Inference of gene regulatory networks: a genetical genomics approach - - PowerPoint PPT Presentation

Inference of gene regulatory networks: a genetical genomics approach

Matthieu Vignes

http://carlit.toulouse.inra.fr/wikiz/index.php/Matthieu_VIGNES INRA - Unit´ e BIA, Toulouse (France)

SMPGD 2010 - Marseilles, France - 15 January 2010

Introduction Genetical genomics Conclusion

Outline

(long) Introduction Biological facts Modelling omics data with HMRF Back to a biological introduction: genetical genomics Genetical genomics : reconstructing gene regulatory networks Existing methods Leads to use Markovian modelling in a genetical genomics context Artificial data set simulation Learning with Bayesian Networks or with SEM regression Preliminary results Conclusion Summary and perspectives Some reading

Introduction Genetical genomics Conclusion

Biology needs integration

Molecular Biology dogma

literal description (DNA) design (transcription, pRNA) blueprint (mRNA) construction (translation) finished product: ”the” cell (Over)simplification: life = information transmission from 1 generation to the other to get these ”survival machine” or living

• rganisms.

Introduction Genetical genomics Conclusion

Biology needs integration

Molecular Biology dogma

literal description (DNA) design (transcription, pRNA) blueprint (mRNA) construction (translation) finished product: ”the” cell (Over)simplification: life = information transmission from 1 generation to the other to get these ”survival machine” or living

• rganisms. But ”Can a biologist fix a radio ?” (Yuri Lazebnik

2002) → interactions between components (and environement).

Introduction Genetical genomics Conclusion

Example of an integrated omics data modelling

• Data: gene (individual) expr. data ⊕ interaction (pairwise)

data between entities.

Introduction Genetical genomics Conclusion

Example of an integrated omics data modelling

• Data: gene (individual) expr. data ⊕ interaction (pairwise)

data between entities.

• Goal: clustering of genes into meaningful groups.

Introduction Genetical genomics Conclusion

Example of an integrated omics data modelling

• Data: gene (individual) expr. data ⊕ interaction (pairwise)

data between entities.

• Goal: clustering of genes into meaningful groups.
• Data features: dependencies between objects, noise,

high-dimensionality and some observations can be missing.

Introduction Genetical genomics Conclusion

Example of an integrated omics data modelling

• Data: gene (individual) expr. data ⊕ interaction (pairwise)

data between entities.

• Goal: clustering of genes into meaningful groups.
• Data features: dependencies between objects, noise,

high-dimensionality and some observations can be missing.

• Chosen modelling: Hidden Markov Random Field. New

instantiation of an mean-field like EM algorithm to estimate parameters and achieve clustering.

Introduction Genetical genomics Conclusion

Example of an integrated omics data modelling

• Data: gene (individual) expr. data ⊕ interaction (pairwise)

data between entities.

• Goal: clustering of genes into meaningful groups.
• Data features: dependencies between objects, noise,

high-dimensionality and some observations can be missing.

• Chosen modelling: Hidden Markov Random Field. New

instantiation of an mean-field like EM algorithm to estimate parameters and achieve clustering.

• SpaCEM3 software (http://spacem3.gforge.inria.fr);

validated in image-like simulated datasets.

Introduction Genetical genomics Conclusion

SFmiss performance - NMAR case, D=1

0% 30% 60% 80% 90% true e = 0.54% e = 1.20% e = 2.77% e = 6.39% e = 22.50%

Figure: 1D synthetic data: data histogram (1st row) and classification error rate e (2nd row)

Introduction Genetical genomics Conclusion

Comparing performances of several algorithms, NMAR case - D = 4

Figure: Misclassified data percentage in an 128 × 128-image with K = 4 groups, obs. are left- and right-censored (NMAR).

Introduction Genetical genomics Conclusion

Workflow of a computational biology data analysis with

• ur method

(from Blanchet & Vignes, J. Comput. Biol. 2009)

Introduction Genetical genomics Conclusion

Real data clustering stability

Introduction Genetical genomics Conclusion

Biological features of clusters

• Modularity

Introduction Genetical genomics Conclusion

Biological features of clusters

• Modularity
• Interpretability of

cluster profiles

Introduction Genetical genomics Conclusion

Biological features of clusters

• Modularity
• Interpretability of

cluster profiles

• GO term

representativity

Introduction Genetical genomics Conclusion

Biological features of clusters

• Modularity
• Interpretability of

cluster profiles

• GO term

representativity

• Link to metabolic

pathways

Introduction Genetical genomics Conclusion

The geneticist’s point of view

• Phenotype: observed characteristic (anatomical, morphological,

molecular, physiological, ethological) or trait in a living organism.

