1. Gene-gene and gene-environment interactions Manuel Ferreira Massachusetts General Hospital Harvard Medical School Center for Human Genetic Research

2. Slides can be found at: http://pngu.mgh.harvard.edu/~mferreira/

3. Outline 2. What is epistasis? 3. Study designs and tests to detect epistasis 4. Application to genome-wide datasets 1. G-G and G-E interactions in the context of gene mapping

4. 1. G-G and G-E in context

5. chromosome 4 DNA sequence SNP (single nucleotide polymorphism) …GGCGGTGTTCCGGGCCATCACCATTGCGGG CCGGATCAACTGCCCTGTGTACATCACCAAG GTCATGAGCAAGAGTGCAGCCGACATCATCG CTCTGGCCAGGAAGAAAGGGCCCCTAGTTTT TGGAGAGCCCATTGCCGCCAGCCTGGGGACC GATGGCACCCATTACTGGAGCAAGAACTGGG CCAAGGCTGCGGCGTTCGTGACTTCCCCTCC CCTGAGCCCGGACCCTACCACGCCCGACTA… Find disease-causing variation The Human Genome

6. ? Gene effect Environmental effect The environment modifies the effect of a gene A gene modifies the effect of an environment G x E interaction Gene-environment interaction S.Purcell ©

7. Epistasis Gene effect Epistasis: one gene modifies the effect of another Gene × gene interaction S.Purcell ©

8. 2. Definition(s) of epistasis

9. AA Aa aa BB Bb bb Epistasis or not ? 113 224 335

10. Definitions of epistasis Biological Statistical Individual-level phenomenon Population-level phenomenon S.Purcell ©

11. Gene RED Pigment 1 Pigment 2 ? Final pigment Gene YELLOW

12. Gene RED Pigment 1 Pigment 2 Final pigment Gene YELLOW AA Aa aa BB Bb bb

13. Gene RED Gene YELLOW Pigment 1 Pigment 2 Final pigment X Aa aa BB Bb bb Bateson (1909)

14. Gene RED Gene YELLOW Pigment 1 Pigment 2 Final pigment X AA BB Bb bb Bateson (1909)

15. Gene RED Gene YELLOW Pigment 1 Pigment 2 Final pigment Introduced the concept of epistasis as a “masking effect”, whereby a variant or allele at one locus prevents the variant at another locus from manifesting its effect. AA Aa aa BB Bb bb Mendelian concept, closer to biological definition of interaction between 2 molecules Bateson (1909)

16. Fisher (1918) 022 133 133 0 1 1 Gene RED Gene YELLOW Epistasis defined as the extent to which the joint contribution of two alleles in different loci towards a phenotype deviates from that expected under a purely additive model. AA Aa aa BB Bb bb 022 022 122 122 AA Aa aa 022 Expected Observed Mathematical concept, closer to statistical definition of interaction between 2 variables on a linear scale.

17. Dominance is defined as the extent to which the joint contribution of two alleles in the same locus towards a phenotype deviates from that expected by a purely additive model. 0 1 2 AA Aa aaAA Aa aaAA Aa aa AA Aa aa Epistasis defined as the extent to which the joint contribution of two alleles in different loci towards a phenotype deviates from that expected under a purely additive model. AdditiveDominant Recessive Genotypic mean

18. Epistasis is very similar... Deviation from additivity between loci. Within locus: Between loci: Locus A Locus B Additive No effect Additive No effect bb Bb BB BB Bb bb 0 1 2 3 4 AA Aa aaAA Aa aaAA Aa aa Genotypic mean

19. Locus A AdditiveDominant Recessive Additive Dominant Recessive Locus B Between loci: Additive (ie. NO epistasis)

20. Locus A AdditiveDominant Recessive Additive Dominant Recessive Locus B 012 123 234 022 133 244 002 113 224 012 234 234 022 133 133 002 224 224 012 012 234 022 022 133 002 002 224 AA Aa aaAA Aa aaAA Aa aa BB Bb bb BB Bb bb BB Bb bb 1 1 1 1 2 0 1 0 0 2 0 2 Between loci: Additive (ie. NO epistasis)

21. 000 011 011 000 012 023 000 001 012 000 000 004 224 242 422 111 111 118 AA Aa aaAA Aa aaAA Aa aa BB Bb bb BB Bb bb Between loci: Non-Additive (ie. epistasis) 0 0 1 0 1 0 1 0 1 0 0 0

22. 113 224 335 AA Aa aa BB Bb bb Epistasis or not ?

23. Statistical definition of epistasis is scale dependent Defined epistasis as a departure from an additive model across loci. Crucial assumption: genotype effects are measured on the appropriate scale.

