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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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Presentation on theme: "Inferring Quantitative Models of Regulatory Networks From Expression Data Iftach Nachman Hebrew University Aviv Regev Harvard Nir Friedman Hebrew University."— Presentation transcript:

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

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

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

4 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

5 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( )

6 Modeling Transcription Rate Steady state equations: G TF Concentration of free promoters Concentration of bound promoters Concentration of TF dd bb

7 Modeling Transcription Rate G TF dd bb  = 1  = 4  = 20  = 250 TF activity Transcription rate TF activity Time  = 1  = 4  = 20  = 250 Trans rate Time

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

9 P(State) General Two Regulator Function TF 2 TF 1 G  b = 0  a = 0  c = 0  d =1  b = 1  c = 1 bb aa cc dd 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

10 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

11 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

12 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

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

14 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

15 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

16 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

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

18 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

19 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 G1G G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 3 Problem: Scoring structures is costly  Requires non-linear parameter optimization  Impractical on real data

20 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

21 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

22 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

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

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

25 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

26 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

27 Model Learning Conclusions Kinetic parameters G4G4 TF 2 TF 1 G3G3 G2G2 G1G1 TF 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

28 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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