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Accounting for genetic interactions improves modeling of individual quantitative trait phenotypes in yeast

Nature Genetics volume 49, pages 497–503 (2017)Cite this article

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Abstract

Experiments in model organisms report abundant genetic interactions underlying biologically important traits, whereas quantitative genetics theory predicts, and data support, the notion that most genetic variance in populations is additive. Here we describe networks of capacitating genetic interactions that contribute to quantitative trait variation in a large yeast intercross population. The additive variance explained by individual loci in a network is highly dependent on the allele frequencies of the interacting loci. Modeling of phenotypes for multilocus genotype classes in the epistatic networks is often improved by accounting for the interactions. We discuss the implications of these results for attempts to dissect genetic architectures and to predict individual phenotypes and long-term responses to selection.

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Figure 1: Many QTLs involved in pairwise interactions are part of highly interconnected epistatic networks.
Figure 2: Epistatic network regulating growth on IAA-containing medium.
Figure 3: Epistatic networks contain hub QTL capacitor alleles of both BY and RM origin that moderate growth-increasing or growth-decreasing effects of segregating alleles at radial QTLs.
Figure 4: Biases in additive-model-based estimates of phenotypes are largest in the genotype classes with the greatest or poorest expected growth.
Figure 5: Simulations show that the additive genetic variances contributed by the loci in the epistatic network regulating growth on IAA-containing medium are highly dependent on the allele frequencies at the other loci in the same network.

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References

  1. Hill, W.G., Goddard, M.E. & Visscher, P.M. Data and theory point to mainly additive genetic variance for complex traits. PLoS Genet. 4, e1000008 (2008).

    Article  Google Scholar 

  2. Bloom, J.S., Ehrenreich, I.M., Loo, W.T., Lite, T.-L.V. & Kruglyak, L. Finding the sources of missing heritability in a yeast cross. Nature 494, 234–237 (2013).

    Article  CAS  Google Scholar 

  3. Bloom, J.S. et al. Genetic interactions contribute less than additive effects to quantitative trait variation in yeast. Nat. Commun. 6, 8712 (2015).

    Article  CAS  Google Scholar 

  4. Polderman, T.J.C. et al. Meta-analysis of the heritability of human traits based on fifty years of twin studies. Nat. Genet. 47, 702–709 (2015).

    Article  CAS  Google Scholar 

  5. Cheverud, J.M. & Routman, E.J. Epistasis and its contribution to genetic variance components. Genetics 139, 1455–1461 (1995).

    CAS  PubMed  PubMed Central  Google Scholar 

  6. Carlborg, O. & Haley, C.S. Epistasis: too often neglected in complex trait studies? Nat. Rev. Genet. 5, 618–625 (2004).

    Article  CAS  Google Scholar 

  7. Mackay, T.F.C. Epistasis and quantitative traits: using model organisms to study gene–gene interactions. Nat. Rev. Genet. 15, 22–33 (2014).

    Article  CAS  Google Scholar 

  8. Nelson, R.M., Pettersson, M.E. & Carlborg, Ö. A century after Fisher: time for a new paradigm in quantitative genetics. Trends Genet. 29, 669–676 (2013).

    Article  CAS  Google Scholar 

  9. Gerke, J., Lorenz, K. & Cohen, B. Genetic interactions between transcription factors cause natural variation in yeast. Science 323, 498–501 (2009).

    Article  CAS  Google Scholar 

  10. Le Rouzic, A., Siegel, P.B. & Carlborg, O. Phenotypic evolution from genetic polymorphisms in a radial network architecture. BMC Biol. 5, 50 (2007).

    Article  Google Scholar 

  11. Le Rouzic, A. & Carlborg, Ö. Evolutionary potential of hidden genetic variation. Trends Ecol. Evol. 23, 33–37 (2008).

    Article  Google Scholar 

  12. Carlborg, O., Jacobsson, L., Ahgren, P., Siegel, P. & Andersson, L. Epistasis and the release of genetic variation during long-term selection. Nat. Genet. 38, 418–420 (2006).

    Article  CAS  Google Scholar 

  13. Paixão, T. & Barton, N.H. The effect of gene interactions on the long-term response to selection. Proc. Natl. Acad. Sci. USA 113, 4422–4427 (2016).

    Article  Google Scholar 

  14. Rönnegård, L. & Valdar, W. Detecting major genetic loci controlling phenotypic variability in experimental crosses. Genetics 188, 435–447 (2011).

    Article  Google Scholar 

  15. Rönnegård, L. & Valdar, W. Recent developments in statistical methods for detecting genetic loci affecting phenotypic variability. BMC Genet. 13, 63 (2012).

    Article  Google Scholar 

  16. Rutherford, S.L. & Lindquist, S. Hsp90 as a capacitor for morphological evolution. Nature 396, 336–342 (1998).

    Article  CAS  Google Scholar 

  17. True, H.L. & Lindquist, S.L. A yeast prion provides a mechanism for genetic variation and phenotypic diversity. Nature 407, 477–483 (2000).

