Checking Consistency Between Expression Data and Large ...Project Symbiose - IRISA November 2006....
Transcript of Checking Consistency Between Expression Data and Large ...Project Symbiose - IRISA November 2006....
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Checking Consistency Between ExpressionData and Large Scale Regulatory Networks:
A Case Study
Carito Guziolowski, Philippe Veber, Michel Le Borgne,Ovidiu Radulescu, Anne Siegel
Project Symbiose - IRISA
November 2006
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How to study a large scale system ?
1 Construct a model from interaction knowledge2 Test its self-consistency and correct it3 Validation with experimental data (variations of products)4 Infer variations of new products
Compare this inference with microarray results
Applied in E. Coli regulatory network (≈ 1000 nodes)Method: Qualitative modelling
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Qualitative modelling object: Interaction graph
Signed and oriented graphNodes: products of a regulatorynetworkArcs: influences over production
A→ C :Increase of product A influences production of CArcs are labeled as:
+ : activation– : repression? : double-signed
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Constructing interaction graph for E. ColiSource: RegulonDB http://regulondb.ccg.unam.mx/index.html
Synchronized with Ecocyc from 2005 (Salgado et al.,Bioinformatics, 2006.)
Genes, transcription factors, interactions, growth conditionsNodes
Transcription factors (proteins)genes4 Protein-complexes: IHF , HU, RcsB and GatR
Interactions
genA→ genB: genA producesprotein A that regulates genB
genA→ PC: genA producesprotein A that is part ofprotein-complex PC.
PC → genB: PC is aprotein-complex that regulatesgenB
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Interaction graph for E. Coli
Large scale network
Hierarchical structure (87% ofgenes are regulated by 13%)Ma et al., Nucleic Acid Res., 32. 2004.
160 doubled-signed interactions
7 global factors (> 80 successors):CRP, FNR, IHF, FIS, ArcA, NarLand Lrp
Number of nodes 1258Number of interactions 2526Nodes without successor 1101Nodes with more than 80 successors 7protein complex 4
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Qualitative equations from interaction graph
Main interest: variation of quantities of products between 2equilibrium statesRemark: Not interested in trajectoriesExample with 4 products:
sign(∆C) ≈ sign(∆A)
sign(∆A) ≈ –sign(∆B)
sign(∆D) ≈ sign(∆A)–sign(∆B)–sign(∆C)
sign(∆A) : +, –, ?
Natural additions and multiplications among signs:
Qualitative equality: + ≈ ?, – ≈ ?
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Qualitative equations from interaction graph
Main interest: variation of quantities of products between 2equilibrium statesRemark: Not interested in trajectoriesExample with 4 products:
sign(∆C) ≈ sign(∆A)
sign(∆A) ≈ –sign(∆B)
sign(∆D) ≈ sign(∆A)–sign(∆B)–sign(∆C)
sign(∆A) : +, –, ?
Natural additions and multiplications among signs:
Qualitative equality: + ≈ ?, – ≈ ?
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Qualitative equations from interaction graph
Main interest: variation of quantities of products between 2equilibrium statesRemark: Not interested in trajectoriesExample with 4 products:
sign(∆C) ≈ sign(∆A)
sign(∆A) ≈ –sign(∆B)
sign(∆D) ≈ sign(∆A)–sign(∆B)–sign(∆C)
sign(∆A) : +, –, ?
Natural additions and multiplications among signs:
Qualitative equality: + ≈ ?, – ≈ ?
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Qualitative equations from interaction graph
Main interest: variation of quantities of products between 2equilibrium statesRemark: Not interested in trajectoriesExample with 4 products:
sign(∆C) ≈ sign(∆A)
sign(∆A) ≈ –sign(∆B)
sign(∆D) ≈ sign(∆A)–sign(∆B)–sign(∆C)
sign(∆A) : +, –, ?
Natural additions and multiplications among signs:
Qualitative equality: + ≈ ?, – ≈ ?
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Qualitative equations from interaction graph
Main interest: variation of quantities of products between 2equilibrium statesRemark: Not interested in trajectoriesExample with 4 products:
sign(∆C) ≈ sign(∆A)
sign(∆A) ≈ –sign(∆B)
sign(∆D) ≈ sign(∆A)–sign(∆B)–sign(∆C)
sign(∆A) : +, –, ?
Natural additions and multiplications among signs:
+ + – = ? + + + = + – + – = – +× – = – +× + = + –× – = +? + – = ? ? + + = ? ? + ? = ? ?× – = ? ?× + = ? ?× ? = ?
Qualitative equality: + ≈ ?, – ≈ ?
