Post on 17-Jan-2016
description
Scalable Algorithms for Analysis of Genomic Diversity Data
Bogdan Paşaniuc
Department of Computer Science & EngineeringUniversity of Connecticut
Main form of variation between individual genomes: single nucleotide polymorphisms (SNPs)
High density in the human genome: 1x107 out of 3109 base pairs
Vast majority bi-allelic 0/1 encoding
Single Nucleotide Polymorphisms
… ataggtccCtatttcgcgcCgtatacacgggActata …… ataggtccGtatttcgcgcCgtatacacgggTctata …… ataggtccCtatttcgcgcCgtatacacgggTctata …
Haplotypes and Genotypes
Haplotype: description of SNP alleles on a chromosome 0/1 vector: 0 for major allele, 1 for minor
Diploids: two homologous copies of each autosomal chromosome One inherited from mother and one from father
Genotype: description of alleles on both chromosomes 0/1/2 vector: 0 (1) - both chromosomes contain the major (minor)
allele; 2 - the chromosomes contain different alleles
021200210011000110001100010
+ two haplotypes per individual
genotype
Introduction
Haplotype data exact DNA sequence function
Haplotypes increased power of association
Directly determining haplotype data is expensive and time consuming
Cost effective high-throughput technologies to determine genotype data
Need for computational methods for inferring haplotypes from genotype data: genotype phasing problem
Outline
Background on genomic diversity The genotype phasing problem Hidden Markov Model of Haplotype
Diversity Genotype Imputation DNA Barcoding Conclusions
Genotype Phasing
For a genotype with k 2’s there are 2k-1 possible pairs of haplotypes explaining it
g: 0010212 ?
h1:0010111
h2:0010010
h3:0010011
h4:0010110
Computational approaches to genotype phasing Statistical methods: PHASE, Phamily, PL, GERBIL … Combinatorial methods: Parsimony, HAP, 2SNP, ENT …
Minimum Entropy Genotype Phasing
Phasing – function f that assigns to each genotype g a pair of haplotypes (h,h’) that explains g
Coverage of h in f – number of times h appears in the image of f Entropy of a phasing:
)||2
),cov(log(
||2
),cov()(
0),cov(: G
fh
G
fhfEntropy
fhh
Minimum Entropy Genotype Phasing [Halperin&Karp 04]: Given a set of genotypes, find a phasing with minimum entropy
ENT Algorithm
InitializationStart with random phasing
Iterative improvement stepWhile there exists a genotype whose re-phasing decreases the entropy, find the genotype that yields the highest decrease in entropy and re-phase it
Min Entropy Objective is uninformative for long genotypes each haplotype compatible with 1 genotype all haplotypes have
coverage of 1 entropy of all phasings = -log(1/2G)
Overlapping Window approach
Entropy is computed over short windows of size l+f l “locked” SNPs previously phased f “free” SNPs are currently phased
locked free
…4321
g1
gn
…
…
Only phasings consistent with the l locked SNPs are considered
Effect of Window Size
Experimental setup (1)
International HapMap Project, Phase II datasets 3.7 million SNP loci 3 populations:
CEU, YRI: 30 trios JPT+CHB: 90 unrelated individuals
Reference haplotypes obtained using PHASE Accuracy
Relative Genotype Error (RGE): percentage of missing genotypes inferred differently as reference method
Relative Switching Error (RSE): number of switches needed to convert inferred haplotype pairs into the reference haplotype pairs
Experimental setup (2)
Compared algorithms ENT 2SNP [Brinza&Zelikovsky 05] Pure Parsimony Trio Phasing (ILP)
[Brinza et al. 05] PHASE [Stephens et al 01] HAP [Halperin&Eskin 04] FastPhase [Scheet&Stephens 06]
Results on HapMap Phase II Panels
Averages over the 22 chromosomes Runtime:
ENT few hours PHASE months of CPU time on cluster of 238
nodes
Results on [Orzack et al 03] dataset
[Orzack et al. 03] 80 unrelated genotypes over 9 SNPs Haplotypes determined experimentally
Ranking of algorithms remains the same Slight underestimation of true error rate