    Article  CAS  Google Scholar 

  18. Gibson, G. & Dworkin, I. Uncovering cryptic genetic variation. Nat. Rev. Genet. 5, 681–690 (2004).

    Article  CAS  Google Scholar 

  19. Paaby, A.B. & Rockman, M.V. Cryptic genetic variation: evolution's hidden substrate. Nat. Rev. Genet. 15, 247–258 (2014).

    Article  CAS  Google Scholar 

  20. Falconer, D.S. & Mackay, T.F.C. Introduction to Quantitative Genetics 4th edn (Longmans Green, 1996).

  21. Bateson, W. Facts limiting the theory of heredity. Science 26, 649–660 (1907).

    Article  CAS  Google Scholar 

  22. Monnahan, P.J. & Kelly, J.K. Epistasis is a major determinant of the additive genetic variance in Mimulus guttatus. PLoS Genet. 11, e1005201 (2015).

    Article  Google Scholar 

  23. Bergman, A. & Siegal, M.L. Evolutionary capacitance as a general feature of complex gene networks. Nature 424, 549–552 (2003).

    Article  CAS  Google Scholar 

  24. Masel, J. & Siegal, M.L. Robustness: mechanisms and consequences. Trends Genet. 25, 395–403 (2009).

    Article  CAS  Google Scholar 

  25. Queitsch, C., Sangster, T.A. & Lindquist, S. Hsp90 as a capacitor of phenotypic variation. Nature 417, 618–624 (2002).

    Article  CAS  Google Scholar 

  26. Dworkin, I., Palsson, A., Birdsall, K. & Gibson, G. Evidence that Egfr contributes to cryptic genetic variation for photoreceptor determination in natural populations of Drosophila melanogaster. Curr. Biol. 13, 1888–1893 (2003).

    Article  CAS  Google Scholar 

  27. Lachowiec, J., Shen, X., Queitsch, C. & Carlborg, Ö. A genome-wide association analysis reveals epistatic cancellation of additive genetic variance for root length in Arabidopsis thaliana. PLoS Genet. 11, e1005541 (2015).

    Article  Google Scholar 

  28. Yvert, G. et al. Trans-acting regulatory variation in Saccharomyces cerevisiae and the role of transcription factors. Nat. Genet. 35, 57–64 (2003).

    Article  CAS  Google Scholar 

  29. Lang, G.I., Murray, A.W. & Botstein, D. The cost of gene expression underlies a fitness trade-off in yeast. Proc. Natl. Acad. Sci. USA 106, 5755–5760 (2009).

    Article  CAS  Google Scholar 

  30. Brem, R.B., Storey, J.D., Whittle, J. & Kruglyak, L. Genetic interactions between polymorphisms that affect gene expression in yeast. Nature 436, 701–703 (2005).

    Article  CAS  Google Scholar 

  31. Slessareva, J.E., Routt, S.M., Temple, B., Bankaitis, V.A. & Dohlman, H.G. Activation of the phosphatidylinositol 3-kinase Vps34 by a G protein α subunit at the endosome. Cell 126, 191–203 (2006).

    Article  CAS  Google Scholar 

  32. Fogel, S., Welch, J.W. & Maloney, D.H. The molecular genetics of copper resistance in Saccharomyces cerevisiae—a paradigm for non-conventional yeasts. J. Basic Microbiol. 28, 147–160 (1988).

    Article  CAS  Google Scholar 

  33. Perlstein, E.O., Ruderfer, D.M., Roberts, D.C., Schreiber, S.L. & Kruglyak, L. Genetic basis of individual differences in the response to small-molecule drugs in yeast. Nat. Genet. 39, 496–502 (2007).

    Article  CAS  Google Scholar 

  34. Sadhu, M.J., Bloom, J.S., Day, L. & Kruglyak, L. Mapping without crosses. Science 352, 1113–1116 (2016).

    Article  CAS  Google Scholar 

  35. Csárdi, G. & Nepusz, T. The igraph software package for complex network research. InterJournal, Complex Systems 1695, 1695 (2006).

    Google Scholar 

  36. Aulchenko, Y.S., Ripke, S., Isaacs, A. & van Duijn, C.M. GenABEL: an R library for genome-wide association analysis. Bioinformatics 23, 1294–1296 (2007).

    Article  CAS  Google Scholar 

  37. Smyth, G.K. Generalized linear models with varying dispersion. J. R. Stat. Soc. B 51, 47–60 (1989).

    Google Scholar 

Download references

Acknowledgements

Funding was provided by the Howard Hughes Medical Institute and by NIH grants R01 GM102308 (L.K.) and F32 GM116318 (M.J.S.) and Swedish Research Council grant 621-2012-4632 (Ö.C.).

