Transcript Qualitative Simulation of Genetic Regulatory Networks

Qualitative Simulation of the Carbon
Starvation Response in Escherichia coli
Delphine Ropers1 Hidde de Jong1
Johannes Geiselmann1,2
1INRIA Rhône-Alpes
2Laboratoire Adaptation
Pathogénie des Microorganismes
Faculté de Médecine et Pharmacie
Université Joseph Fourier CNRS UMR 5163
Email: [email protected]
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
2
Escherichia coli
 The average human gut contains about 1 kg of bacteria

Normally, approximatively 0.1% are E. coli
1 µm
2 µm
Rocky Mountain Laboratories, NIAID, NIH

E. coli, along with other enterobacteria, synthesize vitamins which
are absorbed by our body (e.g., vitamin K, B-complex vitamins)
3
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
Storz and Hengge-Aronis (2000), Bacterial Stress Responses, ASM Press
Heat shock
Nutritional stress
Cold shock
Osmotic stress
…
4
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)
>4h
time
5
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
6
Analysis of carbon starvation response
 Modeling and experimental studies directed at understanding
how network controls 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

7
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
protein
P
P
gene
fis
gyrAB
P1-P’1 P2
cya
promoter
FIS
GyrAB
CYA
DNA
supercoiling
cAMP•CRP
TopA
CRP
tRNA
rRNA
P1-P4
Signal (lack of carbon source)
topA
P1 P2
rrn
P1
P2
crp
Ropers et al. (2006),
BioSystems, 84(2):124-152
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 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, …
9
Modeling of carbon starvation network
 Modular structure of carbon starvation network
P
fis
gyrAB
P
P1-P’1
P2
cya
FIS
GyrAB
CYA
Supercoiling
Activation
Superhelical
density of DNA
CRP•cAMP
TopA
Signal (lack of carbon source)
CRP
tRNA
rRNA
P1-P4
topA
P1
P2
rrn
P1
P2
crp
Ropers et al. (2006),
BioSystems, 84(2):124-152
10
Modeling of carbon starvation network
 Can the initial model explain the carbon starvation response
of E. coli cells?
P
P
fis
gyrAB
P1-P’1 P2
cya
FIS
GyrAB
CYA
DNA
supercoiling
cAMP•CRP
TopA
Signal (lack of carbon source)
CRP
tRNA
rRNA
P1-P4
topA
P1 P2
rrn
P1
P2
crp
 Translation of biological data into a mathematical model
11
Modeling of carbon starvation network
 Ordinary differential equations to describe evolution of
concentration of network components
Good compromise between expressiveness of formalism and available data
 Kinetic ODE model of 12 variables and 46 parameters

Regulation of gene expression (Hill)

Formation of biochemical complexes (mass action)

Enzymatic reactions (Michaelis-Menten)
12
Modeling of carbon starvation network
13
Modeling of carbon starvation network
 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
14
From nonlinear kinetic model to PL model
 Model simplification consists in reducing classical nonlinear
kinetic model to PL model
Nonlinear kinetic model
Time-scale separation
Nonlinear reduced kinetic model
Piecewise-linear approximation
Piecewise-linear model
15
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
Schneider et al. (2003), Curr. Opin. Microbiol., 6:151-156
RNA PolRNA Pol
FIS
P1
P2
rrn
stable RNAs
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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
Schneider et al. (2003), Curr. Opin. Microbiol., 6:151-156
Nonlinear model:
FIS
.
xrrn  rrn1 h+( xFIS , FIS ,n) + rrn2 – rrn xrrn
h+(
P1 P2
xFIS , FIS ,n) 
rrn
stable RNAs
FIS
xFIS n
xFIS n + θFISn
Piecewise-linear model:
.
xrrn  rrn1 s+( xFIS , FIS ) + rrn2 – rrn xrrn
rrn2  rrn  rrn,
(rrn1 + rrn2)  rrn  rrn
17
Modeling of crp regulation by CRP·cAMP
 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
Barnard et al. (2004), Curr. Opin. Microbiol., 7:102-108
RNA Pol RNA Pol
P1
P2
crp
CRP• cAMP
crp mRNAs
CRP
18
Modeling of crp regulation by CRP·cAMP
 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
Barnard et al. (2004), Curr. Opin. Microbiol., 7:102-108
 Formation of CRP•cAMP in presence of carbon starvation
signal CYA
ATP + CYA*
CRP• cAMP
Activation
K1
CYA*•ATP
k2
CYA* + cAMP
k3
degradation/export
Signal
cAMP + CRP
K4
CRP•cAMP
CRP
P1
P2
crp
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Modeling of crp regulation by CRP·cAMP
CYA
Nonlinear model:
.
xCYA* ·ATP  ….
Mass-action kinetics
x. CYA*  … ….
.
xCRP·cAMP  … ….