Many of which are inherited from parents (Mendel’s peas...).

Introduction Genetical genomics Conclusion

The geneticist’s point of view

• Phenotype: observed characteristic (anatomical, morphological,

molecular, physiological, ethological) or trait in a living organism.

Many of which are inherited from parents (Mendel’s peas...).

• Traits carried out by DNA, more precisely by genes (=

information units). Exist in different forms or alleles (mutations); inheritance is complicated by recombination of chromosomes.

Introduction Genetical genomics Conclusion

The geneticist’s point of view

• Phenotype: observed characteristic (anatomical, morphological,

molecular, physiological, ethological) or trait in a living organism.

Many of which are inherited from parents (Mendel’s peas...).

• Traits carried out by DNA, more precisely by genes (=

information units). Exist in different forms or alleles (mutations); inheritance is complicated by recombination of chromosomes.

• Polymorphisms (several shapes) control gene expression or the

affinity between a protein and its target. Can be (i) complex and (ii) quantitative (= discrete)

Introduction Genetical genomics Conclusion

The geneticist’s point of view

• Phenotype: observed characteristic (anatomical, morphological,

molecular, physiological, ethological) or trait in a living organism.

Many of which are inherited from parents (Mendel’s peas...).

• Traits carried out by DNA, more precisely by genes (=

information units). Exist in different forms or alleles (mutations); inheritance is complicated by recombination of chromosomes.

• Polymorphisms (several shapes) control gene expression or the

affinity between a protein and its target. Can be (i) complex and (ii) quantitative (= discrete) → plenty of causal relationships to decipher.

Introduction Genetical genomics Conclusion

Gene Regulatory Networks, Genetical Genomics

• Highlighted links, association/causal dependencies between

gene (products). Formalism of Gene Regulatory Networks (GRN) we ultimately aim at inferring.

Angiogenic signaling network (Adollahi et al. 2007)

Introduction Genetical genomics Conclusion

Gene Regulatory Networks, Genetical Genomics

• Abundance of genomics data (= measurements of cell

component activity). Can be directly used to infer GRN (Wehrli et al. 2006, Bansal et al. 2007).

Introduction Genetical genomics Conclusion

Gene Regulatory Networks, Genetical Genomics

• Abundance of genomics data (= measurements of cell

component activity). Can be directly used to infer GRN (Wehrli et al. 2006, Bansal et al. 2007).

• Genetical Genomics (Jansen and Nap, 2001): combine genetic

information (perturbation of the network) and genomic measures.

Introduction Genetical genomics Conclusion

Gene Regulatory Networks, Genetical Genomics

• Abundance of genomics data (= measurements of cell

component activity). Can be directly used to infer GRN (Wehrli et al. 2006, Bansal et al. 2007).

• Genetical Genomics (Jansen and Nap, 2001): combine genetic

information (perturbation of the network) and genomic measures.

• Grail: understand genetic mechanisms (i) allowing observed

diversity and (ii) able to accomplish many diverse functions.

Introduction Genetical genomics Conclusion

Gene Regulatory Networks, Genetical Genomics

• Abundance of genomics data (= measurements of cell

component activity). Can be directly used to infer GRN (Wehrli et al. 2006, Bansal et al. 2007).

• Genetical Genomics (Jansen and Nap, 2001): combine genetic

information (perturbation of the network) and genomic measures.

• Grail: understand genetic mechanisms (i) allowing observed

diversity and (ii) able to accomplish many diverse functions.

• More pragmatically: exploiting genetic context and observed

(e-)traits to reconstruct GRN

Introduction Genetical genomics Conclusion

Gene Regulatory Networks, Genetical Genomics

• Abundance of genomics data (= measurements of cell

component activity). Can be directly used to infer GRN (Wehrli et al. 2006, Bansal et al. 2007).

• Genetical Genomics (Jansen and Nap, 2001): combine genetic

information (perturbation of the network) and genomic measures.

• Grail: understand genetic mechanisms (i) allowing observed

diversity and (ii) able to accomplish many diverse functions.

• More pragmatically: exploiting genetic context and observed

(e-)traits to reconstruct GRN or less ambitiously: identify genes with strong regulatory roles.

Introduction Genetical genomics Conclusion

Biological ingredients

3 mechanisms to link genotype to the observed e-traits

⊕

Physical map Linkage map

Applications: medical and agricultural genetics, genetic engineering as well as in basic evolutionary biology.

