Mod
Mod
é
é
lisation
lisation
, simulation et
, simulation et
analyse
analyse
qualitatives
qualitatives
de
de
r
r
é
é
seaux d'interactions
seaux d'interactions
,
,
application au cycle
application au cycle
cellulaire mammif
cellulaire mammif
è
è
re
re
Claudine Chaouiya
Technologies Avancées pour le Génome et la Clinique
(TAGC) INSERM ERM 206, Luminy Marseille - France
Contents
Contents
1.
Motivation
2.
Logical modelling of regulatory networks
The formalism
GINsim, a dedicated software
Recent developments to handle large models
3.
Dynamical analysis of a generic Boolean model for the
control of the mammalian cell cycle
Daughter
cell(s)
DNA
synthesis
Mitosis
Resting state
S
G2
M
G0
G1
Eukaryotic cell
DNA
synthesis
Resting state
S
G2
M
G0
G1
Restriction point
Spindle
checkpoint
G2/M
Daughter
cell(s)
Mitosis
Checkpoints
Checkpoints
Eukaryotic cell
S
G2
M
G0
G1
Rb
E2F
Cyclin D
Cdk4/6
APC/Cdc20
APC/Cdh1
Cyclin A
Cdk1/2
Cyclin B
Cdk1
p27
Cyclin E
Cdk2
Rb
p27
Main
Main
molecular actors
molecular actors
Eukaryotic cell
Kohn
Dynamical modelling
Dynamical modelling
Why ?
To build an integrated and coherent synthesis
To gain rigorous global, functional understanding
To predict the behaviour of the system in new situations
To design interesting new experiments
How ?
Regulatory graphs
Qualitative
modelling: Boolean or
logical
formalisms
Quantitative modelling: ODE, Stochastic equations
The core oscillator
Tyson & Novak (2001),
J Theor Biol
210
: 249-63.
Yeast cell cycle
Chen
et al.
(2004),
Mol Biol Cell
15
: 3841-62.
Mammalian cell cycle
Novak & Tyson (2004),
J Theor Biol
230
: 563-79.
Limits
of the differential modelling approach:
•
Scarcity
of
quantitative information
(shape of interactions and kinetic parameters)
•
Numerical
dynamical characterisation
(simulations)
•
Scaling up
is
difficult
Motivation
Motivation
Differential modelling
Motivation
Motivation
A
B
A
B
b
b
DNA
mRNA
transcription
translation
protein
a
a
activation
inhibition
!
no c
onsu
mpti
on
"quantity" of protein
!
level of expression of the corresponding gene
Genetic regulatory networks, a schematic view
Overview of the
Overview of the
logical
logical
formalism
formalism
Regulatory Graphs
!
nodes
!
genes
G
={g
1
,g
2
,...,g
n
} set of
genes
,
regulatory products
…
for each g
i
!
expression level x
i
"
{0, max
i
}
!
arcs
!
interactions (oriented),
!
label
!
interval of expression levels of the source for which the
interaction is
operating
!
logical parameters
!
e
ffects of combinations
of regulatory actions
(given a set X of incoming interactions, K
j
(X) defines to which value
gene g
j
should tend)
R.Thomas
(1973) Boolean formalization of genetic control Circuits. JTB, 42(3):563-85.
Chaouiya C, Remy E, Mossé B, Thieffry, D (2003).
LNCIS
294
: 119-26.
Overview of the
Overview of the
logical
logical
formalism
formalism
Regulatory Graphs
!
nodes
!
genes
G
={g
1
,g
2
,...,g
n
} set of
genes
,
regulatory products
…
for each g
i
!
expression level x
i
"
{0, max
i
}
!
arcs
!
interactions (oriented),
!
label
!
interval of expression levels of the source for which the
interaction is
operating
!
logical parameters
!
e
ffects of combinations
of regulatory actions
(given a set X of incoming interactions, K
j
(X) defines to which value
gene g
j
should tend)
R.Thomas
(1973) Boolean formalization of genetic control Circuits. JTB, 42(3):563-85.
Chaouiya C, Remy E, Mossé B, Thieffry, D (2003).
LNCIS
294
: 119-26.
