wi’08structure population sub-structure. wi’08structure projects harish/nitin gaurav (tuesday)...
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Wi’08 Structure
Population sub-structure
Wi’08 Structure
Projects• Harish/Nitin• Gaurav (Tuesday)• Stefano/Hossein (Tuesday)• Nisha/Yu• David• Jian/Josue (Tuesday)
Wi’08 Structure
Population sub-structure confounds association
• Consider an association test in a recently admixed population
• Suppose location A increases susceptibility to a disease common in Africans.
• Let locus B associate with skin-color.• As expected, locus A is associated
with the disease• Unexpectedly, locus B also shows
association• The problem arises because the
assumption of a random mating population is no longer true– The population has structure!
0 .. 1 D0 .. 1 N0 .. 0 D1 .. 1 N0 .. 1 D0 .. 1 D0 .. 1 D0 .. 1 D0 .. 1 D
1 .. 0 N1 .. 0 N0 .. 0 D1 .. 1 D1 .. 0 N1 .. 0 N1 .. 0 N1 .. 0 N1 .. 0 N
A B
Afr
ican
Euro
pean
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Population sub-structure can increase LD
• Consider two populations that were isolated and evolving independently.
• They might have different allele frequencies in some regions.
• Pick two regions that are far apart (LD is very low, close to 0)
0 .. 10 .. 10 .. 01 .. 10 .. 10 .. 10 .. 10 .. 10 .. 1
1 .. 01 .. 00 .. 01 .. 11 .. 01 .. 01 .. 01 .. 01 .. 0
Pop. A
Pop. B
p1=0.1q1=0.9P11=0.1D=0.01
p1=0.9q1=0.1P11=0.1D=0.01
Wi’08 Structure
Recent ad-mixing of population
• If the populations came together recently (Ex: African and European population), artificial LD might be created.
• D = 0.15 (instead of 0.01), increases 10-fold
• This spurious LD might lead to false associations
• Other genetic events can cause LD to increase, and one needs to be careful
0 .. 10 .. 10 .. 01 .. 10 .. 10 .. 10 .. 10 .. 10 .. 1
1 .. 01 .. 00 .. 01 .. 11 .. 01 .. 01 .. 01 .. 01 .. 0
Pop. A+B
p1=0.5q1=0.5P11=0.1D=0.1-0.25=0.15
Wi’08 Structure
Determining population sub-structure
• Given a mix of people, can you sub-divide them into ethnic populations.
• Turn the ‘problem’ of spurious LD into a clue. – Find markers that are too far apart to show LD– If they do show LD (correlation), that shows the
existence of multiple populations.– Sub-divide them into populations so that LD
disappears.
Wi’08 Structure
Determining Population sub-structure• Same example as before:• The two markers are too
similar to show any LD, yet they do show LD.
• However, if you split them so that all 0..1 are in one population and all 1..0 are in another, LD disappears
0 .. 10 .. 10 .. 01 .. 10 .. 10 .. 10 .. 10 .. 10 .. 1
1 .. 01 .. 00 .. 01 .. 11 .. 01 .. 01 .. 01 .. 01 .. 0
Wi’08 Structure
Iterative algorithm for population sub-structure
• Define• N = number of individuals (each has a single
chromosome)• k = number of sub-populations. • Z {1..k}N is a vector giving the sub-
population. – Zi=k’ => individual i is assigned to population k’
• Xi,j = allelic value for individual i in position j• Pk,j,l = frequency of allele l at position j in
population k
Wi’08 Structure
Example• Ex: consider the
following assignment• P1,1,0 = 0.9• P2,1,0 = 0.1
0 .. 10 .. 10 .. 01 .. 10 .. 10 .. 10 .. 10 .. 10 .. 10 .. 1
1 .. 01 .. 00 .. 01 .. 11 .. 01 .. 01 .. 01 .. 01 .. 01 .. 0
1111111111
2222222222
P1,1,0
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Goal• X is known.• P, Z are unknown. • The goal is to estimate Pr(P,Z|X)• Various learning techniques can be employed.
