Haplotype Discovery and Modeling

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

)()1()(

)(

01

1

ii

ii yfyf

yf

11/11

12

11/11

ˆn

yn

ii

10/10

10/10

1

1 11ˆ n

ii

n

i

n

iiii

n

yy

10/10

10/10

1

1 10

)1(

)1(ˆ

n

ii

n

i

n

iiii

n

yy

20

1

21

1 1

20

21

1

22

2 )ˆ)(1()ˆ()ˆ()ˆ()ˆ(1

ˆ10/1011/11

ii

n

iii

n

i

n

iii

n

ii yyyyy

n

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