Linkage Disequilibrium

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Linkage Disequilibrium

• Joe Mychaleckyj
• Center for Public Health Genomics
• 982-1107
• jcm6t_at_virginia.edu

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Today well 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)
Genetic Data Analysis II Bruce S Weir
x
x
x
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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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2N (ie very large diversity possible)
SNP1 SNP2 SNP3 A / T C / G A /
G A C G A C A
T G G
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 EQUILIBRIUM (How many haplotypes in
total ?)
LINKAGE DISEQUILIBRIUM Haplotype Frequency p(ab)?
p(a) x p(b)
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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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LINKAGE EQUILIBRIUM
Not a Punnett Square!
SNP2 Allele B b
SNP1 Allele A a
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)
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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 Lewontins LD
Parameter (Lewontin 1960)
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LINKAGE DISEQUILIBRIUM
SNP2 Allele B b
SNP1 Allele A a
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)
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b B
What is the LD ? ? 0 p(ab) ? p(a)
p(b)
0.16
0.04
p(a)0.20
a A
p(B)0.80
0.14
0.66
p(b)0.30 p(B)0.70
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 lt 0
• Dmax min (p(A)p(b), p(a)p(B)) D gt 0
• Again, 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)
• D1 or -1 suggests that no recombination has
  taken place between markers
• Beware rare markers - may not have enough
  power/sample size to detect 4th haplotype

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D Interpretation
b B
b B
0.06
0.14
p(a)0.20
0.2
0
p(a)0.20
a A
a A
p(A)0.80
0.7
P(A)0.80
0.1
0.56
0.24
p(b)0.30 p(B)0.70
p(b)0.30 p(B)0.70
D0 Dmax undefined
DDmax 0.14 D 1
p(a) 0.2
p(b) 0.3
D1 (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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SNP1
SNP1
SNP2
n3 haplotypes
A B
A
Recombination
n2 haplotypes
A b
a B
a
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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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SNP1
SNP2
Probability Recombination occurs ? Probability
Recombination does not occur 1-?
Initial LD between SNP1 - SNP2 D0 After 1
generation Preservation of LD D1
D0(1-?) After t generations Dt D0 (1- ?)t
NB Overly simple model - does not account for
allele frequency drift over time
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Dt D0 (1-?)t
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r2 LD Parameter (Hill Robertson, 1968)
r2 D2 p(a)p(b)p(A)p(B)

• 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

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r2 Interpretation
b B
b B
0.06
0.14
p(a)0.20
0.2
0
p(a)0.20
a A
a A
p(A)0.80
0.7
p(A)0.80
0.1
0.56
0.24
p(b)0.30 p(B)0.70
p(b)0.30 p(B)0.70
D0 Dmax undefined
DDmax 0.14 D 1
r2 0
r2 0.14/0.24 0.58
p(a) 0.2
p(b) 0.3
r2 ? 1 Correlation is not perfect, even though
D 1 r2 1 if D 1 and p(a) p(b) 0.3
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r2 Interpretation
p(a) 0.3
p(b) 0.3
Only 2 haplotypes r2 1 Correlation is
perfect D 1 (less than 4 haplotypes) p(a)
p(b) ( 0.3 in this example)

• r21 when there is perfect correlation between
  markers and one genotype predicts the other
  exactly
• Only 2 haplotypes present
• D 1 ?gt 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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Common Measures of Linkage Disequilibrium
-1 D 1 0 r2 1
Recombination
Correlation
Other LD Measures exist, less common usage
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Visualizing LD metrics
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SNP 1 2 3 4 5 6
D






SNP1 SNP2 SNP3 SNP4 SNP5 SNP6
1.0
0.8
0.6
0.2
0
Not usually worried about sign of D
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Haploview TCN2 (r2)
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http//www.hapmap.org
Launched October 2002
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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) gt5
• 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,151591-1593. 2005.

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ENCODE project

• Aim To compare the genome-wide resource to a
  more complete database of common variationone 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
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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 gt 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 17
• Cluster of common (frequent SNPs In high LD)
• 518 SNPs, spanning 800 kb
• 25 in EUR, 9 in AFR, missing in CHN
• Genes
• Microtubule-associated protein tau
• Mutations associated with a variety of
  neurodegeneartive disorders
• Gene coding for a protease similar to
  presenilins
• Mutations result in Alzheimers disease
• Gene 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