CIRM (Marseille Luminy)
3 - 7 novembre 2008
Comité d'organisation. C.
Chaouiya, E.
Remy, P.
Ruet.
Comité scientifique. A.
Cornish-Bowden, J.
Demongeot, J.-L.
Gouzé, M.
Kaufman, C.
Soulé, D.
Thieffry.
La rencontre se dérourela au CIRM, et est organisée par les
membres du projet ANR MaReBio (Mathématiques des Réseaux Biologiques). Il s'agit d'un projet ANR jeunes chercheurs (ANR-05-JCJC-0126-01), créé en novembre 2005.
La rencontre est soutenue par les institutions suivantes: ANR, IML, CIRM, Conseil Général des Bouches-du-Rhône, Ville de Marseille, BioMAGNet.
La plupart des processus biologiques est contrôlée par des réseaux de régulations, comportant différents
types d'interactions moléculaires. Le développement des analyses moléculaires et génétiques, ainsi que les
expériences à grande échelle de génomique fonctionnelle, ont permis d'identifier des réseaux d'interactions
contrôlant des processus biologiques cruciaux, comme le cycle cellulaire, ou différents processus développementaux.
Ces réseaux sont d'une telle complexité que le recours aux outils mathématiques et informatiques s'avère
indispensable. Il s'agit d'analyser la structure et la dynamique de ces réseaux pour en comprendre le fonctionnement.
Cette analyse, confrontée aux données biologiques, doit permettre de confirmer la topologie des
interactions ou de réviser leur définition en proposant des hypothèses sur de nouveaux acteurs moléculaires
ou de nouvelles interactions.
Le thème de la rencontre porte plus particulièrement sur le lien (caractérisé dans certains cas) entre les
propriétés structurales du réseau d'interactions et les propriétés dynamiques induites. En particulier, il est
important, pour de tels systèmes dynamiques, d'identifier le type de leurs attracteurs (par exemple, états
stables ou attracteurs cycliques). Ainsi, le rôle des circuits de régulation est bien connu par les modélisateurs.
L'objectif est donc de faire le point sur l'avancement et les perspectives des travaux dans ce domaine. Il s'agira
d'aborder plus spécifiquement le cas des modélisations discrètes, mais il sera certainement bénéfique de faire
le lien avec ce qui est connu dans le domaine de modélisations continues (par exemple différentielles).
Nous souhaitons donc faire le point sur une thématique essentielle dans le domaine de la modélisation
et l'analyse de réseaux biologiques, identifier les perspectives de recherche et renforcer les liens entre les
chercheurs actifs dans le domaine. Pour cela, nous solliciterons la participation de mathématiciens et bioinformaticiens
dont les travaux portent sur la question abordée, et nous ferons un appel à contributions élargi,
permettant ainsi d'initier de nouvelles collaborations.
Tout au long de la semaine, des temps pour la discussion seront préservés, gardant ainsi le principe
d'atelier de travail. La participation et la formation d'étudiants et jeunes chercheurs constitue l'un des
objectifs essentiels de la rencontre, en particulier dans le cadre des groupes de travail.
Description des thématiques:
- Modélisations discrètes des réseaux génétiques (modélisation logique, automates....).
- Processus concurrents (réseaux de Petri, pi-calculs,...).
- Des modélisations continues aux qualitatives (équations différentielles linéaires par morceaux, équations
discrètes).
- Circuits de regulation : rôles dynamiques et biologiques (règles de Thomas).
- Composition et modularité des réseaux.
Appel à soumissions.
Les jeunes chercheurs (thésards ou postdocs) souhaitant participer et faire
une présentation orale de leur travaux dans un domaine lié à la thématique de la rencontre ont été invités à soumettre un résumé (maximum 2 pages, format pdf) à:
ruet at iml.univ-mrs.fr
au plus tard le 1er septembre 2008. Les auteurs ont été informés de la décision d'acceptation avant le 1er octobre 2008.
