Modeling and Simulation of Genetic Regulatory Networks in Bacteria

Transcription

1 Modeling and Simulation of Genetic Regulatory Networks in Bacteria Hidde de Jong IBIS group INRIA Grenoble Rhône Alpes 655, avenue de l Europe Montbonnot, Saint Ismier CEDEX Hidde.de-Jong@inria.fr

2 INRIA Grenoble Rhône Alpes and IBIS IBIS: systems biology group of INRIA and Joseph Fourier University/CNRS Analysis of bacterial regulatory networks by means of models and experiments Involves computer scientists, molecular biologists, physicists, 2

3 Overview 1. Genetic regulatory networks in bacteria 2. Motivations for modeling and simulation 3. Modeling regulatory networks by means of ordinary differential equations 4. Examples 5. Research challenges 3

4 Bacteria Bacteria were first observed by Antonie van Leeuwenhoek in 1676, using a single lens microscope of his own design van Leeuwenhoek A (1684), Philosophical Transactions ( ) 14: "In the morning I used to rub my teeth with salt and rinse my mouth with water and after eating to clean my molars with a toothpick... I then most always saw, with great wonder, that in the said matter there were many very little living animalcules, very prettily a moving. The biggest sort had a very strong and swift motion, and shot through the water like a pike does through the water; mostly these were of small numbers." 4

5 Impact of bacteria on humans Bacteria as disease agents Tuberculosis, cholera, syphilis, anthrax, leprosy, bubonic plague, Plaque in Weymouth, England Spread of bulbonic plague over Europe Bacteria in food industry (fermentation) Cheese, yoghurt, Bacteria in environmental and biotechnology Sewage treatment, bioremediation, synthesis of chemicals, biofuels, 5

6 Bacterial cells bacterial cells in 1 g of soil and 106 bacterial cells in 1 ml of fresh water 10 times as many bacterial cells as human cells in human body Wide range of shapes (spheres, rods, spirals, ), typically μm in length Madigan et al. (2003), Brock Biology of Microorganisms, Prentice Hall, 10th ed. 6

7 Bacteria as living systems Bacteria possess characteristics shared by most living systems Madigan et al. (2003), Brock Biology of Microorganisms, Prentice Hall, 10th ed. 7

8 Proteins are building blocks of cell Proteins are essential building blocks in machine and coding functions of the cell Cells as biochemical machines and as coding devices Single cell contains 1900 different kinds of proteins and total protein molecules (E. coli) Madigan et al. (2003), Brock Biology of Microorganisms, Prentice Hall, 10th ed. 8

9 Synthesis and degradation of proteins RNA polymerase DNA transcription ribosome effector molecule translation modified protein mrna protein post translational modification degradation protease 9

10 Transcription RNA polymerase Purves et al. (2003), Life 10

11 Synthesis and degradation of proteins genes prots/transcription translation.html 11

12 Regulation of synthesis and degradation transcription factor RNA polymerase DNA modified protein RBS small RNA kinase mrna protease ribosome response regulator Mostly transcriptional regulation in bacteria, but sometimes regulation on all four levels 12

13 Transcriptional regulation Purves et al. (2003), Life 13

14 Transcriptional regulation Transcription regulator Crp bound to DNA Purves et al. (2003), Life 14

15 Genetic regulatory networks Regulation of synthesis and degradation of proteins is achieved by other proteins or protein complexes Transcription regulators, proteases, but also ribosomes, RNA polymerases Direct and indirect regulatory influences give rise to genetic regulatory network protein complex AB protein A metabolite E F protein D protein C protein B DF gene c gene a gene b gene g 15

16 Genetic regulatory networks Regulation of synthesis and degradation of proteins is achieved by other proteins or protein complexes Ribosomes, RNA polymerases, transcription regulators, proteases, Direct and indirect regulatory influences give rise to genetic regulatory network protein D protein A protein C protein B gene c gene a gene b gene g 16

