1. Qualitative Simulation of the Carbon Starvation Response in Escherichia coli: Utilization of the Reporter Genes gfp and lux Delphine Ropers, 1 Danielle Bonaccio, 2 Hidde de Jong, 1 Dominique Schneider, 2 Johannes Geiselmann 2 1 INRIA Rhône-Alpes, Grenoble 2 Laboratoire Adaptation et Pathogénie des Microorganismes, Université Joseph Fourier, Grenoble Email: Delphine.Ropers@inrialpes.fr Web: http://www-helix.inrialpes.fr/article593.html JOBIM satellite meeting, July 9 th, 2005

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 based on gene reporter assays 5.Work in progress

3. 3 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

4. 4 Network controlling stress response vResponse of E. coli to nutritional stress conditions controlled by network of global regulators of transcription vNo global view of functioning of network available, despite abundant knowledge on network components Shen-Orr et al. (2002), Nat. Genet., 31(1):64-68

5. 5 Analysis of carbon starvation response vObjective: modeling and experimental studies directed at understanding how network controls nutritional stress response First step: analysis of the carbon starvation response in E. coli rrn P1P2 CRP crp cya CYA cAMPCRP FIS TopA topA GyrAB P1-P4 P1P2 P1-P’1 P gyrAB P Signal (lack of carbon source) DNA supercoiling fis tRNA rRNA Ropers et al. (2005), Biosystems, to appear protein gene promoter

6. 6 Qualitative modeling and simulation de Jong, Gouzé et al. (2004), Bull. Math. Biol., 66(2):301-340 vMethod for qualitative simulation of large and complex genetic regulatory networks using coarse-grained models 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, Biotechnol. Prog., 2004, 20(3):670-8 vMethod related to logical approaches and qualitative reasoning approaches Thomas, d’Ari (1990), Biological Feedback, CRC Press Kuipers (1994), Qualitative Reasoning, MIT Press

7. 7 PL models of genetic regulatory networks vGenetic regulatory networks modeled by class of piecewise- linear (PL) differential equations Use of step functions to describe regulatory interactions b B a A x a   a s - (x a,  a2 ) s - (x b,  b1 ) –  a x a. x b   b s - (x a,  a1 ) s - (x b,  b2 ) –  b x b. x : protein concentration ,  : rate constants  : threshold concentration x s - (x, θ)  0 1 Glass, Kauffman (1973), J. Theor. Biol., 39(1):103-129

8. 8 Domains in phase space vPhase space divided into domains by threshold planes Regulatory and switching domains xbxb xaxa  a1 max a 0 max b  a2  b1  b2.... x a   a s - (x a,  a2 ) s - (x b,  b1 ) –  a x a. x b   b s - (x a,  a1 ) s - (x b,  b2 ) –  b x b.

9. 9  In every regulatory domain D, system monotonically tends towards target equilibrium set  (D) Analysis in regulatory domains vExtension of PL differential equations to differential inclusions using Filippov approach Gouzé, Sari (2002), Dyn. Syst., 17(4):299-316 xbxb xaxa  a1 max a 0 max b  a2  b1  b2 x a   a s - (x a,  a2 ) s - (x b,  b1 ) –  a x a. x b   b s - (x a,  a1 ) s - (x b,  b2 ) –  b x b. D3D3 xa  a– a xaxa  a– a xa. x b  –  b x b. model in D 3 : model in D 1 : D1D1 xa  a– a xaxa  a– a xa. x b   b –  b x b.  (D 1 )  { (  a /  a,  b /  b ) }  (D1) (D1)  (D3) (D3)  (D 3 )  { (  a /  a, 0 ) }

10. 10 Qualitative abstraction of dynamics vDiscrete abstraction of continuous dynamics: state transition graph consisting of qualitative states and transitions  a1 max a 0 max b  a2  b1  b2 QS 1  (D1) (D1) D1D1 D2D2 D3D3 D4D4 D7D7 D5D5 D6D6 D1D1 D8D8 D9D9 D 10 D 11 D 12 D 13 D 14 D 15 D 16 D 17 D 18 D 24 D 20 D 21 D 22 D 23 D 19 D 25 QS 3 QS 2 QS 1 QS 4 QS 5 QS 10 QS 15 QS 20 QS 25 QS 24 QS 23 QS 22 QS 21 QS 16 QS 11 QS 6 QS 7 QS 12 QS 17 QS 18 QS 19 QS 13 QS 14 QS 8 QS 9 QS 3 QS 2 D2D2 D3D3

