Joe Mychaleckyj

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Linkage Disequilibrium

Joe MychaleckyjCenter for Public Health

Genomics982-1107

jcm6t@virginia.edu

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Joe Mychaleckyj

Today we’ll cover…

• Haplotypes• Linkage Disequilibrium• Visualizing LD• HapMap

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References

Principles of Population Genetics, Fourth Edition (Hardcover) by Daniel L. Hartl, Andrew G. Clark (Author)

xx

x

Genetic Data Analysis II Bruce S WeirQuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

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References

Statistical Genetics: Gene Mapping Through Linkage and Association Eds Benjamin M. Neale, Manuel A.R. Ferreira, Sarah E. Medland, Danielle Posthuma

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SNP1 SNP2 SNP3

[A / T] [C / G] [A / G]

A C G

A C A

T G G

2N (ie very large diversity possible)

Haplotype: specific combination of alleles occurring (cis) on the same chromosome (segment of chromosome)

N SNPs - How many Haplotypes are possible ?

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Terminology

• Haplotype: Specific combination (phasing) of alleles occurring (cis) on the same chromosomal segment

• Linkage/Linked Markers: Physical co-location of markers on the same chromosome

• Diplotype: Haplogenotype ie pair of phased haplotypes one maternally, one paternally inherited

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SNP2 [ B / b ]SNP1 [ A / a ]

Major Allele Freq: p(A) p(B)

Minor Allele Freq: p(a) p(b)

Independently segregating SNPs:

Haplotype Frequency p(ab) = p(a) x p(b)

LINKAGE DISEQUILIBRIUM

Haplotype Frequency p(ab)≠ p(a) x p(b)

LINKAGE EQUILIBRIUM

(How many haplotypes in total ?)

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Linkage Disequilibrium

• Non-random assortment of alleles at 2 (or more) loci

• The closer the markers, the stronger the LD since recombination will have occurred at a low rate

• Markers co-segregate within and between families

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SNP1 Allele

A

a

SNP2 Allele

B b

p(A)p(B)

p(a)p(B)

p(A)p(b) p(A)

p(a)p(b) p(a)

p(B) p(b)

Example:

p(A)p(B)+p(a)p(B)=p(B){ p(A)+p(a)} = p(B)

* LINKAGE EQUILIBRIUM *Not a Punnett

Square!

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SNP2 [ B / b ]SNP1 [ A / a ]

Major Allele Freq: p(A) p(B)

Minor Allele Freq: p(a) p(b)

LINKAGE DISEQUILIBRIUM

Haplotype Frequency p(ab) = p(a) p(b) + D

(sign of D is generally arbitrary, unless comparing D values between populations or studies)

D: Lewontin’s LD Parameter (Lewontin 1960)

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SNP1 Allele

A

a

SNP2 Allele

B b

p(A)p(B)+D

p(a)p(B)-D

p(A)p(b)-D p(A)

p(a)p(b)+D p(a)

p(B) p(b)

p(A)p(B)+D + p(a)p(B)-D =p(B){ p(A)+p(a)} = p(B)

* LINKAGE DISEQUILIBRIUM *

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0.16 0.04

0.14 0.66

a

A

b B

p(a)=0.20

p(B)=0.80

p(b)=0.30 p(B)=0.70

What is the LD ?

≠ 0

p(ab) ≠ p(a) p(b)

p(ab) = p(a) p(b) + D

0.16 = 0.2 x 0.3 + D

D = 0.1

Since p(ab) = p(a)p(b)+ D

+D was used and D is +ve here, but arbitrary

eg can relabel alleles A,B as minor

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Range of D values (-ve to +ve)

D has a minimum and maximum value that depends on the allele frequencies of the markers

Since haplotype frequencies cannot be -ve

p(aB) = p(a)p(B) - D ≥ 0 D ≤ p(a)p(B)

p(Ab) = p(A)p(b) - D ≥ 0 D ≤ p(A)p(b)

These cannot both be true, so D ≤ min( p(a)p(B), p(A)p(b) )

p(ab) = p(a)p(b) + D ≥ 0 D ≥ -p(a)p(b)

p(AB) = p(A)p(B) + D ≥ 0 D ≥ -p(A)p(B)

