Download Gene-Environment Interaction

Gene-Environment
Interaction
AGES workshop, Fall 2012
Lindon Eaves – Introduction
Tim York – Lots of slides
Sarah Medland – Making it work
Genotype x Environment
Interaction
• Genetic control of sensitivity to the
environment
• Environmental control of gene expression
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
Alternative Approach
GxE =
“Environmental modulation” of
path from genotype to
phenotype
See e.g. Purcell
“a,c,e modulated by covariate”
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” (?)
“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”)
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
Genotype x Environment
Interaction
Where does GxE go in “ACE”
model?
• AxE -> “E”
• AxC -> “A”
See Jinks, JL and Fulker, DW (1970) Psych.
Bulletin
Contributions of Genetic, Shared Environment,
Genotype x Shared Environment Interaction
Effects to Twin/Sib Resemblance
Shared
Environment
Additive
Genetic Effects
Genotype x Shared
Environment
Interaction
MZ Pairs
1
1
1x1=1
DZ Pairs/Full Sibs
1
½
1x½=½
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.
Contributions of Genetic, Unshared
Environment, Genotype x Unshared
Environment Interaction Effects to Twin/Sib
Resemblance
Unshared
(Unique)
Environment
Additive
Genetic Effects
Genotype x
Unshared
Environment
Interaction
MZ Pairs
0
1
0x1=0
DZ Pairs/Full Sibs
0
½
0x½=0
If gene-(unshared) environment interaction is not explicitly modeled,
it will be subsumed into the E term in the classic twin model.
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
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]
GxE: A biometrical genetic model
A
A
1
2
M
g2
g1
b
a
E
e
P
b=m + g1A1 + g2A2
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
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)
No GxE: Genetic covariances and correlations
No G x E: Genetic Covariance as Function of Environment
No G x E: Genetic Correlation as Function of Environment
viro
nm
e
nt
alpha=0.5, gamma1=0.0, gamma2=0.0
me
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Tw
in 1
En
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e
Tw
in 2
En
Tw
in 2
En
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varia
c Co
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rrelat
tic Co
Gene
ti
Gene
Tw
in 1
nt
alpha=0.5, gamma1=0.0, gamma2=0.0
Scalar GxE: Genetic covariances and correlations
Scalar G x E: Genetic Covariance as Function of Environment
Scalar G x E: Genetic Correlation as Function of Environment
me
n
t
alpha=0.5, gamma1=0.4, gamma2=0.0
En
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1E
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Tw
in 2
1E
nvi
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Tw
in 2
En
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lation
Corre
nce
varia
tic
Gene
tic Co
Gene
Tw
in
alpha=0.5, gamma1=0.4, gamma2=0.0
Non-Scalar GxE: Genetic covariances and
correlations
Non-scalar G x E: Genetic Covariance as Function of Environment
Non-scalar G x E: Genetic Correlation as Function of Environment
tic
Gene
tic
Gene
la
Corre
nm
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alpha=0.5, gamma1=0.0, gamma2=0.4
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in 1
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En
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rianc
Cova
Tw
in 1
alpha=0.5, gamma1=0.0, gamma2=0.4
Mixed GxE: Genetic covariances and correlations
Mixed G x E: Genetic Covariance as Function of Environment
Mixed G x E: Genetic Correlation as Function of Environment
tic
Gene
viro
nm
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nt
alpha=0.5, gamma1=0.4, gamma2=0.3
En
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in 1
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in 2
En
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in 2
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Corre
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varia
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Gene
Tw
in 1
t
alpha=0.5, gamma1=0.4, gamma2=0.3
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].
Modulation of gene
expression by measured
environment
[and environmental modulation of
non-genetic paths]
Ways to Model Gene-Environment
Interaction in Twin Data
• Multiple Group Models
– (parallel to testing for sex effects using
multiple groups)
Sex Effects
Females
1.0 (MZ) / .5 (DZ)
A1
aF
C1
cF
P1
E1
eF
Males
1.0
1.0 (MZ) / .5 (DZ)
A2
aF
C2
cF
P2
E2
eF
A1
aM
C1
cM
P1
E1
eM
1.0
A2
aM
C2
cM
P2
E2
eM
Sex Effects
Females
1.0 (MZ) / .5 (DZ)
A1
aF
C1
cF
E1
eF
P1
aF = aM ?
Males
1.0
1.0 (MZ) / .5 (DZ)
A2
aF
C2
cF
E2
A1
eF
P2
aM
C1
cM
E1
eM
1.0
A2
aM
P1
cF = cM ?
C2
cM
P2
eF = eM ?
E2
eM
GxE Effects
Urban
1.0 (MZ) / .5 (DZ)
A1
aF
C1
cF
E1
eF
P1
aU = aR ?
Rural
1.0
1.0 (MZ) / .5 (DZ)
A2
aF
C2
cF
E2
A1
eF
P2
aM
C1
cM
E1
eM
1.0
A2
aM
P1
cU = cR ?
C2
cM
P2
eU = eR ?
E2
eM
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
Standard model
• Means vector
(m
m
• Covariance matrix
a + c + e

