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eQTL mapping Dataset The model Experiments Conclusions Estimating the contribution of non-genetic factors to gene expression using Gaussian Process Latent Variable Models Nicol` o Fusi and Neil Lawrence Learning and Inference in

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eQTL mapping Dataset The model Experiments Conclusions

Estimating the contribution of non-genetic factors to gene expression using Gaussian Process Latent Variable Models

Nicol`

  • Fusi and Neil Lawrence

Learning and Inference in Computational Systems Biology

31st March 2010

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eQTL mapping Dataset The model Experiments Conclusions

1 eQTL mapping 2 Dataset 3 The model 4 Experiments 5 Conclusions

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eQTL mapping Dataset The model Experiments Conclusions

Outline

1 eQTL mapping 2 Dataset 3 The model 4 Experiments 5 Conclusions

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eQTL mapping Dataset The model Experiments Conclusions

Expression Quantitative Trait Loci - eQTL

Transcript abudance is regulated by polymorphisms in the regulatory elements Statistical methods can be used to discover which polymorphism affects the expression levels of a gene This mapping sometimes is obfuscated by non-genetic factors

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eQTL mapping Dataset The model Experiments Conclusions

Expression Quantitative Trait Loci - eQTL

Transcript abudance is regulated by polymorphisms in the regulatory elements Statistical methods can be used to discover which polymorphism affects the expression levels of a gene This mapping sometimes is obfuscated by non-genetic factors

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eQTL mapping Dataset The model Experiments Conclusions

Expression Quantitative Trait Loci - eQTL

Transcript abudance is regulated by polymorphisms in the regulatory elements Statistical methods can be used to discover which polymorphism affects the expression levels of a gene This mapping sometimes is obfuscated by non-genetic factors

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eQTL mapping Dataset The model Experiments Conclusions

Outline

1 eQTL mapping 2 Dataset 3 The model 4 Experiments 5 Conclusions

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eQTL mapping Dataset The model Experiments Conclusions

Single Nucleotide Polymorphisms

A single nucleotide polymorphism is a variation in the DNA sequence that affects only one nucleotide. They make up about 90% of all human genetic variation They capture 84% of the total genetic variation in gene expression

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eQTL mapping Dataset The model Experiments Conclusions

Single Nucleotide Polymorphisms

A single nucleotide polymorphism is a variation in the DNA sequence that affects only one nucleotide. They make up about 90% of all human genetic variation They capture 84% of the total genetic variation in gene expression

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eQTL mapping Dataset The model Experiments Conclusions

Single Nucleotide Polymorphisms

A single nucleotide polymorphism is a variation in the DNA sequence that affects only one nucleotide. They make up about 90% of all human genetic variation They capture 84% of the total genetic variation in gene expression

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eQTL mapping Dataset The model Experiments Conclusions

The Hapmap dataset

a multi-country effort to identify and catalog genetic similarities and differences in human beings 3.1 million human single nucleotide polymorphisms have been genotyped 270 individuals from 4 geographically diverse populations (Hapmap phase II)

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eQTL mapping Dataset The model Experiments Conclusions

The Hapmap dataset

a multi-country effort to identify and catalog genetic similarities and differences in human beings 3.1 million human single nucleotide polymorphisms have been genotyped 270 individuals from 4 geographically diverse populations (Hapmap phase II)

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eQTL mapping Dataset The model Experiments Conclusions

The Hapmap dataset

a multi-country effort to identify and catalog genetic similarities and differences in human beings 3.1 million human single nucleotide polymorphisms have been genotyped 270 individuals from 4 geographically diverse populations (Hapmap phase II)

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eQTL mapping Dataset The model Experiments Conclusions

Project GENEVAR - GENe Expression VARiation

Gene expression data from EBV-transformed lymphoblastoid cell lines (Stranger et al., Nature Genetics 2007) 270 individuals from Hapmap phase I and II 47,293 gene probes

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eQTL mapping Dataset The model Experiments Conclusions

Project GENEVAR - GENe Expression VARiation

Gene expression data from EBV-transformed lymphoblastoid cell lines (Stranger et al., Nature Genetics 2007) 270 individuals from Hapmap phase I and II 47,293 gene probes

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eQTL mapping Dataset The model Experiments Conclusions

Project GENEVAR - GENe Expression VARiation

Gene expression data from EBV-transformed lymphoblastoid cell lines (Stranger et al., Nature Genetics 2007) 270 individuals from Hapmap phase I and II 47,293 gene probes

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eQTL mapping Dataset The model Experiments Conclusions

Outline

1 eQTL mapping 2 Dataset 3 The model 4 Experiments 5 Conclusions

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eQTL mapping Dataset The model Experiments Conclusions

Confounding factors

Several studies have shown that non-genetic factors can obfuscate associations: Known Factors: age, sex, ethnicity, ... Batch effects: optical effects Unknown factors

