Phasing of 2-SNP Genotypes

1

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

2
Outline

• Molecular biology terms
• Motivation
• Problem formulation
• Previous work
• Our contribution
• Phasing of 2-SNP genotypes
• Phasing of multi-SNP genotypes
• Results

3
Molecular biology terms

• Human Genome all the genetic material in the
  chromosomes, length 3109 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
• Wild type SNPs are referred as 0
• Mutated SNPs are referred as 1
• Genotypes
• Homozygous SNPs are referred as 0 (mixture of
  00) or 1 (mixture of 11)
• Heterozygous SNPs are referred as 2 (mixture of
  01,10)

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 (h20k 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

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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
01
Example
21
01
11
0 0
22
1 1
0 1
22
1 0
10
Odds of cis- or trans- phasing

• Odds ratio of being phased cis- / trans-

Additive odds ratio is better (also noticed in
PHASE)
LD (linkage disequilibrium) between SNPs i and j
11
Confidence in cis- or trans- phasing

• Closer pairs of SNPs are more linked (less
  crossovers)
• The confidence cij in phasing 2 SNPs i and j
• is inverse proportional to squared distance

Logarithm is for sign-indication of cis-/trans-
preference cij 0 means cis- with certainty
cij cij gt 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 true in 22)

j
i
Genotypes
? 1 0 2 1 1 0 1 0 1
? 01 2
? 00 2
1 1 0 0 1 0 0 2 0 1
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
13
Haplotype frequencies in 22

• Random mating model gt Hardy-Weinberg Equilibrium
  (HWE)

(F00F01F10F11)2 F002 F012 F102 F112
2F00F01 2F00F10 2F00F11 2F01F10 2F01F11
2F10F11
G00 G01 G10 G11 G02
G20 G22 G21
G12

• Even single-SNP haplotype frequencies may deviate
  from HWE

• Accordingly we adjust expectation of 2-SNP
  haplotype frequencies

• Compute expected haplotype frequencies in 22 as
  best fitting to observed deviation in
  single-site haplotype frequencies

14
Phasing of multi-SNP genotypes

• Genotype graph for genotype g is a weighted
  complete graph G(g ) where
• Vertices 2s i.e., heterozygous SNPs in g
• Weight w(i,j) cij confidence in phasing 2
  SNPs i and j
• Phasing of 2 heterozygous SNPs
• cij gt 0 ? cis-edge 22 00 11
• cij lt 0 ? trans-edge 22 01 10
• Phasing Genotype graph coloring
• Color all vertices in two colors such that
• any 2 vertices connected with a cis-edge have
  the same color, and
• any 2 vertices connected with a trans-edge have
  opposite colors

a b c d
a
2 1 2 0 1 2 0 2 0 1
Genotype
1 1 0 0 1 0 0 1 0 1
Haplotype 1
b
c
Haplotype 2
0 1 1 0 1 1 0 0 0 1
d
15
Genotype graph coloring
Frequent conflicts when coloring genotype graph G
since it has cycles Genotype Graph Coloring
Problem Find coloring with total weight
(number) of conflicting edges minimized
Exact solution ILP slow and not accurate
Heuristic solution Find maximum spanning
tree (MST) of G and color MST instead of G
16
2SNP algorithm

• For each pair of SNPs do
• Collect statistics on haplotype/genotype
  frequencies
• Compute weights reflecting likelihood of
  trans-/cis-
• For each genotype g do
• Find MST for the complete graph G(g ) where
  vertices are heterozygous sites
• Color G(g ) vertices and phase based on coloring
• For each haplotype h with ?s (missing SNP
  values) do
• Find a haplotype h closest to h (with minimum
  number of mismatches)
• Replace ?s in h with the known SNP value in h
• Runtime (two bottlenecks)
• O(nm) computing haplotype frequencies for 20m
  pairs of SNPs in each genotype, n is number
  of genotypes, m number of SNPs.
• O(n2m) missing data recovery, finding number of
  mismatches for any two haplotypes

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
  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 7p152, 7q2113, 2p163, 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
Chromosome-Wide Phasing
Entire chromosomes for 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
21
Conclusion
2SNP method Several orders of magnitude
faster Scalable for genome-wide study Phase 10000
SNPs in less than one hour Same accuracy as PHASE
and Gerbil