11. 11  a1 max a 0 max b  a2  b1  b2 Inequality constraints on parameters vState transition graph, and hence qualitative dynamics, may vary with parameter values  (D1) (D1) QS 6 QS 2 QS 1 QS 7 D1D1  (D1) (D1) D1D1 QS 6 QS 1 D2D2 D6D6 D7D7 D6D6  However, state transition graph is identical for certain inequality constraints on parameters , , and    b1   b2  max b   a1   a2  max a  a2   a /  a  max a  b2   b /  b  max b  a /  a  b /  b

12. 12 Qualitative simulation QS 1  a1 max a 0 max b  a6  b1  b2 D1D1 vQualitative simulation determines all qualitative states that are reachable from initial state through successive transitions  b1 max b xbxb QS 1  b2 QS 2 QS 3 QS 4  a1 max a xaxa QS 1  a2 QS 2 QS 3 QS 4 QS 2 QS 3 QS 4

13. 13 Genetic Network Analyzer (GNA) http://www-helix.inrialpes.fr/gna vQualitative simulation method implemented in Java: Genetic Network Analyzer (GNA) de Jong et al. (2003), Bioinformatics, 19(3):336-344

14. 14 Model of carbon stress response network vStress response network modeled by qualitative PL model 7 differential equations, with 46 inequality constraints rrn P1P2 CRP crp cya CYA cAMPCRP FIS TopA topA GyrAB P1-P4 P1P2 P1-P’1 P gyrAB P Signal (lack of carbon) DNA supercoiling fis tRNA rRNA Ropers et al. (2005), Biosystems, to appear

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 Simulation of stress response network vSimulation of transition from exponential to stationary phase State transition graph with 26 states generated in < 1 s, single equilibrium state CYA FIS GyrAB Signal TopA rrn CRP

17. 17 Insight into carbon starvation response vSequence of qualitative events leading to adjustment of growth of cell after carbon starvation signal rrn P1P2 CRP crp cya CYA cAMPCRP FIS TopA topA GyrAB P1-P4 P1P2 P1-P’1 P gyrAB P Signal (lack of carbon) DNA supercoiling fis tRNA rRNA Role of positive feedback loop involving Fis and CRPcAMP

18. 18 Extension of stress response network vModel does not reproduce observed downregulation of negative supercoiling

19. 19 Simulation of response to carbon upshift vSimulation of transition from stationary to exponential phase after carbon upshift State transition graph with 75 states generated in < 1 s, qualitative cycle CYA FIS GyrAB Signal TopA rrn CRP equilibrium state equilibrium state

20. 20 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 cAMPCRP 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

21. 21 Experimental validation of model predictions vSimulations yield novel predictions that call for experimental verification Comparison with observed qualitative evolution of protein concentrations Fusion of gene of interest to reporter gene, whose expression reflects expression of gene of interest vMonitoring gene expression by means of gene reporter system vCharacteristics of the chosen gene reporter system (lux and gfp) Easily assayable, visible signal Highly sensitive, allowing real-time measurements of gene expression in living cells (either isolated or in population) Measurements automatically carried out at high sampling frequency Low cost

22. 22 Gene reporter constructions vIntegration of gene reporter into chromosome or plasmid gyrA l Transcriptional fusion: reporter gene under control of promoter region vTwo types of gene fusion bla ori reporter gene low-copy plasmid DNA region preceding gene of interest gyrA l Translational fusion: reporter gene under control of both promoter region and sequences required for translation

23. 23 Global regulator GFP or Luciférase E. coli genome Reporter gene  Integration of the gene reporter system into bacterial cell  Real-time measurement of reporter-gene expression in bacterial population Time-series measurement of fluorescence or luminescence Time rrnB GFP 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 13:30:0014:30:0015:30:0016:30:00 Intensity Monitoring gene expression: population

24. 24  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 Luciférase E. coli genome Reporter gene Mihalcescu et al. (2004), Nature, 430(6995):81-85 Cts/cell Time (min) gyrA GFP

25. 25 Difficulties of experimental validation vDesign and construction of reporter genes Takes always more time than one thinks! vDetermination of experimental conditions Idem: sticking bacteria on plates, signal acquisition, GFP bleaching,... vMeasurement of gene expression in populations vs single cells Easier to carry out in populations, but less informative vRelation between reporter gene and gene of interest Not that clear: different rates of protein decay vAnalysis of raw data F Far from trivial: noise filtering, data fitting,...

26. 26 Work in progress vModel predictions verified? vWe will know soon! CYA FIS GyrAB Signal TopA rrn CRP