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eQTL mapping Dataset The model Experiments Conclusions

Confounding factors

Several studies have shown that non-genetic factors can obfuscate associations: Known Factors: age, sex, ethnicity, ... Batch effects: optical effects Unknown factors

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eQTL mapping Dataset The model Experiments Conclusions

Confounding factors

Several studies have shown that non-genetic factors can obfuscate associations: Known Factors: age, sex, ethnicity, ... Batch effects: optical effects Unknown factors

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

Modelling non-genetic factors

Our model is inspired by Stegle et al, Lecture notes in Computer Science (2006). We model non-genetic factors as unobserved latent variables. Gene expression levels are described as a linear function of SNP data and non-genetic factors Y = SV + XW + µ1⊤ + ǫ

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eQTL mapping Dataset The model Experiments Conclusions

dual Probabilistic Principal Component Analysis

We learn the parameters by: Marginalizing W, V, µ, ǫ Maximizing the log-likelihood with respect to the latent variables (X) For a particular choice of priors over W and V this approach is equivalent to probabilistic Principal Component Analysis

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eQTL mapping Dataset The model Experiments Conclusions

dual Probabilistic Principal Component Analysis

We put Gaussian priors over W, V and µ: P(W) =

D

  • i=1

N(wi|0, αwI) P(V) =

D

  • i=1

N(vi|0, αvI) P(µ) = N(µ|0, αµI)

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eQTL mapping Dataset The model Experiments Conclusions

dual Probabilistic Principal Component Analysis

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eQTL mapping Dataset The model Experiments Conclusions

dual Probabilistic Principal Component Analysis

The likelihood of Y can be then written as P(Y|W, X, S, µ) =

D

  • j=1

N(yj|Wxj + Vsj + µ, σ2I) Marginalizing W, V, µ, ǫ we obtain the marginal likelihood P(Y|X) =

D

  • j=1

N(yj|0, αwXX⊤ + αvSS⊤ + αµ + σ2I)

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eQTL mapping Dataset The model Experiments Conclusions

dual Probabilistic Principal Component Analysis

The likelihood of Y can be then written as P(Y|W, X, S, µ) =

D

  • j=1

N(yj|Wxj + Vsj + µ, σ2I) Marginalizing W, V, µ, ǫ we obtain the marginal likelihood P(Y|X) =

D

  • j=1

N(yj|0, αwXX⊤ + αvSS⊤ + αµ + σ2I)

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eQTL mapping Dataset The model Experiments Conclusions

Population structure

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eQTL mapping Dataset The model Experiments Conclusions

Accounting for population structure

C = αwXX⊤ + αvSS⊤ + αµ + σ2I C = αwXX⊤ + αvSS⊤ + αpPP⊤ + αµ + σ2I C = αwXX⊤ + αvSS⊤ + αpPP⊤ + αgGG⊤ + αµ + σ2I

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eQTL mapping Dataset The model Experiments Conclusions

Accounting for population structure

C = αwXX⊤ + αvSS⊤ + αµ + σ2I C = αwXX⊤ + αvSS⊤ + αpPP⊤ + αµ + σ2I C = αwXX⊤ + αvSS⊤ + αpPP⊤ + αgGG⊤ + αµ + σ2I

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eQTL mapping Dataset The model Experiments Conclusions

Accounting for population structure

C = αwXX⊤ + αvSS⊤ + αµ + σ2I C = αwXX⊤ + αvSS⊤ + αpPP⊤ + αµ + σ2I C = αwXX⊤ + αvSS⊤ + αpPP⊤ + αgGG⊤ + αµ + σ2I

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eQTL mapping Dataset The model Experiments Conclusions

Outline

1 eQTL mapping 2 Dataset 3 The model 4 Experiments 5 Conclusions

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eQTL mapping Dataset The model Experiments Conclusions

eQTL scan using data from Hapmap and GENEVAR

At each locus we compute the log-odds score: Li = log10

  • n

P(Ym|sn,j, θi,n) P(Ym|θbkg)

  • (1)

The significance of an association is evaluated via permutation testing.

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eQTL mapping Dataset The model Experiments Conclusions

Traditional eQTL scan

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eQTL mapping Dataset The model Experiments Conclusions

eQTL scan accounting for non-genetic factors

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eQTL mapping Dataset The model Experiments Conclusions

Traditional eQTL scan

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eQTL mapping Dataset The model Experiments Conclusions

eQTL scan accounting for non-genetic factors

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eQTL mapping Dataset The model Experiments Conclusions

Outline

1 eQTL mapping 2 Dataset 3 The model 4 Experiments 5 Conclusions

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eQTL mapping Dataset The model Experiments Conclusions

Conclusions

We presented a model that explicitly accounts for non-genetic factors Using this model we can detect an higher number of significant associations Many extensions are possible (future work)