Introduction Genetical genomics Conclusion

Outline

(long) Introduction Biological facts Modelling omics data with HMRF Back to a biological introduction: genetical genomics Genetical genomics : reconstructing gene regulatory networks Existing methods Leads to use Markovian modelling in a genetical genomics context Artificial data set simulation Learning with Bayesian Networks or with SEM regression Preliminary results Conclusion Summary and perspectives Some reading

Introduction Genetical genomics Conclusion

Learning networks in genetical genomics

◮ Pairwise algo. (Ghazalpour et al.,

PLOS Gen., 2006) co-expression network + module cis-eQTL

Introduction Genetical genomics Conclusion

Learning networks in genetical genomics

◮ Pairwise algo. (Ghazalpour et al.,

PLOS Gen., 2006) co-expression network + module cis-eQTL

◮ Equation-based algo. (Liu et al.,

Genetics, 2008): greedy SEM with expr. levels and genotypes as covar., pre-filtered by eQTL info. ⊲ Nathalie Keussayan’s MSc. (with B. Mangin). New MSc. to start 2010.

Introduction Genetical genomics Conclusion

Learning networks in genetical genomics

◮ Pairwise algo. (Ghazalpour et al.,

PLOS Gen., 2006) co-expression network + module cis-eQTL

◮ Equation-based algo. (Liu et al.,

Genetics, 2008): greedy SEM with expr. levels and genotypes as covar., pre-filtered by eQTL info. ⊲ Nathalie Keussayan’s MSc. (with B. Mangin). New MSc. to start 2010.

◮ Network-based algo. (Zhu et al.,

PLoS Comput. Biol., 2007): MCMC algo.

• n BN structures with BIC and eQTL info.

as a prior. ⊲ Jimmy Vandel MSc. (with Simon de Givry). Staying with us for a PhD .

Introduction Genetical genomics Conclusion

Inferring a MRF with genetical genomics data

• 1. Estimating weights -as a measure of uncertainty- on putative

edges and fixing those on edges defined by expert knowledge.

Introduction Genetical genomics Conclusion

Inferring a MRF with genetical genomics data

• 1. Estimating weights -as a measure of uncertainty- on putative

edges and fixing those on edges defined by expert knowledge.

• ...could lead to the inference of N(N − 1)/2 parameters.
• Alternative: partial learning of a MRF (extended to pairwise

MF).

Introduction Genetical genomics Conclusion

Inferring a MRF with genetical genomics data

• 1. Estimating weights -as a measure of uncertainty- on putative

edges and fixing those on edges defined by expert knowledge.

• ...could lead to the inference of N(N − 1)/2 parameters.
• Alternative: partial learning of a MRF (extended to pairwise

MF).

• 2. Triplet Markov fields (Blanchet & Forbes, IEEE PAMI 2008)

allowing objects to be assigned to overlapping subclasses seem an interesting lead to model genetic background of a gene by introducing an additional blanket that could encode genetic dependencies in the population.

Introduction Genetical genomics Conclusion

Inferring a MRF with genetical genomics data

• 1. Estimating weights -as a measure of uncertainty- on putative

edges and fixing those on edges defined by expert knowledge.

• ...could lead to the inference of N(N − 1)/2 parameters.
• Alternative: partial learning of a MRF (extended to pairwise

MF).

• 2. Triplet Markov fields (Blanchet & Forbes, IEEE PAMI 2008)

allowing objects to be assigned to overlapping subclasses seem an interesting lead to model genetic background of a gene by introducing an additional blanket that could encode genetic dependencies in the population.

• ...application at present limited to supervised classification.
• Optimality to include genetics?

Introduction Genetical genomics Conclusion

A recipe for genetical genomics artificial dataset generation

(Collaboration with Alberto de la Fuente, CRS4, Pula, Italy)

• Choose a network with features

as close as possible to know features of realistic biological networks → http://www.

comp-sys-bio.org/AGN/.

Introduction Genetical genomics Conclusion

A recipe for genetical genomics artificial dataset generation

(Collaboration with Alberto de la Fuente, CRS4, Pula, Italy)

• Choose a network with features

as close as possible to know features of realistic biological networks → http://www.

comp-sys-bio.org/AGN/.

• Simulate genotype from a RIL population: pop size,

chromosome size, number and distribution of markers (incl.error and missingness) → CarthaG` ene.

Introduction Genetical genomics Conclusion

A recipe for genetical genomics artificial dataset generation

(Collaboration with Alberto de la Fuente, CRS4, Pula, Italy)

• Choose a network with features

as close as possible to know features of realistic biological networks → http://www.

comp-sys-bio.org/AGN/.

• Simulate genotype from a RIL population: pop size,

chromosome size, number and distribution of markers (incl.error and missingness) → CarthaG` ene.