17 Complexity of genetic regulatory networks Most genetic regulatory networks of biological interest are large and complex E. coli has 4200 genes coding for several hundreds of transcription factors Network of transcription regulators in E. coli Martinez Antonio et al. (2003), Curr. Opin. Microbiol., 6(5):

18 Analysis of genetic regulatory networks Abundant knowledge on components and interactions of genetic regulatory networks in many bacteria Scientific knowledge bases and databases Bibliographic databases Currently little understanding of how global dynamics emerges from local interactions between components Response of cell to external perturbation Differentiation of cell Shift from structure to dynamics of networks «functional genomics», «integrative biology», «systems biology», Kitano (2002), Science, 295(5560):564 18

19 Experimental tools Study of dynamics of genetic regulatory networks requires powerful experimental tools High throughput, low cost, reliable, precise, Different methods for monitoring gene expression, measuring different quantities: Western blots: protein abundance Northern blots: (relative) mrna abundance DNA microarrays: (relative) mrna abundance Reporter genes: promoter activity, mrna abundance. Measurements on population of cells, more recently also measurements on individual cells Longo and Hasty (2006), Mol. Syst. Biol., msb

20 Reporter gene systems Most experimental techniques do not allow measurement of gene expression at high precision and sampling density Use of fluorescent reporter gene systems for real time monitoring of gene expression in living cells Cloning of promoter of gene of interest on plasmid carrying promoter fluorescent reporter gene (gfp) promoter bla gfp reporter gene gene a ori 20

21 Real time monitoring of gene expression Integration of reporter gene systems into bacterial cell E. coli genome Global regulator excitation Reporter gene GFP emission Measurements of dynamics of gene expression at high resolution in populations and individual cells 21

22 Mathematical methods and computer tools Modeling and simulation indispensable for dynamic analysis of genetic regulatory networks: understanding role of individual components and interactions suggesting missing components and interactions Mathematical methods supported by computer tools required for modeling and simulation: precise and unambiguous description of network systematic derivation of behavior predictions First models of genetic regulatory networks date back to early days of molecular biology Regulation of lac operon Goodwin (1963), Temporal Organization in Cells 22

23 Hierarchy of modeling formalisms Variety of modeling formalisms exist, describing system on different levels of detail de Jong (2002), J. Comput. Biol., 9(1): Hasty et al. (2001), Nat. Rev. Genet., 2(4): Smolen et al. (2000), Bull. Math. Biol., 62(2): Szallassi et al. (2006), System Modeling in Cellular Biology, MIT Press Graphs precision Ordinary differential equations abstraction Stochastic master equations 23

24 Ordinary differential equation models Cellular concentration of proteins, mrnas, and other molecules at time point t represented by continuous variable xi(t) R 0 Regulatory interactions, controlling synthesis and degradation, modeled by ordinary differential equations dx = x = f. (x), dt where x = [x1,, xn] and f (x) is rate law Kinetic theory of biochemical reactions provides basis for specification of rate law Heinrich and Schuster (1996), The Regulation of Cellular Systems Cornish Bowden (1995), Fundamentals of Enzyme Kinetics 24

25 Cross inhibition network Cross inhibition network consists of two genes, each coding for transcription regulator inhibiting expression of other gene protein protein gene promoter promoter gene Cross inhibition network is example of positive feedback, important for differentiation Thomas and d Ari (1990), Biological Feedback 25

26 ODE model of cross inhibition network x. a = κa f (xb) γa xa x. b = κb f (xa) γb xb f (x ) 1 0 xa = concentration protein A xb = concentration protein B κa, κb > 0, production rate constants γa, γb > 0, degradation rate constants n θ f (x) =, θ > 0 threshold n n θ + x θ x 26

27 ODE model of cross inhibition network x. a = κa f (xb) γa xa x. b = κb f (xa) γb xb xa = concentration protein A xb = concentration protein B κa, κb > 0, production rate constants γa, γb > 0, degradation rate constants Implicit modeling assumptions: Ignore intermediate gene products (mrna) Ignore gene expression machinery (RNA polymerase, ribosome) Simplification of complex interactions of regulators with DNA to single response function 27

