Evolution, maintenance and allelic architecture of complex traits

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traits Genetics Shamil Sunyaev GENOTYPE PHENOTYPE Functional

and Harvard Simple and Comple Phenotypes Comple traits are

1 Why are we doing genetics? Evolution, maintenance and allelic architecture of comple traits Genetics Shamil Sunyaev GENOTYPE PHENOTYPE Functional Biology Broad Institute of M.I.T. and Harvard Simple and Comple Phenotypes Comple traits are heritable but not in Mendelian fashion Simple phenotype Comple phenotype Comple traits are heritable but not in Mendelian fashion

2 Inheritance at each locus is Mendelian. Loci are independent Quantitative Trait Loci (QTLs) Phenotype is additive over locus effects -> normal distribution Dichotomous comple traits such as disease Liability distribution Liability threshold Locus 1 Locus 2 Locus 3 Locus 4 Locus 1 Locus 2 Locus 3 Locus 4 Locus 5 Locus 6 Locus 7 Locus 5 Locus 6 Locus 7 Population variation is fully described by variance Variance decomposition V = V G + V E Y Variance around the mean Genetic contribution Everything else Variance of means Components of genetic variance Regression Main (additive) effects V G = V A + V D + V I + V M Genetic interactions Y Dominant effects New mutations AA Aa aa

Additive variance Heritability Broad sense Additive variance VA is variance eplained by the model H2 = Y j = βi ij + ε VG V i Narrow sense VA = 2 βi2 i (1 i ) h2 = i Estimating heritability VA V With

3 Additive variance Heritability Broad sense Additive variance VA is variance eplained by the model H2 = Y j = βi ij + ε VG V i Narrow sense VA = 2 βi2 i (1 i ) h2 = i Estimating heritability VA V With genotypic information in hand Regress phenotype on genotype 1 1 Cov(MP,O) = VA + VI 2 4 Additive variance Y j = βi ij + ε VA = 2 βi2 i (1 i ) i i Narrow sense heritability Narrow sense heritability V Cov(MP,O) h2 = A V V (MP) In the Ideal World Regress phenotype on genotype h2 = VA V Current GWAS eplain a minor fraction of heritability Y = βi i + ε i Identify significant and reproducible associations. Estimate effect sizes. Estimate additive variance. known 2 V A = 2 β i i (1 i ) i Reality: missing heritability 2 VA Cov(MP,O) h = << V V (MP) Height %, Blood lipids 12%

4 Likely reasons for missing heritability Questions about allelic architecture 1. Common variants of weak effect 2. Rare variants of larger effect 3. Epistatic interactions Cov(MP,O) = 1 2 V + 1 A 4 V I How many loci are involved? Is variation underlying the trait rare or common? What is the distribution of effect sizes of variants involved in the trait? What is the role of epistasis and dominance? Why is epistasic variance commonly disregarded? GG interactions In human genetics, epistatic interactions between common variants have not been observed. In a model with two (or several) loci, contribution of epistatic variance is relatively small. Long term response to selection in model organisms seems to contradict the importance of epistasis. Any evidence for or against epistasis? Why is epistasic variance might be of importance? A non-linear model involving many loci would generate a large epistaticvariance. Interactions would be statistically undetectable. The model would not generate significant deviations from the observations. As an eample, we may consider a model with multiple pathways involved.

Evidence in favor of the highly polygenic model Evidence in favor of the highly polygenic model Evidence in favor of the highly polygenic model Estimating additive variance using Random Effect Model

Common SNPs eplain a large proportion of the heritability for human height Jian Yang 1, Beben Benyamin 1, Brian P McEvoy 1, Scott Gordon 1, Anjali K Henders 1, Dale R Nyholt 1, Pamela A Madden 2,

5 Evidence in favor of the highly polygenic model Evidence in favor of the highly polygenic model Evidence in favor of the highly polygenic model Estimating additive variance using Random Effect Model ANALYSIS We can model effects of individual variants as random effects distributed as N(0,σ 2 ). Common SNPs eplain a large proportion of the heritability for human height Jian Yang 1, Beben Benyamin 1, Brian P McEvoy 1, Scott Gordon 1, Anjali K Henders 1, Dale R Nyholt 1, Pamela A Madden 2, Andrew C Heath 2, Nicholas G Martin 1, Grant W Montgomery 1, Michael E Goddard 3 & Peter M Visscher 1 Random effect model is a model with error terms drawn from a multivariate normal distribution. In the infinitesimal model, co-variance matri can be approimated using IBS (not IBD). AA Aa aa Genotypes Normalized genotypes Normalized genotypes 0 E() Var() 2q 2 pq 1 E() Var() p q 2 pq 2 E() Var() 2 p 2 pq Y i = β j ij +ε j ij Normalized genotype of individual i at SNP j In the matri form: y = β +ε Two important matrices: If SNP1 is causal and SNP2 is not, the apparent association of SNP2 is: β^ 2 = β 1 r 12 LD = 1 M T In non-normalized genotypes β^ 2 = β 1 r 12 Var( 1 ) Var( 2 ) GRM = 1 N T