Effect of pedigree information
Outline
Background on genomic diversity The genotype phasing problem Hidden Markov Model of Haplotype
Diversity Genotype Imputation DNA Barcoding Conclusions
Founder Haplotypes
Haplotypes in the current population arose from small number of founder haplotypes by mutation and recombination events
Obtained using HaploVisual www.cs.helsinki.fi/u/prastas/haplovisual/
HMM Model
Similar to models proposed by [Schwartz 04, Rastas et al. 05, Kimmel&Shamir 05, Scheet&Stephens 06]
Models the ancestral haplotype population Paths with high transition probability “founder”
haplotypes Transitions from one founder to other founder
recombination events Emissions mutation events
HMM Training
Previous works use EM training of HMM based on unrelated genotype data
2-step procedure: 1. Infer haplotypes using ENT
Uses all available pedigree information
2. Baum-Welch training on inferred haplotypes Maximizes the likelihood of the haplotypes
Maximum Probability Genotype Phasing
Phase G as pair (h1,h2) = argmax P(h1)P(h2) Maximum phasing probability:
How hard is to compute maximum phasing probability in the HMM? Conjectured to be NP-hard [Rastas et al 07]
Theorem Cannot approximate P(G) within O(n1/2 -), unless
ZPP=NP, where n is the number of SNP loci
)()( MAX)( 21 hPhPGP
Complexity of Computing Maximum Phasing Probability
Reduction from Max Clique
Transitions1,1/2 Initial transition 2deg(v)+1(2)/α All haps prob 1/α
Complexity of Computing Maximum Phasing Probability
H representing clique of size k will be emitted along k paths P(H) = k/α
By construction H’ (complement of H) can be emitted along second block
G = 22…22 P(G)=max(P(H))2
G has a clique of size k or more iff P(G) ≥ (k/α)2
Maximum probability genotype phasing is NP-hard
Heuristic Decoding Algorithms
Viterbi Decoding Maximum probability of emitting a haplotype pair that
explain G along two HMM paths Efficiently computed using Viterbi’s algorithm
Posterior Decoding For each SNP choose the states that are most likely at
that locus given the genotype G Find most likely emissions at each SNP to explain G Efficiently computed using forward and backward
algorithm
Sampling from the HMM posterior distribution generate pairs of haplotypes that explain G conditional
on the haplotype distribution represented by the HMM Combine the sample into a single phasing
Greedy Likelihood Decoding
Uses forward values computed by forward algorithm fh(i,q) = the total probability of emitting the first i alleles
of the haplotype h and ending up at state q at level i. P(H|M)= ∑fh(n,q)
Constructs (h, h’) with (x,y) at SNP i, s.t. the probability of the phasing up to locus i, given the already determined phasing for the first i, is maximized
2 variants: left-to-right or right-to-left
),(),()'|'P( )|P( ']1...1[]1...1[]1...1[]1...1[ qifqifhyhhxhii Qqh
Qqhiiii
Combined Greedy Likelihood decoding
Left to right phasing Right to left phasing
Combined phasing
SNP i
P(Comb. phasing at SNP i) = ∑ fh(i,q)bh(i,q) x ∑ fh’(i,q)bh’(i,q)
SNP i that gives best improvement found in O(Kn) time given forward and backward values for the 4 haplotypes
hh’
hh’
Tweaking a Phasing by Local Switching
New phasing obtained by switching at SNP i
P (new phasing) = ∑ fh(i,q) bh(i,q) x ∑ fh’(i,q) bh’(i,q)
SNP i that gives best improvement found in O(Kn) time given forward and backward values for the 2 haplotypes
Iterative 1-OPT procedure
While there exists a SNP that improves the likelihood of the phasing obtained by switching at that SNP, find the SNP that yields the highest increase and perform switching
SNP i
Experimental Setup
ADHD dataset Chromosome X genotype data from the Genetic Association Information
Network (GAIN) study on Attention Deficit Hyperactivity Disorder (ADHD) 958 parent-child trios from the International Multi-site ADHD Genetics
(IMAGE) project Phased the children as unrelated on a 50 SNP window
