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

2. Outline 1. Aim 2. The Human Genome 3. Principles of Linkage Analysis
4. Parametric Linkage Analysis
5. Nonparametric Linkage Analysis

3. 1. Aim

4. QTL mapping
LOCALIZE and then IDENTIFY a locus that regulates a trait (QTL)
Nucleotide or sequence of nucleotides with variation in the population, with different variants associated with different trait levels.

5. 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

6. 2. Human Genome

7. 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

8. DNA polymorphisms Microsatellites SNPs >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

9. Diploid zygote >1 cell
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 -
chr1
- B
- B
G1 phase
S phase
M phase
Haploid gametes
Diploid zygote 1 cell
Diploid zygote >1 cell

10. DNA recombination ♁ NR R R Diploid gamete precursor cell NR
22 + 1
22 + 1
A - NR
(♂)
B -
A -
- A
chr1
2 (22 + 1)
2 (22 + 1)
B -
- B ♁
Meiosis
- A 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

11. DNA recombination between linked loci
22 + 1
A -
B - NR
(♂)
A -
- A
B -
- B
2 (22 + 1) ♁
Meiosis
- A NR
- B ♂
(♂)
(♁) ♁
A -
- A
A -
- A
B -
- B
B -
- B
A -
B - NR
(♁)
A -
- A
B -
- B
Diploid gamete precursor
- A
- B NR
Haploid gamete precursors
Hap. gametes

12. 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 ≤ 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

13. 3. Principles of Linkage Analysis

14. Linkage Analysis requires genetic markersMn θ
0.5
0.5 .4 .3 .3 .4
0.5
.15 M1 M2 Mn θ
0.5
.35
.22
.26
.35
0.5
0.5 .4 .3 .1 .3 .4 M1 M2 Mn

15. Linkage Analysis: Parametric vs. Nonparametric
Gene
Chromosome
Recombination
Genetic factors M Q A
Mode of inheritance
Correlation D
Phe C
Environmental factors E
Adapted from Weiss & Terwilliger 2000

16. 4. Parametric Linkage Analysis

17. Autosomal dominant, Q1 predisposing allele
Linkage with informative phase known meiosis
Gene ♂
Chromosome ♁
M1..6
Q1,2
Autosomal dominant, Q1 predisposing allele
M2M5Q2Q2
M1M6Q1Q? M1 Q1
Informative
Phase known
M1M2Q1Q2
M1Q1/M2Q2
M3M4Q2Q2 M2 Q2
M1Q1/M3Q2
M2Q2/M3Q2
M1Q1/M4Q2
M1Q1/M4Q2
M2Q2/M4Q2
M2Q1/M3Q2
NR: M1Q1
NR: M2Q2
θMQ = 1/6 = 0.17
(~20.8 cM)
R: M1Q2
R: M2Q1

18. Linkage with informative phase unknown meiosisQ1 M1 Q2
Q2Q2
Q1Q? M2 Q2 M2 Q1
Informative
Phase unknown
M1M2Q1Q2
M1Q2/M2Q1
M1Q1/M2Q2
M3M4Q2Q2
M1Q1/M3Q2
M2Q2/M3Q2
M1Q1/M4Q2
M1Q1/M4Q2
M2Q2/M4Q2
M2Q1/M3Q2
M1Q1/M2Q2 P N
M1Q2/M2Q1 P N
NR: M1Q1
½(1-θ) 3
R: M1Q1 ½θ 3
NR: M2Q2
½(1-θ) 2
R: M2Q2 ½θ 2
R: M1Q2 ½θ
NR: M1Q2
½(1-θ)
R: M2Q1 ½θ 1
NR: M2Q1
½(1-θ) 1 + +

19. 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

20. Parametric Linkage Analysis - summaryQ M1 M2 Mn θ
0.5
0.5 .4 .3 .3 .4
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

21. Outline 1. Aim 2. The Human Genome 3. Principles of Linkage Analysis
4. Parametric Linkage Analysis
5. Nonparametric Linkage Analysis

22. 5. Nonparametric Linkage Analysis

23. Approach Parametric: genotype marker locus & genotype trait locus
(latter inferred from phenotype according to a specific disease model)
Parameter of interest: θ between 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...

24. Phenotypic similarity between relatives
Squared trait differences
Squared trait sums
Trait cross-product
Trait variance-covariance matrix
Affection concordance T2 T1

25. Inheritance vector (M)
Genotypic similarity between relatives
IBS Alleles shared Identical By State “look the same”, may have the
same DNA sequence but they are not necessarily derived from a
known common ancestor M1 M2 M3 M3
IBD Alleles shared
Identical By Descent
are a copy of the
same
ancestor
allele Q1 Q2 Q3 Q4 M1 M2 M3 M3 Q1 Q2 Q3 Q4
IBS
IBD M1 M3 M1 M3 2 1 Q1 Q3 Q1 Q4 1
Inheritance vector (M) 1

26. Genotypic similarity between relatives -
Inheritance vector (M)
Number of alleles shared IBD
Proportion of alleles shared IBD - M1 M3 M2 M3 1 1 Q1 Q3 Q2 Q4 M1 M3 M1 M3 1 1
0.5 Q1 Q3 Q1 Q4 M1 M3 M1 M3 2 1 Q1 Q3 Q1 Q3

27. Genotypic similarity between relatives -D
22n

28. H:\manuel - Copy folder “Linkage” to C:\
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 to
(i) and
(ii)

29. Practical E F G A1A2 A3A4 A1A3 A1A3 A2A4 Exercice 2 A1A2 A1A3 A1A3
(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
A1A3
A1A3
A2A4
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:

30. IBD at a marker Singlepoint IBD IBD at a ‘grid’ Multipoint IBD 5 cM M1Mn
IBD at a marker
Singlepoint IBD
5 cM M1 M2 Mn
IBD at a ‘grid’
Multipoint IBD

31. Statistics that incorporate both phenotypic and genotypic similarities
Phenotypic similarity
0.5 1
Genotypic similarity ( )

32. Phenotypic dissimilarity
Haseman-Elston regression – Quantitative traits
0.5 1
Phenotypic dissimilarity =
b ×
Genotypic similarity c

33. VC ML – Quantitative & Categorical traits
method
0.5 1
H1:
H0:
e.g. LOD=3

34. Genome-wide linkage analysis (e.g. VC)
Individual LOD scores can be expressed as P values (Pointwise)
LOD Chi-sq (n-df) P value
(x4.6)
True positive k
Theoretical (Lander & Kruglyak 1995)
LOD
LOD = 3.6, Chi-sq = 16.7, P =
Type I error

35. 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