Linear Mied Model (LMM) Polygenic scores Our model Y i = β j ij +ε j We have to fit markers individually Y i = β 1 1 + β j ij +ε ~ β 1 1 +ε ' j=2 For each SNP we can fit the model Y i = β i + u i +ε

6 Linear Mied Model (LMM) Polygenic scores Our model Y i = β j ij +ε j We have to fit markers individually Y i = β β j ij +ε ~ β 1 1 +ε ' j=2 For each SNP we can fit the model Y i = β i + u i +ε We can construct a simple additive estimate of the phenotype using all markers Y^ i = j β^ j ij ε ~ N ( 0, Iσ 2 ) u ~ MVN ( 0,GRM ) A multitude of small effects Distribution of apparent effect sizes β True effects Estimates of heritability from eome sequencing studies Back-calculating heritability from prediction in independent samples! r 2 # Y^,Y " $ & % h 2 h 2 h 2 + M N Evidence in favor of the highly polygenic model Rare variants

Stabilizing selection is the most common type of selection on a quantitative trait Technically, non-neutral genetic variation should not eist!

Mutation/selection balance From evolutionary perspective common genetic disease should not eist: natural selection should remove disease-causing alleles from the Theory 2: Common diseases are due to

7 Stabilizing selection is the most common type of selection on a quantitative trait Technically, non-neutral genetic variation should not eist! Forces to maintain variation: Selection Mutation Stabilizing selection Selection may be related or unrelated to the trait Why does a common genetic disease eist? Mutation/selection balance From evolutionary perspective common genetic disease should not eist: natural selection should remove disease-causing alleles from the Theory 2: Common diseases are due to multiple deleterious alleles in mutation-selection balance Theory 1: Disease late onset (after the reproductive age) Changed environment and lifestyle (Selection direction reversal) Compensatory positive effect Balancing selection Frequency dependent selection Antagonistic pleiotropy (Trade Off) MEDICALLY detrimental polymorphisms are not EVOLUTIONARY deleterious Eamples: APOE (Alzheimer s disease), AGT (Hypertension), CYP3A (Hypertension) Weak selection High mutation rate CURRENT ESTIMATE: ~0 new mutations per genome ~1-2 new amino acid changes per genome Eamples: LDL-C, HDL-C, Triglyceride, Blood pressure, Colorectal adenomas Functional class (fover within class baseline) (fover within class baseline) Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics 12

8 Functional class Functional class (fover within class baseline) (fover within class baseline) growth Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics 12 Functional class Functional class Nonsense Missense Missense (fover within class baseline) growth (fover within class baseline) growth Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics 12 Functional class Functional class Nonsense Nonsense Missense Missense Benign (fover within class baseline) purifying selection growth (fover within class baseline) purifying selection growth Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics 12

9 Functional class Functional class Nonsense Nonsense Probably damaging Possibly damaging Possibly damaging Missense Missense Benign Benign (fover within class baseline) purifying selection growth (fover within class baseline) purifying selection growth Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics Kiezun, Garimella, Do, Stitziel, et al. Nature Genetics 12 Combine all non-synonymous variants in a single test Study design Theory: 1) Most new missense mutations are functional (mutagenesis, genetics, comparative genomics) 2) Most new missense mutations are only weakly deleterious ( genetics) 3) Most functional missense mutations are likely to influence phenotype in the same direction (mutagenesis, medical genetics) Lowest values Highest values Data: multiple candidate gene studies HDL-C, LDL-C, Triglycerides, BMI, Blood pressure, Colorectal adenomas Quantitative trait This is a direct association! This is a direct association! Disease Control Disease Control Functional variants Neutral variants

Studies of large s (many thousands of individuals) are required to achieve high statistical power. Kryukov et al., PNAS 09, Kiezun et al.

10 Simulations suggest that Mendelian genetics vs. comple trait genetics Sequencing studies would be able to identify many genes involved in biology of the trait under study. Studies of large s (many thousands of individuals) are required to achieve high statistical power. Kryukov et al., PNAS 09, Kiezun et al., Nature Genetics 12 Eample: HDL-Cholesterol Variance eplained by rare variants Adopted from Brewer et al., 03 What can we learn about allelic architecture from data available in 13? Simulate various architectures Match the results with GWAS studies Match the results with polygenic scores Match the results with sequencing data Variance eplained by rare variants

Regulatory variants Regulation: variants in promoters, enhancers, silencers, insulators What can we learn about allelic architecture from first principles and data available in 1918?

