what is the goal of qtl study?
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Yandell © 2003 JSM 2003 1
Dimension Reductionfor Mapping mRNA Abundance
as Quantitative Traits
Brian S. YandellUniversity of Wisconsin-Madison
www.stat.wisc.edu/~yandell/statgen[Lan et al. 2003 Genetics 164(4): August 2003]
Yandell © 2003 JSM 2003 2
what is the goal of QTL study?• uncover underlying biochemistry
– identify how networks function, break down– find useful candidates for (medical) intervention– epistasis may play key role– statistical goal: maximize number of correctly identified QTL
• basic science/evolution– how is the genome organized?– identify units of natural selection– additive effects may be most important (Wright/Fisher debate)– statistical goal: maximize number of correctly identified QTL
• select “elite” individuals– predict phenotype (breeding value) using suite of characteristics
(phenotypes) translated into a few QTL– statistical goal: mimimize prediction error
Yandell © 2003 JSM 2003 3
what is a QTL?• QTL = quantitative trait locus (or loci)
– trait = phenotype = characteristic of interest– quantitative = measured somehow
• glucose, insulin, gene expression level
• Mendelian genetics– allelic effect + environmental variation
– locus = location in genome affecting trait• gene or collection of tightly linked genes
• some physical feature of genome
Yandell © 2003 JSM 2003 4
typical phenotype assumptions• normal "bell-shaped" environmental variation• genotypic value GQ is composite of m QTL• genetic uncorrelated with environment
22
2
)var(
)var()|(var
)|(
Q
Q
Q
G
Gh
QY
GQYE
8 9 10 11 12 13 14 15 16 17 18 19 20
qq QQ
Qqdatahistogram
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why worry about multiple QTL?• so many possible genetic architectures!
– number and positions of loci– gene action: additive, dominance, epistasis– how to efficiently search the model space?
• how to select “best” or “better” model(s)?– what criteria to use? where to draw the line?– shades of gray: exploratory vs. confirmatory study– how to balance false positives, false negatives?
• what are the key “features” of model?– means, variances & covariances, confidence regions– marginal or conditional distributions
Yandell © 2003 JSM 2003 6
0 5 10 15 20 25 30
01
23
rank order of QTL
addi
tive
eff
ect
Pareto diagram of QTL effects
54
3
2
1
major QTL onlinkage map
majorQTL
minorQTL
polygenes
(modifiers)
Yandell © 2003 JSM 2003 7
advantages of multiple QTL approach• improve statistical power, precision
– increase number of QTL detected
– better estimates of loci: less bias, smaller intervals
• improve inference of complex genetic architecture– patterns and individual elements of epistasis
– appropriate estimates of means, variances, covariances• asymptotically unbiased, efficient
– assess relative contributions of different QTL
• improve estimates of genotypic values– less bias (more accurate) and smaller variance (more precise)
– mean squared error = MSE = (bias)2 + variance
Yandell © 2003 JSM 2003 8
epistasis in parallel pathways(Gary Churchill)
• Z keeps trait value low
• Neither E1nor E2 is rate limiting
• Loss of function alleles are segregating from parent A
at E1and from parent B at E2
Z
X
Y
E1
E2
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epistasis in a serial pathway(Gary Churchill)
ZX YE1 E2• Z keeps trait value high
• Neither E1 nor E2 is rate limiting
• Loss of function alleles are segregating from parent B
at E1and from parent A at E2
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epistasis examples(Doebley Stec Gustus 1995; Zeng pers. comm.)