28 Bistability of cross inhibition network Analysis of steady states in phase plane xa x. a = 0 x. b = 0 0 κa xa = 0 : xa = γa f (xb) κb. xb = 0 : xb = f (x ) a γb. xb System is bistable: two stable and one unstable steady state. For almost all initial conditions, system will converge to one of two stable steady states (differentiation) System returns to steady state after small perturbation 28

29 Switching in cross inhibition network Transient perturbation may cause irreversible switch from one steady state to the other Temporary disable one of the inhibitors x. a = κa γa xa x. b = κb f (xa) γb xb 29

30 Switching in cross inhibition network Transient perturbation may cause irreversible switch from one steady state to the other System evolves to new steady state xa x. a = 0 x. b = 0 0 κa xa = 0 : xa = γ a κb. xb = 0 : xb = f (x ) a γb. xb 30

31 Switching in cross inhibition network Transient perturbation may cause irreversible switch from one steady state to the other Enable again inhibitor x. a = κa f (xb) γa xa x. b = κb f (xa) γb xb 31

32 Switching in cross inhibition network Transient perturbation may cause irreversible switch from one steady state to the other System remains in new steady state xa x. a = 0 x. b = 0 0 κa xa = 0 : xa = γa f (xb) κb. xb = 0 : xb = f (x ) a γb. xb 32

33 Bifurcation in cross inhibition network Switching of cross inhibition network can be interpreted as sequence of bifurcations, induced by change in parameter x. a = κa f (α xb) γa xa x. b = κb f (xa) γb xb xa x. a = 0 xa x. a = 0 x. b = 0 xb 0 xa x. a = 0 x. b = 0 xb 0 α = 1 value of α x. b = 0 xb 0 α = 0 33

34 Construction of cross inhibition network Construction of cross inhibition network in vivo Gardner et al. (2000), Nature, 403(6786): Differential equation model of network. α1 u = u β 1 + v. α2 v = v γ 1 + u 34

35 Experimental test of model Experimental test of mathematical model (bistability and switching) Gardner et al. (2000), Nature, 403(6786):

36 Bacteriophage λ infection of E. coli Response of E. coli to phage λ infection involves decision between alternative developmental pathways: lysis and lysogeny Ptashne, A Genetic Switch, Cell Press,

37 Bistability in phage λ Lytic and lysogenic pathways involve different patterns of gene expression Ptashne, A Genetic Switch, Cell Press,

38 Control of phage λ fate decision Cross inhibition feedback between CI and Cro plays key role in establishment of lysis or lysogeny Induction of lysis after DNA damage Santillán, Mackey (2004), Biophys. J., 86(1):

39 Simple model of phage λ fate decision Differential equation model of cross inhibition feedback network involved in phage λ fate decision mrna and protein, delays, thermodynamic description of gene regulation Santillán, Mackey (2004), Biophys. J., 86(1):

40 Analysis of phage λ model Bistability (lysis and lysogeny) only occurs for certain parameter values Switch from lysogeny to lysis involves bifurcation from one monostable regime to another, due to change in degradation constant Santillán, Mackey (2004), Biophys. J., 86(1):

41 Extended model of phage λ infection Differential equation model of the extended network underlying decision between lysis and lysogeny McAdams, Shapiro (1995), Science, 269(5524):

42 Simulation of phage λ infection Numerical simulation of promoter activity and protein concentrations in (a) lysogenic and (b) lytic pathways Cell follows one of two pathways for different initial conditions 42

43 Measurements of phage λ infection Use of fluorescent reporter genes to follow phage promoters over time, both in populations and in individual cells Kobiler et al. (2005), Proc. Natl. Acad. Sci. USA, 102(12): Amir et al. (2007), Mol. Syst. Biol., 3:71 43

44 Challenges for modelers ODE models provide well developed theoretical framework, but difficult to apply due to lack of quantitative data on parameters Genetic regulatory networks are basically systems of biochemical reactions: different types of models to take into account noise and stochasticity Mostly small networks have been studied, by upscaling to large networks of dozens or even hundreds of genes, proteins, metabolites, From model systems to organisms of medical and biotechnical interest 44

