Transcript epistasis in mice

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 age
7000
Distribution of repeatabilities
Frequency
6000
5000
4000
3000
2000
1000
0
05 . 15 . 25 . 35
0.
0
0
0
45 . 55 . 65 . 75
0.
0
0
0
85
0.
Repeatability
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
n=0
1
1D genome scan for
QTL n+1
Step I Detect
Marginal
Effects
Randomization test for adding QTL n+1
to model Mn
No
Yes
2
3
Significant?
Add QTL n+1 to
model Mn, n=n+1
Terminate scan for
marginal QTL effects
Return to 1
Continue at 2
Randomization test
type I
Derive threshold for 0 vs
two interacting QTL without
significant marginal effects
Randomization test
type II
For all QTL significant by
their marginal effects
Derive thresholds for a
second interacting QTL
conditional on the marginal
effects of the first QTL
2D genome scan (E)
Step II Detect
QTL
Pairs
4 for epistatic QTL pairs
5
For all putative QTL
pairs
2
No of QTLs in pair with
significant marginal effects
No evaluation
necessary
1
Evaluate significance
using threshold type II
Significant?
Step III Evaluate
Epistasis
6
Randomization test
type III
For all significant
QTL pairs
Model selection
randomization test
CTC meeting, Oxford, 2003
0
Evaluate significance
using threshold type I
“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)
20
Chromosome
Genome-wise 5% threshold
Test statistic
15
10
5
0
0.000
2.000
4.000
6.000
8.000
Morgan
10.000
12.000
14.000
16.000
Carlborg, deKoning, and Haley 2003
CTC meeting, Oxford, 2003
A flavour of the results
IGF2r (Chr. 17)
20
4-41
6-78
8-45
9-20
Chromosome
Genome-wise 5% threshold
14-54 16-64 17-44 19-10
4-41
6-78
F
S
S
S
Test statistic
15
S
E
10
5
8-45
F
9-20
E
14-54
E
16-64
17-44
19-10
0
0.000
2.000
4.000
6.000
8.000
Morgan
10.000
12.000
14.000
IGF2R***
S
S
E
F
Ph 9
en 8.8
oty
pic 8.6
me 8.4
an 8.2
8
7.8
DD
BB Chr 4, mrk 41
BB
DD
Chr 9, mrk 20
CTC meeting, Oxford, 2003
16.000
Carlborg, deKoning, and Haley 2003
A flavour of the results
IGF2R***
IGF2R***
Ph
en
ot
yp
ic
m
ea
n
9
9
8.8
8.6
8.4
8.2
8
7.8
8.8
Phenotypic 8.6
mean
8.4
DD
BB Chr 4, mrk 41
BB
8.2
DD
BB
Chr 14, mrk 54
8
BB
DD
Chr 6, mrk 78
DD
Chr 16, mrk 64
IGF2R***
IGF2R***
Phe 9
not
ypi 8.8
c
8.6
me
an 8.4
8.2
8
DD
7.8
BB
BB
Chr 14, mrk 54
Chr 4, mrk 41
9.2
9
8.8
Phenotypic 8.6
mean
8.4
8.2
8
7.8
DD
BB
BB
DD
Chr 17, mrk 44
CTC meeting, Oxford, 2003
DD
Chr 4, mrk 41
Acknowledgements
CTC meeting, Oxford, 2003