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Inferring Quantitative Models of Regulatory Networks From Expression Data Iftach Nachman Hebrew University Aviv Regev Harvard Nir Friedman Hebrew University

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Goal: Reconstruct Cellular Networks Biocarta. http://www.biocarta.com/ u Structure u Function u Dynamics Conditions Genes Common approach: Interaction Networks Different semantics for networks u Boolean, probabilistic, differential equations, …

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A Major Assumption… mRNA tr. rate protein active protein mRNA mRNA degradation TF G G G Activation signal Hidden mRNA Observed

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Realistic Regulation Modeling u Model the closest connection u Active protein levels are not measured u Transcript rates are computed from expression data and mRNA decay rates u Realistic biochemical model of transcription rates TF G G Hidden Observed proteinmRNA mRNA tr. rate active protein Activation signal mRNA degradation Hidden Observed

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OnOff Modeling Transcription Rate Simplest case: one activator G TF mRNA transcripts G TF On [McAdams & Arkin, 1997; Ronen et al, 2002] P( ) Avg rate = + P( )

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Modeling Transcription Rate Steady state equations: G TF Concentration of free promoters Concentration of bound promoters Concentration of TF dd bb

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Modeling Transcription Rate G TF dd bb = 1 = 4 = 20 = 250 TF activity Transcription rate TF activity Time = 1 = 4 = 20 = 250 Trans rate Time

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[Buchler et al, 2003; Setty et al, 2002] General Two Regulator Function TF 2 TF 1 G P(State) a b c d 11 X 22 G TF Similar models for other modes of binding: u Competitive binding u Cooperative binding

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P(State) General Two Regulator Function TF 2 TF 1 G b = 0 a = 0 c = 0 d =1 b = 1 c = 1 bb aa cc dd X X X X = Average Rate Rate “AND” gate “OR” gate a b c d [Buchler et al, 2003; Setty et al, 2002] Avg rate = function of TF concentrations Few parameters: Affinity parameters Rate parameters

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Models of Regulatory Networks Regulators (activity) Target Genes (trans. rate) G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 3 G5G5 G6G6 G7G7 Noise Observed rates ? Predicted rates TF activity Time Trans rate Time

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Learning Learning From Data Transcription rates Expression data mRNA decay rates Kinetic parameters G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 2 + Gradient ascent

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TF 1 TF 2 G4G4 TF 1 G3G3 G2G2 G1G1 Learning Cell Cycle Experiment Transcription rates Expression data mRNA decay rates Kinetic parameters + Biological Databases [YPD] ChIP location [Lee et. al] 7 regulators & 141 target genes Cell cycle gene expression [Spellman et. al] + mRNA decay rates [Wang et al] Transcription rates

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M/G1 G1 S S/G2 G2/M predictionsinput parameters 0 2 1 Cell Cycle Experiment 17x141 = 2397 Data points 466 parameters 17x7 = 119 Regulator activity values

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G1G2G1G2 FKH1 FKH2 G1G2G1G2 SWI5 ACE2 Regulator Activity Profiles u When are they active? Known biology: u SWI4 & MBP1: mid-late G1 u FHK1: S/G2 u FKH2: G2/M u SWI5: M/G1 G1G2G1G2 MBP1 SWI4 Reconstructed activity profiles match direct experimental knowledge

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Regulator Activity Profiles u When are they active? u Could we reconstruct these from mRNA profiles? Known biology: u SWI5 is transcriptionally regulated u MCM1 is not Regulator’s own mRNA is not sufficient to reconstruct activity levels mRNA profile SWI5 Activity mRNA MCM1 Activity mRNA

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Regulator Activity Profiles u When are they active? u Could we reconstruct these from mRNA profiles? u Could we reconstruct these from target’s transcription rate? Avg target rate

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M/G1 G1 S S/G2 G2/M input predictions Cell Cycle Experiment How well are we doing? residue

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Model Learning ab initio Learning Transcription rates Learning Expression data mRNA decay rates Kinetic parameters G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 2 + Big assumption: u Network topology is given u Unrealistic, even for well understood systems + Challenge: Reconstruct network topology? Number of regulators Their joint effect on target genes

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How Do We Learn Structure? Standard approach: hill climbing search G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 -17.23 -23.13 -19.19 G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 3 Problem: Scoring structures is costly Requires non-linear parameter optimization Impractical on real data

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Pred(G|TF,Y) Ideal regulator Time Pred(G|TF) TF G Y Step 1: Compute optimal hypothetical regulator Time regulators Step 2: Search for “similar” regulator TF 1 TF 2 TF 3 TF 4 Activity level Target Profile Ideal Regulator Method Goal: Consider adding edges Idea: Score only promising candidates

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Parent(s) activity Predicted(G|TF,TF 2 ) Time regulators TF 1 TF 2 TF 3 TF 4 Step 3: Add new parent and optimize parameters Time Step 1: Compute optimal hypothetical regulator Step 2: Search for “similar” regulator Pred(G|TF,Y) Ideal regulator Y Target Profile TF G TF 2 Crucial point: Choice of similarity measure u Principled approach see [Nachman et al UAI04] u Provides approximation to Δlikelihood Ideal Regulator Method Goal: Consider adding edges Idea: Score only promising candidates

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New regulator: “centroid” of selected ideal regulators Adding New Regulator Ideal regulators Idea: Introduce hidden regulator for genes with similar ideal regulator TF new G1G1 G2G2 G4G4 G1G1 G2G2 G3G3 G4G4 G5G5 Y1Y1 Y2Y2 Y3Y3 Y4Y4 Y5Y5 Time

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M/G1 G1 S S/G2 G2/M Input rates 0 2 1 Curated prior knowledge 466 params ab initio from scratch 461 params Ab initio Structure Learning

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Input rates Curated prior knowledge 466 params ab initio from scratch 461 params M/G1 G1 S S/G2 G2/M 0 2 1 Ab initio Structure Learning

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0 20 40 60 80 100 120 H2 SWI5 H4 SWI4 Significant target overlap & correlated activity Significant target overlap & weak correlation H1 MBP1 H3 FKH2 curated ab initio target genes regulators Regulators: ab initio vs. curated H1 H2H4H3H5H6 H7 SWI4MBP1ACE2FKH1SWI5MCM1FKH2

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curated ab initio target genes regulators u Significant agreement with “known” topology Both in structure & dynamics u Improved predictions Regulators: ab initio vs. curated SWI4MBP1ACE2FKH1SWI5MCM1FKH2 H1 H2H4H3H5H6 H7

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Model Learning Conclusions Kinetic parameters G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 2 + + Transcription rates Network (prior knowledge) G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 u Realistic model, based on first principles u Learning procedure Reconstruct unobserved activity profiles Reconstruct network topology u Insights into Structure & Dynamics Function

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Future Directions u Prior knowledge u ChIP location u Cis-regulatory elements External perturbations Internal feedback G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 3 G5G5 G6G6 G7G7

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