11 Regulatory variants Regulation: variants in promoters, enhancers, silencers, insulators What can we learn about allelic architecture from first principles and data available in 1918? Phenotypic variation is stable in Many comple and quantitative traits have intermediate heritability Quantitative traits are normally distributed Selection can be directional and stabilizing Selection can be direct and apparent (pleiotropic) Fitness optimum Fitness optimum Mean phenotype Mean phenotype Deleterious allele Deleterious allele Beneficial allele Deleterious allele Pleiotropic selection Direct selection Parameters of the model Heritability by allele frequency Effective size: N=, Minor allele frequency 0.5

12 Quantitative trait variation is Can we constrain allelic architecture based on the trait s distribution? Stable over time Has an intermediate heritability Phenotypic Distribution skew (asymmetry) variance (heritability) 60 Normally distributed ecess kurtosis (thickness of tails) Properties of trait distributions Phenotype of an individual Heritability and E. Kurtosis for several traits k Height + LDL cholesterol + Blood glucose HfastingL + Blood Pressure HsystolicL + Blood pressure HdiastolicL + QT interval + Age of menarche h Intermediate heritability Integral constraints on genotype-phenotype map

13 Parameterization The simplest model: two effect sizes s s -β 0 β Two effect sizes model Using Asymptotics for strong selection (large -S). Assuming intermediate heritability, h 2 = 0.5. Suppose measured maimum Ma β= κ/h 2 Parameterization Allowed parameter values for eponential DFE Log HsL 0 Log HLL ú ú ú ú ú ú ú ú t = 0.1, b\ = ú t = 0.2, b\ = ú t = 0.3, b\ = ú t = 0.4, b\ = ú t = 0.5, b\ = ú t = 1, b\ = ú t = 2, b\ = ú t = 4, b\ = θ corresponds to,000 genes Step 1 Population genetic model Forward evolutionary simulations DNA sequence variation Model parameters Demographic history Mutation rate Recombination rate Distribution of selection coefficients Empirically observed values # singletons / Mb Frequency spectra for synonymous and missense sites Pairwise linkage Constraining allelic architecture based on results of genomic studies Step 2 Effect size Step 3 Disease models Genetic architecture (frequencies and effect sizes of causal alleles) Linkage Frequency Case/control sampling In silico genetic studies Mutational target size (# of base pairs, T) Degree of coupling () between selection coefficients and phenotypic effects GWAS Polygene score Sequencing studies Sample size Disease prevalence Disease heritability Sibling relative risk Affected sib-pair linkage LOD scores Discovery GWAS p-value distribution Number of GWS loci replicated Polygenic score R 2 Eome and genome sequencing and genotyping studies

60 15 5 CDKAL1 TCF7L2 CDKN2A/B IGF2BP2 SLCA8 HHE JAZF1 IRS1 FTO HNF1B 15 5 60 60 15 5 15 5 60 60 15 5 Sibling risk Affected sib pair genomewide linkage GWAS DIAGRAMv1 discovery: N=K replication:

25Mb target (N = 0 loci) T = 1.25Mb target (N = 0 loci) 1.8-3.4 54,59-60 + 4.2 (0.3) 2.4 (0.5) 2.2 (0.8) Best LOD score 61 in ASPs: 2.2 62 2 GWS loci best p = 1e-23 e T = 3.

7 9 12 15 Chromosome 0.14 0.12 0. 0.08 0.06 0.04 CDKAL1 1 3 5 7 9 12 15 P < 1e 4 P < 0.01 P < 0.

5 TCF7L2 -log(p) -log(p) Tight coupling to selection (τ = 1) 1 2 3 4 5 6 1 2 3 4 5 6 Best LOD Score Best LOD Score ++ 0-0 (0) GWS loci 0-3 (2) GWS loci 11-19 (12) GWS loci best p = 3e-05 best p =

5) 1 3 5 7 9 11 14 17 1 3 5 7 9 11 14 17 Chromosome -log(p) -log(p) No coupling to selection (τ = 0) 1 2 3 4 5 6 Best LOD Score 1 3 5 7 9 11 14 17 1 3 5 7 9 11 14 17 Chromosome -log(p) -log(p) Weak

