1. Qualitative Simulation of the Carbon Starvation Response in Escherichia coli Delphine Ropers INRIA Rhône-Alpes 655 avenue de l’Europe Montbonnot, 38334 Saint Ismier CEDEX, France Email: Delphine.Ropers@inrialpes.fr Web: http://www-helix.inrialpes.fr/article593.html

2. 2 Overview 1.Introduction: nutritional stress response in E. coli 2.Qualitative modeling and simulation of genetic regulatory networks 3.Modeling of carbon starvation response in E. coli 4.Experimental validation of model predictions 5.Work in progress

3. 3 Stress response in Escherichia coli vBacteria able to adapt to a variety of changing environmental conditions Nutritional stress Osmotic stress Heat shock Cold shock … vStress response in E. coli has been much studied Model for understanding adaptation of pathogenic bacteria to their host

4. 4 Nutritional stress response in E. coli vResponse of E. coli to nutritional stress conditions: transition from exponential phase to stationary phase Changes in morphology, metabolism, gene expression, … log (pop. size) time > 4 h

5. 5 Network controlling stress response vResponse of E. coli to nutritional stress conditions controlled by large and complex genetic regulatory network Cases et de Lorenzo (2005), Nat. Microbiol. Rev., 3(2):105-118 vNo global view of functioning of network available, despite abundant knowledge on network components

6. 6 Analysis of carbon starvation response vObjective: modeling and experimental studies directed at understanding how network controls nutritional stress response

7. 7 Qualitative modeling and simulation vCurrent constraints on modeling and simulation: l Knowledge on molecular mechanisms rare l Quantitative information on kinetic parameters and molecular concentrations absent vMethod for qualitative simulation of large and complex genetic regulatory networks using coarse-grained models de Jong, Gouzé et al. (2004), Bull. Math. Biol., 66(2):301-340 Batt G. et al. (2005), Hybrid Systems: Computation and Control, LNCS 3414, 134-150. vMethod used to simulate initiation of sporulation in Bacillus subtilis and quorum sensing of Pseudomonas aeruginosa de Jong et al. (2004), Bull. Math. Biol., 66(2):261-300 Viretta and Fussenegger (2004), Biotechnol. Prog., 20(3):670-8

8. 8 PL differential equation models vGenetic networks modeled by class of differential equations using step functions to describe regulatory interactions x a   a s - (x a,  a2 ) s - (x b,  b ) –  a x a. x b   b s - (x a,  a1 ) –  b x b. x : protein concentration ,  : rate constants  : threshold concentration x s - (x, θ)  0 1 vDifferential equation models of regulatory networks are piecewise-linear (PL) Glass and Kauffman (1973), J. Theor. Biol., 39(1): 103-129 b B a A

9. 9 vAnalysis of the dynamics in phase space vPhase space partition: unique derivative sign pattern in domains vQualitative abstraction yields state transition graph vAbstraction preserves unicity of derivative sign pattern  a1 0 max b  a2 bb max a Qualitative analysis of network dynamics x a   a s - (x a,  a2 ) s - (x b,  b ) –  a x a. x b   b s - (x a,  a1 ) –  b x b. x a   a –  a x a. x b   b –  b x b... x a > 0 x b < 0 D5:D5: 0 <  a1 <  a2 <  a /  a < max a 0 <  b <  b /  b < max b...... x a > 0 x b > 0 x a > 0 x b < 0 x a = 0 x b < 0 D1:D1: D5:D5: D7:D7:  a1 0 max b  a2 bb max a  a  a  b  b D 12 D 22 D 23 D 24 D 17 D 18 D 21 D 20 D1D1 D3D3 D5D5 D7D7 D9D9 D 15 D 27 D 26 D 25 D 11 D 13 D 14 D2D2 D4D4 D6D6 D8D8 D 10 D 16 D 19

10. 10 vPredictions well adapted to comparison with available experimental data: changes of derivative sign patterns vModel validation: comparison of derivative sign patterns in observed and predicted behavior Validation of qualitative models.. x a < 0 x b > 0 x a > 0 x b > 0 x a = 0 x b = 0.... D1:D1: D 17 : D 18 : Concistency? Yes 0 xbxb time 0 xaxa x a > 0. x b > 0.. x a < 0.