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Qualitative equations from interaction graph
Main interest: variation of quantities of products between 2equilibrium statesRemark: Not interested in trajectoriesExample with 4 products:
sign(∆C) ≈ sign(∆A)
sign(∆A) ≈ –sign(∆B)
sign(∆D) ≈ sign(∆A)–sign(∆B)–sign(∆C)
sign(∆A) : +, –, ?
Natural additions and multiplications among signs:
+ + – = ? + + + = + – + – = – +× – = – +× + = + –× – = +? + – = ? ? + + = ? ? + ? = ? ?× – = ? ?× + = ? ?× ? = ?
Qualitative equality: + ≈ ?, – ≈ ?
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Solving a qualitative system
Qualitative equation for node i :
sign(∆Xi) ≈∑
j∈pred(i)
sign(j → i)sign(∆Xj)
All the influences over a given node arrive through itsclosest neighborsThis equation is true overknown mathematical hypothesis
Solution of the qualitative system:Assignment of each variable to + or –All equations are satisfied
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Solving a qualitative system
Qualitative equation for node i :
sign(∆Xi) ≈∑
j∈pred(i)
sign(j → i)sign(∆Xj)
Solution of the qualitative system:Assignment of each variable to + or –All equations are satisfied
C ≈ A
A ≈ −B
D ≈ A− B − C
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Solving a qualitative system
Qualitative equation for node i :
sign(∆Xi) ≈∑
j∈pred(i)
sign(j → i)sign(∆Xj)
Solution of the qualitative system:Assignment of each variable to + or –All equations are satisfied
C ≈ A
A ≈ −B
D ≈ A− B − C
A = +, B = –, C = +, D = +
+ ≈ ++ ≈ −(–)
+ ≈ +− (–)− (+)
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Solving a qualitative system
Qualitative equation for node i :
sign(∆Xi) ≈∑
j∈pred(i)
sign(j → i)sign(∆Xj)
Solution of the qualitative system:Assignment of each variable to + or –All equations are satisfied
C ≈ A
A ≈ −B
D ≈ A− B − C
+ ≈ ++ ≈ −(–)
+ ≈ +− (–)− (+)
4 sets of variations(among 16) are solutions
A B C D+ – + ++ – + –– + – +– + – –
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(In)Consistency of E.Coli qualitative system
1100 qualitative equations
Study of solutions
PYQUALI: Python library developped at IRISAEquations represented by a Ternary Diagram of Decision(TDD) of 31100 nodesStudy of equivalent reduced system
The qualitative system for the transcriptionalnetwork of E.Coli does not have any solution.
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Corrections
Problem (automatically detected by PYQUALI):
IHF ≈ ihfA + ihfB (1)
ihfA ≈ −IHF (2)
ihfB ≈ −IHF (3)
Inconsistent system (no
valuation is solution)ihfA ihfB IHF Conflict+ + + (2), (3)+ + − (1)+ − + (1)+ − − (1)− + + (1)− + − (1)− − + (1)− − − (2), (3)
Solution: Adding sigma-factor interactions
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Corrections
Problem (automatically detected by PYQUALI):
IHF ≈ ihfA + ihfB (1)
ihfA ≈ −IHF (2)
ihfB ≈ −IHF (3)
Inconsistent system (no
valuation is solution)ihfA ihfB IHF Conflict+ + + (2), (3)+ + − (1)+ − + (1)+ − − (1)− + + (1)− + − (1)− − + (1)− − − (2), (3)
Solution: Adding sigma-factor interactions
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Corrections
Problem (automatically detected by PYQUALI):
IHF ≈ ihfA + ihfB (1)
ihfA ≈ −IHF (2)
ihfB ≈ −IHF (3)
Inconsistent system (no
valuation is solution)ihfA ihfB IHF Conflict+ + + (2), (3)+ + − (1)+ − + (1)+ − − (1)− + + (1)− + − (1)− − + (1)− − − (2), (3)
Solution: Adding sigma-factor interactionsA σ factor associates to RNAP allowing thetranscription of different subset of genes
Protein Gene Functionσ70 rpoD Transcribes most genes in growing cellsσ38 rpoS The starvation/stationary phase sigma-factorσ28 rpoF The flagellar sigma-factorσ32 rpoH The heat shock sigma-factorσ24 rpoE The extracytoplasmic stress sigma-factorσ54 rpoN The nitrogen-limitation sigma-factorσ19 fecI The ferric citrate sigma-factor
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CorrectionsProblem (automatically detected by PYQUALI):
IHF ≈ ihfA + ihfB (1)
ihfA ≈ −IHF (2)
ihfB ≈ −IHF (3)
Inconsistent system (no
valuation is solution)ihfA ihfB IHF Conflict+ + + (2), (3)+ + − (1)+ − + (1)+ − − (1)− + + (1)− + − (1)− − + (1)− − − (2), (3)
Solution: Adding sigma-factor interactions
IHF ≈ ihfA + ihfB
ihfA ≈ −IHF + rpoD + rpoS
ihfB ≈ −IHF + rpoD + rpoS
Consistent system (18
solutions among 32)rpoD rpoS ihfA ihfB IHF+ + + + ++ + + − ++ + − + +− − − − −− − − + −− − + − −
+/− −/+ + + ++/− −/+ + − ++/− −/+ + − −+/− −/+ − + ++/− −/+ − + −+/− −/+ − − −
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Self-consistent graph for E. Coli