– maxP,Z Pr(X|P,Z) (Max likelihood estimate)– maxP,Z Pr(X|P,Z) Pr(P,Z) (MAP)– Sample P,Z from Pr(P,Z|X)
• Here a Bayesian (MCMC) scheme is employed to sample from Pr(P,Z|X). We will only consider a simplified version
Wi’08 Structure
Algorithm:Structure
• Iteratively estimate – (Z(0),P(0)), (Z(1),P(1)),.., (Z(m),P(m))
• After ‘convergence’, Z(m) is the answer.
• Iteration– Guess Z(0)
– For m = 1,2,..• Sample P(m) from Pr(P | X, Z(m-1))• Sample Z(m) from Pr(Z | X, P(m))
• How is this sampling done?
(Z1,P1)
(Z3,P3)
(Z4,P4)
(Z2,P2)
Wi’08 Structure
Example
• Choose Z at random, so each individual is assigned to be in one of 2 populations. See example.
• Now, we need to sample P(1) from Pr(P | X, Z(0))
• Simply count• Nk,j,l = number of people in
population k which have allele l in position j
• pk,j,l = Nk,j,l / N
0 .. 10 .. 10 .. 01 .. 10 .. 10 .. 10 .. 10 .. 10 .. 10 .. 1
1 .. 01 .. 00 .. 01 .. 11 .. 01 .. 01 .. 01 .. 01 .. 01 .. 0
1221121212
1221121221
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Example• Nk,j,l = number of people in
population k which have allele l in position j
• pk,j,l = Nk,j,l / Nk,j,*• N1,1,0 = 4• N1,1,1 = 6• p1,1,0 = 4/10• p1,2,0 = 4/10 • Thus, we can sample P(m)
0 .. 10 .. 10 .. 01 .. 10 .. 10 .. 10 .. 10 .. 10 .. 10 .. 1
1 .. 01 .. 00 .. 01 .. 11 .. 01 .. 01 .. 01 .. 01 .. 01 .. 0
1221121212
1221121221
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Sampling Z• Pr[Z1 = 1] = Pr[”01” belongs to population 1]?• We know that each position should be in
linkage equilibrium and independent.• Pr[”01” |Population 1] = p1,1,0 * p1,2,1
=(4/10)*(6/10)=(0.24) • Pr[”01” |Population 2] = p2,1,0 * p2,2,1 =
(6/10)*(4/10)=0.24• Pr [Z1 = 1] = 0.24/(0.24+0.24) = 0.5
Assuming, HWE, and LE
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Sampling
• Suppose, during the iteration, there is a bias.
• Then, in the next step of sampling Z, we will do the right thing
• Pr[“01”| pop. 1] = p1,1,0 * p1,2,1 = 0.7*0.7 = 0.49
• Pr[“01”| pop. 2] = p2,1,0 * p2,2,1 =0.3*0.3 = 0.09
• Pr[Z1 = 1] = 0.49/(0.49+0.09) = 0.85• Pr[Z6 = 1] = 0.49/(0.49+0.09) = 0.85• Eventually all “01” will become 1
population, and all “10” will become a second population
0 .. 10 .. 10 .. 01 .. 10 .. 10 .. 10 .. 10 .. 10 .. 10 .. 1
1 .. 01 .. 00 .. 01 .. 11 .. 01 .. 01 .. 01 .. 01 .. 01 .. 0
1112121211
2221221221
Wi’08 Structure
Allowing for admixture• Define qi,k as the fraction of individual i
that originated from population k.• Iteration
– Guess Z(0)
– For m = 1,2,..• Sample P(m),Q(m) from Pr(P,Q | X, Z(m-1))• Sample Z(m) from Pr(Z | X, P(m),Q(m))
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Estimating Z (admixture case)• Instead of estimating Pr(Z(i)=k|X,P,Q), (origin
of individual i is k), we estimate Pr(Z(i,j,l)=k|X,P,Q)
i,1i,2
j
€
Pr(Z i, j,l = k | X,P,Q) =qi,k Pr(X i, j,l | Z i, j,l = k,P)
qi,k' Pr(X i, j ,l | Z i, j ,l = k',P)k'
∑
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Results: Thrush data• For each
individual, q(i) is plotted as the distance to the opposite side of the triangle.
