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

Slides can be found at:

Outline 3. What is epistasis? 4. Study designs and tests to detect epistasis 5. Application to genome-wide datasets 1. G-G and G-E in the context of gene mapping 2. Genetic concepts

1. G-G and G-E in context

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

Common disease

GenotypeRisk of disease DD0.01 Dd0.012 dd Disease prevalence ~1 in 100 Each extra d allele increases risk by ~1.2 times Frequency of d in controls~ 5% Frequency of d in cases~ 6% Common disease, polygenic effects

? Gene-environment correlation 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 ©

Linkage disequilibrium (LD) Epistasis Gene effect Epistasis: one gene modifies the effect of another Gene × gene interaction S.Purcell ©

2. Genetic concepts

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)

Effect of a locus on disease risk can be expressed as: Genotype Penetrances Genotype Relative Risks Genotype Odds Ratios Effect of a locus on a continuous trait usually expressed as: Genotype Means

Genotype penetrance Probability of developing disease for a given genotype Example: P(D=affected | G=AABB) = 0.01 P(D=affected | G) P(D=unaffected | G=AABB) = P(D=unaffected | G) Penetrance scale P(D=affected | G)

Genotype relative risk (RR) Risk of developing disease for a given genotype, relative to the risk for a reference genotype Example: RR(AABb) = P(D=affected | G=AABB) P(D=affected | G) P(D=affected | G = ref) P(D=affected | G=AABb) RR(AABb) ∞ = 2.6 Relative risk scale

P(D=unaffected | G = ref) Genotype odds ratio (OR) Odds of developing disease for a given genotype, relative to the odds for a reference genotype Example: OR(AABb) = P(D=unaffected | G=AABb) P(D=affected | G) P(D=unaffected | G) P(D=affected | G=AABb) OR(AABb) ∞ P(D=unaffected | G=AABB) P(D=affected | G=AABB) P(D=affected | G = ref) = 2.7 Odds ratio scale

Penetrances Relative RisksOdds Ratios Disease trait Genotype Means Continuous trait

3. Definition(s) of epistasis

AA Aa aa BB Bb bb Epistasis or not ?

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

Requires: 1) Variation between individuals 2) Effect on disease Requires: 1) Correct statistical definition of effect S.Purcell ©

Gene RED Pigment 1 Pigment 2 ? Final pigment Gene YELLOW

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

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

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

Gene RED Gene YELLOW Pigment 1 Pigment 2 Final pigment 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)

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 AA Aa aa 022 Expected Observed Fisher (1918) Mathematical concept, closer to statistical definition of interaction between 2 variables on a linear scale.

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 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

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 AA Aa aaAA Aa aaAA Aa aa Genotypic mean

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

Locus A AdditiveDominant Recessive Additive Dominant Recessive Locus B AA Aa aaAA Aa aaAA Aa aa BB Bb bb BB Bb bb BB Bb bb Between loci: Additive (ie. NO epistasis)

AA Aa aaAA Aa aaAA Aa aa BB Bb bb BB Bb bb Between loci: Non-Additive (ie. epistasis)

AA Aa aa BB Bb bb Epistasis or not ?

Statistical epistasis is scale dependent AA Aa aa BB Bb bb Defined epistasis as a departure from the genotype effects expected under an additive model. Crucial assumption: genotype effect is measured on the appropriate scale Epistasis? Linear OR Scale NO YES

AA Aa aa AA Aa aa log (x) No departure from additivity Significant departure from additivity log (x)

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

4. Designs and methods to detect epistasis

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

Methods 1. Regression 2. Linkage Disequilibrium 3. Transmission distortion

+ 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

+ 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

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

Methods 2. LD-based BB Bb bb p(a) = 0.2 p(b) = AA Aa aa AA Aa aa A a B b B b ~ 0 ~ 0.02 Cases Controls Genotype frequencies Haplotype frequencies LD Epistasis model BB Bb bb BB Bb bb Epistasis induces LD in cases, even for unlinked loci:

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

DTNBP1 MUTEDPLDNSNAPAPCNO BLOC1S1BLOC1S2 BLOC1S3 -log10(p-value) p=0.05 Dysbindin-1 by itself shows no evidence of association with Scz 373 Irish schizophrenics 812 controls Standard single SNP analyses Genes in 5q GABA cluster S.Purcell ©

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

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

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

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

Case-only designs offer efficient detection of epistasis

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

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

5. Application to genome-wide datasets

# SNPs # pairs , , , ,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.

Multiple testing increases false positives

# SNPs # pairs P-value needed e ,225 4e ,750 4e-7 250,000 31,249,880,000 2e , ,999,750,000 4e-13 P-value required for experiment-wide significance must be adjusted for the number of tests performed

Chromosome

A B C D E F G H I J 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

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