Phasing of 2-SNP Genotypes Based on Non-Random Mating Model Dumitru Brinza Alexander Zelikovsky Department of Computer Science Georgia State University Atlanta, USA

Molecular biology terms Motivation Problem formulation Previous work Outline Molecular biology terms Motivation Problem formulation Previous work Our contribution Phasing of 2-SNP genotypes Phasing of a complete genotype Results

Molecular biology terms Human Genome – all the genetic material in the chromosomes, length 3×109 base pairs Difference between any two people occur in 0.1% of genome SNP – single nucleotide polymorphism site where two or more different nucleotides occur in a large percentage of population. Genotype – The entire genetic identity of an individual, including alleles, SNPs, or gene forms. (e.g., AC CT TG AA AC TG) Haplotype – A single set of chromosomes (half of the full set of genetic material). (e.g., A C T A A T) Genotype is a mixture of two haplotypes.

From ACTG to 0,1,2 notations  Haplotype: Genotypes: Wild type SNPs are notated as 0 Mutated SNPs are notated as 1 Genotypes: Homozygous SNPs are notated as 0,1 (mixture of 00,11) Heterozygous SNPs are notated as 2 (mixture of 01,10) homozygous haplotype SNP heterozygous Two haplotypes per individual Genotype for the individual  1 0 1 0 0 1 1 1 0 2 1 2 0 2

Motivation Haplotype may contain large amount of genetic markers, which are responsible for human disease. Haplotypes may increase the power of association between marker loci and phenotypic traits. Evolutionary tree can be reconstructed based on haplotypes. Physical phasing (haplotypes inferring) is too expensive. Great need in computational methods for extracting haplotype information from the given genotype information. Existing methods are either extremely slow or less accurate for genome-wide study.

Phasing problem (Haplotype inference) Inferring haplotypes or genotype phasing is resolution of a genotype into two haplotypes Given: n genotype vectors (0, 1 or 2), Find: n pairs of haplotype vectors, one pair of haplotypes per each genotype explaining genotypes For individual genotype with h heterozygous sites there are 2h-1 possible haplotype pairs explaining this genotype (h=20k for the genome-wide). also there are around 10% missing data. This is hopeless without genetic model

Previous work PHASE – Bayesian statistical method (Stephens et al., 2001, 2003) HAPLOTYPER – proposed a Monte Carlo approach (Niu et al., 2002) Phamily – phase the trio families based on PHASE (Acherman et al., 2003) GERBIL – statistical method using maximum likelihood (ML), MST and expectation-maximization (EM) (Kimmel and Shamir, 2005) SNPHAP – use ML/EM assuming Hardy-Weinberg equilibrium (Clayton et al., 2004)

Contribution We explore phasing of genotypes with 2 SNPs which have ambiguity when the both sites are heterozygous. There are two possible phasing and the phasing problem is reduced to inferring their frequencies. Having the phasing solution for 2-SNP genotypes, we propose an algorithm for inferring the complete haplotypes for a given genotype based on the maximum spanning tree of a complete graph with vertices corresponding to heterozygous sites and edge weights given by the inferred 2-SNP frequencies. Extensive experimental validation of proposed methods and comparison with the previously known methods

Phasing of 2-SNP genotypes At least one SNP is homozygous – phasing is well defined: Both SNPs are heterozygous – ambiguity Cis- phasing Trans- phasing 01 01 or Example 01 21 01 11 0 0 22 1 1 0 1 22 1 0

Certainty of cis- or trans- phasing Normally odds ratio of being phased cis- or trans- Modified odds ratio better describes cis- or trans- phasing LD (linkage disequilibrium) between endpoints i and j

Certainty of cis- or trans- phasing Higher LD between pairs of closer SNPs We discard falsely encountered LD between non-linked SNPs which are far apart Logarithm stays for sign, cij ≤ 0 means cis- with certainty |cij| cij > 0 means trans- with certainty |cij| 0 0 22 i j 1 1 0 1 22 i j 0 1

Certainty of cis- or trans- phasing n – number of genotypes F00, F01, F10, F11 – true haplotype frequencies (observed + expected in 22) i j Genotypes ? 1 0 2 1 1 0 1 0 1  #01 + 2 1 1 0 0 1 0 0 2 0 1  #00 + 2 *  0 1 2 0 1 2 0 1 0 1  (#00 + 1 , #11 + 1) or (#01 + 1 , #10 + 1) 2 1 1 0 1 1 0 ? 0 1  #11 + 2 0 1 1 0 1 2 0 0 2 1  #10 + 1 , #11 + 1