• The assignment is reliable, and there is evidence of admixture.
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NJ versus Structure:thrush data
• Objective function is different in standard clustering algorithms!
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Population Structure in isolated human populations
• 377 locations (loci) were sampled in 1000 people from 52 populations.
• 6 genetic clusters were obtained, which corresponded to 5 geographic regions (Rosenberg et al. Science 2003)
AfricaEurasia East Asia
America
Ocea
nia
Wi’08 Structure
Population sub-structure:research problem• Systematically explore the effect of
admixture. Can admixture be predicted for a locus, or for an individual
• The sampling approach may or may not be appropriate. Formulate as an optimization/learning problem:– (w/out admixture). Assign individuals to sub-
populations so as to maximize linkage equilibrium, and hardy weinberg equilibrium in each of the sub-populations
– (w/ admixture) Assign (individuals, loci) to sub-populations
Wi’08 Structure
Population Substructure Conclusions• Populations substructure (violating the
assumption of random mating) can create artificial linkage disequlibrium, and false associations
• One way out of it is to identify and sub-divide the populations into sub-populations.
• Another approach is to ‘correct’ for the effects of structure.
Wi’08 Structure
Detecting structural variations
Wi’08 Structure
Genomic variation• Inherited phenotypes arise from genetic variation
– Point mutations, indels, genetic recombination, but also….– Structural Variation
• Insertions, deletions, translocations, inversions, fissions, fusions….
deletions
inversions
translocations
Wi’08 Structure
Fluoroscent in situ hybridization
• (Cancer genomes show extensive structural variation)
• Historically, larger structural variations (easily observed under a microscope were commonly studied, mostly in the context of diseases…
Wi’08 Structure
HapMap and other projects
• The development of molecular techniques (sequencing, genotyping) shifted interest onto smaller scale mutations. They were assumed to be the dominant source of genetic variation
• It turns out that structural variation in normal populations is more common than assumed.
Wi’08 Structure
1. Inversions and HapMap
A
AA
A
A
ACC
GG
G
G
T
TT
G
G
GAG
A
AA
G
A
A GGA
CTCA
• SNP data is seemingly oblivious to Inversions (& other structural polymorphisms)
• Can we detect a signal for inversion polymorphisms in SNPs?
A
A
A
AA
G
G
G
G
GG
G
GG
reference genome sequence
population
Wi’08 Structure
Array-CGH
Garnis et al. Molecular Cancer 2004
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CNVs dominate, possibly because of technology
Wi’08 Structure
Structural variations
• Structural variants are common, but non CNVs are hard to detect.
• Some of the translocations are important in disease
Wi’08 Structure
2. Variations in tumor genomes
• Fusion observed in leukemia, lymphoma, and sarcomas
• “Philadelphia Translocation” Drugs target this fusion protein
• Can we detect fused genes in tumors?
Wi’08 Structure
3. Assaying for specific variations
• Most tumors start off with a single cell, which then proliferate.
• Drugs like Gleevec are used well after cancer has taken hold.
• Can we detect the cancer early by detecting the genomic abnormality?
– If a very few cells in the person are cancerous, can we still detect it?
• Can we track a patient through his treatment?
Wi’08 Structure
Today
• Detection of inversion polymorphisms (& other copy neutral variation) using genotype data.
