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what is the goal of QTL study?

Dimension Reduction for Mapping mRNA Abundance as Quantitative Traits Brian S. Yandell University of Wisconsin-Madison www.stat.wisc.edu/~yandell/statgen [Lan et al. 2003 Genetics 164 (4): August 2003]. what is the goal of QTL study?. uncover underlying biochemistry

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what is the goal of QTL study?

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  1. Dimension Reductionfor Mapping mRNA Abundance as Quantitative TraitsBrian S. YandellUniversity of Wisconsin-Madisonwww.stat.wisc.edu/~yandell/statgen[Lan et al. 2003 Genetics 164(4): August 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 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 JSM 2003

  4. typical phenotype assumptions • normal "bell-shaped" environmental variation • genotypic value GQ is composite of m QTL • genetic uncorrelated with environment data histogram JSM 2003

  5. 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 JSM 2003

  6. Pareto diagram of QTL effects major QTL on linkage map (modifiers) minor QTL major QTL 3 polygenes 2 4 5 1 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 JSM 2003

  8. X E1 Z E2 Y epistasis in parallel pathways(Gary Churchill) • Z keeps trait value low • Neither E1nor E2 is rate limiting • Loss of function alleles are segregating from parent A at E1and from parent B at E2 JSM 2003

  9. epistasis in a serial pathway(Gary Churchill) • Z keeps trait value high • Neither E1 nor E2 is rate limiting • Loss of function alleles are segregating from parent B at E1and from parent A at E2 E1 E2 X Y Z JSM 2003

  10. epistasis examples(Doebley Stec Gustus 1995; Zeng pers. comm.) 1 9 traits 1,4,9 1: dom-dom interaction 4: add-add interaction 9: rec-rec interaction (Fisher-Cockerham effects) 4 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) JSM 2003

  12. idea of mapping microarrays(Jansen Nap 2001) JSM 2003

  13. goal: unravel biochemical pathways(Jansen Nap 2001) JSM 2003

  14. central dogma via microarrays(Bochner 2003) JSM 2003

  15. coordinated expression in mouse genome (Schadt et al. 2003 Nature) expression pleiotropy in yeast genome (Brem et al. 2002 Science) JSM 2003

  16. glucose insulin (courtesy AD Attie) JSM 2003

  17. Insulin Requirement decompensation JSM 2003 from Unger & Orci FASEB J. (2001) 15,312

  18. Type 2 Diabetes Mellitus JSM 2003 from Unger & Orci FASEB J. (2001) 15,312

  19. 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,… JSM 2003

  20. LOD map for PDI: cis-regulationLan et al. (2003 submitted) JSM 2003

  21. Multiple Interval MappingSCD1: multiple QTL plus epistasis! JSM 2003

  22. 2-D scan: assumes only 2 QTL! epistasis LOD joint LOD JSM 2003

  23. trans-acting QTL for SCD1(no epistasis yet: see Yi, Xu, Allison 2003) dominance? JSM 2003

  24. Bayesian model assessment:chromosome QTL pattern for SCD1 JSM 2003

  25. 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 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 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 JSM 2003

  28. PC simply rotates & rescalesto find major axes of variation JSM 2003

  29. multivariate screenfor gene expressing mapping principal components PC1(red) and SCD(black) PC2 (22%) PC1 (42%) JSM 2003

  30. mapping first diabetes PC as a trait JSM 2003

  31. pFDR for PC1 analysis prior probability fraction of posterior found in tails 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 JSM 2003

  33. pFDR and QTL posterior • positive false detection rate • pFDR = pr( no QTL at  | Y,X,  in  ) • pFDR = pr(H=0)*size pr(m=0)*size+pr(m>0)*power • power = posterior = pr(QTLin  | 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 JSM 2003

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