45 Qualitative Modelling and Simulation of Bacterial Regulatory Networks Hidde de Jong1 Delphine Ropers1 Johannes Geiselmann1,2 1 2 INRIA Grenoble Rhône Alpes Laboratoire Adaptation Pathogénie des Microorganismes CNRS UMR 5163 Université Joseph Fourier Hidde.de-Jong@inrialpes.fr Object 3

46 Overview 1. Bacterial regulatory networks: carbon starvation response in E. coli 2. Qualitative simulation of genetic regulatory networks using piecewise linear models 3. Qualitative simulation of carbon starvation response in Escherichia coli: model predictions and validation 4. Perspectives 46

47 Escherichia coli stress responses E. coli is able to adapt to a variety of stresses in its environment Model organism for understanding of decision making processes in single cell organisms E. coli is easy to manipulate in the laboratory Model organism for understanding adaptation of pathogenic bacteria to their host Storz and Hengge Aronis (2000), Bacterial Stress Responses, ASM Press Heat shock Nutritional stress Cold shock Osmotic stress 2 µm 47

48 Response of E. coli to carbon starvation Response of E. coli to carbon starvation conditions: transition from exponential phase to stationary phase Changes in morphology, metabolism, gene expression, log (pop. size) > 4 h time 48

49 Carbon starvation response network Response of E. coli to carbon source availability is controlled by large and complex regulatory network Global regulators of transcription form backbone of network Ropers et al. (2006), Biosystems, 84(2): Network senses carbon source availability and global regulators coordinate adaptive response of bacteria 49

50 Modeling of carbon starvation network No global view of functioning of network available, despite abundant knowledge on network components Modeling and simulation indispensable for dynamic analysis of network: Understanding role of individual components and interactions Suggesting missing components and interactions Making novel predictions of system behavior Mathematical methods supported by computer tools allow modeling and simulation of network: 50

51 Modeling of carbon starvation network Well established theory for kinetic modeling of bacterial regulatory networks using ODE models Heinrich and Schuster (1996), The Regulation of Cellular Systems, Chapman & Hall Goldbeter (1997), Biochemical Oscillations and Cellular Rhythms, Cambridge University Press Szallasi et al. (2006), System Modeling in Cellular Biology, MIT Press Practical problems encountered by modelers: Knowledge on molecular mechanisms rare Quantitative information on kinetic parameters and molecular concentrations absent Large models Even in the case of well studied E. coli network! 51

52 Qualitative modeling and simulation Possible strategies to overcome problems Parameter estimation from experimental data Parameter sensitivity analysis Model simplifications Intuition: essential properties of system dynamics robust against reasonable model simplifications Qualitative modeling and simulation of large and complex genetic regulatory networks using simplified models de Jong, Gouzé et al. (2004), Bull. Math. Biol., 66(2): Relation with discrete, logical models of gene regulation Thomas and d Ari (1990), Biological Feedback, CRC Press 52

53 PL differential equation models Genetic networks modeled by class of differential equations using step functions to describe regulatory interactions x. a = κa s (xa, θa2) s (xb, θb ) γa xa x. b = κb s (xa, θa1) γb xb s (x, θ) 1 0 θ x x : protein concentration θ : threshold concentration κ, γ : rate constants Differential equation models of regulatory networks are piecewise linear (PL) Glass and Kauffman (1973), J. Theor. Biol., 39(1):

54 Mathematical analysis of PL models Analysis of dynamics of PL models maxb x. a = κa γa xa x. b = κb γb xb κb/γb θb D1 0 θa1 θa2 κa/γa maxa x. a = κa s (xa, θa2) s (xb, θb ) γa xa x. b = κb s (xa, θa1) γb xb Glass and Kauffman (1973), J. Theor. Biol., 39(1):