1.0
1.5
2.0
2.5
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3.5
4.0
4.5
geno
typi
c va
lue
aa Aa AA
bb
BbBB 1.0
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2.5
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geno
typi
c va
lue
bb Bb BB
aa
AaAA
-1.0
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effe
ct +
/- 2
se
a1 d1 a2 d2 iaa iad ida idd
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0ge
noty
pic
valu
e
aa Aa AA
bbBb
BB2
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geno
typi
c va
lue
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aa
Aa
AA
-40
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0ef
fect
+/-
2 s
e
a1 d1 a2 d2 iaa iad ida idd
02
46
geno
typi
c va
lue
aa Aa AA
bb
BbBB 02
46
geno
typi
c va
lue
bb Bb BB
aa
AaAA -2-1
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23
effe
ct +
/- 2
se
a1 d1 a2 d2 iaa iad ida idd
traits 1,4,91: dom-dom interaction4: add-add interaction9: rec-rec interaction(Fisher-Cockerham effects)
4
91
Yandell © 2003 JSM 2003 11
why map gene expressionas a quantitative trait?
• cis- or trans-action?– does gene control its own expression? – evidence for both modes (Brem et al. 2002 Science)
• mechanics of gene expression mapping– measure gene expression in intercross (F2) population– map expression as quantitative trait (QTL technology)– adjust for multiple testing via false discovery rate
• research groups working on expression QTLs– review by Cheung and Spielman (2002 Nat Gen Suppl)
– Kruglyak (Brem et al. 2002 Science)
– Doerge et al. (Purdue); Jansen et al. (Waginingen)
– Williams et al. (U KY); Lusis et al. (UCLA)
– Dumas et al. (2000 J Hypertension)
Yandell © 2003 JSM 2003 12
idea of mapping microarrays(Jansen Nap 2001)
Yandell © 2003 JSM 2003 13
goal: unravel biochemical pathways(Jansen Nap 2001)
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central dogma via microarrays(Bochner 2003)
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coordinated expression in mouse genome (Schadt et al. 2003 Nature)
expression pleiotropy
in yeast genome(Brem et al.
2002 Science)
Yandell © 2003 JSM 2003 16
glucose insulin
(courtesy AD Attie)
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Insulin Requirement
from Unger & Orci FASEB J. (2001) 15,312
decompensation
Yandell © 2003 JSM 2003 18
Type 2 Diabetes Mellitus
from Unger & Orci FASEB J. (2001) 15,312
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studying diabetes in an F2
• segregating cross of inbred lines– B6.ob x BTBR.ob F1 F2– selected mice with ob/ob alleles at leptin gene (chr 6)– measured and mapped body weight, insulin, glucose at various ages
• (Stoehr et al. 2000 Diabetes)– sacrificed at 14 weeks, tissues preserved
• gene expression data– Affymetrix microarrays on parental strains, F1
• key tissues: adipose, liver, muscle, -cells• novel discoveries of differential expression (Nadler et al. 2000 PNAS; Lan et
al. 2002 in review; Ntambi et al. 2002 PNAS)– RT-PCR on 108 F2 mice liver tissues
• 15 genes, selected as important in diabetes pathways• SCD1, PEPCK, ACO, FAS, GPAT, PPARgamma, PPARalpha, G6Pase, PDI,
…
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LOD map for PDI: cis-regulationLan et al. (2003 submitted)
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0 50 100 150 200 250 300
02
46
8LO
D
chr2 chr5 chr9
0 50 100 150 200 250 300
-0.5
0.0
0.5
1.0
effe
ct (
add=
blue
, do
m=
red)
chr2 chr5 chr9
Multiple Interval MappingSCD1: multiple QTL plus epistasis!
Yandell © 2003 JSM 2003 22
2-D scan: assumes only 2 QTL!
epistasis LOD
joint LOD
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trans-acting QTL for SCD1(no epistasis yet: see Yi, Xu, Allison 2003)
dominance?
