1. Sharlee Climer, Alan R. Templeton, and Weixiong Zhang
SplittingHeirs: Inferring Haplotypes by Optimizing Resultant Dense Graphs
Sharlee Climer, Alan R. Templeton, and Weixiong Zhang
ACM-BCB, Niagara falls
August 2010

2. Overview Introduction Definition of haplotype inference problem
Previous approaches
SplittingHeirs
Experimental results

3. Introduction Only 0.1% of human DNA has variation
Most of this variation is due to Single Nucleotide Polymorphisms (SNPs)
Most SNPs have only two variants, or alleles, within a population
Broad definition of haplotype:
A set of alleles for a given set of SNPs in relatively close proximity on a chromosome
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4. Introduction DNA is transcribed to produce RNA
RNA is translated, ultimately producing proteins
Variation in non-coding regions might have an effect on regulation
SNPs throughout the genome may be of interest
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5. Introduction Humans are diploid
Pairs of chromosomes
Common sequencing produces a meld of the two haplotypes, referred to as a genotype
Computational methods used to infer a pair of haplotypes from a genotype
Phasing the genotype G C T T
SNP1
SNP2
G C
T T
G T A C + C T A G ?
C T A C + G T A G

6. Importance of accuracy when inferring haplotypes from genotypes
SNP1
SNP2
SNP1
SNP2
C C
T C
G C
T T
Importance of accuracy when inferring haplotypes from genotypes
Frequently an early step in expensive and vitally important studies

7. Introduction Possible to identify the separate haplotypes directly
Only feasible for very small studies
Useful for testing accuracy of computational methods
Andres et al. [Genet. Epi. 2007] found computational methods had poor accuracy and confidence levels were error prone
PHASE [Stephens et al., AJHG 2001]
fastPhase [Scheet and Stephens, AJHG 2006]
HAP [Halperin and Eskin, Bioinformatics 2004]
GERBIL [Kimmel and Shamir, PNAS 2005]
Errors in confidence levels suggest that the models might not fully capture biological properties

8. Problem Definition G T A C C T A G 1 1 0 0 0 1 0 1 2 1 0 2
Let ‘0’ and ‘1’ represent the two possible alleles for a given SNP
Haplotype represented by a string of binary values
Genotype for a pair of haplotypes
‘0’ if both alleles are ‘0’
‘1’ if both alleles are ‘1’
‘2’ if heterozygous
G T A C
C T A G

9. Problem Definition
For k heterozygous sites, there are 2k-1 feasible solutions
Not apparent which solution is more likely than another
Population-level characteristics
There tends to be relatively few unique haplotypes
There tends to be clusters of haplotypes that are similar to each other
Some haplotypes are relatively common

10. Problem Definition
Given a set of genotypes drawn from a population: 1) Find the set of haplotypes that exist in the set 2) For each genotype, determine the pair of haplotypes that is mostly likely to exist in the given individual
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11. Example Example problem Display solutions as graphs g1: 1111 0001
5 individuals
8 SNP sites
Display solutions as graphs
Each node represents a unique haplotype
Edge weight
Measure of difference between haplotypes
Set equal to the number of sites that differ between the haplotypes
Edges with smallest distances are shown
g1:
g2:
g3:
g4:
g5:

12. Example Solution found by: 5 unique haplotypes
g1:
g2:
g3:
g4:
g5:
Solution found by:
Clark’s Subtraction Method [Mol. Biol. And Evol. 1990]
Pure Parsimony [Gusfield, CPM’03]
EM [Excoffier and Slatkin, Mol. Biol.Evol. 1995]
5 unique haplotypes
Haplotypes are not very similar to each other

13. Example No Perfect Phylogeny solution Solution found by HAP
6 unique haplotypes
Haplotypes are slightly more similar to each other

14. Example Solution found by PHASE 9 unique haplotypes
g1:
g2:
g3:
g4:
g5:
Solution found by PHASE
9 unique haplotypes
Haplotypes are more similar to each other

15. Example PHASE favors pair-wise similarities
g1:
g2:
g3:
g4:
g5:
PHASE favors pair-wise similarities
Essentially evaluating a nearest-neighbor graph

16. SplittingHeirs where di = the weight of edge i
SplittingHeirs favors cluster-wide similarities, as well as reduced cardinality
Cast as a Mixed Integer Linear Program (MIP)
Minimize:
where
di = the weight of edge i
h = the cardinality of the haplotype set
u = a weighting factor

17. SplittingHeirs
Enforce cluster-wide similarities by requiring a minimum density of edges in the graph
Additional constraint:
where
e = number of edges
a is a configurable parameter
Can be decreased for highly diverse sample
Can be increased for sample with low diversity

18. Example Solution found by SplittingHeirs 8 unique haplotypes
Haplotypes are quite similar to each other

19. Results
Tested on 7 sets of haplotype data for which the true phase is known
n is the number of individuals
m is the number of sites
# Ambiguous is the number of genotypes that have more than one feasible solution

20. Results

21. Results

22. Conclusions
Introduced a biologically intuitive model that optimizes cluster-wide similarities and reduced cardinality
Globally optimal solutions can be computed for small regions
Candidate locus studies
Future work
Speed up computation
Use model to guide an approximation method
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23. Acknowledgments Olin Fellowship NIH grants NSF grants
P50-GM065509
R01-GM087194A2
U01-GM063340
NSF grants
IIS
DBI
Alzheimer’s Association grant
Thanks to:
Taylor Maxwell
Gerold Jaeger