55 Mathematical analysis of PL models Analysis of dynamics of PL models maxb x. a = κa γa xa x. b = γb xb θb D5 0 θa1 θa2 κa/γa maxa x. a = κa s (xa, θa2) s (xb, θb ) γa xa x. b = κb s (xa, θa1) γb xb Glass and Kauffman (1973), J. Theor. Biol., 39(1):

56 Mathematical analysis of PL models Analysis of dynamics of PL models in phase space maxb θb D3 0 θa1 θa2 maxa x. a = κa s (xa, θa2) s (xb, θb ) γa xa x. b = κb s (xa, θa1) γb xb Extension of PL differential equations to differential inclusions using Filippov approach Gouzé and Sari (2002), Dyn. Syst., 17(4):

57 Mathematical analysis of PL models Analysis of dynamics of PL models in phase space maxb θb 0 D7 θa1 θa2 maxa x. a = κa s (xa, θa2) s (xb, θb ) γa xa x. b = κb s (xa, θa1) γb xb Extension of PL differential equations to differential inclusions using Filippov approach Gouzé and Sari (2002), Dyn. Syst., 17(4):

58 Qualitative analysis of network dynamics Phase space partition: unique derivative sign pattern in regions Discrete abstraction yields state transition graph Alur et al. (2000), Proc. IEEE, 88(7): maxb θb 0 D20 D18 D16 D10 D21 D19 D17 D11 D24 D23 D25 D26 D27 D22 D12 D13 D14 D15 D1 D3 D5 D7 D9 D D D θa1 2 4 D θa2 6 8 maxa D21 D24 D19 D23 D17 D22 D20 D 18 D16 D10 D11 D25 D12 D1 x. a > 0 1 D : x. > 0 b D3 D2 D13 D27 D26 D15 D14 D9 D5 D7 D4 D6 x.a > 0 D5: x. < 0 b D8 x.a = 0 D : x. < 0 b 7 State transition graph conservative approximation of continuous dynamics Batt et al. (2008), Automatica, 44(4):

59 Qualitative analysis of network dynamics State transition graph invariant for parameter constraints maxb κb/γb θb D11 1 D 0 D11 D12 D 3 D θa1 D12 1 D3 0 < θa1 < θa2 < κa/γa < maxa 0 < θb < κb/γb < maxb θa2 κa/γa maxa 59

60 Qualitative analysis of network dynamics State transition graph invariant for parameter constraints maxb κb/γb θb D11 1 D 0 D11 D12 D 3 D θa1 D12 1 D3 0 < θa1 < θa2 < κa/γa < maxa 0 < θb < κb/γb < maxb θa2 κa/γa maxa 60

61 Qualitative analysis of network dynamics State transition graph invariant for parameter constraints maxb κb/γb θb D11 1 D 0 D11 D12 D 3 D κb/γb 0 D3 1 D11 D12 D1 3 D κa/γa θa1 0 < θb < κb/γb < maxb 0 < κa/γa < θa1 < θa2 < maxa D11 D1 0 < θa1 < θa2 < κa/γa < maxa θa2 κa/γa maxa θa1 maxb θb D12 θa2 maxa 0 < θb < κb/γb < maxb Batt et al. (2008), Automatica, 44(4):

62 Use of state transition graph Analysis of steady states and limit cycles of PL models Attractor states in graph correspond (under certain conditions) to stable Casey et al. (2006), J. Math Biol., 52(1):27 56 steady states of PL model Attractor cycles in graph correspond (under certain conditions) to stable Glass and Pasternack (1978), J. Math Biol., 6(2): limit cycles of PL model Edwards (2000), Physica D, 146(1 4): maxb D24 D19 D23 D D17 D22 18 D16 θb 0 D21 D20 D10 θa1 θa2 maxa D11 D25 D12 D1 D3 D2 D13 D26 D14 D5 D7 D4 D6 D27 D15 D9 D8 62