.
xCRP  CRP 1 + CRP 2 h+( xCRP·cAMP , CRP·cAMP ,n) – CRP xCRP ·
CRP• cAMP
Activation
Signal
CRP
P1
P2
crp
Reduced nonlinear model:
xCRP · cAMP =
k2 xCYA xCRP
k2 xCYA + k3 K4
Quasi-steady-state approximation
.
xCRP ·  CRP1 + CRP2 h+( xCRP·cAMP , CRP·cAMP ,n) – CRP xCRP ·
Piecewise-linear model:
CYA concentration (M)
CRP concentration (M)
.
xCRP  CRP1 + CRP2 s+(xCYA , CYA1) s+(xCRP , CRP1) s+(xSIGNAL , SIGNAL) – CRP xCRP .
20
Model of carbon starvation network
 PLDE model of 7 variables and 36 parameter inequalities
21
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
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Simulation of stress response network
 Simulation of transition from exponential to stationary phase
State transition graph with 27 states, 1 stable steady state
CRP
GyrAB
TopA
CYA
rrn
FIS
Signal
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Insight into nutritional stress response
 Sequence of qualitative events leading to adjustment of
growth of cell after nutritional stress signal
Role of the mutual inhibition of Fis and CRP•cAMP
P
fis
gyrAB
P
P1-P’1
P2
cya
FIS
GyrAB
CYA
Supercoiling
Activation
Superhelical
density of DNA
CRP•cAMP
TopA
Signal (lack of nutrients)
CRP
tRNA
rRNA
P1-P4
topA
P1
P2
rrn
P1
P2
crp
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Validation of carbon starvation response 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):6361-6370
.
.
EF(xfis < 0  EF(xfis = 0  xrrn < rrn) )
True

“cya transcription is negatively regulated by the complex cAMP-CRP”
Kawamukai et al. (1985), J. Bacteriol., 164(2):872-877
.
AG(xcrp > 3crp  xcya > 3cya  xs > s → EF xcya < 0)

True
“DNA supercoiling decreases during transition to stationary phase”
Balke, Gralla (1987), J. Bacteriol., 169(10):4499-4506
.
.
EF( (xgyrAB < 0  xtopA > 0)  xrrn < rrn)
False
25
Suggestion of missing interaction
 Model does not reproduce observed downregulation of negative
supercoiling
Missing interaction in the network?
P
fis
gyrAB
P
P1-P’1
P2
cya
FIS
GyrAB
CYA
Supercoiling
Activation
Superhelical
density of DNA
CRP•cAMP
TopA
Signal (lack of nutrients)
CRP
tRNA
rRNA
P1-P4
topA
P1
P2
rrn
P1
P2
crp
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Extension of stress response network
 Model does not reproduce observed downregulation of negative
supercoiling
Missing component in the network?
P
P
P1 P2nlpD
gyrAB
P1-P’1 P2
σS
GyrAB
CYA
Supercoiling
gyrI
Activation
TopA
P5 P1-P4
Ropers et al. (2006)
rpoS
cya
FIS
GyrI
P
fis
Stress
signal
RssB
CRP
tRNA
rRNA
topA
P1
P1 P2
rrn
P2
crp
PA
rssA PB rssB
27
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
.
.
xa
xa = 0
xa
xa = 0
A
a
B
a
.
b
.
xb = 0
0
xb
xb = 0
0
b
xb
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Preliminary results
 Analysis of subsystem of carbon starvation response network
CYA
CRP• cAMP
Activation
Signal
CRP
P1
P2
crp
 Good correspondence of qualitative dynamics of reduced NL
and PL models
29
Reporter gene systems
 Simulations yield predictions that cannot be verified with
currently avaliable experimental data
 Use of reporter gene systems to monitor gene expression
rrnB
fis
promoter region
crp
bla
nlpD
rpoS
gfp or lux
reporter
gene
cloning promoter
regions on plasmid
topA
gyrB
ori
gyrA
30
Monitoring of gene expression
 Integration of fluorescent or luminescent reporter gene systems
into bacterial cell
E. coli
genome
Global
regulator
E. coli
genome
Global
regulator
emission
excitation
Reporter
gene
Reporter
operon
GFP
emission
Luciferase
 Expression of reporter gene reflects expression of host gene of
interest
31
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
Well with
bacterial
culture
Different gene reporter
system in wells
96-well microplate
 Upshift experiments in M9/glucose medium
32
Analysis of reporter gene expression data
 Wellreader: Matlab program for analysis of reporter gene
expression data
luminescence intensity
fis reporter
33
Data analysis issues
 Outlier detection
 Data smoothing and interpolation by means of cubic
smoothing splines
 Computation of reporter concentration, promoter activity, host
protein concentration
34
Preliminary results on model validation
 Validation of E. coli carbon starvation response model by
means of time-course expression data
fis
topA
crp
gyrB
rrnB
rpoS
35
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 welladapted 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
36
Further work
 Monitoring reporter-gene expression in single cell
Collaboration with Irina Mihalcescu (Université Joseph Fourier, Grenoble)
 Extensions of carbon starvation model


Inclusion of additional global regulators involved in carbon starvation
response
Composite models of E. coli stress response on genetic and metabolic
level
Collaboration with Daniel Kahn (INRIA Rhône-Alpes, Lyon)
37
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
38
39
Insight into response to carbon upshift
 Sequence of qualitative events leading to adjustment of cell
growth after a carbon upshift
Role of the negative feedback loop involving Fis and DNA supercoiling
P
fis
gyrAB
P
P1-P’1
P2
cya
FIS
GyrAB
CYA
DNA
supercoiling
cAMP•CRP
TopA
Signal (lack of carbon)
CRP
tRNA
rRNA
P1-P4
topA
P1
P2
rrn
P1
P2
crp
40