These cannot both be true, so D ≥ max( -p(a)p(b), -p(A)p(B) )

* Similar equations if we had defined p(ab) = p(a)p(b) - D

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Limits of D LD Parameter

Limits of D are a function of allele frequencies

Standardize D by rescaling to a proportion of its maximal value for the given allele frequencies (D') D’ = D

Dmax

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D’ (Lewontin, 1964)

D’ = D / Dmax

Dmax = min (p(A)p(B), p(a)p(b)) D < 0

Dmax = min (p(A)p(b), p(a)p(B)) D > 0Again, sign of D’ depends on definition

D’ = 1 or -1 if one of p(A)p(B), p(A)p(b), p(a)p(B), p(a)p(b) = 0

= Complete LD (ie only 3 haplotypes seen)D’=1 or -1 suggests that no recombination has

taken place between markersBeware rare markers - may not have enough

power/sample size to detect 4th haplotype

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D’ Interpretation

0.06 0.14

0.24 0.56

a

A

b B

p(a)=0.20p(A)=0.80

p(b)=0.30 p(B)=0.70

0.2 0

0.1 0.7

a

A

b B

p(a)=0.20P(A)=0.80

p(b)=0.30 p(B)=0.70

D=0 ; Dmax undefined D=Dmax =0.14 ; D’ = +1

p(a) = 0.2

p(b)= 0.3

D’=1 (perfect LD using D’ measure - No recombination between marker - Only 3 haplotypes are seen

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Creation of LD

• Easiest to understand when markers are physically linked

• Creation of LD– Mutation– Founder effect– Admixture– Inbreeding / non-random mating– Selection– Population bottleneck or stratification– Epistatic interaction

• LD can occur between unlinked markers• Gametic phase disequilibrium is a more

general term

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A

a

A B

A b

a B

SNP1

SNP1

SNP2

Recombinationn=2 haplotypesn=2 haplotypes

n=3 haplotypesn=3 haplotypes

SNP1

SNP2

A B

A b

a B

a b

n=4 haplotypesn=4 haplotypes

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Destruction of LD

• Main force is recombination • Gene conversion may also act at

short distances (~ 100-1,000 bases)

• LD decays over time (generations of interbreeding)

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Initial LD between SNP1 - SNP2: D0

After 1 generation

Preservation of LD:D1 = D0(1-θ)

After t generations:Dt = D0 (1- θ)t

SNP1 SNP2 Probability Recombination occurs = θ

Probability Recombination does not occur = 1-θ

NB: Overly simple model - does not account for allele frequency drift over time

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QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Dt = D0 (1-θ)t

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r2 LD Parameter (Hill & Robertson, 1968)

• Squared correlation coefficient varies 0 - 1

• Frequency dependent• Better LD measure for allele correlation

between markers - predictive power of SNP1 alleles for those at SNP2

• Used extensively in disease gene or phenotype mapping through association testing

r2 = D2

p(a)p(b)p(A)p(B)

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r2 Interpretation

0.06 0.14

0.24 0.56

a

A

b B

p(a)=0.20p(A)=0.80

p(b)=0.30 p(B)=0.70

0.2 0

0.1 0.7

a

A

b B

D=0 ; Dmax undefined D=Dmax =0.14 ; D’ = +1

r2 = 0 r2 = 0.14/0.24 = 0.58

p(a) = 0.2

p(b) = 0.3r2 ≠ 1 Correlation is not perfect, even

though D’ = 1

r2 = 1 if D’ = 1 and p(a) = p(b) = 0.3

p(a)=0.20p(A)=0.80

p(b)=0.30 p(B)=0.70

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r2 Interpretationp(a) = 0.3

p(b) = 0.3Only 2 haplotypes:

r2 = 1 Correlation is perfect

D’ =1 (less than 4 haplotypes)

p(a) = p(b) (= 0.3 in this example)

• r2=1 when there is perfect correlation between markers and one genotype predicts the other exactly

– Only 2 haplotypes present

• D’ = 1 ≠> r2 = 1• No recombination AND markers must have

identical allele frequency– SNPs are of similar age

• Corollary– Low r2 values do not necessarily = high recombination– Discrepant allele frequencies