63 Use of state transition graph Determine reachability of attractors of PL models from given initial states: qualitative simulation D D D19 D23 D17 D22 21 D20 D 18 D16 D10 D11 Kuipers (1994), Qualitative Reasoning, MIT Press 24 D25 D12 D1 D3 D2 D13 D26 D27 D15 D14 D5 D7 D4 D6 D9 D8 Simulation algorithms based on symbolic computation instead of numerical simulation Use of inequality constraints between parameters 63

64 Use of state transition graph Paths in state transition graph represent predicted sequences of qualitative events Model validation: comparison of predicted and observed sequances of qualitative events D xa D18 D16 0 time xb 0 21 D24 D19 D23 D17 D22 D20 Concistency?.. x > 0 xa > 0 b.. x > 0 xa < 0 b time Yes D10 D11 D25 D12 D1 x. a > 0 1 D:. xb > 0 D3 D2 D13 D27 D26 D5 D7 D4 D6 x.a < 0 D17: x. > 0 b D15 D14 D9 D8 x. a= 0 D : x. = 0 b 18 Need for automated and efficient tools for model validation 64

65 Model validation by model checking Dynamic properties of system can be expressed in temporal logic (CTL) x a.. There Exists a Future state where xa > 0 and xb > 0 and starting from that state,.. there Exists a Future state where xa < 0 and xb > EF(xa > 0 xb > 0 EF(xa < 0 xb > 0) ) 0 time xb 0.. x > 0 xa > 0 b.. x > 0 xa < 0 time b Model checking is automated technique for verifying that state transition graph satisfies temporal logic statements Efficient computer tools available for model checking Batt et al. (2005), Bioinformatics, 21(supp. 1): i19 i28 Monteiro et al. (2008), Bioinformatics, in press 65

66 Genetic Network Analyzer (GNA) Qualitative analysis of PL models implemented in Java: Genetic Network Analyzer (GNA) Distribution by Genostar SA de Jong et al. (2003), Bioinformatics, 19(3): helix.inrialpes.fr/gna 66

67 Analysis of bacterial regulatory networks Applications of qualitative simulation: Initiation of sporulation in Bacillus subtilis de Jong, Geiselmann et al. (2004), Bull. Math. Biol., 66(2): Quorum sensing in Pseudomonas aeruginosa Viretta and Fussenegger, Biotechnol. Prog., 2004, 20(3): Onset of virulence in Erwinia chrysanthemi Sepulchre et al., J. Theor. Biol., 2007, 244(2):

68 Analysis of carbon starvation network Objective: better understanding of functioning of carbon starvation response network in E. coli Combined use of models and experiments Which network components and which interactions have to be taken into account? Start with the simplest possible representation of network Consider key global regulators for carbon starvation response, such as Fis, CRP camp, and DNA supercoiling level Gutierrez Ríos et al. (2007), BMC Microbiol., 7:53 68

69 Simple representation of network Simple representation of carbon starvation response network structured around key global regulators Ropers et al. (2006), Biosystems, 84(2):

70 Modeling of carbon starvation network Can we make sense of the carbon starvation response of E. coli using this simple network? How do global regulators bring about growth arrest when carbon sources are running out? Translation of biological data into a mathematical model 70

71 Modeling of carbon starvation network Nonlinear ODE model of 12 variables and 46 parameters Regulation of gene expression (Hill) Enzymatic reactions (Michaelis Menten and mass action) Formation of biochemical complexes (mass action) 71

72 Modeling of carbon starvation network Model reduction strategies to obtain PL models ODE model 12 variables, 46 parameters Quasi steady state approximation Reduced ODE model Piecewise linear approximation PLDE model Reduced model are easier to analyze, little loss of precision 72

73 Modeling of carbon starvation network 73

74 Modeling of carbon starvation network Model reduction strategies to obtain PL models ODE model Fast 12 variables, 46 parameters Quasi steady state approximation Reduced ODE model 7 variables, 43 parameters Slow Piecewise linear approximation PLDE model 7 variables, 36 parameter inequalities Reduced model are easier to analyze, little loss of precision 74

75 Steady states of carbon starvation model Analysis of steady states of PL model of carbon starvation network: two stable steady states Steady state corresponding to exponential phase conditions Steady state corresponding to stationary phase conditions 75

