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TRANSCRIPT
Lecture 7.0 1
The informatics of SNPs and haplotypes
Gabor T. MarthDepartment of Biology, Boston [email protected]
CGDN Bioinformatics WorkshopFebruary 20, 2006
Lecture 7.0 2
Why do we care about variations?
underlie phenotypic differences
cause inherited diseases
allow tracking ancestral human history
Lecture 7.0 3
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
Lecture 7.0 4
Steps of SNP discovery
Sequence clustering
Cluster refinement
Multiple alignment
SNP detection
Lecture 7.0 5
Computational SNP mining – PolyBayes
2. Use sequence quality information (base quality values) to distinguish true mismatches from sequencing errors sequencing error true polymorphism
1. Utilize the genome reference sequence as a template to organize other sequence fragments from arbitrary sources
Two innovative ideas:
Lecture 7.0 6
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
Lecture 7.0 7
genome reference sequence
1. Fragment recruitment (database search)
2. Anchored alignment
3. Paralog identification
4. SNP detection
SNP discovery with PolyBayes
Lecture 7.0 8
Polymorphism discovery SW
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Marth et al. Nature Genetics 1999
Lecture 7.0 9
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
Lecture 7.0 10
Het detection = Diploid base calling
Homozygous T
Homozygous C
Heterozygous C/T Automated detection of heterozygous positions in diploid individual samples
Lecture 7.0 11
Large SNP mining projects
Sachidanandam et al. Nature 2001
~ 8 million
ESTWGS
BAC
genome reference
Lecture 7.0 12
Variation structure is heterogeneous
chromosomal averages
polymorphism density along chromosomes
Lecture 7.0 13
What explains nucleotide diversity?
5
6
7
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
5
6
7
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
Lecture 7.0 14
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
Lecture 7.0 15
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
Lecture 7.0 16
Mutation rate
accgttatgtaga accgctatgtaga
MRCA
actgttatgtaga accgctatataga
MRCA
• higher mutation rate (µ) gives rise to more SNPS
5
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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 genome
CpG content
SN
P d
ensi
ty
Lecture 7.0 17
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)
Lecture 7.0 18
Population subdivision
unique unique
shared
• geographically subdivided populations will have differences between their respective variation structures
Lecture 7.0 19
Recombination
acggttatgtaga accgttatgtaga
accgttatgtaga
acggttatgtaga
acggttatgtaga
acggttatgtaga
accgttatgtaga
accgttatgtaga
accgttatgtaga
acggttatgtaga
Lecture 7.0 20
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
Lecture 7.0 21
Modeling genetic drift: Genealogy
present generation
randomly mating population, genealogy evolves in a non-deterministic fashion
Lecture 7.0 22
Modeling genetic drift: Mutation
mutation randomly “drift”: die out, go to higher frequency or get fixed
Lecture 7.0 23
Modulators: Natural selection
negative (purifying) selection
positive selection
the genealogy is no longer independent of (and hence cannot be decoupled from) the mutation process
Lecture 7.0 24
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.
Lecture 7.0 25
Models of demographic history
past
present
stationary expansioncollapse
MD(simulation)
AFS(direct form)
history
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bottleneck
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Lecture 7.0 26
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
Lecture 7.0 27
Model: processes that generate SNPs
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simulation procedures
3/5 1/5 2/5
Lecture 7.0 28
Models of demographic history
past
present
stationary expansioncollapse
MD(simulation)
AFS(direct form)
history
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
0.1
1 2 3 4 5 6 7 8 9 10
bottleneck
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Lecture 7.0 29
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
0.3
0.4
• best model is a bottleneck shaped population size history
present N1=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
Lecture 7.0 30
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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?
Lecture 7.0 31
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
Lecture 7.0 32
Model-based prediction
computational model encapsulating what we know about the process
genealogy + mutations
allele structure
arbitrary number of additional replicates
Lecture 7.0 33
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
por
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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
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Pro
port
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of A
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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
Mu
tatio
na
l Age
(g
en
era
tion
s)
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
Mu
tatio
na
l Age
(g
en
era
tion
s)
Mutational Size (i)
average age of polymorphism
Prediction – allele frequency and age
Lecture 7.0 34
How to use markers to find disease?
Lecture 7.0 35
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
Lecture 7.0 36
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)
Lecture 7.0 37
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
Lecture 7.0 38
Haplotype blocks
Daly et al. Nature Genetics 2001
• experimental evidence for reduced haplotype diversity (mainly in European samples)
Lecture 7.0 39
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
Lecture 7.0 40
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
Lecture 7.0 41
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
Lecture 7.0 42
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
Lecture 7.0 43
Haplotype inference
• Parsimony approach: minimize the number of different haplotypes that explains all diploid genotypes in the sample Clark
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
Lecture 7.0 44
Haplotype inference
http://pga.gs.washington.edu/
Lecture 7.0 45
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
Lecture 7.0 46
Annotations – haplotype blocks
• Dynamic programming approach Zhang 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
Lecture 7.0 47
Haplotype tagging SNPs (htSNPs)
Find groups of SNPs such that each possible pair is in strong LD (above threshold).
CarlsonAJHG 2005
Lecture 7.0 48
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
Lecture 7.0 49
Samples from a single population?
(random 60-chromosome subsets of 120 CEPH chromosomes from 60 independent individuals)
Lecture 7.0 50
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.
Lecture 7.0 51
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
Lecture 7.0 52
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
Lecture 7.0 53
Generating data-relevant haplotypes1. 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.
Lecture 7.0 54
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.
Lecture 7.0 55
M-site haplotypes as composites of overlapping K-site haplotypes
1. generate K-site sets
2. build M-site composites
M
Lecture 7.0 56
Piecing together K-site sets
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000001010011100101110111 this should work to the degree to which the
constraint at overlapping markers preserves long-range marker association
Lecture 7.0 57
Building composite haplotypes
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A composite haplotype is built from a complete path through the (M-K+1) K-sites.
Lecture 7.0 58
3-site composite haplotypes
a typical 3-site composite
30 CEPH HapMap reference individuals (60 chr)
Hinds et al. Science, 2005
Lecture 7.0 59
3-site composite vs. data
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Lecture 7.0 60
3-site composites: the “best case”
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1. generate K-site sets
Lecture 7.0 61
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.
Lecture 7.0 62
4-site composite haplotypes
4-site composite
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Lecture 7.0 63
“Best-case” 4 site composites
Composite of exact 4-site sub-haplotypes
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Lecture 7.0 64
Variability across 4-site composites
Lecture 7.0 65
Variability across 4-site composites
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Lecture 7.0 66
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
Lecture 7.0 67
http://bioinformatics.bc.edu/marthlab