11. 11 Genetic Network Analyzer (GNA) de Jong et al. (2003) Bioinformatics Batt et al. (2005), Bioinformatics Page et al. (2006) http://www-helix.inrialpes.fr/gna Integration into environment for explorative genomics by Genostar Technologies SA vQualitative simulation method implemented in Java: Genetic Network Analyzer (GNA)

12. 12 Initiation of sporulation in Bacillus subtilis vValidation of method by analysis of well-understood network Control of initiation of sporulation in Bacillus subtilis ? division cycle sporulation- germination cycle metabolic and environmental signals

13. 13 Model of sporulation network vPiecewise-linear model of network controlling sporulation 11 differential equations, with 59 inequality constraints de Jong, Geiselmann et al. (2004), Bull. Math. Biol., 66(2): 261-300

14. 14 Model of carbon starvation network E. coli vCarbon starvation network modeled by PL model 7 differential equations, with 36 inequality constraints Ropers et al. (2006), BioSystems, in press

15. 15 ( x FIS ) n + K o n ( x FIS ) n f rrnP1 ( x FIS ) = Hill rate law:  FIS f rrnP1 ( x FIS )  s + ( x FIS,  FIS ) Step-function approximation: Modeling of rrn module FIS rrn P1P2 stable RNAs  Regulatory mechanism of control by FIS at promoter rrn P1 FIS binds to multiple sites in promoter region FIS forms a cooperative complex with RNA polymerase. x rrn   rrn 1 s + ( x FIS,  FIS ) +  rrn 2 –  rrn x rrn Schneider et al. (2003), Curr. Opin. Microbiol., 6:151-156

16. 16 ATP + CYA* K1K1 CYA*ATPCYA* + cAMP cAMP + CRP K4K4 k2k2 CRPcAMP k3k3 degradation/export Modeling of CRP activation CRP cAMP Activation CRP CYA Signal crp P1P2 vCRP activation in presence of carbon starvation signal vModeling of CRP activation using mass-action law Quasi steady-state assumption simplifies model k 2 x CYA + k 3 K 4 k 2 x CYA x CRP x CRP cAMP =

17. 17  Regulatory mechanism of control by CRP cAMP at crp P2 CRP cAMP binds to a single site CRP cAMP forms a cooperative complex with RNA polymerase Modeling of crp activation by CRP · cAMP Barnard et al. (2004), Curr. Opin. Microbiol., 7:102-108 CRP cAMP Activation CRP CYA Signal crp P1P2 CYA concentration (M) CRP concentration (M) ( x CRPcAMP ) n + K o n ( x CRPcAMP ) n f crpP2 ( x CRPcAMP ) = Rate law: k 2 x CYA + k 3 K 4 k 2 x CYA x CRP x CRPcAMP = Step-function approximation: f crpP2  s + (x CYA,  CYA ) s + (x CRP,  CRP ) s + (x SIGNAL,  SIGNAL ) x crp   crp 1 +  crp 2 s + (x CYA,  CYA 1 ) s + (x CRP,  CRP 1 ) s + (x SIGNAL,  SIGNAL ) –  crp x crp.

18. 18 Simulation of stress response network vQualitative analysis of attractors: two equilibrium states Stable state, corresponding to exponential-phase conditions Stable state, corresponding to stationary-phase conditions

19. 19 Simulation of stress response network vSimulation of transition from exponential to stationary phase State transition graph with 27 states generated in < 1 s, 1 stable equilibrium state CYA FIS GyrAB Signal TopA rrn CRP

20. 20 Insight into carbon starvation response vSequence of qualitative events leading to adjustment of growth of cell after carbon starvation signal Superhelical density of DNA rrn P1P2 Activation CRP crp cya CYA CRPcAMP FIS TopA topA GyrAB P1-P4 P1P2 P1-P’1 P gyrAB P Signal (lack of carbon source) Supercoiling fis tRNA rRNA Role of the mutual inhibition of FIS and CRP cAMP

