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Qualitative Simulation of the Carbon Starvation Response in Escherichia coli Delphine Ropers 1 Hidde de Jong 1 Johannes Geiselmann 1,2 1 INRIA Rhône-Alpes 2 Laboratoire Adaptation Pathogénie des Microorganismes Faculté de Médecine et Pharmacie Université Joseph Fourier CNRS UMR

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2 Overview 1.Carbon starvation response of Escherichia coli 2.Qualitative modeling, simulation, and analysis of carbon starvation network 3.Experimental validation of carbon starvation model

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3 Escherichia coli vThe average human gut contains about 1 kg of bacteria l Normally, approximatively 0.1% are E. coli l E. coli, along with other enterobacteria, synthesize vitamins which are absorbed by our body (e.g., vitamin K, B-complex vitamins) Rocky Mountain Laboratories, NIAID, NIH 2 µm 1 µm

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4 Escherichia coli stress responses vE. coli is able to adapt and respond to a variety of stresses in its environment Model organism for understanding adaptation of pathogenic bacteria to their host Nutritional stress Osmotic stress Heat shock Cold shock … Storz and Hengge-Aronis (2000), Bacterial Stress Responses, ASM Press

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5 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

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6 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): vNo global view of functioning of network available, despite abundant knowledge on network components

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7 Analysis of carbon starvation response vWhich network components and which interactions to take into account? l Impossible to model the whole network E. coli genome: ~4500 genes (~150 transcription factor genes) l Start with the simplest possible representation of the carbon starvation response in E. coli vModeling and experimental studies directed at understanding how network controls carbon starvation response

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8 Analysis of carbon starvation response vModeling and experimental studies directed at understanding how network controls carbon starvation response vBottom-up strategy: 1) Initial model of carbon starvation response 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. (2006), BioSystems, 84(2): protein gene promoter

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9 Analysis of carbon starvation response vBottom-up strategy: 1) Initial model of the carbon starvation response Search and curate data available in the literature and databases 2) Experimental verification of model predictions 3) Extension of model to take into account wrong predictions Additional global regulators: IHF, HNS, ppGpp, FNR, LRP, ArcA, … vModeling and experimental studies directed at understanding how network controls carbon starvation response

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10 vModular structure of carbon starvation network Ropers et al. (2006), BioSystems, 84(2): Modeling of carbon starvation network

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11 Modeling of carbon starvation network vCan the initial model explain the carbon starvation response of E. coli cells? vTranslation of biological data into a mathematical model

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12 Modeling of carbon starvation network vOrdinary differential equations to describe evolution of concentration of network components Good compromise between expressiveness of formalism and available data vKinetic ODE model of 12 variables and 46 parameters l Regulation of gene expression (Hill) l Formation of biochemical complexes (mass action) l Enzymatic reactions (Michaelis-Menten)

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13 Modeling of carbon starvation network

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14 v Current constraints on kinetic modeling of E. coli network: Knowledge on molecular mechanisms incomplete Quantitative information on kinetic parameters and molecular concentrations mostly absent v Possible strategies to overcome the constraints Parameter sensitivity analysis Model simplifications v Intuition: essential properties of system dynamics robust against moderate changes in kinetic parameters and rate laws Modeling of carbon starvation network

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15 From nonlinear kinetic model to PL model vModel simplification consists in reducing classical nonlinear kinetic model to PL model Nonlinear kinetic model Nonlinear reduced kinetic model Piecewise-linear model Time-scale separation Piecewise-linear approximation

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16 RNA Pol FIS RNA Pol Modeling of rrn regulation vRegulatory mechanism of FIS control of promoter rrn P1 l FIS binds to multiple sites in promoter region l FIS forms a cooperative complex with RNA polymerase P1P2 rrn stable RNAs Schneider et al. (2003), Curr. Opin. Microbiol., 6:

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17 Nonlinear model: Modeling of rrn regulation FIS rrn P1P2 stable RNAs Schneider et al. (2003), Curr. Opin. Microbiol., 6: vRegulatory mechanism of FIS control of promoter rrn P1 l FIS binds to multiple sites in promoter region l FIS forms a cooperative complex with RNA polymerase. x rrn rrn 1 h + ( x FIS, FIS,n) + rrn 2 – rrn x rrn x FIS n + θ FIS n x FIS n h + ( x FIS, FIS,n) FIS Piecewise-linear model:. x rrn rrn 1 s + ( x FIS, FIS ) + rrn 2 – rrn x rrn rrn 2 rrn rrn, ( rrn 1 + rrn 2 ) rrn rrn

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18 CRP cAMP RNA Pol Modeling of crp regulation by CRP · cAMP Barnard et al. (2004), Curr. Opin. Microbiol., 7: crp P1P2 Regulatory mechanism of CRPcAMP control of crp P2 promoter CRPcAMP binds to a single site CRPcAMP forms a cooperative complex with RNA polymerase CRP crp mRNAs

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19 Modeling of crp regulation by CRP · cAMP Barnard et al. (2004), Curr. Opin. Microbiol., 7: CRP cAMP Activation CRP CYA Signal crp P1P2 Regulatory mechanism of CRPcAMP control of crp P2 promoter CRPcAMP binds to a single site CRPcAMP forms a cooperative complex with RNA polymerase Formation of CRPcAMP in presence of carbon starvation signal ATP + CYA* K1K1 CYA*ATPCYA* + cAMP cAMP + CRP K4K4 k2k2 CRPcAMP k3k3 degradation/export