14 CDKAL1 TCF7L2 CDKN2A/B IGF2BP2 SLCA8 HHE JAZF1 IRS1 FTO HNF1B Sibling risk Affected sib pair genomewide linkage GWAS DIAGRAMv1 discovery: N=K replication: N=65K DIAGRAMv3 + Metabochip meta-analysis: N=85K Polygene score logistic regression 19 a b c d -log(p) -log(p) Nagelkerke's R 2 Empirical T2D T = 2kb target (N = 0 loci) T = 1.25Mb target (N = 0 loci) T = 1.25Mb target (N = 0 loci) , (0.3) 2.4 (0.5) 2.2 (0.8) Best LOD score 61 in ASPs: GWS loci best p = 1e-23 e T = 3.75Mb target (N = 10 loci) (65) GWS loci best p = 4e (4) GWS loci 39 GWS loci (25) GWS loci 99-2 (99) GWS loci best p = 1e-139 best p = 1e-18 best p = 2e-33 best p = 4e Chromosome CDKAL P < 1e 4 P < 0.01 P < 0.1 P < 0.5 TCF7L2 -log(p) -log(p) Tight coupling to selection (τ = 1) Best LOD Score Best LOD Score (0) GWS loci 0-3 (2) GWS loci (12) GWS loci best p = 3e-05 best p = 6e-09 best p = 6e Chromosome -log(p) -log(p) Moderate coupling to selection (τ = 0.5) Chromosome -log(p) -log(p) No coupling to selection (τ = 0) Best LOD Score Chromosome -log(p) -log(p) Weak coupling to selection (τ = 0.1) 2.2 (0.1) Best LOD Score 0-1 (1) GWS loci best p = 5e GWS loci 1-2 (1) GWS loci 8-18 (15) GWS loci (65) GWS loci (17) GWS loci Nagelkerke's R P < 1e 4 P < 0.01 P < 0.1 P < 0.5 Nagelkerke's R P < 1e 4 P < 0.01 P < 0.1 P < 0.5 Nagelkerke's R P < 1e 4 P < 0.01 P < 0.1 P < 0.5 Nagelkerke's R Chromosome P < 1e 4 P < 0.01 P < 0.1 P < 0.5 Allelic architecture constraints Etreme models are ecluded. A broad range of models is still consistent with the data. Rare variants may eplain less than 25% of heritability and more than 80% of heritability e e e e e P G WAS P G WAS P G WAS P G WAS P G WAS Eome Sequencing Project Comple phenotypes (common diseases) Heart GO PI: Stephen Rich University of Virginia Program Officer: Deborah Applebaum-Bowden Lung GO PIs: Michael Bamshad U. of Washington Kathleen Barnes, Johns Hopkins University Women s Health Initiative Sequencing Program PI: Rebecca Jackson Ohio State University PIs: Debbie Nickerson, Mark Rieder, Jay Shendure, & Phil Green PIs: Stacey Gabriel & David Altshuler Study design Results: Aggregate of very rare variants Burden of T1 risk BURDEN alleles: risk test 1% threshold Early onset MI cases: Men < Women < 60 Most likely to be genetically influenced 00 Controls without MI: Men > 60 Women > 70 Observed ( logp) Age Epected ( logp)

15 // // // // // // // // // // // // // // // // // // // Results: Aggregate of very rare variants Burden of T1 risk BURDEN alleles: risk test 1% threshold 7 6 Observed ( logp) 5 Due to lack of 4 association? 3 Due to lack of power? Epected ( logp) Goldstein et al, JCI, 52:1544, 1973 Unique to cases Unique to controls Observed in cases and controls D37E 84 mutations found in 6,078 cases 39 mutations found in 6,241 controls A B RM L60H M92fs R93Q R94W Q95 Q97 E98D E99K A5S E116 R143fs Q145R G164R G185C S197G P215L A222V R233W E255G R259S A262S P272Q L277P E279D R289C T292I Q295 Q313 A315V P319L H321L G334V R343C L363Q // // // RM E81K R94W Q97 E98D E99K Q145R E168D G175A G185C V213M P215L I246M E255G E255K V281M Q283R R289C A315V H321L L363R Unique to cases Unique to controls Q33 S70fs S99 Q2 g.ivs3+1a>g E1 C155 R3 Y419 g.ivs9+1a>g Y489 g.ivs+1g>a W533 g.ivs12+2c>t C68I Q770 L804fs 24 mutations found in 4,703 cases 2 mutations found in 5,090 controls C143 I687fs LDL cholesterol (mg/dl) Non-Carriers Benign Possibly damaging Variant class Probably damaging Disruptive Goldstein et al, JCI, 52:1544, 1973

POPULATION GENETICS Winter 2005 Lecture 18 Quantitative genetics and QTL mapping

POPULATION GENETICS Winter 2005 Lecture 18 Quantitative genetics and QTL mapping - from Darwin's time onward, it has been widely recognized that natural populations harbor a considerably degree of genetic