Decoding alg. TweakingViterbi 11.814 11.571
Posterior 26.736 11.940HMM Sampling 15.323 11.826Greedy left to
right 12.154 11.693Greedy right to
left 13.283 12.057Greedy
combined 11.838 11.510Random phasing 50.559 14.764
Method TweakingENT 13.513 11.705
fastPHASE 12.035 11.231PHASE v
2.1 10.393 11.2192SNP 14.497 11.729
BEAGLE r=1 11.862 11.705
BEAGLE r=4 10.442 11.304
Outline
Background on genomic diversity The genotype phasing problem Hidden Markov Model of Haplotype
Diversity Genotype Imputation DNA Barcoding Conclusions
Genome-wide case-control association studies
Preferred method for finding the genetic basis of human diseases
1. Large number of markers (SNPs) typed in cases and controls
2. Statistical test of association disease-correlated locus
Disease causal SNPs unlikely to be typed directly
Limited coverage of current genotyping platforms
Vast number of SNPs present across the human genome
Genotype Imputation
Imputation of genotypes at un-typed SNP loci Powerful technique for increasing the power of
association studies Typed markers in conjunction with catalogs of
SNP variation (e.g. HapMap) predictors for SNP not present on the array
Challenge: Optimally combining the multi-locus information from current + multi-locus variation from HapMap
HMM Based Genotype Imputation
1. Integrate the HapMap variation information into the HMM• Train HMM using the haplotypes from the panel
related to the studied population (e.g. CEU panel: Utah residents with ancestry from northern and western Europe)
2. Compute probabilities of missing genotypes given the typed genotype data
• gi is imputed as x, where )|,(argmax }2,1,0{ MxgGPx ix
)|(
)|,(),|(
MGP
MxgGPMGxgP i
i
Related Problems
Missing Data Recovery Fill in the genotypes uncalled by the
genotyping algorithm
Genotype Error Detection and Correction If gi is present, then the increase in
likelihood obtained by replacing gi with x is:
)|(
)|(
MGP
MGP xgi
Likelihood Computation
P(G|M) = probability with which M emits any two haplotypes that explain G along any pair of paths.
Computed in O(nK3) by a 2-path extension of the forward algorithm followed by a factor K speed-up [Rastas07]
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Experimental Setup
WTCCC Dataset Genotype data of the 1958 birth cohort from the
The Welcome Trust Consortium genome-association study
1,444 individuals from this cohort were typed using both the Affymetrix 500k platform and a custom Illumina 15k platform
Affymetrix data + CEU HapMap haplotypes used to impute genotypes at the SNP loci present of the Illumina chip and not on the Affymetrix chip
The actual Illumina genotypes were then used to estimate the imputation accuracy
Results
Estimates of the allele 0 frequencies based on Imputation vs. Illumina 15k
Results
Accuracy and missing data rate for imputed genotypes for different thresholds.
Dashed line = missing data rateSolid line = discordance rate
Effect of Errors and Missing Data
Added additional 1% genotyping errors and 1% missing genotypes
TP Rate = correctly flagged errors out of total errors insertedFP Rate = incorrectly flagged genotype out of total correct genotypes Error Correction Accuracy = correctly recovered out of flagged ones
Error Detection Error CorrectionMissing Data
Recovery Imputatio
n
TP
Rate(%)FP
Rate(%) Accuracy(%) Error Rate(%)Error
Rate(%)EDC+MDR+IM
P 69.46 0.20 97.16 7.62 6.49MDR+IMP - - - 7.72 6.63
IMP - - - - 6.64
Outline
Background on genomic diversity The genotype phasing problem Hidden Markov Model of Haplotype
Diversity Genotype Imputation DNA Barcoding Conclusions
DNA barcoding
Recently(2003) proposed by taxonomists as a tool for rapid species identification
Use short DNA region as “fingerprint” for species
Region of choice: cytochrome c oxidase subunit 1
mitochondrial gene ("COI", 648 base pairs long).