Haplotype frequencies in 22 Chosen to fit best Hardy-Weinberg equilibrium adjusted to observed deviation in single-site genotype distribution Hardy-Weinberg Equilibrium (HWE): (F00+F01+F10+F11)2 = F002 + F012 + F102 + F112 + 2F00F01 + 2F00F10 + 2F00F11 + 2F01F10 + 2F01F11 + 2F10F11 G00 G01 G10 G11 G02 G20 G22 G21 G12 Observed deviation from HWE in one SNP (F0+F1)(F0+F1-2x)= (F0+x)2 + (F1+x)2 + 2(F0F1-x2) xG0 yG1 zG2 Haplotype frequencies in 22 are chosen to fit best Hardy-Weinberg equilibrium adjusted to observed deviation in single-site genotype distribution HWE deviation in 2 SNPs based on HWE deviation in each SNP (F00+F01+F10+F11)2 = F002 + F012 + F102 + F112 + 2F00F01 + 2F00F10 + 2F00F11 + 2F01F10 + 2F01F11 + 2F10F11 xxG00 xyG01 yxG10 yyG11 xzG02 zxG20 zzG22 zyG21 yzG12

Phasing of a complete genotype Genotype graph for genotype g is a complete graph G(g ) where: Vertices = heterozygous SNPs in g (I,j)-edge weight w(I,j)=cis-/trans- likelihood phasing Phasing of 2 heterozygous SNPs Cis- edge: 22 = 00 + 11 Trans- edge: 22 = 01 + 10 Graph coloring Color all vertices in two colors such that any 2 vertices connected with the cis- edge have the same color, and any 2 vertices connected with trans- edge have opposite colors a b c d a Genotype 2 1 2 0 1 2 0 2 0 1 Haplotype #1 1 1 0 0 1 0 0 1 0 1 b c Haplotype #2 0 1 1 0 1 1 0 0 0 1 d

Phasing of a complete genotype Graph coloring Conflicts are solved using Maximum Spanning Tree (MST) 1 2 1 1 2 1 2 2 3 1 1 3

2SNP algorithm Collect statistics on haplotype/genotype frequencies for any 2 SNPs For each 2 SNPs compute weights reflecting likelihood of trans-/cis- For each genotype g: Find Maximum Spanning Tree for the complete graph G(g ) where vertices are heterozygous sites Color G(g ) vertices and phase based on colors Missing data recovery Recover each missing site based on the closest haplotype (Hamming distance) with the phased site Runtime (two bottlenecks) O(nm) – computing haplotype frequencies for 20×m pair of SNPs in each genotype, n is number of genotypes, m number of SNP’s. O(n2m) – missing data recovery, comparison of n genotypes by Hamming distance

Datasets Chromosome 5q31: 129 genotypes with 103 SNPs derived from the 616 KB region of human Chromosome 5q31 (Daly et al., 2001). Yoruba population (D): 30 genotypes with SNPs from 51 various genomic regions, with number of SNPs per region ranging from 13 to 114 (Gabriel et al., 2002). Random matching 5q31: 128 genotypes each with 89 SNPs from 5q31 cytokine gene generated by random matching from 64 haplotypes of 32 West African Hull et al. (2004). HapMap datasets: 30 genotypes of Utah residents and Yoruba residents available on HapMap by Dec 2005. The number of SNPs varies from 52 to 1381 across 40 regions including ENm010, ENm013, ENr112, ENr113 and ENr123 spanning 500 KB regions of chromosome bands 7p15:2, 7q21:13, 2p16:3, 4q26 and 12q12 respectively, and two regions spanning the gene STEAP and TRPM8 plus 10 KB upstream and downstream.

Unrelated individuals phasing validation Phasing methods can be validated on simulated data (haplotypes are known) The validation on real data is usually performed on the trio data Offspring haplotypes are mostly known (inferred from parents haplotypes) Error types Single-Site error Number of SNPs in offspring phased haplotypes which differ from SNPs inferred from trio data, divide by (total number of SNPs) x (total number of haplotypes) Individual error Number of correctly phased offspring genotypes (no Single-Site errors) divide by total number of genotypes Switching error Minimum number of switches which should be done in pair of haplotypes of offspring phased genotype such that both haplotypes will coincide with haplotypes inferred from trio data, divide by total number of heterozygous positions in offspring genotypes.

Results

Conclusion Entire genome (30 Trios from Hapmap) Average Errors: Single-site: 3.3% Switching: 8.8% #SNPs 1.5K runtime 2 sec 2.5K 8 sec 5.0K 25 sec 10.0K 55 sec 20.0K 220 sec 40.0K 17 min 60.0K 35 min 80.0K 70 min 2SNP method Several orders of magnitude faster Scalable for genome-wide study Same accurate as PHASE and Gerbil