21. 21 Extension of carbon starvation network Ropers et al. (2006) Missing component in the network? vModel does not reproduce observed downregulation of negative supercoiling

22. 22 Simulation of response to carbon upshift vSimulation of transition from stationary to exponential phase after carbon upshift State transition graph with 300 states generated in < 1 s, qualitative cycle CYA FIS CRP GyrAB Signal TopA rrn equilibrium state equilibrium state

23. 23 Insight into response to carbon upshift vSequence of qualitative events leading to adjustment of cell growth after a carbon upshift rrn P1P2 CRP crp cya CYA Activation FIS TopA topA GyrAB P1-P4 P1P2 P1-P’1 P gyrAB P Signal (lack of carbon) DNA supercoiling fis tRNA rRNA Role of the negative feedback loop involving Fis and DNA supercoiling

24. 24 Experimental validation of model predictions vSimulations yield novel predictions that call for experimental verification Comparison with observed qualitative evolution of protein concentrations vMonitoring gene expression by means of gene reporter system Reporter gene under control of promoter region of gene of interest promoter region bla ori gfp or lux reporter gene gene reporter system on plasmid Reporter gene expression reflects expression of gene of interest

25. 25 Global regulator GFP or Luciferase E. coli genome Reporter gene  Integration of the gene reporter system into bacterial cell Monitoring gene expression: population  Real-time measurement of reporter-gene expression in bacterial population Time-series measurement of fluorescence or luminescence rrn GFP

26. 26  Integration of the gene reporter system into bacterial cell  Real-time measurement of reporter-gene expression in individual bacteria Monitoring gene expression: single cell Phase contrast Fluorescence Global regulator GFP or Luciferase E. coli genome Reporter gene Mihalcescu et al. (2004), Nature, 430(6995):81-85 Cts/cell Time (min) gyrA GFP

27. 27 Work in progress vModel predictions verified? vWe will know soon! CYA FIS GyrAB Signal TopA rrn CRP

28. 28 Conclusions vUnderstanding of functioning and development of living organisms requires analysis of genetic regulatory networks From structure to behavior of networks vNeed for mathematical methods and computer tools well- adapted to available experimental data Coarse-grained models and qualitative analysis of dynamics vBiological relevance attained through integration of modeling and experiments Models guide experiments, and experiments stimulate models

29. 29 Contributors Grégory Batt, INRIA Rhône-Alpes, France Danielle Bonaccio, Université Joseph Fourier, Grenoble, France Hidde de Jong, INRIA Rhône-Alpes, France Hans Geiselmann, Université Joseph Fourier, Grenoble, France Jean-Luc Gouzé, INRIA Sophia-Antipolis, France Irina Mihalcescu, Université Joseph Fourier, Grenoble, France Michel Page, INRIA Rhône-Alpes/Université Pierre Mendès France, Grenoble, France Corinne Pinel, Université Joseph Fourier, Grenoble, France Delphine Ropers, INRIA Rhône-Alpes, France Tewfik Sari Université de Haute Alsace, Mulhouse, France Dominique Schneider Université Joseph Fourier, Grenoble, France

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31. 31 Automated verification of properties vUse of model-checking techniques to verify (observed) properties of dynamics of network EF(x a >0 Λ x b >0 Λ EF(x a =0 Λ x b <0))...... x a <0 x b =0.. x a <0 x b >0. x a >0 x b <0. x a =0 x b <0.. x a >0 x b >0.. x a =0 x b =0.. QS 1 QS 3 QS 4 QS 5 QS 7 QS 8 QS 6 QS 2 There E xists a F uture state where x a >0 and x b >0 and starting from that state, there E xists a F uture state where x a =0 and x b <0.... Yes! l transition graph transformed into Kripke structure Batt et al. (2005), Bioinformatics, 21(supp. 1): i19-i28 l properties expressed in temporal logic

32. 32 Casey et al. (2005), J. Math. Biol., in press vAnalysis of stability of attractors, using properties of state transition graph Definition of stability of equilibrium points on surfaces of discontinuity Analysis of attractors of PL systems vSearch of attractors of PL systems in phase space Combinatorial, but efficient algorithms  a1 max a 0 max b  a2  b1  b2