C
B
[2,3]
[1,1]
[1,1]
A
K
C(
A
[2,3],B
[1,1])
K
C(
A
[1,1],B
[1,1])
K
C(
B
[1,1])
K
C(
A
[2,3])
K
C(
A
[1,1])
K
C(
#
)
Overview of the
Overview of the
logical
logical
formalism
formalism
State Transition Graphs
!
nodes
!
states [x
0
,x
1,
...,x
n
]
!
arcs
!
transitions between states
(dynamics)
x
0
,x
1
...x
j
...,x
n
?
g
j
I
j
(x)
set of interactions operating on g
j
in state x
if K
j
(
I
j(x)
)
!
x
j
, gene g
j
receives a
call for updating
if K
j
(
I
j(x)
) > x
j
then g
j
is
called to increase
if
K
j
(
I
j(x)
) < x
j
then g
j
is called to decrease
$
Overview of the
Overview of the
logical
logical
formalism
formalism
State Transition Graphs
!
nodes
!
states [x
0
,x
1,
...,x
n
]
!
arcs
!
transitions between states
(dynamics)
x
0
,x
1
...x
j
...,x
n
?
g
j
I
j
(x)
set of interactions operating on g
j
in state x
C
B
[2,3]
[1,1]
[1,1]
A
1 1 0
K
C(A
[1,1],B
[1,1])=1
1 1 1
Overview of the
Overview of the
logical
logical
formalism
formalism
State Transition Graphs
!
nodes
!
states [x
0
,x
1,
...,x
n
]
!
arcs
!
transitions between states
(dynamics)
+
-
+
0
,1,
1
,1,
1
x
0
$
x
2
%
x
4
$
1
,
1
,
0
,
1
,
2
synchronous
all updating calls executed
simultaneously
synchronous / asynchronous updating assumptions
asynchronous
a unique call for updating executed at each step
lack of delay information
&
all possible transitions
generated
+
-
+
0
,1,
1
,1,
1
1
,1,1,1,1
0,1,
0
,1,1
0,1,1,1,
2
"
Logical
parameters
effects of combinations of
incoming interactions
K
B
(
#
)=0
K
B
({A,1})=1
K
B
({A,2})=0
" A graph describes the interactions between
genes or regulatory products
" Discrete levels of expression associated to
each gene (logical variables)
" Levels associated to each interaction
[1]
[1]
[1]
[2]
[1]
ABC
B
$
A
$
A
B
C
Overview of the
GINsim
GINsim
, a
, a
dedicated
dedicated
software
software
graph analysis toolbox
core simulator
GINML parser
user interface
graph
analysis
graph
editor
simulation
State transition graph
Regulatory graph
Available at
http://gin.univ-mrs.fr/GINsim
Regulatory graphs
!
A regulatory product G with n boolean regulators
!
2
n
parameters
parameters are set to 0 by default
how to ease the definition of the logical rules ?
State transition graphs
!
Goals:
determination of attractors (stable states, cyclic attractors)
reachability, properties on the trajectories
!
State explosion
"
Using the relation between properties of the regulatory graph and
induced dynamical properties
"
Limitation of the construction, yet keeping relevant properties
Handling large models
Efficient representation of the logical function
logical rules definition
state stransition graph construction
stable state determination
regulatory circuit analysis
Beyond the asynchronous / synchronous dichotomy
Handling large models
A
r
1
r
2
r
3
r
1
r
2
r
2
{0,1,2}
{0,1}
{0,1}
{0,1,2}
3*2*2 logical parameters
2
1
1
2
2
0
1
2
2
1
0
2
2
0
0
2
2
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
A
r
3r
2r
1r
2
r
3
r
3
r
3
r
3
r
3
r
3
0 0 0 1
0 1 2 2 2 2 2 2
Logical function as an OMDD
Logical function as an OMDD
A
r
1
r
2
r
3
r
1
r
2
r
2
{0,1,2}
{0,1}
{0,1}
{0,1,2}
3*2*2 logical parameters
2
1
1
2
2
0
1
2
2
1
0
2
2
0
0
2
2
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
A
r
3r
2r
1r
2
r
3
r
3
r
3
r
3
r
3
r
3
0 0 0 1
0 1 2 2 2 2 2 2
Logical function as an OMDD
Logical function as an OMDD
A
r
1
r
2
r
3
r
1
r
2
0
1
2
r
2
r
3
{0,1,2}
{0,1}
{0,1}
{0,1,2}
3*2*2 logical parameters
2
1
1
2
2
0
1
2
2
1
0
2
2
0
0
2
2
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
A
r
3r
2r
1!