| Lundi 3 | | |
| 11h15 - 11h45 |
|
Accueil et présentation à l'annexe (salles 1-2) du CIRM |
| 11h45 - 12h30 |
M. Kaufman |
From structure to dynamics: Frequency tuning in the p53-Mdm2 network |
| 12h30 - 14h |
Déjeuner |
| 14h - 14h45 |
A. Bockmayr |
Temporal constraints in the logical analysis of regulatory networks |
| 14h45 - 15h10 |
H. Siebert |
Feedback circuits and attractors of Boolean regulatory networks |
| 15h10 - 15h40 |
Café |
| 15h40 - 16h25 |
H. Matsuno |
Hypothesis creation from the pathway simulation on hybrid Petri net |
| 16h25 - 17h10 |
M. Heiner |
Time Petri nets for modelling and analysis of biochemical networks |
| 17h10 - 17h55 |
V. Schächter |
Systematic refinement of a global metabolic model of Acinetobacter baylyi using gene essentialities |
| Mardi 4 | | |
| 9h - 9h45 |
F. Fages |
From reaction graphs to influence graphs and back: a theorem |
| 9h45 - 10h10 |
G. Batt |
Quantitative robustness estimate of gene network properties |
| 10h10 - 10h35 |
F. Corblin |
Generalizing the discrete analyses of genetic networks using constraints |
| 10h35 - 10h55 |
Café |
| 10h55 - 11h40 |
A. Benecke |
Context-dependent complexity reduction of probability landscapes for the gene network inference problem |
| 11h40 - 12h05 |
M. Pedicini |
TH1/2 differentiation in an agent-based model |
| 12h05 - 12h30 |
A. Ciliberto |
How to make bistability disappear and appear again in enzmyatic reaction networks |
| 12h30 - 14h |
Déjeuner |
| Après-midi |
Groupes de travail |
Inverse ingeneering (R. Laubenbacher), Méthodes formelles (F. Fages) |
| Mercredi 5 | | |
| 9h - 9h45 |
R. Thomas |
Itération ciblée selon la nature du point fixe recherché |
| 9h45 - 10h10 |
J.-L. Gouzé |
Stability of biological networks with high degradation rates |
| 10h10 - 10h35 |
V. Baldazzi |
Qualitative simulation of carbon starvation responses in E. coli |
| 10h35 - 10h55 |
Café |
| 10h55 - 11h40 |
J. Aracena |
On the number and robustness of attractors in Boolean networks |
| 11h40 - 12h05 |
B. Luna Olivera |
Some issues about discrete-time regulatory networks |
| 12h05 - 12h30 |
M. Chaves |
Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics |
| 12h30 - 14h |
Déjeuner |
| Après-midi |
Libre |
|
| Jeudi 6 | | |
| 9h - 9h45 |
R. Laubenbacher |
The dynamics of conjunctive Boolean networks |
| 9h45 - 10h10 |
A. Richard |
Circuits positifs et négatifs dans les systèmes dynamiques discrets modélisant les réseaux de gènes |
| 10h10 - 10h35 |
A. Naldi |
Réduction de graphes de régulation logiques preservant les comportements essentiels |
| 10h35 - 10h55 |
Café |
| 10h55 - 11h40 |
B. Fernandez |
Symbolic dynamics of piecewise affine biological networks
|
| 11h40 - 12h05 |
M. Maurin |
Modeling of genetic regulatory network in stochastic pi-calculus: application to the lambda-phage |
| 12h05 - 12h30 |
L. Paulevé |
Temporal parameters within pi-calculus modeling of gene regulatory networks |
| 12h30 - 14h |
Déjeuner |
| Après-midi |
Groupes de travail |
Règles de Thomas (C. Soulé), Réseaux de réseaux (J. Carneiro) |
| Vendredi 7 | | |
| 9h45 - 10h30 |
A. Cornish-Bowden |
Est-il possible de construire un modèle d'un organisme dans l'ordinateur ? |
| 10h30 - 10h55 |
Café |
| 10h55 - 11h20 |
J. Carneiro |
Intercellular networks: wiring and rewiring dynamics |
| 11h20 - 11h45 |
F. Alves |
A continuous 3D model for spatial patterning in Drosophila early development |
| 11h45 - 12h30 |
J. Demongeot |
Robustesse dans les réseaux de régulation. Une approche générique |
| 12h30 - 14h |
Déjeuner |
- F. Alves
A continuous 3D model for spatial patterning in Drosophila early development.
I will present a continuous three-dimensional model for the spatial coordination of the gap gene regulatory network in Drosophila early development. The modeling framework is based on the analysis of the gene expression regulation in discrete points in space by non-linear differential equations, and relies on the de-coupling between the reaction and the diffusion components of the system.
Reflecting the combinatorial complexity of transcriptional regulation, gene expression is described individually in each nucleus and the overall behavior is quantitatively studied in time and space, considering the syncytial blastoderm as a three-dimensional system. The model predicts the wildtype expression patterns of the maternal and gap proteins, the aberrant patterns triggered by ectopic gene expression, as well as the patterns observed in loss-of-function mutants. This modeling strategy identifies the key factors responsible for the spatial organization of the early Drosophila embryo and represents a stepping stone to more complex approaches. I?m especially interested in discussing if connections can be established with the discrete models.
