Wi’08Structure Population sub-structure

Wi’08Structure Projects Harish/Nitin Gaurav (Tuesday) Stefano/Hossein (Tuesday) Nisha/Yu David Jian/Josue (Tuesday)

Wi’08Structure 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! D N D N D N D D N A B African European

Wi’08Structure 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) Pop. A Pop. B p 1 =0.1 q 1 =0.9 P 11 =0.1 D=0.01 p 1 =0.9 q 1 =0.1 P 11 =0.1 D=0.01

Wi’08Structure 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 Pop. A+B p 1 =0.5 q 1 =0.5 P 11 =0.1 D= =0.15

Wi’08Structure 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’08Structure 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

Wi’08Structure 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. – Z i =k’ => individual i is assigned to population k’ X i,j = allelic value for individual i in position j P k,j,l = frequency of allele l at position j in population k

Wi’08Structure Example Ex: consider the following assignment P 1,1,0 = 0.9 P 2,1,0 = P 1,1,0

Wi’08Structure Goal X is known. P, Z are unknown. The goal is to estimate Pr(P,Z|X) Various learning techniques can be employed. – max P,Z Pr(X|P,Z) (Max likelihood estimate) – max P,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’08Structure 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? (Z 1,P 1 ) (Z 3,P 3 )(Z 4,P 4 )(Z 2,P 2 )

Wi’08Structure 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 N k,j,l = number of people in population k which have allele l in position j p k,j,l = N k,j,l / N

Wi’08Structure Example N k,j,l = number of people in population k which have allele l in position j p k,j,l = N k,j,l / N k,j,* N 1,1,0 = 4 N 1,1,1 = 6 p 1,1,0 = 4/10 p 1,2,0 = 4/10 Thus, we can sample P (m)

Wi’08Structure Sampling Z Pr[Z 1 = 1] = Pr[”01” belongs to population 1]? We know that each position should be in linkage equilibrium and independent. Pr[”01” |Population 1] = p 1,1,0 * p 1,2,1 =(4/10)*(6/10)=(0.24) Pr[”01” |Population 2] = p 2,1,0 * p 2,2,1 = (6/10)*(4/10)=0.24 Pr [Z 1 = 1] = 0.24/( ) = 0.5 Assuming, HWE, and LE

Wi’08Structure 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] = p 1,1,0 * p 1,2,1 = 0.7*0.7 = 0.49 Pr[“01”| pop. 2] = p 2,1,0 * p 2,2,1 =0.3*0.3 = 0.09 Pr[Z 1 = 1] = 0.49/( ) = 0.85 Pr[Z 6 = 1] = 0.49/( ) = 0.85 Eventually all “01” will become 1 population, and all “10” will become a second population

Wi’08Structure Allowing for admixture Define q i,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) )

Wi’08Structure 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,1 i,2 j

Wi’08Structure 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.

Wi’08Structure NJ versus Structure:thrush data Objective function is different in standard clustering algorithms!

Wi’08Structure 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) Africa EurasiaEast Asia America Oceania

Wi’08Structure 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’08Structure 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’08Structure Detecting structural variations

Wi’08Structure 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’08Structure 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’08Structure 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’08Structure 1. Inversions and HapMap A A A A A AC C G G G G T T T G G G AG A A A G A AG GA CT CA SNP data is seemingly oblivious to Inversions (& other structural polymorphisms) Can we detect a signal for inversion polymorphisms in SNPs? A A A A A G G G G G G G G G reference genome sequence population

Wi’08Structure Array-CGH Garnis et al. Molecular Cancer 2004

Wi’08Structure CNVs dominate, possibly because of technology

Wi’08Structure Structural variations Structural variants are common, but non CNVs are hard to detect. Some of the translocations are important in disease

Wi’08Structure 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’08Structure 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’08Structure 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’08Structure Chr. 17 Inversion

Wi’08Structure Inversion polymorphisms

Wi’08Structure Common inverted haplotype

Wi’08Structure LLR statistic computation Multi-allelic markers are chosen in blocks around the putative breakpoints LD is measured using multi-allelic D-statistic M1M1 M2M2 M3M3 M4M4 LD 24 LD 34 LD 13 LD 12 Bansal et al. Genome Research, 2007

Wi’08Structure LLR l M1M1 M2M2 M3M3 M4M4 LD 13 d 12 d 13

Wi’08Structure LLR R M1M1 M2M2 M3M3 M4M4 LD 24 LD 34 d 12 d 24

Wi’08Structure 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

Wi’08Structure Power Difficult to simulate inversions using the coalescent We simulated inversions on HapMap data. (a) varying frequency, 500kb inversion (b) varying length

Wi’08Structure 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’08Structure Inversions with secondary evidence 18 regions had highly homologous repeat sequence, 11 with inverted repeats (p-value against random distribution of inversion breakpoints)

Wi’08Structure Inversions with secondary evidence

Wi’08Structure 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’08Structure 1.2Mb Chr 10 (CHB+JPT) Inversion supported by fosmid evidence (Tuzun et al. 2005)

Wi’08Structure 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’08Structure ICAp69 Islet cell antigen (ICAp69) gene

Wi’08Structure 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.

Wi’08Structure Conclusions for the class Genetic variations are important to our understanding of evolution and genotype- phenotype relationship

Wi’08Structure Topics covered 1. We started (and finished) by considering sources of variation 2. Models of evolution of population under natural assumptions 1. HW/Linkage equlibrium 2. 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 selection 5. Association testing 6. Population sub-structure 7. Detecting structural variation

Wi’08Structure Algorithmic diversions 1. Phylogeny reconstruction (perfect phylogeny, distance-based methods) 2. Optimization using (Integer-) Linear programming, simulated annealing and other paradigms 3. Greedy algorithms, dynamic programming 4. Stochastic sampling methods (MCMC, Gibbs sampling) 5. Statistical tests for significance 6. Efficient simulation techniques 1. Coalescent for populations 2. Simulating genotype/phenotype associations