Number of nodes 1529Number of interactions 3883Nodes without successor 1365Nodes with more than 80 successors 10sigma-factors 6protein complex 4
Add interactions among sigma factors and itsrelated genes
Sigma factors are considered as external nodes:no equation
Protein Gene Induced Genesσ70 rpoD 1047σ38 rpoS 114σ54 rpoN 100σ24 rpoE 48σ32 rpoH 29σ19 fecI 7
Regulatory network of E.coli with sigmafactors interactions is self-consistent
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Validation: Experimental data related to NutritionalStress
Population of E.coli grows exponentially untila nutrional stress
Variation of products between 2 equilibriumstates:
Exponential phaseStationary phase
40 experimental data (from RegulonDB) Ropers et al., Biosystems, 2004.
gene effectacnA +acrA +adhE +appB +appC +appY +blc +bolA +
gene effectcsiE +cspD +dnaN +dppA +fic +gabP +gadA +gadB +
gene effectgadC +hmp +hns +hyaA +ihfA −ihfB −lrp +mpl +
gene effectosmB +osmE +osmY +otsA +otsB +polA +proP +proX +
gene effectrecF +rob +sdaA −sohB −treA +yeiL +yfiD +yihI −
Inconsistency: There does not exist a solution of the quali-tative system that agree with the observed values
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Solving inconsistency of the observations (Problem)Inconsistent subgraph: (automatically detected by PYQUALI)
24 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA+ + + + + + ++ + + − + + ++ + − + + + +− − − − − − −− − − + − − −− − + − − − −+ − + + + − +− + + + + + +− + + + + + −
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ − − − − − −+ − − − − − +− − − − − + –
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Solving inconsistency of the observations (Problem)Inconsistent subgraph: (automatically detected by PYQUALI)
4 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA+ + + + + + ++ + + − + + ++ + − + + + +– – – – – – –− − − + − − −− − + − − − −+ − + + + − +− + + + + + +− + + + + + −
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ – – – – – –+ – – – – – +– + – – – + –
Subset of observations:
ihfA = –ihfB = –blc = +dppA = +
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Solving inconsistency of the observations (Problem)Inconsistent subgraph: (automatically detected by PYQUALI)
1 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA+ + + + + + ++ + + − + + ++ + − + + + +– – – – – – –− − − + − − −− − + − − − −+ − + + + − +− + + + + + +− + + + + + −
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ – – – – – –+ – – – – – +– + – – – + –
Subset of observations:
ihfA = –ihfB = –blc = +dppA = +
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Solving inconsistency of the observations (Problem)Inconsistent subgraph: (automatically detected by PYQUALI)
0 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA+ + + + + + ++ + + − + + ++ + − + + + +– – – – – – –− − − + − − −− − + − − − −+ − + + + − +− + + + + + +− + + + + + −
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ – – – – – –+ – – – – – +– + – – – + –
Subset of observations:
ihfA = –ihfB = –blc = +dppA = +
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Changing values of observations ?Inconsistent subgraph: (automatically detected by PYQUALI)
24 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA+ + + + + + ++ + + − + + ++ + − + + + +− − − − − − −− − − + − − −− − + − − − −+ − + + + − +− + + + + + +− + + + + + −
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ − − − − − −+ − − − − − +− − − − − + –
Corrections over thevalues of ihfA andihfB
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Changing values of observations ?Inconsistent subgraph: (automatically detected by PYQUALI)
4 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA
+ + + + + + ++ + + − + + ++ + − + + + +− − − − − − −− − − + − − −− − + − − − −+ – + + + – +– + + + + + +– + + + + + –
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ − − − − − −+ − − − − − +− + − − − + −
Corrected observations:ihfA = +ihfB = +blc = +dppA = +
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Changing values of observations ?Inconsistent subgraph: (automatically detected by PYQUALI)
3 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA
+ + + + + + ++ + + − + + ++ + − + + + +− − − − − − −− − − + − − −− − + − − − −+ – + + + – +– + + + + + +– + + + + + –
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ − − − − − −+ − − − − − +− + − − − + −
Corrected observations:ihfA = +ihfB = +blc = +dppA = +
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Changing values of observations ?Inconsistent subgraph: (automatically detected by PYQUALI)