 Za 2 + c 2

2
2
2


2
2
2
a +c +e 
Model-fitting approach to GxE
A
C
a
c
E
e
A
C
a
c
E
e
m
M
m
Twin 1
Twin 2
M
Model-fitting approach to GxE
A
a+bXM
m
M
C
c
E
e
Twin 1
A
a+bXM
C
c
E
e
Twin 2
m
M
Individual specific moderators
A
a+bXM1
C
c
E
e
A
a+bXM2
C
c
E
e
m
M
m
Twin 1
Twin 2
M
E x E interactions
A
a+bXM1
C
E
c+bYM1
e+bZM1
A
a+bXM2
C
c+bYM2
e+bZM2
m
M
E
m
Twin 1
Twin 2
M
‘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
‘Definition variables’ in Mx
create dynamic var/cov structure
• Common uses:
1. To model changes in variance
components as function of some
variable (e.g., age, SES, etc)
2. As covariates/effects on the means (e.g.
age and sex)
1.0 (MZ) / .5 (DZ)
• Classic Twin Model:
Var (T) = a2 + c2 + e2
A1
a
C1
c
E1
e
1.0
A2
C2
a
c
Twin 1
E2
e
Twin 2
• Moderation Model:
Var (T) =
(a + βXM)2 + (c + βYM)2 + (e + βZM)2
A
a + βXM
C
e + βZM
c + βyM
m + βMM
Purcell 2002,
Twin Research
E
T
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
A
a + βXM
C
E
e + βZM
c + βyM
m + βMM
T
Additional Things to Consider
• Unstandardized versus standardized
effects
Additional Things to Consider
Unstandardized versus standardized effects
ENVIRONMENT 1
ENVIRONMENT 2
Unstandardized
Variance
Standardized
Variance
Unstandardized
Variance
Standardized
Variance
Genetic
60
0.60
60
0.30
Common
environmental
35
0.35
70
0.35
Unique
environmental
5
0.05
70
0.35
Total variance
100
200
Environment may not
modulate all the genes
C.f. Biometrical genetic model –
Different genes may control main
effect and sensitivity/slope
AS
aM
AU
aS + βXSM
aU + βXUM
βXS indicates moderation
of shared genetic effects
M
T
BXU indicates moderation
of unique genetic effects
on trait of interest
Genotype-Environment
Covariance/Correlation (rGE)
see e.g. RB Cattell (1965)
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)
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
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
Getting it to work
SARAH!!!!
Practical (1):
Using Multiple Group Models to
test for GxE
Adding Covariates to Means Model
A
C
a
c
E
e
A
C
a
c
E
e
m+bMM1
M
m+bMM2
Twin 1
Twin 2
M
Matrix Letters as Specified in Mx
Script
A
C
E
a+bXM1 c+bYM1
a +aM*D1
e+eM*D1
Twin 1
C
a+bXM2 c+cM*D2 e+b M
Z 2
a+aM*D2
e+eM*D2
Twin 2
M
m+bMM2
m+bMM1
mu+b*D1
E
c+bYM2
c+cM*D1 e+b M
Z 1
M
A
Main effects and moderating effects
mu+b*D2
Practical (2):
Using Definition Variables
to test for GxE
Matrix Letters as Specified in Mx
Script
A
C
E
a+bXM1 c+bYM1
a +aM*D1
c+cM*D1 e+b M
Z 1
Twin 1
C
E
c+bYM2
e+eM*D1
M
A
a+bXM2 c+cM*D2 e+b M
Z 2
a+aM*D2
e+eM*D2
Twin 2
M
m
m
mu
mu
‘Definition variables’ in Mx
create dynamic var/cov structure
• Common uses:
1. To model changes in variance
components as function of some
variable (e.g., age, SES, etc)
2. As covariates/effects on the means (e.g.
age and sex)
Definition variables used as
covariates
General model with age and sex as covariates:
yi = a + b1(agei) + b2 (sexi) + e
Where yi is the observed score of individual i, a
is the intercept or grand mean, b1 is the
regression weight of age, agei is the age of
individual i, b2 is the deviation of males (if sex
is coded 0= female; 1=male), sexi is the sex of
individual i, and e is the residual that is not
explained by the covariates (and can be
decomposed further into ACE etc).
Allowing for a main effect of X
• Means vector
(m + bX1i
m + bX 2 i 
• Covariance matrix
a + c + e

 Za 2 + c 2

2
2
2


2
2
2
a +c +e 
Common uses of definition
variables in the means model
• Incorporating covariates (sex, age, etc)
• Testing the effect of SNPs (association)
• In the context of GxE, controlling for rGE