Qualitative Simulation of the Carbon Starvation Response in Escherichia coli

Delphine Ropers1 Hidde de Jong1 Johannes Geiselmann1,2

1INRIA Rhône-Alpes2Laboratoire Adaptation Pathogénie des Microorganismes

Faculté de Médecine et PharmacieUniversité Joseph Fourier CNRS UMR 5163

Email: Delphine.Ropers@inrialpes.fr

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

3

Escherichia coli

Rocky Mountain Laboratories, NIAID, NIH2 µm

1 µm

4

Escherichia coli stress responses E. 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

5

Nutritional stress response in E. coli

Response 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

6

Network controlling stress response Response 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

No global view of functioning of network available, despite abundant knowledge on network components

7

Analysis of carbon starvation response

Which network components and which interactions to take into account?

Impossible to model the whole network

E. coli genome: ~4500 genes (~150 transcription factor genes)

Start with the simplest possible representation of the carbon

starvation response in E. coli

Modeling and experimental studies directed at understanding how network controls carbon starvation response

8

Analysis of carbon starvation response Modeling and experimental studies directed at understanding

how network controls carbon starvation response

Bottom-up strategy:

1) Initial model of carbon starvation response

rrnP1 P2

CRP

crp

cya

CYA

cAMP•CRP

FIS

TopA

topA

GyrAB

P1-P4P1 P2

P2P1-P’1

P

gyrABP

Signal (lack of carbon source)DNA

supercoiling

fis

tRNArRNA

Ropers et al. (2006),BioSystems, 84(2):124-152

protein

gene

promoter

9

Analysis of carbon starvation response

Bottom-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, …

Modeling and experimental studies directed at understanding how network controls carbon starvation response

10

Modular structure of carbon starvation network

Superhelical density of DNA

rrnP1 P2

Activation

CRP

crp

cya

CYA

CRP•cAMP

FIS

TopA

topA

GyrAB

P1-P4P1 P2

P2P1-P’1

P

gyrABP

Signal (lack of carbon source)Supercoiling

fis

tRNArRNA

Ropers et al. (2006),BioSystems, 84(2):124-152

Modeling of carbon starvation network

11

Modeling of carbon starvation network Can the initial model explain the carbon starvation response of E. coli cells?

Translation of biological data into a mathematical model

rrnP1 P2

CRP

crp

cya

CYA

cAMP•CRP

FIS

TopA

topA

GyrAB

P1-P4P1 P2

P2P1-P’1

P

gyrABP

Signal (lack of carbon source)DNA

supercoiling

fis

tRNArRNA

12

Modeling of carbon starvation network

13

Modeling of carbon starvation network

14

Current constraints on kinetic modeling of E. coli network:

• Knowledge on molecular mechanisms incomplete

• Quantitative information on kinetic parameters and molecular

concentrations mostly absent

Possible strategies to overcome the constraints

• Parameter sensitivity analysis

• Model simplifications

Intuition: essential properties of system dynamics robust against moderate changes in kinetic parameters and rate laws

Modeling of carbon starvation network

15

From nonlinear kinetic model to PL model

Model 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

16

RNA Pol

FIS

RNA Pol

Modeling of rrn regulation Regulatory mechanism of FIS control of promoter rrn P1

FIS binds to multiple sites in promoter region

FIS forms a cooperative complex with RNA polymerase

P1 P2 rrn

stable RNAs

Schneider et al. (2003), Curr. Opin. Microbiol., 6:151-156

17

Nonlinear model:

Modeling of rrn regulation

FIS

rrnP1 P2

stable RNAs

Schneider et al. (2003), Curr. Opin. Microbiol., 6:151-156

Regulatory mechanism of FIS control of promoter rrn P1 FIS binds to multiple sites in promoter region

FIS forms a cooperative complex with RNA polymerase

.xrrn rrn1 h+( xFIS , FIS ,n) + rrn

2 – rrn xrrn

xFIS n + θFIS

n

xFIS n

h+( xFIS , FIS ,n)

FISPiecewise-linear model:

.xrrn rrn1 s+( xFIS , FIS ) + rrn

2 – rrn xrrn

rrn2 rrn rrn, (rrn

1 + rrn2) rrn rrn

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CRP• cAMP

RNA PolRNA Pol

Modeling of crp regulation by CRP·cAMP

Barnard et al. (2004), Curr. Opin. Microbiol., 7:102-108

crpP1 P2

Regulatory mechanism of CRP•cAMP control of crp P2 promoter CRP•cAMP binds to a single site CRP•cAMP forms a cooperative complex with RNA polymerase

CRP

crp mRNAs

19

Modeling of crp regulation by CRP·cAMP

Barnard et al. (2004), Curr. Opin. Microbiol., 7:102-108

CRP• cAMP Activation

CRP

CYA

Signal

crpP1 P2

Regulatory mechanism of CRP•cAMP control of crp P2 promoter CRP•cAMP binds to a single site CRP•cAMP forms a cooperative complex with RNA polymerase

Formation of CRP•cAMP in presence of carbon starvation signal

ATP + CYA*K1

CYA*•ATP CYA* + cAMP

cAMP + CRPK4

k2

CRP•cAMP

k3degradation/export

20

Modeling of crp regulation by CRP·cAMP

Nonlinear model:xCYA* ·ATP ….

xCRP CRP 1 + CRP

2 h+( xCRP·cAMP , CRP·cAMP ,n) – CRP xCRP ·

xCYA* … ….

.

.

.

.xCRP·cAMP … ….

.

Piecewise-linear model:

xCRP CRP1 + CRP

2 s+(xCYA , CYA1) s+(xCRP , CRP

1) s+(xSIGNAL , SIGNAL) – CRP xCRP .

