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Introduction to QTL mapping. Manuel Ferreira. Boulder Introductory Course 2006. Outline. 1. Aim.

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Introduction to QTL mapping

Manuel Ferreira

Boulder Introductory Course 2006

Outline

1. Aim

2. The Human Genome

3. Principles of Linkage Analysis

4. Parametric Linkage Analysis

5. Nonparametric Linkage Analysis

1. Aim

QTL mapping

LOCALIZE and then IDENTIFY a locusthat regulates a trait (QTL)

Nucleotide or sequence of nucleotides with variation in the population, with different variants associated with different trait levels.

For a heritable trait...

Linkage:

localize region of the genome where a QTL that regulates the trait is likely to be harboured

Family-specific phenomenon:

Affected individuals in a family share the same

ancestral predisposing DNA segment at a given QTL

Association:

identify a QTL that regulates the trait

Population-specific phenomenon:

Affected individuals in a population share the same

ancestral predisposing DNA segment at a given QTL

2. Human Genome

DNA structure

A DNA molecule is a linear backbone of alternating sugar residues and phosphate groups

Attached to carbon atom 1’ of each sugar is a nitrogenous base: A, C, G or T

Two DNA molecules are held together in anti-parallel fashion by hydrogen bonds between bases [Watson-Crick rules]

Antiparallel double helix

A gene is a segment of DNA which is transcribed to give a protein or RNA product

Only one strand is read during gene transcription

Nucleotide: 1 phosphate group + 1 sugar + 1 base

DNA polymorphisms

Microsatellites

>100,000

Many alleles, (CA)n, very

informative, even, easily automated

SNPs

10,054,521 (25 Jan ‘05)

10,430,753 (11 Mar ‘06)

Most with 2 alleles (up to 4), not very

informative, even, easily automated

A

B

DNA organization

22 + 1

2 (22 + 1)

2 (22 + 1)

2 (22 + 1)

A -

A -

A -

B -

Mitosis

B -

B -

chr1

A -

A -

A -

- A

A -

- A

B -

B -

B -

- B

B -

- B

A -

- A

- A

B -

- B

- B

chr1

G1 phase

S phase

M phase

Haploid gametes

Diploid zygote 1 cell

Diploid zygote >1 cell

DNA recombination

22 + 1

22 + 1

A -

NR

(♂)

B -

A -

- A

chr1

2 (22 + 1)

2 (22 + 1)

B -

- B

- A

Meiosis

R

chr1

(♂)

(♁)

- B

A -

A -

- A

- A

chr1

B -

B -

- B

- B

A -

R

chr1

chr1

chr1

chr1

(♁)

A -

- A

B -

chr1

Diploid gamete precursor cell

B -

- B

- A

chr1

NR

- B

Haploid gamete precursors

chr1

Hap. gametes

DNA recombination between linked loci

22 + 1

A -

NR

B -

(♂)

A -

- A

B -

- B

2 (22 + 1)

- A

Meiosis

NR

- B

(♂)

(♁)

A -

A -

- A

- A

B -

B -

- B

- B

A -

NR

B -

(♁)

A -

- A

B -

- B

Diploid gamete precursor

- A

- B

NR

Haploid gamete precursors

Hap. gametes

Human Genome - summary

DNA is a linear sequence of nucleotides partitioned into 23 chromosomes

Two copies of each chromosome (2x22 autosomes + XY), from

paternal and maternal origins. During meiosis in gamete precursors,

recombination can occur between maternal and paternal homologs

Recombination fraction between loci A and B (θ)

Proportion of gametes produced that are recombinant for A and B

If A and B are very far apart: 50%R:50%NR - θ = 0.5

If A and B are very close together: <50%R - 0 ≤ θ < 0.5

Recombination fraction (θ) can be converted to genetic distance (cM)

Haldane: eg. θ=0.17, cM=20.8

Kosambi: eg. θ=0.17, cM=17.7

3. Principles of Linkage Analysis

Linkage Analysis requires genetic markers

Q

M1

Mn

M2

.3

.4

.4

.3

0.5

0.5

θ

0.5

.15

M1

Mn

M2

.35

.22

.35

.26

0.5

θ

0.5

0.5

.4

.3

.3

.4

.1

M1

Mn

M2

Linkage Analysis: Parametric vs. Nonparametric

Gene

Chromosome

Recombination

Genetic factors

M

Q

A

Mode of inheritance

Correlation

D

Phe

C

E

Environmental factors

Adapted from Weiss & Terwilliger 2000

4. Parametric Linkage Analysis

Linkage with informative phase known meiosis

Gene

Chromosome

M1..6

Q1,2

Autosomal dominant, Q1 predisposing allele

M2M5Q2Q2

M1M6Q1Q?

M1

Q1

Informative

Phase known

M1Q1/M2Q2

M3M4Q2Q2

M1M2Q1Q2

M2

Q2

M1Q1/M3Q2

M2Q2/M3Q2

M1Q1/M4Q2

M1Q1/M4Q2

M2Q2/M4Q2

M2Q1/M3Q2

NR: M1Q1

NR: M2Q2

(~20.8 cM)

θMQ = 1/6 = 0.17

R: M1Q2

R: M2Q1

Linkage with informative phase unknown meiosis

M1

Q1

M1

Q2

Q2Q2

Q1Q?