• Compute gene expression data from gene activity ODE →

COmplex PAthway SImulator (COPASI,

http://www.copasy.org/) for steady-state expression levels. Note: expr. levels need to be discretized with BN: k-means, log-scale, mixture, box-plot...?

Introduction Genetical genomics Conclusion

Bayesian Networks (BN)

Definition of BN

Directed Acyclic Graph (DAG) & P(V ) = p

i=1 P(Vi | Vpa(Vi), with

Vi := Mi ⊗ Gi. Clever init.: encompassing network with putative eQTL → MCQTL http://carlit.toulouse.inra.fr/MCQTL/.

Introduction Genetical genomics Conclusion

Bayesian Networks (BN)

Definition of BN

Directed Acyclic Graph (DAG) & P(V ) = p

i=1 P(Vi | Vpa(Vi), with

Vi := Mi ⊗ Gi. Clever init.: encompassing network with putative eQTL → MCQTL http://carlit.toulouse.inra.fr/MCQTL/.

Tested Algorithms (Matlab’s BayesNet, K.Murphy and P. Leray)

• 1. Scoring algorithms: BIC (+ penalty for genetic linkage) with

structure exploration strategies: Maximum Weight Spanning Tree (MWST), K2 (node ordering), Greedy Search (GS).

• 2. Independance algorithms: χ2 or Likelihood Ratio Test (LRT) with

Introduction Genetical genomics Conclusion

Structural Equation Modelling (SEM)

⊲ Y = Y .B + X.Θ + ǫ

where: Y matrix of transcript levels (n × p) X matrix of genotypes (n × q) Bkm direct effect of level of gene k on level of gene m (Bii = 0). Θjm direct effect of marker j on expression of gene m.

Introduction Genetical genomics Conclusion

Structural Equation Modelling (SEM)

⊲ Y = Y .B + X.Θ + ǫ

where: Y matrix of transcript levels (n × p) X matrix of genotypes (n × q) Bkm direct effect of level of gene k on level of gene m (Bii = 0). Θjm direct effect of marker j on expression of gene m.

⊲ Gene-by-gene regression Yk = Y\k ∗ βk + X ∗ Θk + ǫk βk’s and Θk’s need to be estimated as regression coefficients.

Introduction Genetical genomics Conclusion

Structural Equation Modelling (SEM)

⊲ Y = Y .B + X.Θ + ǫ

where: Y matrix of transcript levels (n × p) X matrix of genotypes (n × q) Bkm direct effect of level of gene k on level of gene m (Bii = 0). Θjm direct effect of marker j on expression of gene m.

⊲ Gene-by-gene regression Yk = Y\k ∗ βk + X ∗ Θk + ǫk βk’s and Θk’s need to be estimated as regression coefficients. ⊲ Values signif. = 0 allow us to infer network structure.

Introduction Genetical genomics Conclusion

Lasso estimation of parameters in the SEM

• Idea 1 Least Square: unbiased but variance on estimator

becomes a problem since typically n ≪ p.

Introduction Genetical genomics Conclusion

Lasso estimation of parameters in the SEM

• Idea 1 Least Square: unbiased but variance on estimator

becomes a problem since typically n ≪ p.

• Idea 2 Biased estimations: v2.α ridge (not parcimonious), v2.β

best subset (fixed number of variables can have coef.= 0), v2.final Lasso (Tibshirani 1996, selects and reduces variables).

Introduction Genetical genomics Conclusion

Lasso estimation of parameters in the SEM

• Idea 1 Least Square: unbiased but variance on estimator

becomes a problem since typically n ≪ p.

• Idea 2 Biased estimations: v2.α ridge (not parcimonious), v2.β

best subset (fixed number of variables can have coef.= 0), v2.final Lasso (Tibshirani 1996, selects and reduces variables).

• βk = arg min
• |Yk − [Y\kX].βk|L2 + λ|βk|L1
• (|

βk|L1 ≤ τ, βk =t [Bk θk])

Introduction Genetical genomics Conclusion

Lasso estimation of parameters in the SEM

• Idea 1 Least Square: unbiased but variance on estimator

becomes a problem since typically n ≪ p.

• Idea 2 Biased estimations: v2.α ridge (not parcimonious), v2.β

best subset (fixed number of variables can have coef.= 0), v2.final Lasso (Tibshirani 1996, selects and reduces variables).

• βk = arg min
• |Yk − [Y\kX].βk|L2 + λ|βk|L1
• (|

βk|L1 ≤ τ, βk =t [Bk θk]) We used the Least Angle Regression (LAR) algo. (lars in R) to compute X.ˆ β, with cross-validation, BIC and Meinshausen criteria to determine the best λ.