CYA concentration (M) CRP concentration (M)

CRP• cAMP Activation

CRP

CYA

Signal

crpP1 P2

Mass-action kinetics

Reduced nonlinear model:

k2 xCYA + k3 K4

k2 xCYA xCRP

xCRP · cAMP =

xCRP · CRP1 + CRP

2 h+( xCRP·cAMP , CRP·cAMP ,n) – CRP xCRP ·.

Quasi-steady-state approximation

21

Model of carbon starvation network

PLDE model of 7 variables and 36 parameter inequalities

22

Attractors of stress response network

Analysis of attractors of PL model: two steady states

• Stable steady state, corresponding to exponential-phase conditions

• Stable steady state, corresponding to stationary-phase conditions

23

Simulation of stress response network

Simulation of transition from exponential to stationary phase

State transition graph with 27 states, 1 stable steady state

CYA

FIS

GyrAB

Signal

TopA

rrn

CRP

24

Insight into nutritional stress response

Sequence of qualitative events leading to adjustment of growth of cell after nutritional stress signal

Superhelical density of DNA

rrnP1 P2

Activation

CRP

crp

cya

CYA

CRP•cAMP

FIS

TopA

topA

GyrAB

P1-P4P1 P2

P2P1-P’1

P

gyrABP

Signal (lack of nutrients)Supercoiling

fis

tRNArRNA

Role of the mutual inhibition of Fis and CRP•cAMP

25

Validation of carbon starvation response model

Validation of model using model checking “Fis concentration decreases and becomes steady in stationary phase”

“cya transcription is negatively regulated by the complex cAMP-CRP”

“DNA supercoiling decreases during transition to stationary phase”

EF(xfis < 0 EF(xfis = 0 xrrn < rrn) ). .

TrueAG(xcrp > 3crp xcya > 3

cya xs > s → EF xcya < 0).

True

FalseEF( (xgyrAB < 0 xtopA > 0) xrrn < rrn). .

Ali Azam et al. (1999), J. Bacteriol., 181(20):6361-6370

Kawamukai et al. (1985), J. Bacteriol., 164(2):872-877

Balke, Gralla (1987), J. Bacteriol., 169(10):4499-4506

26

Suggestion of missing interaction Model does not reproduce observed downregulation of negative

supercoiling

Superhelical density of DNA

rrnP1 P2

Activation

CRP

crp

cya

CYA

CRP•cAMP

FIS

TopA

topA

GyrAB

P1-P4P1 P2

P2P1-P’1

P

gyrABP

Signal (lack of nutrients)Supercoiling

fis

tRNArRNA

Missing interaction in the network?

27

Extension of stress response network

Activation Stress signal

CRP

crp

cya

CYA

fis

FIS

Supercoiling

TopA

topA

GyrAB

P1-P4P1 P2

P2P1-P’1

rrnP1 P2

P

gyrABP

tRNArRNA

Ropers et al. (2006)

GyrI

gyrIP

rpoSP1 P2nlpD

σS

RssB

rssAPA PB rssB

P5

Missing component in the network?

Model does not reproduce observed downregulation of negative supercoiling

28

Assessment of model reduction

Monte-Carlo simulation studies to compare qualitative dynamics of NL and PLDE models

Generate random parameter and initial conditions sets and numerically

simulate NL model

Check whether sequences of derivative sign patterns of numerical

solutions are included in transition graph for PLDE model

xb

xa

0

xb = 0 .

xa = 0 .

b

B

a

A

xb

xa

0

xb = 0 .

xa = 0 .

b

a

29

Analysis of subsystem of carbon starvation response network

Good correspondence of qualitative dynamics of reduced NL and PL models

Preliminary results

CRP• cAMP Activation

CRP

CYA

Signal

crpP1 P2

30

Reporter gene systems

Use of reporter gene systems to monitor gene expression

promoter region

bla

ori

gfp or luxreporter

gene

cloning promoter regions on plasmid

Simulations yield predictions that cannot be verified with currently avaliable experimental data

rrnB

fis

crp

rpoS

topA

gyrB

gyrA

nlpD

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

Expression of reporter gene reflects expression of host gene of interest

Global regulator

Luciferase

E. coli genome

Reporter operon

emission

32

Real-time monitoring: microplate reader Use of automated microplate reader to monitor in parallel in

single experiment expression of different reporter genes fluorescence/luminescent intensity

absorbance (OD) of bacterial culture

Upshift experiments in M9/glucose medium

96-well microplate

Well withbacterial culture

Different gene reporter system in wells

33

Analysis of reporter gene expression data

Wellreader: Matlab program for analysis of reporter gene expression data

fis reporter

luminescence intensity

34

Data analysis issues

Outlier detection

Data smoothing and interpolation by means of cubic smoothing splines

Computation of reporter concentration, promoter activity, host protein concentration

35

Preliminary results on model validation

Validation of E. coli carbon starvation response model by means of time-course expression data

fis crp gyrB

topA rrnB rpoS

36

Conclusions

Understanding of functioning and development of living organisms requires analysis of genetic regulatory networks

From structure to behavior of networks

Need for mathematical methods and computer tools well-adapted to available experimental data

Coarse-grained models and qualitative analysis of dynamics

Biological relevance attained through integration of modeling and experiments

Models guide experiments, and experiments stimulate models

37

Further work

38

Contributors and sponsorsGrégory 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

39

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Insight into response to carbon upshift

Sequence of qualitative events leading to adjustment of cell growth after a carbon upshift

rrnP1 P2

CRP

crp

cya

CYA

cAMP•CRP

FIS

TopA

topA

GyrAB

P1-P4P1 P2

P2P1-P’1

P

gyrABP

Signal (lack of carbon)

DNA supercoiling

fis

tRNArRNA

Role of the negative feedback loop involving Fis and DNA supercoiling