Gene-Environment Interaction

1. Gene-Environment Interaction AGES workshop, Fall 2012 Lindon Eaves – Introduction Tim York – Lots of slides Sarah Medland – Making it work

2. Genotype x Environment Interaction • Genetic control of sensitivity to the environment • Environmental control of gene expression

3. The Biometrical Genetic Approach: GxE =Genetic Control of “Sensitivity” to environment See e.g. Mather and Jinks. Like any other phenotype – individual differences in sensitivity may be genetic

4. Alternative ApproachGxE =“Environmental modulation” of path from genotype to phenotype See e.g. Purcell “a,c,e modulated by covariate”

5. CARE! Results depend on scale – often remove GxE (and other “interactions” – e.g. epistasis) by change in scale Often try to choose units so model is additive/linear and simple. “Simplicity is truth” (?)

6. “Environment” • Micro-environment (unmeasured, random) “E” and “C” in twin models • Macro-environment (measured, ?”fixed”) SES, life events, exposure, smoking • “Independent” (of genotype) • “Correlated with genotype – of individual (“active/evocative”) or relative (“passive”)

7. Animals, Plants and Microorgansims • GxE common property of genetic systems • Ranking of lines/strains changes over environments: ?“genetic correlation across environments” • Polygenic: genes affecting response to E widely distributed across genome (Caligari and Mather) • GxE usually small relative to main effects of G and E (“power”?) • Can select separately for means and slopes (“different genes cause GxE”) • Some genes affect response to specific environmental features (Na, K, rain, diet, separation) • Some genes affect response to overall quality of environment (“stress”) • GxE adaptive – own genetic architecture (A,D etc) – genetic vulnerability, resilience, sensation-seeking, harm avoidance (rGE) • GxE scale dependent – choose units of measurement

8. Genotype x Environment Interaction

9. Where does GxE go in “ACE” model? • AxE -> “E” • AxC -> “A” See Jinks, JL and Fulker, DW (1970) Psych. Bulletin

10. Contributions of Genetic, Shared Environment, Genotype x Shared Environment Interaction Effects to Twin/Sib Resemblance In other words—if gene-(shared) environment interaction is not explicitly modeled, it will be subsumed into the A term in the classic twin model.

11. Contributions of Genetic, Unshared Environment, Genotype x Unshared Environment Interaction Effects to Twin/Sib Resemblance If gene-(unshared) environment interaction is not explicitly modeled, it will be subsumed into the E term in the classic twin model.

12. Testing for GxE and GxC • Plot absolute within MZ pair differences against pair means (CARE!!) • Plot absolute within DZ pair differences against shared measured environment

13. Basic Model (1960’s) Yi |E = gi + biE + di Yi |E = phenotype of ith genotype in environment E gi = main effect (“intercept”) of ith genotype bi = slope (“sensitivity”) of ith genotype in response to environment (gi , bi) ~ N[m,G]

14. GxE: A biometrical genetic model A2 M A1 g2 g1 b a b=m + g1A1 + g2A2 P E e

15. ith phenotype in kth level of measured environment • Pi|Mk= aA1i + (m + g1A1i + g2A2i)Mk+ eEik • aA1i + (m + g1A1i + g2A2i)Mk+ eEik • = ck+ (a+ g1Mk)A1i + g2MkA2i+ eEik

16. Expected twin covariance conditional on environments of first and second twins Cov(Pi1|Mk ,Pi2|Ml ) = [a2 + ag1(Mk+Ml)+(g12+g22)MkMl]r + Cov(Ei1k,Ei2l) r= genetic correlation (1 in MZs)

17. No GxE: Genetic covariances and correlations

18. Scalar GxE: Genetic covariances and correlations

19. Non-Scalar GxE: Genetic covariances and correlations

20. Mixed GxE: Genetic covariances and correlations

21. Note: Can’t separate components of “mixed” GxE unless you have same or related genotypes (MZ and/or DZ pairs) in concordant and discordant environments. [c.f. Analysis of sex limited gene effects].

