CTC meeting, Oxford, 2003

Epistatic QTL for gene expression in mice; potential for BXD expression data

Dirk-Jan de Koning*, Örjan Carlborg*, Robert Williams†, Lu Lu†,

Chris Haley*

*Roslin Institute, UK

†University of Tennessee Health Science Center, USA

CTC meeting, Oxford, 2003

Introduction

• Genetical genomics: exciting new tool

• Analysis tools for experimental crosses widely available

• More complex models have been proposed

• Scale-up from 10 to 10K traits NOT trivial

CTC meeting, Oxford, 2003

Data

• 29 BXD RI lines

• 587 markers spanning all chromosome

• Array data for 12,242 genes– 77 arrays– Normalized: µ=8, σ2=2– 1 - 4 replicates/line

CTC meeting, Oxford, 2003

Research questions

• Proportion of variation in gene expression due to epistasis?

• Epistasis more prevalent for certain types of genes?

• For epistatic pairs of genes: both trans or 1 cis?

• Magnitude of epistasis in relation to differences between founder lines and deviation of F1

CTC meeting, Oxford, 2003

Data and analysis issues

• What is the repeatability?

• What to do with outliers?

• Means or single observations?

• If means: weighted or un-weighted?

• If weighted: what weights?

• Single marker mapping or interval mapping?

CTC meeting, Oxford, 2003

Repeatability• Upper limit of heritability

• Mixed linear model in Genstat

• No consistent effect of sex and ageDistribution of repeatabilities

0

1000

2000

3000

4000

5000

6000

7000

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

Repeatability

Fre

qu

ency

CTC meeting, Oxford, 2003

Outliers

• Outliers identified as individual expression measures + or – 3 s.d. from mean

• 3 treatments of outliers:– Ignore– Remove– Shrink to 3 s.d.

CTC meeting, Oxford, 2003

(Weighted) analysis of means

• Weighted analyses should reflect difference in number of replicates

• 3 types of weighting:– No weighting– Inverse of variance

• Very crude estimate• Strong effect of small SE!

– Use expected reduction in variance:• n/[1+r(n-1)]

CTC meeting, Oxford, 2003

QTL analysis*1. Single QTL genome scan using least

squares

2. 2-dimensional scan fitting all pair-wise combinations of interacting QTL:

• exhaustive search• Only additive x additive interaction

3. Permutation test: analyses ‘approximated’ using GA

* Carlborg and Andersson, Genetical Research, 2002

CTC meeting, Oxford, 2003

1D genome scan for QTL n+1

Randomization test for adding QTL n+1 to model Mn

Add QTL n+1 to model Mn, n=n+1

2D genome scan (E) for epistatic QTL pairs

Randomization test type I

Derive thresholds for a second interacting QTL

conditional on the marginal effects of the first QTL

For all QTL significant by their marginal effects

Significant?

For all putative QTL pairs

Model selection randomization test

No of QTLs in pair with significant marginal effects

Evaluate significance using threshold type II

Evaluate significance using threshold type I

Significant?

No evaluation necessary

2

1

0

For all significant QTL pairs

Step I - DetectMarginal Effects

Step II - DetectQTLPairs

Step III - Evaluate Epistasis

n=0

Yes No

Derive threshold for 0 vs two interacting QTL without significant marginal effects

Randomization test type II

Randomization test type III

1

2

3

4

5

6

Terminate scan for marginal QTL effects

Return to 1 Continue at 2

CTC meeting, Oxford, 2003

“Training” data• 96 trait pseudo-randomly selected:

proportional representation of r

• Individual phenotypes– 3 treatments of outliers

• mean phenotypes– 3 treatments of outliers– 3 type of weighting– IM vs. single marker

• Many scenarios to be evaluated

CTC meeting, Oxford, 2003

Computational considerations

• Means (29) vs. ind. measurements (77)• Single marker vs. IM:

– 587 vs. 2100 tests for 1D scan– 343,982 vs. 4,410,000 tests for 2D scan

• 1,000 genome-wide randomisations for 12,442 traits…

100.000 CPU hours on 512 processor Origin 3800 at CSAR, Manchester (£50K)

CTC meeting, Oxford, 2003

A flavour of the results

IGF2r (Chr. 17)

0

5

10

15

20

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000

Morgan

Tes

t st

ati

stic

Chromosome

Genome-wise 5% threshold

Carlborg, deKoning, and Haley 2003

CTC meeting, Oxford, 2003

A flavour of the results

4-41 6-78 8-45 9-20 14-54 16-64 17-44 19-10

4-41 F S S S S 6-78 E 8-45 F 9-20 E

14-54 E S 16-64 S 17-44 E

19-10 F

IGF2r (Chr. 17)

0

5

10

15

20

0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000

Morgan

Tes

t st

ati

stic

Chromosome

Genome-wise 5% threshold

Carlborg, deKoning, and Haley 2003

BB DD BB DD 7.8 8 8.2 8.4 8.6 8.8 9 Ph

enotypic mean

Chr 9, mrk 20 Chr 4, mrk 41

IGF2R***

CTC meeting, Oxford, 2003

A flavour of the results

BB DD BB DD

7.8 8 8.2 8.4 8.6 8.8 9 Phenotypic mean

Chr 6, mrk 78 Chr 4, mrk 41

IGF2R***

BB DD

BB DD 7.8 8 8.2 8.4 8.6 8.8 9 9.2

Phenotypic mean

Chr 17, mrk 44 Chr 4, mrk 41

IGF2R***

BB DD BB DD

7.8 8 8.2 8.4 8.6 8.8 9 Phe

notypic mean

Chr 14, mrk 54 Chr 4, mrk 41

IGF2R***

BB DD

BB DD 8 8.2

8.4 8.6 8.8

9 Phenotypic

mean

Chr 16, mrk 64 Chr 14, mrk 54

IGF2R***

CTC meeting, Oxford, 2003

Acknowledgements