M2

M2

Q2

Q1

Informative

Phase unknown

M1Q1/M2Q2

M1M2Q1Q2

M3M4Q2Q2

M1Q2/M2Q1

M1Q1/M3Q2

M2Q2/M3Q2

M1Q1/M4Q2

M1Q1/M4Q2

M2Q2/M4Q2

M2Q1/M3Q2

M1Q2/M2Q1

M1Q1/M2Q2

P

P

N

N

3

3

½θ

½(1-θ)

R: M1Q1

NR: M1Q1

R: M2Q2

½θ

NR: M2Q2

2

2

½(1-θ)

NR: M1Q2

R: M1Q2

½θ

0

0

½(1-θ)

NR: M2Q1

R: M2Q1

1

1

½(1-θ)

½θ

+

+

Parametric LOD score calculation

Overall LOD score for a given θ is the sum of all family LOD scores at θ

eg. LOD=3 for θ=0.28

Parametric Linkage Analysis - summary

Q

M1

Mn

M2

.3

.4

.4

.3

θ

0.5

0.5

0.5

.1

For each marker, estimate the θ that yields highest LOD score across all families

This θ (and the LOD) will depend upon the mode of inheritance assumed

MOI determines the genotype at the trait locus Q and thus determines the

number of meiosis which are recombinant or nonrecombinant. Limited to

Mendelian diseases.

Markers with a significant parametric LOD score (>3) are said to be linked

to the trait locus with recombination fraction θ

Outline

1. Aim

2. The Human Genome

3. Principles of Linkage Analysis

4. Parametric Linkage Analysis

5. Nonparametric Linkage Analysis

5. Nonparametric Linkage Analysis

Approach

Parametric: genotype marker locus & genotype trait locus

(latter inferred from phenotype according to a specific disease model)

Parameter of interest: θbetween marker and trait loci

Nonparametric: genotype marker locus & phenotype

If a trait locus truly regulates the expression of a phenotype, then two

relatives with similar phenotypes should have similar genotypes at a

marker in the vicinity of the trait locus, and vice-versa.

Interest: correlation between phenotypic similarity and marker genotypic

similarity

No need to specify mode of inheritance, allele frequencies, etc...

Phenotypic similarity between relatives

Squared trait differences

Squared trait sums

Trait cross-product

Trait variance-covariance matrix

Affection concordance

T2

T1

Genotypic similarity between relatives

IBSAlleles shared Identical By State “look the same”, may have the

same DNA sequence but they are not necessarily derived from a

known common ancestor

M3

M1

M2

M3

Q3

Q1

Q2

Q4

IBDAlleles shared

Identical By Descent

are a copy of the

same

ancestor

allele

M1

M2

M3

M3

Q1

Q2

Q3

Q4

IBD

IBS

M1

M3

M1

M3

2

1

Q1

Q4

Q1

Q3

0

0

1

0

1

Inheritance vector (M)

Genotypic similarity between relatives -

Inheritance vector (M)

Number of alleles shared IBD

Proportion of alleles shared IBD -

M2

M3

M1

M3

0

0

0

1

1

0

Q2

Q4

Q1

Q3

M1

M3

M1

M3

0

0

1

0

0.5

1

Q1

Q4

Q1

Q3

M1

M3

M1

M3

0

0

0

0

2

1

Q1

Q3

Q1

Q3

Genotypic similarity between relatives -

D

A

B

C

22n

Practical

Aim

(1) Estimate IBD with MERLIN; (2) IBD estimation can be influenced by genotyped individuals and allele frequencies; (3) compute

H:\manuel - Copy folder “Linkage” to C:\

1. Open with Notepad: pr1.ped pr1.dat pr1.map pr1.freq

2. Start>Run>C:/Linkage/pfe32.exe

3. Run Command Prompt

4. Keep a File Explorer window open

Exercice1

(1) Estimate IBD for pedigrees A, B and C in the previous slide

(2) Change allele frequencies (pr1.freq) from 0.25 0.25 0.25 0.25 to

(i) 0.45 0.25 0.25 0.05 and

(ii) 0.05 0.25 0.25 0.45

Practical

A1A2

A3A4

A1A3

A2A4

A1A3

Exercice 2

(1) Modify pr1.ped and estimate IBD probabilities and between twin 1 and twin 2 for pedigrees E, F and G:

E

F

G

A1A2

A1A3

A1A3

A1A3

A1A3

A2A4

A1A3

A1A3

P(IBD=0)

0.08

0.00

0.00

P(IBD=1)

0.31

0.20

0.00

P(IBD=2)

0.61

0.80

1.00

0.77

0.90

1.00

Allele frequencies on pr1.freq: 0.25 0.25 0.25 0.25

M1

Mn

M2

IBD at a marker

Singlepoint IBD

5 cM

M1

Mn

M2

IBD at a ‘grid’

Multipoint IBD

Statistics that incorporate both phenotypic and genotypic similarities

Phenotypic similarity

0.5

1

0

Genotypic similarity ( )

Haseman-Elston regression – Quantitative traits

0.5

1

0

Phenotypic dissimilarity

=

b ×

Genotypic similarity

+ c

VC ML – Quantitative & Categorical traits

method

0.5

1

0

H1:

H0:

e.g. LOD=3

Genome-wide linkage analysis (e.g. VC)

Individual LOD scores can be expressed as P values (Pointwise)

LOD Chi-sq (n-df) P value

2.1 9.67 0.0009

(x4.6)

True positive

Theoretical(Lander & Kruglyak 1995)

k

LOD

LOD = 3.6, Chi-sq = 16.7, P = 0.000022

Type I error

Nonparametric Linkage Analysis - summary

No need to specify mode of inheritance

Models phenotypic and genotypic similarity of relatives

Expression of phenotypic similarity, calculation of IBD

HE and VC are the most popular statistics used for linkage of

quantitative traits

Other statistics available, specially for affection traits

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