Key assumption: Existence of “barcoding gap”
Inter-species variability >> than intra-species
variability
BOLD: The Barcode of Life Data Systems [Ratnasingham&Hebert07]
http://www.barcodinglife.org Currently: 38,539 species, 388,582
barcodes
DNA barcoding challenges
Efficient algorithms for species identification Millions of species
Meaningful confidence measures BOLD identification system showed to have
unclear confidence measures [Ekrem et al.07]:
New species discovery Sample size optimization
#barcodes per species required Barcode length Barcode quality
Number of regions required
Species identification problem
Several methods proposed for assigning specimens to species
TaxI (Steinke et al.05), Likelihood ratio test (Matz&Nielsen06), BOLD-IDS(Ratnasingham&Hebert 07)…
No direct comparisons on standardized benchmarks This work:
Direct comparison of methods from three main classes
Distance-based, tree-based, and statistical model-based
Explore the effect of repository size #barcodes/species, #species
Given repository containing barcodes from known species and a new barcode find its species
Methods
Distance-based Hamming distance, Aminoacid Similarity,
Convex Score similarity, Tri-nucleotide frequency distance, Combined method
Tree-based Exemplar NJ [Meyer&Paulay05] Profile NJ [Muller et al 04] Phylogenetic transversal
Statistical model-based Likelihood ratio test [Matz&Nielsen06] PWMs Inhomogeneous Markov Chains
Inhomogeneous Markov Chain (IMC)
Takes into account dependencies between consecutive loci
start
A
C
T
G
A
C
T
G
A
C
T
G
A
C
T
G
…
locus 1 locus 2 locus 3 locus 4
1t 2t 3t
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Comparison of representative methods
ACG Birds Bats Guyana Fish Australia CowriesMIN-HD 98.81% 97.59% 100.00% 99.30% 88.80%
IMC 95.27% 97.23% 100.00% 99.58% 89.83%Phylo 93.29% 92.33% 98.55% 99.30% 81.00%
Leave one out experiment
Hesperidia of the ACG 1 [Hajibabaei M. et al, 05]: 4267 barcodes, 561 species Birds of North America [Kerr K.C.R. et al, 07]: 2589 barcodes, 656 species Bats of Guyana [Clare E.L. et al, 06]: 840 barcodes, 96 species Fishes of Australia Container Part [Ward et. al, 05]: 754 barcodes, 211 species Cowries [Meyer and Paulay, 05]: 2036 barcodes, 263 species
Accuracy vs Species size
00.10.20.30.40.50.60.70.80.9
1
0 50 100 1500
0.10.20.30.40.5
0.60.70.80.9
1
0 50 100 150
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150
MIN-HD IMC
Phylo
Accuracy vs. #Species
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
300 600 900 1200 1500
MIN-HD
IMC
Phylo*
Conclusions
Highly scalable method for genotype phasing Several orders of magnitude faster than current
methods Phasing accuracy close to the best methods Exploits all pedigree information available
HMM model of haplotype diversity Hardness result for genotype phasing Improved decoding algorithms for phasing Imputation of genotypes at un-typed SNPs
DNA-barcoding Introduced new methods for species identification Comprehensive comparison to existing methods
Acknowledgments
Prof. Ion Mandoiu
Profs. Sanguthevar Rajasekaran, Alex Russell
Sasha Gusev (Entropy phasing, DNA barcoding)
Justin Kennedy (HMM Imputation and Error detection)
James Lindsay, Sotiris Kentros (DNA barcoding)
References
Genotype phasing: B. Pasaniuc and I.I. Mandoiu. Highly scalable genotype phasing by entropy minimization. In
Proc. 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pages 3482-3486, 2006.
A. Gusev, I.I. Mandoiu, and B. Pasaniuc. Highly scalable genotype phasing by entropy minimization. IEEE/ACM Trans. on Computational Biology and Bioinformatics 5, pp. 252-261, 2008.
HMM model, genotype imputation and error detection: J. Kennedy, I.I. Mandoiu, and B. Pasaniuc. Genotype error detection using hidden Markov
models of haplotype diversity. In Proc. 7th Workshop on Algorithms in Bioinformatics(WABI07) LNBI, pp 73-84, 2007.
J. Kennedy, I.I. Mandoiu, and B. Pasaniuc. GEDI: Genotype Error Detection and Imputation using Hidden Markov Models of Haplotype Diversity. (in preparation).
DNA-barcoding: B. Pasaniuc, S. Kentros and I.I. Mandoiu. DNA Barcode Data Analysis: Boosting
Assignment Accuracy by Combining Distance- and Character-Based Classifiers, The DNA Barcode Data Analysis Initiative (DBDAI): Developing Tools for a New Generation of Biodiversity Data Workshop, 2006.
B. Pasaniuc, S. Kentros and I.I. Mandoiu. Model-based species identification using DNA barcodes, 39th Symposium on the Interface: Computing Science and Statistics, 2007.
B. Pasaniuc, A. Gusev, S. Kentros, J. Lindsay and I.I. Mandoiu. A Comparison of Algorithms for Species Identification Based on DNA Barcodes. 2nd International Barcode of Life Conference, Academia Sinica, Taipei, Taiwan, Sept. 17-21, 2007