7 simplified logical rules
Logical function as an OMDD
Logical function as an OMDD
Role
Role
of
of
regulatory
regulatory
circuits
circuits
A
B
C
D
Positive circuit
A
B
C
D
Negative circuit
Role
Role
of
of
regulatory
regulatory
circuits
circuits
Regulatory circuits are
simple
structures and play a crucial
role in the dynamics of biological systems
Characteristics
Positive circuits
Negative circuits
Number of repressions
Even
Odd
Dynamical property
Circuit
Circuit
functionality
functionality
For
K
A
(
#
)
=K
B
(
#
)=K
C
(
#
)=K
D
(C)=1
(all other parameters=0)
!
only
one stable state
with {A,B,C,D}=
1
0
11
Changing
K
A
(
#
)
to
0
!
two stable states
0
1
00
and
00
11
The
positive cross-inhibitory circuit
involving
B
and
C
is
functional
only in the
absence of A
.
A
B
C
Circuit
Circuit
functionality
functionality
For
K
A
(
#
)
=0
For
K
A
(
#
)
=1
The
negative cross-inhibitory circuit
involving
B
and
C
is
functional
only in the
absence of A
.
Development of a
Feedback circuit analysis algorithm
implemented
as a novel module of
GINsim
(Naldi
et al
, in preparation)
A
!
Nodes
Regulators (proteins...)
Discrete levels of expression
!
Arcs
Directed (signed) interactions
Mammalian cell
Mammalian cell
cycle
cycle
regulatory graph
regulatory graph
Fauré A, Naldi A, Chaouiya C, Thieffry D (2006). Dynamical analysis of a generic Boolean
model for the control of the mammalian cell cycle.
Bioinformatics
(ISMB’06)
22
: e124-31.
Functional relationships
between generic components
Adapted from
!
Nodes
Regulators (proteins...)
Discrete levels of expression
!
Arcs
Directed (signed) interactions
!
Logical parameters
Rules directing the dynamics
Mammalian cell
Mammalian cell
cycle
cycle
regulatory graph
regulatory graph
Adapted from
Defining the logical rules:
"
5 incoming interactions
!
up to 2
5
parameters
"
specifying logical functions covering multiple situations
...
Mammalian cell
Wild-type simulation
Wild-type simulation
In presence of Growth factors:
! unique
cyclic attractor
!
E2F
,
CycE
,
CycA
,
Cdc20
,
Cdh1
,
UbcH10
,
CycB
oscillate
!
Rb
and
p27
inactive
CycD = 1
In absence of
Growth factors
:
! unique
stable state
! (only)
Rb
,
p27
,
Cdh1
active
! quiescence
CycD = 0
Asynchronous
Synchronous
CycD
Rb
E2F CycE
CycA
p27
Cdc20
Cdh1
UbcH10
CycB
CycA
%
CycB
%
Cdh1
$
Cdh1
$
CycA
%
CycB
%
Updating assumptions
Updating assumptions
Terminal strongly
connected component
encompassing 112 states
Asynchronous
Synchronous
Synchronous
state transition
state transition
graph
graph
[CyD, Rb, E2F, CycE, CycA, p27, Cdc20, Cdh1, UbcH10, CycB]
Cdc20
$
Cdc20
%
E2F
$
CycA
%
CycB
%
Cdh1
$
CycA
$
UbcH10
%
CycE
$
E2F
%
Cdh1
%
CycE
%
UbcH10
$
CycB
$
Synchronous cycle
encompassing
7 states
[CyD, Rb, E2F, CycE, CycA, p27, Cdc20, Cdh1, UbcH10, CycB]
Cdc20
$
Cdc20
%
E2F
$
CycA
%
CycB
%
Cdh1
$
CycA
$
UbcH10
%
CycE
$
E2F
%
Cdh1
%
CycE
%
UbcH10
$
CycB
$
Synchronous cycle
encompassing
7 states
[CyD, Rb, E2F, CycE, CycA, p27, Cdc20, Cdh1, UbcH10, CycB]
Cdc20
$
Cdc20
%
E2F
$
CycA
%
CycB
%
Cdh1
$
CycA
$
UbcH10
%
CycE
$
E2F
%
Cdh1
%
CycE
%
UbcH10
$
CycB
$
Synchronous cycle
encompassing
7 states
Both
synchronous
and
asynchronous
assumptions have
their drawbacks...
!
Under the
synchronous
assumption:
- independent processes coupled
- spurious transitions and cycles
- lack of precision
!
Under the
asynchronous
assumption:
- correct pathways buried in many other pathways
- dynamical components often very large
- kinetic information scarse
Hence the usefulness of
mixed (a)synchronous
treatments!
Beyond the
1)
Synthesis rates
slower than
degradation rates
!