• Detection of gene fusion events using sequencing
• PCR based detection of variation in the presence of heterosomy: only a fraction of cells carry the variant genome
Wi’08 Structure
Chr. 17 Inversion
Wi’08 Structure
Inversion polymorphisms
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Common inverted haplotype
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LLR statistic computation
• Multi-allelic markers are chosen in blocks around the putative breakpoints
• LD is measured using multi-allelic D-statistic
M1 M2 M3 M4
LD24 LD34LD13LD12
Bansal et al.Genome Research, 2007
Wi’08 Structure
LLRl
M1 M2 M3 M4
LD13LD13
€
LLRl = log Pr(LD12,LD13 | M1 → M3 → M2 → M4 )Pr(LD12,LD13 | M1 → M2 → M3 → M4 )
⎛ ⎝ ⎜
⎞ ⎠ ⎟
d12d13
Wi’08 Structure
LLRR
M1 M2 M3 M4
LD24 LD34
€
LLRR = log Pr(LD24 ,LD34 | M1 → M3 → M2 → M4 )Pr(LD24 ,LD34 | M1 → M2 → M3 → M4 )
⎛ ⎝ ⎜
⎞ ⎠ ⎟
d12d24
Wi’08 Structure
Inversion polymorphisms in human
• LLRl and LLRr define our inversion statistic • Large positive values for both likelihood ratios
indicate inversion • A permutation test to estimate the significance
of the statistic• Overlapping breakpoints are merged
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Power
• Difficult to simulate inversions using the coalescent• We simulated inversions on HapMap data.• (a) varying frequency, 500kb inversion• (b) varying length
Wi’08 Structure
Inversion polymorphisms
• We used the Phase I phased haplotype data from the International HapMap project – 3 samples: CEU, YRI, Asian: CHB+JPT about 900K
SNPs • The location between two adjacent SNPs was
considered a potential inversion breakpoint • The statistic was computed for every pair of
inversion breakpoints within a certain distance (200kb - 6Mb)
• 176 inversion polymorphisms were detected
Wi’08 Structure
Inversions with secondary evidence
• 18 regions had highly homologous repeat sequence, 11 with inverted repeats (p-value 0.006 against random distribution of inversion breakpoints)
Wi’08 Structure
Inversions with secondary evidence
Wi’08 Structure
1.4Mb inversion at 16p12(CEU+YRI)
• Supported by fosmid pair evidence (Tuzun et al., 2005)• 80kb long inverted repeat• Identical breakpoints in CEU and YRI data• Known chimp repeat
Wi’08 Structure
1.2Mb Chr 10 (CHB+JPT)
• Inversion supported by fosmid evidence (Tuzun et al. 2005)
Wi’08 Structure
Chr 6 Inversion(YRI) & TCBA1
• 66 inversion breakpoints covered by genes• Less than expected by chance (p-value 0.02)• Many overlapping genes are known to be disrupted in disease• T-cell lymphoma breakpoint associated target (TCBA1)
– Structurally disrupted in T-cell lymphoma cell-lines
Wi’08 Structure
ICAp69
• Islet cell antigen (ICAp69) gene
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Inversion Polymorphism summary
• Many inversions (and copy neutral) polymorphisms remain to be detected.
• The genotype LD signal is useful but has low power.– We are investigating other signals to
improve detection• Some of these variations lead to genes
fusing.
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Conclusions for the class
• Genetic variations are important to our understanding of evolution and genotype-phenotype relationship
Wi’08 Structure
Topics covered1. We started (and finished) by considering sources of
variation2. Models of evolution of population under natural
assumptions1. HW/Linkage equlibrium2. Efficient simulation of populations via coalescent theory
3. Evolution under recombinations/recombination hot-spot detection via counting of recombination events
4. Detection of regions under selection5. Association testing6. Population sub-structure7. Detecting structural variation
Wi’08 Structure
Algorithmic diversions1. Phylogeny reconstruction (perfect phylogeny,
distance-based methods)2. Optimization using (Integer-) Linear programming,
simulated annealing and other paradigms3. Greedy algorithms, dynamic programming4. Stochastic sampling methods (MCMC, Gibbs
sampling)5. Statistical tests for significance6. Efficient simulation techniques
1. Coalescent for populations2. Simulating genotype/phenotype associations
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