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Authors and Affiliations

  1. Department of Medical Biochemistry and Microbiology, Uppsala University, Uppsala, Sweden

    Simon K G Forsberg & Örjan Carlborg

  2. Department of Human Genetics, University of California, Los Angeles, Los Angeles, California, USA

    Joshua S Bloom, Meru J Sadhu & Leonid Kruglyak

  3. Howard Hughes Medical Institute, University of California, Los Angeles, Los Angeles, California, USA

    Joshua S Bloom, Meru J Sadhu & Leonid Kruglyak

  4. Department of Biological Chemistry, University of California, Los Angeles, Los Angeles, California, USA

    Joshua S Bloom, Meru J Sadhu & Leonid Kruglyak

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  1. Simon K G Forsberg
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  4. Leonid Kruglyak
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Contributions

Analyses were designed by S.K.G.F., J.S.B., M.J.S., L.K. and Ö.C. Analyses were conducted by S.K.G.F. and Ö.C. The manuscript was written by S.K.G.F. and Ö.C. and incorporates comments by J.S.B., M.J.S. and L.K.

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Correspondence to Örjan Carlborg.

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Integrated supplementary information

Supplementary Figure 1 LOD scores for all significant genetic interactions (n = 266) involving the 330 epistatic QTLs detected in this population.

The left box plot displays the LOD scores for the genetic interactions between hubs (involved in more than four interactions) and radial loci. The right box plot displays the LOD scores for the genetic interactions that do not involve a hub. The p-value is from a two-sided, non-parametric Wilcoxon test.

Supplementary Figure 2 The correlations between the number of genetic interactions that a locus is involved in and its marginal additive and variance heterogeneity effects.

The x axis shows the number of pairwise genetic interactions each locus is involved in. The left y axis shows the marginal additive and the right y axis shows the marginal variance heterogeneity effect on the phenotype. Each dot in the figure represents a locus. The red dots show the marginal effect on the mean of the phenotype (r = 0.42; P < 1 × 10–12), whereas the blue dots show the effect on the phenotypic variability (r = 0.64; P < 1 × 10–12).

Supplementary Figure 3 Phenotypic distributions in segregants with different combinations of alleles across the six loci in 14 epistatic networks affecting growth in different media.

The networks are divided depending on whether the hub QTL is a significant capacitor or not. A Tukey box plot (the bottom/top of the box are the first/third quartiles, the band is the median and the ends of whiskers extend to the lowest/highest data point within 1.5 times the interquartile range) is plotted for each of the 64 genotype classes in every network. Color indicates the genotype at the hub QTL (green/gray boxes for BY/RM alleles, respectively). The x axis represents the six-locus genotype class, where blue/orange dots indicate growth-increasing/growth-decreasing alleles at the five radial QTLs in the network. The black lines through the boxes illustrate the additive-model-based estimates of the phenotypes for the 64 genotype classes. The number above the x axis is the number of segregants in each genotype class.

Supplementary Figure 4 Phenotypic distributions in segregants with a varying number of growth-decreasing alleles at the radial loci across the six loci in 14 epistatic networks affecting growth in different media.

The networks are divided depending on whether the hub QTL is a significant capacitor or not. Each Tukey box plot (the bottom/top of the box are the first/third quartiles, the band is the median and the whiskers extend to the lowest/highest data point within 1.5 times the interquartile range) represents a group of segregants that share the same number of growth-decreasing alleles at the five radial QTLs in the respective networks. The segregants are divided and colored based on the genotype at the hub QTL (green/gray boxes for BY/RM alleles, respectively). The x axis gives the number of growth-decreasing alleles at the radial QTLs and the number of segregants in each group. The regression lines illustrate the fit of linear additive models to segregants with alternative genotypes at the hub QTL.

Supplementary Figure 5 Phenotype estimation bias for the individual multilocus genotype classes in 15 epistatic networks.

The networks are divided depending on whether the hub QTL is a significant capacitor or not. Each y axis gives the cross-validated estimation error (bias) for the six-locus additive model representation of the genotype value of each individual multilocus genotype class as compared to the actual phenotype (y – ŷ). Each Tukey box plot (the bottom/top of the box are the first/third quartiles, the band is the median and the whiskers extend to the lowest/highest data point within 1.5 times the interquartile range) shows the distribution of prediction errors in 1 of the 64 genotype classes in the network. The 32 leftmost box plots represent the genotype classes with the capacitor hub QTL allele (or with the highest h2 in the case of a non-significant capacitor hub). Significant biases, i.e., where the estimation errors deviate significantly from zero, are colored in yellow.

Supplementary Figure 6 Difference in estimation accuracy between additive and epistatic models illustrated as the cross-validation results from the ten epistatic networks where the hub QTL is a significant capacitor.

The y axis gives the difference in cross-validated mean squared error (MSE) between an additive model (MSEadd) and a model including pairwise interactions (MSEepi2). Each dot corresponds to the difference in MSE for one genotype class. The difference is measured as MSEadd – MSEepi2, meaning that positive values correspond to genotype classes where the estimation accuracy is improved when using an epistatic model.

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Forsberg, S., Bloom, J., Sadhu, M. et al. Accounting for genetic interactions improves modeling of individual quantitative trait phenotypes in yeast. Nat Genet 49, 497–503 (2017). https://doi.org/10.1038/ng.3800

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