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Bayesian model assessment:chromosome QTL pattern for SCD1
1 3 5 7 9 11 13 15
0.00
0.05
0.10
0.15
4:1,
2,2*
34:
1,2*
2,3
5:3*
1,2,
35:
2*1,
2,2*
35:
2*1,
2*2,
36:
3*1,
2,2*
36:
3*1,
2*2,
35:
1,2*
2,2*
36:
4*1,
2,3
6:2*
1,2*
2,2*
32:
1,3
3:2*
1,2
2:1,
2
3:1,
2,3
4:2*
1,2,
3
model index
mod
el p
oste
rior
pattern posterior
0.2
0.4
0.6
0.8
model index
post
erio
r /
prio
r
Bayes factor ratios
1 3 5 7 9 11 13 15
3 44 4
55 5
6 65
66
23
2
weak
moderate
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high throughput dilemma• want to focus on gene expression network
– hundreds or thousands of genes/proteins to monitor – ideally capture networks in a few dimensions
• multivariate summaries of multiple traits
– elicit biochemical pathways• (Henderson et al. Hoeschele 2001; Ong Page 2002)
• may have multiple controlling loci– allow for complicated genetic architecture– could affect many genes in coordinated fashion– could show evidence of epistasis– quick assessment via interval mapping may be misleading
Yandell © 2003 JSM 2003 26
why study multiple traits together?• environmental correlation
– non-genetic, controllable by design– historical correlation (learned behavior)– physiological correlation (same body)
• genetic correlation– pleiotropy
• one gene, many functions• common biochemical pathway, splicing variants
– close linkage• two tightly linked genes• genotypes Q are collinear
Yandell © 2003 JSM 2003 27
high throughput:which genes are the key players?
• one approach:
clustering of expression
seed by insulin, glucose• advantage:
subset relevant to trait• disadvantage:
still many genes to study
Yandell © 2003 JSM 2003 28
PC simply rotates & rescalesto find major axes of variation
-5 0 5
-50
5
mRNA1
mR
NA
2
-2 -1 0 1
-2-1
01
2
V1
V2
Yandell © 2003 JSM 2003 29
multivariate screenfor gene expressing mapping
principal componentsPC1(red) and SCD(black)
PC2
(22%
)
PC1 (42%)
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mapping first diabetes PC as a trait
0 50 100 150 200 250 300
0.0
00
0.0
20
loci
his
togr
am
hong7pc.bim summaries with pattern ch2,ch5,ch9
ch2 ch5 ch9
0 50 100 150 200 250 300
-1.0
0.5
addi
tive
ch2 ch5 ch9
0 50 100 150 200 250 300
-2.0
0.0
dom
inan
ce
ch2 ch5 ch9
Yandell © 2003 JSM 2003 31
pFDR for PC1 analysis
0.0 0.2 0.4 0.6 0.8
0.0
0.2
0.4
0.6
0.8
1.0
relative size of HPD region
pr(
H=
0 | p
>si
ze )
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
pr( locus in HPD | m>0 )
BH
pF
DR
(-)
and
size
(.)
00.
050.
10.
150.
2S
tore
y pF
DR
(-)
prior probability
fraction of posterior
found in tails
Yandell © 2003 JSM 2003 32
false detection rates and thresholds
• multiple comparisons: test QTL across genome– size = pr( LOD() > threshold | no QTL at )– threshold guards against a single false detection
• very conservative on genome-wide basis
– difficult to extend to multiple QTL
• positive false discovery rate (Storey 2001)– pFDR = pr( no QTL at | LOD() > threshold )– Bayesian posterior HPD region based on threshold
={ | LOD() > threshold } { | pr( | Y,X,m ) large }
– extends naturally to multiple QTL
Yandell © 2003 JSM 2003 33
pFDR and QTL posterior• positive false detection rate
– pFDR = pr( no QTL at | Y,X, in )
– pFDR = pr(H=0)*sizepr(m=0)*size+pr(m>0)*power
– power = posterior = pr(QTL in | Y,X, m>0 )
– size = (length of ) / (length of genome)
• extends to other model comparisons– m = 1 vs. m = 2 or more QTL
– pattern = ch1,ch2,ch3 vs. pattern > 2*ch1,ch2,ch3
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