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

2. 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

3. 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.

4. 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 2

5. 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.

6. 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

7. 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)

8. 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

9. 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

10. 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

11. 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

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

13. 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 + F F00F01 + 2F00F10 + 2F00F11 + 2F01F10 + 2F01F11 + 2F10F11
G00 G01 G10 G G G G G G12
Observed deviation from HWE in one SNP
(F0+F1)(F0+F1-2x)= (F0+x)2 + (F1+x)2 + 2(F0F1-x2)
xG yG 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 = F F F F F00F01 + 2F00F10 + 2F00F11 + 2F01F10 + 2F01F11 + 2F10F11
xxG00 xyG01 yxG10 yyG11 xzG zxG zzG zyG21 yzG12

14. 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 =
Trans- edge: 22 =
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
Haplotype #1 b c
Haplotype #2 d

15. 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

16. 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

17. 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 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.

18. 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.

19. Results

20. 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