Introduction Genetical genomics Conclusion

BN vs. SEM: advantages and drawbacks

BN SEM Computational time Continuous data Modelling cycles Param./likelihood estim. Non-linear dependencies

Introduction Genetical genomics Conclusion

Results: (i) BN vs. SEM and (ii) with or without genotypes

Network recovery performances (mean on 9 artificial datasets)

Introduction Genetical genomics Conclusion

Outline

(long) Introduction Biological facts Modelling omics data with HMRF Back to a biological introduction: genetical genomics Genetical genomics : reconstructing gene regulatory networks Existing methods Leads to use Markovian modelling in a genetical genomics context Artificial data set simulation Learning with Bayesian Networks or with SEM regression Preliminary results Conclusion Summary and perspectives Some reading

Introduction Genetical genomics Conclusion

Wrap up

• Graphical model steals the show in Systems Biology: examples
• f
• HMRF for the analysis of a gene expression dataset in a

network context and of

• BN or SEM as tools to infer GRN in the genetical genomics

context.

Introduction Genetical genomics Conclusion

Future Work

• HMRF:
• Collaboration at INRA: P. Gammas (Nodule formation in M.

Truncatula), F. Jourdan (metabolomics), M. Sancristobal & N. Villa (detecting modules).

• Include other distributions (multinomial ?) e.g. for ecology.
• Weight on edgdes, model. missing/spurious edges, graph

structure effect, overlapping clustering.

• Triplet models unsupervised clustering.
• Genetical genomics:
• Validate/assess algorithms for network structure recovery in

genetical genomics...Before improving them ?

• Try these methods on a ”real” gold standard dataset (mice,

yeast, A. thaliana ok...What if sunflower or strawberries).

• extension of the lasso: elastic net (Zou and Hastie 2005),

Bayesian lasso (Yi and Xu 2008), group bridge (Huang et al. 2009) . . . or further: Dantzig selector (James and Radchenko 2009).

• ’global’ penalized likelihood computation accounting for the

Introduction Genetical genomics Conclusion

Some references

• R. Tibshirani.

Regression shrinkage and selection via the lasso.

• J. Royal. Statist. Soc B., 58:267-88, 1996.
• R. Jansen and J. Nap.

Genetical genomics: the added value from segregation. Trends Gen., 17:388-91, 2001.

• H. Zou and T. Hastie.

Regularization and variable selection via the elastic net.

• J. R. Statist. Soc. B, 67:301-20, 2005.
• AV. Werhli, M. Grzegorczyk and D. Husmeier.

Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical gaussian models and Bayesian networks. Bioinformatics, 22:2523-31, 2006.

• M. Bansal et al.

How to infer gene networks from expression profiles.

• Mol. Syst. Biol. 3:78, 2007.

Introduction Genetical genomics Conclusion

Some references (cont’d)

• B. Liu et al.

Gene network inference via structural equation modeling in genetical genomics experiments. Genetics, 178:1763-76, 2008.

• N. Yi and S. Xu.

Bayesian LASSO for quantitative trait loci mapping. Genetics, 179:1045-55, 2008.

• J. Blanchet and M. Vignes.

A model-based approach to gene clustering with missing observations reconstruction in a Markov random field framework..

• J. Comput. Biol., 16:475-486, 2009.
• J. Huang et al.

A group bridge approach for variable selection. Biometrika, 96:339-55, 2009.

• M. Vignes et al.

From gene clustering to genetical genomics: analyzing or reconstructing biological networks. Proceedings of the ECCS, Warwick, 2009.

• GM. James and P. Radchenko.

A generalized Dantzig selector with shrinkage tuning. Biometrika, 96:323-37, 2009.

The end

Many thanks to colleagues

in Toulouse: C. Cierco, S. de Givry, B. Mangin, N. Peyrard, R. Sabbadin, T. Schiex, J. Vandel (BIA), P. Gamas, N. Langlade, P. Vincourt (LIPM) and somewhere else: J. Blanchet (SLF/WSL, Switzerland), F. Forbes (INRIA Grenoble), BioSS (Scotland), A. de la Fuente (CRS4, Italy). . .

The end

Many thanks to colleagues

in Toulouse: C. Cierco, S. de Givry, B. Mangin, N. Peyrard, R. Sabbadin, T. Schiex, J. Vandel (BIA), P. Gamas, N. Langlade, P. Vincourt (LIPM) and somewhere else: J. Blanchet (SLF/WSL, Switzerland), F. Forbes (INRIA Grenoble), BioSS (Scotland), A. de la Fuente (CRS4, Italy). . .

and to you for your attention. Questions, critics, remarks. . . welcome ?!