76 Simulation of stress response network Qualitative simulation of carbon starvation response State transition graph with 27 states, paths converge to stationary phase steady state CRP GyrAB TopA CYA rrn FIS Signal 76

77 Insight into carbon starvation response Role of the mutual inhibition of Fis and CRP camp in the adjustment of growth of cells following carbon starvation 77

78 Validation of carbon starvation model Validation of model using model checking Fis concentration decreases and becomes steady in stationary phase Ali Azam et al. (1999), J. Bacteriol., 181(20): EF(xfis < 0 EF(xfis = 0 xrrn < θrrn) ) True cya transcription is negatively regulated by the complex camp CRP Kawamukai et al. (1985), J. Bacteriol., 164(2): AG(xcrp > θ3crp xcya > θ3cya xs > θs EF xcya < 0) True DNA supercoiling decreases during transition to stationary phase.. EF( (xgyrab < 0 xtopa > 0) xrrn < θrrn) Balke, Gralla (1987), J. Bacteriol., 169(10): False 78

79 Suggestion of missing interaction Model does not reproduce observed downregulation of negative supercoiling Missing interaction in the network? 79

80 Extension of stress response network Model does not reproduce observed downregulation of negative supercoiling Missing component in the network? 80

81 Novel predictions Qualitative simulation also yields predictions that cannot be verified with currently available experimental data Damped oscillations at reentry into exponential phase after carbon upshift 81

82 Perspectives: experimental verification Real time monitoring of gene expression using fluorescent and luminescent reporter gene systems E. coli genome Global regulator excitation Reporter gene GFP emission 82

83 Perspectives: network identification Adaptation of methods for hybrid systems identification to PL models of genetic regulatory networks Time series data Switch detection Mode estimation Threshold reconstruction Network inference Drulhe et al. (2008), IEEE Trans. Autom. Control, 53(1): Porreca et al. (2008), J. Comput. Biol., in press 83

84 Perspectives: control and redesign Development of control strategies that interfere with adaptive capacity of bacteria by adding synthetic control networks Sensors of physiological state that activate/inhibit regulators of stress response genes A B Collaboration INRIA INSERM 84

85 Conclusions Modeling of bacterial regulatory networks often hampered by lack of information on parameter values Use of coarse grained PL models that provide reasonable approximation of dynamics Mathematical methods and computer tools for analysis of qualitative dynamics of PL models Weak information on parameter values (inequality constraints) Use of PL models may gain insight into functioning of large and complex networks PL models provide first idea of qualitative dynamics that may guide modeling by means of more accurate models 85

86 Contributors and sponsors Grégory Batt, INRIA Rocquencourt Valentina Baldazzi, INRIA Grenoble Rhône Alpes Guillaume Baptist, Université Joseph Fourier, Grenoble Bruno Besson, INRIA Grenoble Rhône Alpes Hidde de Jong, INRIA Grenoble Rhône Alpes Estelle Dumas, INRIA Grenoble Rhône Alpes Johannes Geiselmann, Université Joseph Fourier, Grenoble Jean Luc Gouzé, INRIA Sophia Antipolis Radu Mateescu, INRIA Grenoble Rhône Alpes Pedro Monteiro, INRIA Grenoble Rhône Alpes/IST Lisbon Michel Page, INRIA Grenoble Rhône Alpes/Université Pierre Mendès France, Grenoble Corinne Pinel, Université Joseph Fourier, Grenoble Caroline Ranquet, Université Joseph Fourier, Grenoble Delphine Ropers, INRIA Grenoble Rhône Alpes Object 4 Ministère de la Recherche, IMPBIO program European Commission, FP6, NEST program INRIA, ARC program Agence Nationale de la Recherche, BioSys program 86

87 Internships at INRIA Challenging problems for biologists, computer scientists, mathematicians, physicists, in a multidisciplinary working environment. Contact: Hidde.de Jong@inria.fr Courtesy Guillaume Baptist (2008) 87