-genome PCR amplification, radiation hybrids, somatic cell hybrids) are expensive and laborious

A

T

C

T

G

C

C

A

Haplotype inference

• Parsimony approach: minimize the number of different haplotypes that explains all diploid genotypes in the sampleClark

Mol Biol Evol 1990

• Maximum likelihood approach: estimate haplotype frequencies that are most likely to produce observed diploid genotypes Excoffier & Slatkin

Mol Biol Evol 1995

• Bayesian methods: estimate haplotypes based on the observed diploid genotypes and the a priori expectation of haplotype patterns informed by Population Genetics Stephens et al.

AJHG 2001

Haplotype inference

http://pga.gs.washington.edu/

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

3 3 3

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.

N

M

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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"000" "001" "010" "011" "100" "101" "110" "111"0

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"000" "001" "010" "011" "100" "101" "110" "111"

000100001101010110011111

000001010011100101110111 this should work to the degree to which

the constraint at overlapping markers preserves long-range marker association

Building composite haplotypes

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"000" "001" "010" "011" "100" "101" "110" "111"

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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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r2 (data)

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)

3-site composites: the “best case”

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“short-range”

“long-range”

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

Variability across 4-site composites

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… is comparable to the variability across data sets.

Utility for association studies?

• No matter how good the resource is, its success to find disease causing variants greatly depend on the allelic structure of common diseases, a question under debate

• Regardless of how we describe human association structure, many questions remain about the relative merits of single-marker vs. haplotype-based strategies for medical association studies

http://clavius.bc.edu/~marthlab/MarthLab