Inference of Regulatory Networks via Systems Genetics

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Inference of Regulatory Networks via Systems
Genetics

• Ina Hoeschele

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Systems Genetics
Infer cells regulatory structure
Infer molecular basis of phenotypes / diseases
Systems Biology
Complex Trait Biology
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Systems Genetics

• Measure DNA sequence polymorphisms on a group of
  related individuals (lt100 to 2000) covering the
  entire genome (e.g. SNPs)
• Several genotypes at each polymorphism (e.g. two,
  0/1)
• Multi-factorial perturbations of a system,
  genetically randomized populations
• Measure molecular and organismal variables, e.g.
• Expression profiling (etraits)
• Expression profiling and disease phenotypes
• Expression profiling, methylation profiling,
  disease
• Metabolite, protein profiling

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Systems Genetics

• The genotypes at some polymorphisms influence
  directly the expression of certain genes
• in cis polymorphism A in gene As promoter
  region influences its transcript abundance
• in trans polymorphism A in gene As coding
  region influences the function of protein A let
  gene A be a regulator of gene B, then both
  polymorphism A and gene A influence the
  expression of gene B

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Systems Genetics

• The genes expression profiles (etraits) have
  both polymorphism and gene (etrait) regulators
• Very large number of targets (regulated genes
  etc.)
• Very large number of potential regulators for
  each target
• Sample size (n) MUCH smaller than number of
  potential regulators (p)
• Targets are co-regulated
• Regulators are correlated
• Regulatory networks are cyclic
• Analyses of regulatory programs should account
  for all of the above

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Systems Genetics

• One target one regulator approach
• YT ? bPR e
• do for each T and each R (except cis analysis)
• low power
• trans YT ? b1YR b2PR e ( cisP)
• better power but does not account for
  co-regulation of multiple targets

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Systems Genetics

• One target all regulators approach
• YT ? ?Rb1RPR ( ?Rb2RYR ) e
• do for each T, still does not account for
  co-regulation
• standard variable selection methods and
  regularization methods tend not to perform well
  (nltltp, correlated regulators)
• May also need to consider interactions among loci
• Often ignored or limited to two-way interactions
• Penalization/Regularization methods
• Constrained OLS, bounds on Lt norm(s) of
  coefficients (t1, 2, )
• Elastic net variable selection (Zou and Hastie
  2005)
• Extension of lasso (compromise with ridge
  regression)
• nltltp, joint selection of correlated predictors
• Bayesian variable selection
• Priors on b
• MCMC ??
• Deterministic (e.g. variational) ??

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Systems Genetics

• Clustering of targets
• Analyze jointly the targets in a cluster
• Single regulator model, multivariate analysis
  costly
• PCA within clusters, analyze PCs separately
• Analyze cluster with all regulator model
  (individual Y model but joint variable selection)
  
• Geronemo iteratively perform clustering and
  selection of clustermodule regulators
  (regression tree) (Lee et al. 2006)

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Systems Genetics

• Biclustering, two-group association
• Find groups of targets regulated by groups of
  polymorphisms
• Biclustering based on matrix of associations btw
  targets and polymorphisms efficient but
  meaningful results?
• Various approaches for two-group association
• Penalized Canonical Correlation Analysis (CCA)
• Represent CCA in regression framework
• Bayesian CCA (probabilistic interpretation, joint
  latent factor model for both groups of variables)
  
• MCMC (convergence issues, see factor analysis)
• deterministic (variational)

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Systems Genetics

• Two-step regulatory network inference
• 1a) Construct an Undirected Dependency Graph
  (UDG) using target data (e.g., expression) only
• 1b) Determine which polymorphisms affects which
  targets and use this information to direct edges
  (e.g., Neto et al. 2008)
• 2a) Perform cis and trans polymorphism analysis
  and combine into an encompassing network (Liu et
  al. 2008)
• 2b) Sparsify the network, using structural
  equation modeling SEM
• extension of linear regression (variables can be
  both response and predictor)
• likelihoods for SEM and LR not the same for
  cyclic networks
• Toward one-step regulatory network inference
• Geronemo (etraits small list (300) of candidate
  regulator genes)

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