2 different priority classes
2)
Components regulated by
similar molecular mechanisms
are grouped into
synchronous
classes
!
synchronous
versus
a
synchronous component sets
Rank Type
Transitions
---1
Asynch. CycD
%
$
, Rb
%
$
, p27
%
$
, Cdh1, E2F
%
, CycE
%
1
Synch. CycA
%
, Cdc20
%
, UbcH10
%
, CycB
%
2
Asynch. E2F
$
, CycE
$
, CycA
$
, Cdc20
$
2
Synch. UbcH10
$
, CycB
$
Mixed
Mixed
(a)
(a)
synchronous assumption
synchronous assumption
example
[CyD, Rb, E2F, CycE, CycA, p27, Cdc20, Cdh1, UbcH10, CycB]
Cdc20
$
Cdc20
%
E2F
$
CycA
%
CycB
%
Cdh1
$
UbcH10
%
CycE
$
CycE
%
CycA
%
CycB
%
Cdh1
$
Cdc20
%
Cdh1
%
Cdh1
$
CycA
$
UbcH10
$
CycB
$
E2F
%
Cdh1
%
E2F
%
Cdh1
%
E2F
%
Mixed state transition
Mixed state transition
graph
graph
Terminal strongly
connected
component
encompassing
Functional regulatory
Functional regulatory
circuits
circuits
132 regulatory circuits
12 functional
10 positive
2 negative
CycB
!
Cdc20
cdh1=0
Rb=0
p27=0
Cdc20=0
CycA
!
E2F
cdh1=0
CycB=0
cdh1=1
CycB=0
UbcH10=0
Functional regulatory
Functional regulatory
circuits
circuits
CycB
!
Cdc20
cdh1=0
Rb=0
p27=0
Cdc20=0
CycA
!
E2F
cdh1=0
CycB=0
cdh1=1
CycB=0
UbcH10=0
Mutant simulations :
Cdh1=1,
the cyclic attractor is lost
1 single stable state for CycD=1
2 stable states for CycD=0
Rb=1,
the cyclic attractor is lost
1 single stable state for CycD=1
1 single stable state for CycD=0
Mutant simulations
Mutant simulations
Rape & Kirshner
(2004)
Expected,
backup
mechanisms
(Emi...) not yet
considered
G1 arrest
No mitotic
checkpoint,
S phase delay
myc
UbcH10
Alevizopoulos
et
al.
(1997)
OK
Cell cycle
arrest
Cell cycle arrest
Ectopic
activity of
p27
Rivard
et al.
(1996)
Additional
activity levels
required for
Rb
Cell cycle
arrest
Viable, less
serum-dependent
p27-/-Bartek
et al.
(1996)
OK
Viable
Viable;
lengthening of
all phases of
the cycle
Rb-/-Reference
Agreement
Simulation
Phenotype
Experiment
!
A preliminary
logical model of the cell cycle control
in
mammals
!
Simulation of
mutants
and other
perturbations
!
Multi-level
modelling whenever needed
!
Feedback circuit
analysis
!
Development of a logical model of the
budding yeast
cell
cycle (collaboration with
Andrea Ciliberto
, IFOM)
- well-known system
- large number of characterised mutants
- existing ODE models for several specific modules
!
Goal:
logical model integrating all relevant modules
Conclusions & prospects
Conclusions & prospects
cell
Budding yeast cell
Budding yeast cell
cycle control
cycle control
Expected event succession for the wild-type
90 simple mutants tested (knock-out / over-expression)
2/3 are consistent
!
Priority classes
for subtler updating policies
!
Regulatory circuit analysis
!
Translation into
Petri Nets
(quantitative extensions)
!
Support of various
formats
for models/simulations: GINML
(XML), SVG, INA, PNML, SBML
!
Model checking
(temporal logics + model checkers)
!
Simplified (default) logical rules
to easily define models
!
Complex attractor identification
Prospects
Prospects
methodological and
TACG Marseille
TACG Marseille
Denis Thieffry
Adrien Fauré
Aurélien Naldi
Acknowledgements
Acknowledgements
Financial support
Financial support
STREP EU project
DIAMONDS
ACI JC
MaReBio
IML Marseille
IML Marseille
Elisabeth Remy
IFOM Milano
IFOM Milano
Andrea Ciliberto
Circuit
Circuit
functionality
functionality
'
"
Functional interaction
- the level of its target is modified (considering the threshold)
- depends on the presence/absence of co-regulators
"
functionality context
- use the logical function to determine the functionality context
K
i
(C) <
'
and K
i
(C
(
{x
i-1
})
"
'
K
i
(C)
"
'
and K
i
(C
(
{x
i-1
}) <
'
x
i
x
i-1
C
"
Functional circuit
- all interactions are functional
- the functionality context is the intersection of all interaction
contexts