24. AA Aa aa AA Aa aa +4 +0.7+0.4 log (x) No departure from additivity Significant departure from additivity 0.00 1.10 0.69 1.39 1.10 1.61 114 225 336 log (x)

25. Penetrances Relative RisksOdds Ratios Disease trait Genotype Means Continuous trait

26. Penetrance scale Linear scale RR scale OR scale Epistasis defined as departure from: Additive model Multiplicative model Genotype effects measured on: Additive: Multiplicative: y = LocusA + LocusB y = LocusA × LocusB

27. 3. Designs and methods to detect epistasis

28. Study designs Family-basedCase-ControlCase-only More robust, fewer assumptions More efficient, powerful

29. Methods 1. Regression 2. “Linkage Disequilibrium” or allelic-association 3. Transmission distortion

30. + m 3. (LocusA × LocusB) Methods y = m 1.LocusA + m 2.LocusB y = (m 1 + m 3.LocusB).LocusA + m 2.LocusB Effect of LocusA on y is modified by LocusB 1. Regression y Continuous traitLinear regression Disease traitLogistic regression

31. + m 3. (LocusA × Env) Methods y = m 1.LocusA + m 2.Env y = (m 1 + m 3.Env).LocusA + m 2.Env Effect of LocusA on y is modified by Env 1. Regression

32. Methods 2. LD-based Epistasis induces “LD” in cases, even for unlinked loci: p(a) = 0.2 p(b) = 0.2 111 111 111.640.160.040 A a B b B b.640.160.040 ~ 0 “LD” Epistasis model.41.21.02.21.10.01.03.01.00 AA Aa aa.41.21.02.21.10.01.03.01.00 Cases Controls BB Bb bb BB Bb bb BB Bb bb AA Aa aa Genotype frequencies “Haplotype frequencies”

33. Methods 2. LD-based BB Bb bb p(a) = 0.2 p(b) = 0.2.41.21.02.21.10.01.03.01.00 111 111 1120 AA Aa aa.40.20.03.20.10.01.03.01.02.640.160.040 AA Aa aa A a B b B b.630.158.054 ~ 0 ~ 0.05 Cases Controls Genotype frequencies “Haplotype frequencies” “LD” Epistasis model BB Bb bb BB Bb bb Epistasis induces “LD” in cases, even for unlinked loci:

34. Two-locus genotypes AA (p A 2 ) Aa (2p A q A ) BB (p B 2 ) Bb (2p B q B ) AABB aa (q A 2 ) bb (q B 2 ) AaBB aa BB AABb AaBb aa Bb AAbb Aabb aa bb Locus A: a A (p A ) (q A ) Locus B: b B (p B ) (q B ) p B + q B = 1 p A + q A = 1 AAbb = Ab / Ab A b A b if and only if AAbb ≠ Ab / Ab A A if b b (2-locus genotype) (haplotype)

35. Methods 2. LD-based In the presence of Epistasis: LD cases > 0 LD cases > LD controls Statistics that measure the strength of association (δ) between two loci Case-ControlCase-only H 0 : δ = 0H 0 : δ Cases = δ Controls LD (D, r 2 ) Correlation

36. Cases (Scz) Controls Genes in 5q GABA cluster Pamela Sklar Tracey Petryshen C&M Pato Pamela Sklar Tracey Petryshen C&M Pato

37. Methods 3. Transmission distortion AA Aa Aa BB probands If the effect of locus A on disease risk is modified by Locus B: AA Aa Aa AA Aa Aa 50% Bb probands 52% bb probands 56% Same applies for Env instead of Locus B

38. aa Aa aa aa Aa Aa AA Aa Aa AA Aa AA Subset of bb probandsSubset of BB probands →100% →0% →100% If variants A and B are in LD (common haplotypes AB / ab) False positive interactions (due to linkage or population stratification) TDT requires assumption of independence between loci

39. Design & Methods Case-ControlCase-onlyFamily-based Regression LD-based  TDT  

40. Case-only designs offer efficient detection of epistasis

41. Case-only design isn’t always valid Gene AGene B Gene AGene B stratification 1. Physical distance 2. Population substructure in case sample

42. LD Fast, often more powerful Less useful for continuous traits and/or family data ProsCons Efficient, powerfulAssumptions Applicable to linked lociLess efficient Few methods that efficiently handle relatives Case-Control Case-only Family-based PLINK Slow(er) Many extensions possible (GxE, covariates, etc) Regression (unlinked loci, no stratification, etc)

43. 4. Application to genome-wide datasets

44. # SNPs # pairs 5 10 50 1,225 500 124,750 250,000 31,249,880,000 500,000 124,999,750,000 An “all pairs of SNPs” approach to epistasis does not scale well… … but it is feasible! ~1 week, running PLINK using ~200 CPUs. >3000 individuals

45. Multiple testing increases false positives

46. # SNPs # pairs P-value needed 5 10 5e-3 50 1,225 4e-5 500 124,750 4e-7 250,000 31,249,880,000 2e-12 500,000 124,999,750,000 4e-13 P-value required for experiment-wide significance must be adjusted for the number of tests performed

47. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Chromosome 13 Chromosomes 1 to 22 Genome-wide epistasis screen in Bipolar-disorder

48. A B C D E F G H I J 1 2 3 4 5 6 7 8 A 1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 B 1 B 2 B 3 B 4 B 5 B 6 B 7 B 8 ……. J 6 J 7 J 8 A single gene-based test 80 allele-based tests

49. Gene-environment Science 2003, 301: 306

50. Gene-environment The Journal of Nutrition 2002, 8S: 132

51. Gene-Gene Nature 2005, 436: 701

52. Further reading Cordell HJ (2002) Human Molecular Genetics 11: 2463-2468. –a statistical review of epistasis, methods and definitions Clayton D & McKeigue P (2001) The Lancet, 358, 1357-60. –a critical appraisal of GxE research Marchini J, Donnelly P & Cardon LR (2005) Nature Genetics, 37, 413-417 –epistasis in whole-genome association studies