22. Modulation of gene expression by measured environment [and environmental modulation of non-genetic paths]

23. Ways to Model Gene-Environment Interaction in Twin Data • Multiple Group Models • (parallel to testing for sex effects using multiple groups)

24. Sex Effects Females Males

25. Sex Effects Females Males aF = aM ? cF = cM ? eF = eM ?

26. GxE Effects Urban Rural aU = aR ? cU = cR ? eU = eR ?

27. Problem: • Many environments of interest do not fall into groups • Regional alcohol sales • Parental warmth • Parental monitoring • Socioeconomic status • Grouping these variables into high/low categories loses a lot of information

28. Standard model • Means vector • Covariance matrix

29. Model-fitting approach to GxE A C E A C E c a e a c e m m Twin 1 Twin 2 M M

30. Model-fitting approach to GxE A C E A C E c a+XM e a+XM c e m m Twin 1 Twin 1 Twin 2 Twin 2 M M

31. Individual specific moderators A C E A C E c a+XM1 e a+XM2 c e m m Twin 1 Twin 1 Twin 2 Twin 2 M M

32. E x E interactions A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 e+ZM1 e+ZM2 m m Twin 1 Twin 1 Twin 2 Twin 2 M M

33. ‘Definition variables’ in Mx • General definition: Definition variables are variables that may vary per subject and that are not dependent variables • In Mx:The specific value of the def var for a specific individual is read into a matrix in Mx when analyzing the data of that particular individual

34. ‘Definition variables’ in Mx create dynamic var/cov structure • Common uses: • To model changes in variance components as function of some variable (e.g., age, SES, etc) • As covariates/effects on the means (e.g. age and sex)

35. Classic Twin Model: Var (T) = a2 + c2 + e2 • Moderation Model: Var (T) = (a + βXM)2 + (c + βYM)2 + (e + βZM)2 Purcell 2002, Twin Research

36. Var (T) = (a + βXM)2 + (c + βYM)2 (e + βZM)2 Where M is the value of the moderator and Significance of βX indicates genetic moderation Significance of βY indicates common environmental moderation Significance of βZ indicates unique environmental moderation BM indicates a main effect of the moderator on the mean

37. Additional Things to Consider • Unstandardized versus standardized effects

38. Additional Things to Consider Unstandardized versus standardized effects

39. Environment may not modulate all the genes C.f. Biometrical genetic model – Different genes may control main effect and sensitivity/slope

40. AS AU aM aS + βXSM aU + βXUM βXS indicates moderation of shared genetic effects BXU indicates moderation of unique genetic effects on trait of interest M T

41. Genotype-Environment Covariance/Correlation (rGE)see e.g. RB Cattell (1965)

42. Gene-environment Interaction • Genetic control of sensitivity to the environment • Environmental control of gene expression Gene-environment Correlation • Genetic control of exposure to the environment • Different genotypes select or create different environments • Different genotypes are exposed to correlated environments (e.g. sibling effects, maternal effects) • Environments select on basis of genotype (Stratification, Mate choice)

43. This complicates interpretation of GxE effects • If there is a correlation between the moderator (environment) of interest and the outcome, and you find a GxE effect, it’s not clear if: • The environment is moderating the effects of genes or • Trait-influencing genes are simply more likely to be present in that environment

44. Ways to deal with rGE • Limit study to moderators that aren’t correlated with outcome • Pro: easy • Con: not very satisfying • Moderator in means model will remove from the covariance genetic effects shared by trait and moderator • Pro: Any interaction detected will be moderation of the trait specific genetic effects • Con: Will fail to detect GxE interaction if the moderated genetic component is shared by the outcome and moderator • Explicitly model rGE using a bivariate framework • Pro: explicitly models rGE • Con: Power to detect BXU decreases with increasing rGE; difficulty converging

45. Getting it to workSARAH!!!!

46. Practical (1): Using Multiple Group Models to test for GxE

47. Adding Covariates to Means Model A C E A C E c a e a c e m+MM1 m+MM2 Twin 1 Twin 2 M M

48. Matrix Letters as Specified in Mx Script A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 c+cM*D1 c+cM*D2 e+ZM1 e+ZM2 a +aM*D1 a+aM*D2 e+eM*D2 e+eM*D1 Twin 1 Twin 2 M M m+MM2 m+MM1 mu+b*D2 mu+b*D1 Main effects and moderating effects

49. Practical (2): Using Definition Variables to test for GxE

50. Matrix Letters as Specified in Mx Script A C E A C E c+YM1 c+YM2 a+XM1 a+XM2 c+cM*D1 c+cM*D2 e+ZM1 e+ZM2 a +aM*D1 a+aM*D2 e+eM*D2 e+eM*D1 Twin 1 Twin 2 M M m m mu mu