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-1 D’ 1

0 r2 1

Common Measures of Linkage Disequilibrium

Recombination

Correlation

Other LD Measures exist, less common usage

Joe Mychaleckyj

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Visualizing LD metrics

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SNP1

SNP2

SNP3

SNP4

SNP5

SNP6

SNP1 2 3 4 5 6

0.2

0.6

0.8

1.0

0

| D’ |

Not usually worried about sign of D’

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Haploview: TCN2 (r2)

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Launched October 2002

http://www.hapmap.org

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International HapMap Project• Initiated Oct 2002• Collaboration of scientists worldwide• Goal: describe common patterns of human

DNA sequence variation• Identify LD and haplotype distributions• Populations of different ancestry

(European, African, Asian)– Identify common haplotypes and population-specific differences

• Has had major impact on:– Understanding of human popualtion history as reflected in genetic

diversity and similarity– Design and analysis of genetic association studies

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HapMap samples

• 90 Yoruba individuals (30 parent-parent-offspring trios) from Ibadan, Nigeria (YRI)

• 90 individuals (30 trios) of European descent from Utah (CEU)

• 45 Han Chinese individuals from Beijing (CHB)

• 44 Japanese individuals from Tokyo (JPT)

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Project feasible because of:

• The availability of the human genome sequence• Databases of common SNPs (subsequently

enriched by HapMap) from which genotyping assays could be designed

• Development of inexpensive, accurate technologies for highthroughput SNP genotyping

• Web-based tools for storing and sharing data• Frameworks to address associated ethical and

cultural issues

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HapMap goals

• Define patterns of genetic variation across human genome

• Guide selection of SNPs efficiently to “tag” common variants

• Public release of all data (assays, genotypes)• Phase I: 1.3 M markers in 269 people

1 SNP/5kb (1.3M markers)

Minor allele frequency (MAF) >5%

• Phase II: +2.8 M markers in 270 people

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http://www.hapmap.org/

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HapMap publications

• The International HapMap Consortium. A Haplotype Map of the Human Genome. Nature 437, 1299-1320. 2005.

• The International HapMap Consortium. The International HapMap Project. Nature 426, 789-796. 2003.

• The International HapMap Consortium. Integrating Ethics and Science in the International HapMap Project. Nature Reviews Genetics 5, 467 -475. 2004.

• Thorisson, G.A., Smith, A.V., Krishnan, L., and Stein, L.D. The International HapMap Project Web site. Genome Research,15:1591-1593. 2005.

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ENCODE project

• Aim: To compare the genome-wide resource to a more complete database of common variation—one in which all common SNPs and many rarer ones have been discovered and tested

• Selected a representative collection of ten regions, each 500 kb in length

• Each 500-kb region was sequenced in 48 individuals, and all SNPs in these regions (discovered or in dbSNP) were genotyped in the complete set of 269 DNA samples

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Comparison of linkage disequilibrium and recombination for two ENCODE regions

Nature 437, 1299-1320. 2005

Joe Mychaleckyj

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LD in Human Populations

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Haplotype Blocks

N SNPs = 2N Haplotypes possible, ie very large diversity possible

But: we do not see the full extent of haplotype diversity in human populations

Extensive LD especially at short distances eg ~20kbases.

Haplotypes are broken into blocks of markers with high mutual LD separated by recombination hotspots

Non-uniform LD across genome

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Haplotype Blocks

Haplotype blocks: at least 80% of observed haplotypes with frequency >= 5% could be grouped into common patterns

Whole Genome Patterns of Common DNA Variation in Three Human Populations, Science 2005, Hinds et al.

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Length of LD spans

r2

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Example: Large block of LD on chromosome 17Cluster of common (frequent SNPs In high LD)518 SNPs, spanning 800 kb25% in EUR, 9% in AFR, missing in CHNGenes:

Microtubule-associated protein tauMutations associated with a variety of neurodegeneartive disordersGene coding for a protease similar to presenilinsMutations result in Alzheimer’s diseaseGene for corticotropin-releasing hormone receptor

• Immune, endocrine, autonomic, behavioral response to stress

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Chromosome 17 LD Region

Prevalent inversion in EUR human population

~25%