2 consistent solutions :rpoD rpoS ihfA ihfB IHF blc dppA
+ + + + + + ++ + + − + + ++ + − + + + +− − − − − − −− − − + − − −− − + − − − −+ – + + + – +– + + + + + +– + + + + + –
+/− −/+ + − + −/+ +/−− + + − + + ++ − + − − − +
+/− −/+ + − − −/+ −+/− −/+ − + + −/+ +/−− + − + + + ++ − − + − − −
+/− −/+ − + − −/+ +/−+ − − − − − −+ − − − − − +− + − − − + −
Corrected observations:ihfA = +ihfB = +blc = +dppA = +
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Solution
Proposed corrections: ihfA = +, ihfB = +
References related to ihfA and ihfB
Data for stationary phase provided by RegulonDB data was incorrect
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Solution
Proposed corrections: ihfA = +, ihfB = +
References related to ihfA and ihfB
Data for stationary phase provided by RegulonDB data was incorrect
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Solution
Proposed corrections: ihfA = +, ihfB = +
References related to ihfA and ihfB
Data for stationary phase provided by RegulonDB data was incorrect
![Page 34: Checking Consistency Between Expression Data and Large ...Project Symbiose - IRISA November 2006. How to study a large scale system ? 1 Construct a model from interaction knowledge](https://reader036.fdocuments.net/reader036/viewer/2022081406/5f16b9f84c520a2cea1755c1/html5/thumbnails/34.jpg)
SolutionProposed corrections: ihfA = +, ihfB = +
References related to ihfA and ihfB
Data for stationary phase provided by RegulonDB data was incorrect
Consistency of E.coli regultory network plus sigma-factors withthe corrected set of 40 observations for Stationary Phase
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Inference
Always from a set of known variations
2 consistent solutions:rpoD rpoS ihfA ihfB IHF blc dppA
+ + + + + + +– + + + + + +
Subset of observations:ihfA = +ihfB = +blc = +dppA = +
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Inference
Always from a set of known variations
2 consistent solutions:rpoD rpoS ihfA ihfB IHF blc dppA
+ + + + + + +– + + + + + +
Subset of observations:ihfA = +ihfB = +blc = +dppA = +
Inference :No inferred value for rpoDrpoS = +IHF = +
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Inference
Always from a set of known variations
2 consistent solutions:rpoD rpoS ihfA ihfB IHF blc dppA
+ + + + + + +– + + + + + +
Subset of observations:ihfA = +ihfB = +blc = +dppA = +
Inference :No inferred value for rpoDrpoS = +IHF = +
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Inference
Always from a set of known variations
2 consistent solutions:rpoD rpoS ihfA ihfB IHF blc dppA
+ + + + + + +– + + + + + +
Subset of observations:ihfA = +ihfB = +blc = +dppA = +
Inference :No inferred value for rpoDrpoS = +IHF = +
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Inferring variations of new products of E.coli network
With 40 observations of Stationary Phase were found 5.2.1016 solutions
From these, 381 (26%) variables maintain always the same sign
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Inferring variations of new products of E.coli network
42 (of 381) products inferred under stationary phase conditiongene valueIHF +ada +agaR +alsR +araC +argP +argR +baeR +cadC +
gene valuecpxR +crp +cusR +cynR +cysB +cytR +dnaA +dsdC +evgA +
gene valuefucR +fur +galR +gcvA +glcC +gntR +ilvY +iscR +lexA +
gene valuelysR +melR +mngR +oxyR +phoB +prpR +rbsR +rhaR +rpoD +
gene valuerpoS +soxR +soxS +srlR +trpR +tyrR +
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Comparing the predictions with MA resultsSource of Microarray data: GEO (Gene Expression Omnibus)Barret et al., Nucleic Acid Res, 33. 2005
Comparison between 2 sets of variations of genes:
Microarray data for stationary phase after 20 minutes: 4025Inferred variations: 381
Number of common genes for both sets: 292
Comparison results for the 381 inferred variations:
Possible reasons of disagreement:
Microarray data related to small variations of certain genesMissing interactions in our model
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Conclusion
We were able to propose methods and algorithms that canhandle automatically (PYQUALI) large scale graphsWhat we are able to do
Test the self-consistency of a networkCheck its consistency with a set of experimental dataPropose corrections to the model or to the experimentaldataInfer new variations of non-observed products
Future workFind the best set of observations to validate a modelFind the best set of observations to infer the mostPropose methods to complete a network (addingmetabolites)
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Thank you!