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Haplotype Discovery and Modeling
Identification of genes
Identify the
PhenotypeMap Clone
QTL Mapping
Marker 1
Marker 2Marker 3
Marker k
QTL
A QTL (quantitative trait locus) is a gene that affects a quantitative trait,
The QTL detected by the markers linked with it is a chromosomal segment,
The DNA structure of a QTL is unknown.
.
.
.
I
II
III
1
1
1
2 4 5
3 5 7
2
2 4 6 8
aaBb
AABb AaBbaabb AaBb
Aabb
AaBb aaBb AaBbAABb AAbb Aabb
aabb
Aabb aaBb
QTL Mapping Based on Linkage
Mapping and sequencing
10000 Kb
100 Kb
Markers
DNA clones
SNPs (‘snips’)
• A SNP is a site in the DNA where different chromosomes differ in the base they have.
SNPs
Paternal allele: CCCGCCTTCTTGGCTTTACA
Maternal allele: CCCGCCTTCTCGGCTTTACA
Paternal allele : CCCGCCTTCTTGGCTTTACA
Maternal allele : CCCGCCTTCTTGGCTTTACA
HapMap
Single Nucleotide Polymorphisms (SNPs)
Insensitive to drug
Sensitive to drug
Detecting specific DNA sequence variantsthat determine complex traits
The International HapMap Consortium (Nature, 2003, 2005)
Allele, Haplotype, and Diplotype
Basic concepts
Haplotyping a Phenotype
Basic concepts
Quantitative Trait Nucleotide (QTN)
Risk Haplotype and Composite Diplotype
Risk haplotype: [AB] = R
Non-risk haplotype: [Ab], [aB], [ab] = r
Composite Diplotype: RR, Rr, rr
A
B B
A A
B B
AA
B B
AA
B B
A
,
Illustrations
Basic concepts
Consider A QTN composed of two SNPs:
RR (2) Rr (1) rr (0)
Study designA random sample of unrelated individuals from a natural population
SNPGroup 1 2 Diplotype Obs. Drug Response Trait
1 AA BB [AB][AB] n11/11 y1 = (y11, …, y1n11/11)T
2 AA Bb [AB][Ab] n11/10 y2 = (y21, …, y2n11/10)T
3 AA bb [Ab][Ab] n11/00 y3 = (y31, …, y3n11/00)T
4 Aa BB [AB][aB] n10/11 y4 = (y41, …, y4n10/11)T
5 Aa Bb [AB][ab] n10/10 y5 = (y51, …, y5n10/10)T
[Ab][aB]
6 Aa bb [Ab][ab] n10/00y6 = (y61, …, y6n10/00)T
7 aa BB [aB][aB] n00/11 y7 = (y71, …, y7n00/11)T
8 aa Bb [aB][ab] n00/10y8 = (y81, …, y8n00/10)T
9 aa bb [ab][ab] n00/00 y9 = (y91, …, y9n00/00)T
Unifying Likelihoodbased on marker (S) and phenotype (y) data
There are two types of parameters:
- Haplotype frequencies (population genetic parameters p) [AB]: p11 = pq+D [Ab]: p10 = p(1-q)-D p – Allele (A) frequency at SNP 1 [aB]: p01 = (1-p)q-Dq – Allele (B) frequency at SNP 2 [ab]: p00 = (1-p)(1-q)+D D – Linkage disequilibrium
- Haplotype effects and variation (quantitative genetic para. q) RR: µ2 = µ + a a = additive effect Rr: µ1 = µ + d d = dominance effect rr: µ0 = µ - a
Liu, Johnson, Casella and Wu, 2004, Genetics
Modeling Haplotype Frequencies
SNPGroup 1 2 Diplotype Frequency Obs.
1 AA BB [AB][AB] p211 n11/11
2 AA Bb [AB][Ab] 2p11p10 n11/10
3 AA bb [Ab][Ab] p210 n11/00
4 Aa BB [AB][aB] 2p11p01 n10/11
5 Aa Bb [AB][ab] 2p11p00 n10/10 [Ab][aB] 2p10p01
6 Aa bb [Ab][ab] 2p10p00 n10/00
7 aa BB [aB][aB] p201 n00/11
8 aa Bb [aB][ab] 2p01p00 n00/10
9 aa bb [ab][ab] p200 n00/00
EM algorithm
E step
M step
Modeling Haplotype Effects SNP Risk Haplotype
1 2 [AB] [Ab] [aB] [ab]1 AA BB [AB][AB] RR rr rr rr2 AA Bb [AB][Ab] Rr Rr rr rr3 AA bb [Ab][Ab] rr RR rr rr4 Aa BB [AB][aB] Rr rr Rr rr5 Aa Bb [AB][ab] Rr rr rr Rr
[Ab][aB] rr Rr Rr rr6 Aa bb [Ab][ab] rr Rr rr Rr7 Aa BB [aB][aB] rr rr RR rr8 Aa Bb [aB][ab] rr rr Rr Rr9 Aa bb [ab][ab] rr rr rr RR
Likelihood L1 L2 L3 L4
Genotypic values of composite diplotypes: RRu2, Rru1, rru0
Mixture Modelassuming that [AB] is the risk haplotype
EM Algorithm
• E step
• M step
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Hypothesis Testing
H0: µ2 = µ1 = µ0 = 0 RR = Rr = rr
H1: At least one of equalities in the H0 does
not hold
LR = –2ln[L0( |y) – L1( |y,S, )]
The threshold is determined empirically by permutation tests
q~ p̂q̂
Genome-wide Scan
LR
SNPs on the Genome
Threshold
Structural Variation in the Human Genome
Haplotype Blocks: Nearby SNPs are often distributed in block-like patterns
Hotspots and Coldspots: SNPs from different blocks have larger recombination rates than those from within blocks
Tag SNPs: Haplotype diversity within each block can be well explained by a small portion of SNPs.
Recombination Hot Spots
Block 1 Block 2 Block 3 Block 4 …
A Genetic StudyA candidate genefor human obesity
SNP A: A, G
SNP B: C, G
Four haplotypes[AC][AG][GC][GG]
• A total of 155 patients selected from a population • Typed for the two SNPs• Measured for body mass index (BMI)• Question: Which haplotype triggers an effect on BMI?
Testing Risk Haplotype LR[AC] 2.32 r[AG] 1.52 r[GC] 3.11 r[GG] 10.35 (p<0.01) R
RR: µ2 = µ + a = 30.83 – 1.77 = 29.06 a = additive effectRr: µ1 = µ + d = 30.83 – 3.05 = 27.78 d = dominance effectrr: µ0 = µ - a = 30.83 + 1.77 = 32.60 • A patient who combines haplotype [GG] with any other haplotypes is normal weight,• A patient who combines any two haplotypes from [AC], [AG] and [GC] is obese,• A patient who has double haplotypes [GG] is overweight
Model Extensions
• Block-Block Interactions (Lin et al. 2007, Bioinformatics)
• Haplotype-Environment Interactions (Wang et al. 2008, Molecular Pain)
• Haplotype Imprinting Effects (Cheng et al., to be submitted)
• Multivariate high-dimensional drug response (PK-PD link, efficacy and toxicity…) – A systems approach
1000-Genome Projects This sequencing effort will
produce most detailed map
of human genetic variation to
support disease studies
Results will help to design the
personalized medication which can
optimize drug therapy