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20 Modeling of crp regulation by CRP · cAMP Nonlinear model: x CYA* ·ATP …. x CRP CRP 1 + CRP 2 h + ( x CRP·cAMP, CRP·cAMP,n) – CRP x CRP · x CYA* … …. .... x CRP·cAMP … ….. Piecewise-linear model: x CRP CRP 1 + CRP 2 s + (x CYA, CYA 1 ) s + (x CRP, CRP 1 ) s + (x SIGNAL, SIGNAL ) – CRP x CRP. CYA concentration (M) CRP concentration (M) CRP cAMP Activation CRP CYA Signal crp P1P2 Mass-action kinetics Reduced nonlinear model: k 2 x CYA + k 3 K 4 k 2 x CYA x CRP x CRP · cAMP = x CRP · CRP 1 + CRP 2 h + ( x CRP·cAMP, CRP·cAMP,n) – CRP x CRP ·. Quasi-steady-state approximation

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21 Model of carbon starvation network vPLDE model of 7 variables and 36 parameter inequalities

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22 Attractors of stress response network vAnalysis of attractors of PL model: two steady states Stable steady state, corresponding to exponential-phase conditions Stable steady state, corresponding to stationary-phase conditions

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23 Simulation of stress response network vSimulation of transition from exponential to stationary phase State transition graph with 27 states, 1 stable steady state CYA FIS GyrAB Signal TopA rrn CRP

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24 Insight into nutritional stress response vSequence of qualitative events leading to adjustment of growth of cell after nutritional stress 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 nutrients) Supercoiling fis tRNA rRNA Role of the mutual inhibition of Fis and CRPcAMP

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25 Validation of carbon starvation response model vValidation of model using model checking l “Fis concentration decreases and becomes steady in stationary phase” l “cya transcription is negatively regulated by the complex cAMP-CRP” l “DNA supercoiling decreases during transition to stationary phase” EF(x fis < 0 EF(x fis = 0 x rrn < rrn ) ).. True AG(x crp > 3 crp x cya > 3 cya x s > s → EF x cya < 0). True False EF( (x gyrAB 0) x rrn < rrn ).. Ali Azam et al. (1999), J. Bacteriol., 181(20): Kawamukai et al. (1985), J. Bacteriol., 164(2): Balke, Gralla (1987), J. Bacteriol., 169(10):

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26 Suggestion of missing interaction vModel does not reproduce observed downregulation of negative supercoiling 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 nutrients) Supercoiling fis tRNA rRNA Missing interaction in the network?

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

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28 Assessment of model reduction vMonte-Carlo simulation studies to compare qualitative dynamics of NL and PLDE models l Generate random parameter and initial conditions sets and numerically simulate NL model l Check whether sequences of derivative sign patterns of numerical solutions are included in transition graph for PLDE model xbxb xaxa 0 x b = 0. x a = 0. b B a A xbxb xaxa 0 x b = 0. x a = 0. bb aa

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29 vAnalysis of subsystem of carbon starvation response network vGood correspondence of qualitative dynamics of reduced NL and PL models Preliminary results CRP cAMP Activation CRP CYA Signal crp P1P2

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30 Reporter gene systems vUse of reporter gene systems to monitor gene expression promoter region bla ori gfp or lux reporter gene cloning promoter regions on plasmid vSimulations yield predictions that cannot be verified with currently avaliable experimental data rrnB fis crp rpoS topA gyrB gyrA nlpD

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31 Global regulator GFP E. coli genome Reporter gene Integration of fluorescent or luminescent reporter gene systems into bacterial cell Monitoring of gene expression excitation emission vExpression of reporter gene reflects expression of host gene of interest Global regulator Luciferase E. coli genome Reporter operon emission

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32 Real-time monitoring: microplate reader vUse of automated microplate reader to monitor in parallel in single experiment expression of different reporter genes l fluorescence/luminescent intensity l absorbance (OD) of bacterial culture vUpshift experiments in M9/glucose medium 96-well microplate Well with bacterial culture Different gene reporter system in wells

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33 Analysis of reporter gene expression data vWellreader: Matlab program for analysis of reporter gene expression data fis reporter luminescence intensity

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34 Data analysis issues vOutlier detection vData smoothing and interpolation by means of cubic smoothing splines vComputation of reporter concentration, promoter activity, host protein concentration

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35 Preliminary results on model validation vValidation of E. coli carbon starvation response model by means of time-course expression data fis crp gyrB topA rrnB rpoS

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36 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

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37 Monitoring reporter-gene expression in single cell Collaboration with Irina Mihalcescu (Université Joseph Fourier, Grenoble) Extensions of carbon starvation model l Inclusion of additional global regulators involved in carbon starvation response l Composite models of E. coli stress response on genetic and metabolic level Collaboration with Daniel Kahn (INRIA Rhône-Alpes, Lyon) Further work

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38 Contributors and sponsors Grégory Batt, Boston University, USA Hidde de Jong, INRIA Rhône-Alpes, France Hans Geiselmann, Université Joseph Fourier, Grenoble, France Jean-Luc Gouzé, INRIA Sophia-Antipolis, France Radu Mateescu, INRIA Rhône-Alpes, 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 Ministère de la Recherche, IMPBIO program European Commission, FP6, NEST program INRIA, ARC program Agence Nationale de la Recherche, BioSys program

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40 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

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