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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]
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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
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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
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typical phenotype assumptions• normal "bell-shaped" environmental variation• genotypic value GQ is composite of m QTL• genetic uncorrelated with environment
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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
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Pareto diagram of QTL effects
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major QTL onlinkage map
majorQTL
minorQTL
polygenes
(modifiers)
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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
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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.)
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traits 1,4,91: dom-dom interaction4: add-add interaction9: rec-rec interaction(Fisher-Cockerham effects)
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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)
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idea of mapping microarrays(Jansen Nap 2001)
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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)
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glucose insulin
(courtesy AD Attie)
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Insulin Requirement
from Unger & Orci FASEB J. (2001) 15,312
decompensation
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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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Multiple Interval MappingSCD1: multiple QTL plus epistasis!
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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
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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
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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
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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
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PC simply rotates & rescalesto find major axes of variation
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multivariate screenfor gene expressing mapping
principal componentsPC1(red) and SCD(black)
PC2
(22%
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PC1 (42%)
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mapping first diabetes PC as a trait
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pFDR for PC1 analysis
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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
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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