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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
40
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
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