1. Inferring Genetic Architecture of Complex Biological Processes Brian S
Inferring Genetic Architecture of Complex Biological Processes Brian S. Yandell University of Wisconsin-Madison 
modern high throughput biology
heritable subsets of complex traits
genetic architecture for meta-traits
causal biochemical networks
13 October 2004
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2. modern high throughput biology
measuring the molecular dogma of biology
DNA  RNA  protein  metabolites
measured one at a time only a few years ago
massive array of measurements on whole systems (“omics”)
thousands measured per individual (experimental unit)
all (or most) components of system measured simultaneously
whole genome of DNA: genes, promoters, etc.
all expressed RNA in a tissue or cell
all proteins
all metabolites
systems biology: focus on network interconnections
chains of behavior in ecological community
underlying biochemical pathways
genetics as one experimental tool
perturb system by creating new experimental cross
each individual is a unique mosaic
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3. 13 October 2004
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4. glucose insulin (courtesy AD Attie) 13 October 2004
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(courtesy AD Attie)

5. studying diabetes in an F2
segregating cross of inbred lines
B6.ob x BTBR.ob  F1  F2  F2.ob/ob
selected mice with ob/ob alleles at leptin gene (chr 6)
mapped body weight, insulin, glucose at various ages (Stoehr et al Diabetes)
sacrificed at 14 weeks, tissues preserved
gene expression data
RT-PCR for a few mRNA on 108 F2 mice liver tissues
(Lan et al Diabetes; Lan et al Genetics)
Affymetrix microarrays on 60 F2 mice liver tissues
U47 A & B chips, RMA normalization
design: selective phenotyping (Jin et al Genetics)
13 October 2004
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6. The intercross (from K Broman)
13 October 2004
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7. interval mapping basics
observed measurements
Y = phenotypic trait
X = markers & linkage map
i = individual index 1,…,n
missing data
missing marker data
Q = QT genotypes
alleles QQ, Qq, or qq at locus
unknown quantities
M = genetic architecture
 = QT locus (or loci)
 = phenotype model parameters
pr(Q|X,) genotype model
grounded by linkage map, experimental cross
recombination yields multinomial for Q given X
f(Y|Q) phenotype model
distribution shape (assumed normal here)
unknown parameters  (could be non-parametric) 
after
Sen & Churchill
(2001 Genetics) M
13 October 2004
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8. genetic architecture: heterogeneity
heterogeneity: different genotypes could yield the same phenotype
multiple genes affecting phenotype in subtle ways
epistatic interactions of multiple genes
genetic architecture: model M
M = {1, 2, 3, (1, 2)} = 3 loci with epistasis between two
 = (1, 2, 3) = loci in model M
q = 0 + 1q + 2q + 3q + (1,2)q = model for genotype mean
Q = (Q1, Q2, Q3) = genotype for each individual at loci 
q = (q1, q2, q3) = possible genotype at loci 
can partition prior on genotypic mean into priors for effects jq
pr(q) = pr(0) prodj in M pr(jq)
13 October 2004
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9. finding heritable traits (from Christina Kendziorski)
probability a trait is heritable
pr(H|Y,Q) = pr(Y|Q,H) pr(H|Q) / pr(Y|Q) Bayes rule
pr(Y|Q) = pr(Y|Q,H) pr(H|Q) + pr(Y|Q, not H) pr(not H|Q)
phenotype given genotype
pr(Y|Q, not H) = f0(Y) = sum f(Y| ) pr() if not H
pr(Y|Q, H) = f1(Y|Q) = productq f0(Yq ) if heritable
Yq = {Yi | Qi =q} = trait values with genotype Q=q
13 October 2004
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10. hierarchical model for expression phenotypes
(EB arrays: Christina Kendziorski)
mRNA phenotype models
given genotypic mean q
common prior on q across all mRNA
(use empirical Bayes to estimate prior)
13 October 2004
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11. expression meta-traits: pleiotropy
what are expression meta-traits?
pleiotropy: a few genes can affect many traits
transcription factors, regulators
weighted averages: Z = YW
principle components, discriminant analysis
inferring genetic architecture is difficult
missing data: genotypes Q not observed
model selection issues
thousands of expression traits
heavy computation load
13 October 2004
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12. PC for two correlated mRNA
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13. PC across microarray functional groups
Affy chips on 60 mice
~40,000 mRNA
2500+ mRNA show DE
(via EB arrays with
marker regression)
1500+ organized in
85 functional groups
2-35 mRNA / group
which are interesting?
examine PC1, PC2
circle size = # unique mRNA
13 October 2004
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14. 2 functional groups factor loadings of PC meta-traits
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15. 13 October 2004
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16. (portion of) chr 4 region?
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17. interplay of pleiotropy & correlation
pleiotropy only
correlation only
both
Korol et al. (2001)
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18. path diagrams (errors omitted)
other correlation
- polygenic
- physiologic
pleiotropy
close linkage Y1 Y1 Q1 Y1 Z Q Q2 Y2 Y2 Y2
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19. PC and DA for mRNA traits PC shows little relation to genotypes DA based on best fit with marker pair D4Mit17 and D15Mit63
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20. interaction plots for DA meta-traits
13 October 2004
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21. interaction plots for SCD (one important expression trait)
13 October 2004
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22. inferring biochemical pathways (with Elias Chaibub)
genetic architecture for meta-traits
list of major genomic regions (QTLs)
correlations across many individual traits
change in gene underlying a QTL
QTL reveals allelic differences in nearby gene
allelic differences cause expression differences
cis-acting: changes expression of its mRNA
trans-acting: changes expression of other mRNA
13 October 2004
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23. graphical models D1 R1 Q P1 cis D2 R2 P2 trans 13 October 2004
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24. open questions model selection and search computation
best selection criteria
efficient search algorithms
search over non-normal models
graphical models for biochemical pathways
computation
fast computation of meta-traits
revealing graphics for diagnostics & inference
13 October 2004
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