- J. Aracena
On the number and robustness of attractors in Boolean networks.
Boolean networks (BNs) have been extensively used as mathematical models of
genetic regulatory networks. The number and robustness of the attractors is a
key feature of the dynamical behavior of a BN. We will exhibit an upper
bound
on the number of fixed points in BNs. In particular, in BNs where each
interaction between the elements of the network is either an activation or an
inhibition, this bound depends on the minimum cardinality of a set of
vertices
meeting all positive cycles of the network (positive feedback vertex set). On
the other hand, we will show a theoretical study about the robustness of the
whole dynamical behavior and the dynamical cycles of a BN with respect to
different deterministic update schedules (parallel, block-sequential,
sequential). For this, we define equivalence classes of update schedules with
the same dynamical behavior in terms of the signed connection digraphs.
- V. Baldazzi
(Slides)
Qualitative simulation of carbon starvation responses in E. coli.
The adaptation of living organisms to their environment is
controlled at the molecular level by large and complex networks of
genes, mRNAs, proteins, metabolites, and their mutual interactions.
We have analyzed the network of global transcription regulators
controlling the adaptation of the bacterium Escherichia coli to
environmental stress conditions. Even though E. coli is one of
the best studied model organisms, it is currently little understood
how a stress signal is sensed and propagated throughout the network
of global regulators, and leads the cell to respond in an adequate
way.
Using standard methods for kinetic modeling and system reduction, we have built a simplified model of the carbon starvation
response network. This model has been analyzed by means of a
qualitative simulation method that is able to overcome the current
lack of quantitative data on kinetic parameters and molecular
concentrations.
In order to test the validity of our approach, we have randomly
sampled parameters inside their physiological range and
systematically compared the dynamics of the original and reduced
models. Piecewise-linear model has proved to correctly predict both
transient and asymptotic behavior of the original system.
We have used the reduced model to simulate the response of E. coli
cells to carbon deprivation. This has allowed us to identify
essential features of the transition between exponential and
stationary phase and to make new predictions on the qualitative
system behavior following a carbon upshift. The model predictions
have been tested experimentally by means of luciferase and
fluorescence reporter systems.
- G. Batt
Quantitative robustness estimate of gene network properties.
The robustness of biological systems behaviors has been demonstrated many times both experimentally and theoretically. In most cases however, the definition of robustness is highly problem-dependent, if not purely informal. An interesting general formal definition of robustness has recently been given by H. Kitano [Mol.Syst.Biol, 2007]. The robustness of a property with respect to a set of perturbations is the average value of the functionality of the system under all perturbations, weighted by the perturbation probabilities. Unfortunately, no indications are given on how to define and quantify the ``functionality" of a system.
Here, we propose an instantiation of this abstract definition, and an effective procedure to estimate it computationally. In this setting, the expected behavior is given as a temporal logic specification, and the behavior of the system under perturbations is simply given by a set of numerical traces. Our technique is rather general since most modeling formalisms provide numerical traces as simulation results and since temporal logics are versatile specification languages adapted to capture the quantitative yet imprecise aspects of cellular behavior. The computation of the robustness estimate is based on the notion of violation degree that measures the distance between the expected behavior and the behavior of the perturbed system [Rizk et al, CMSB'08]. This method has been implemented in the modeling environment Biocham and applied to cell cycle and transcriptional cascade models.
- A. Benecke
Context-dependent complexity reduction of probability landscapes for the
gene network inference problem.
The comprehension of the gene regulatory code in eukaryotes is one of
the major challenges of systems biology, and is a requirement for the
development of novel therapeutic strategies for multifactorial diseases.
Its bi-fold degeneration precludes brute force and statistical
approaches based on the genomic sequence alone. Rather, recursive
integration of systematic, whole-genome experimental data with advanced
statistical regulatory sequence predictions needs to be developed. Such
experimental approaches as well as the prediction tools are only
starting to become available and increasing numbers of genome sequences
and empirical sequence annotations are under continual discovery-driven
change. Furthermore, given the complexity of the question, a decade(s)
long multi-laboratory effort needs to be envisioned. These constraints
need to be considered in the creation of a framework that can pave a
road to successful gene network inference.
We introduce here a concept for such a framework, based entirely on
systematic annotation in terms of probability profiles of genomic
sequence using any type of relevant experimental and theoretical
information and subsequent cross-correlation analysis in
hypothesis-driven model building and testing. We furthermore show how
correlation functions can be developed to analyze the probability
landscape structure. Finally, we develop methodology for complexity
reduction based on systematic context-dependency analysis and subsequent
collapsing of the irrelevant parts of the landscapes.
Probability landscapes, which include as reference set the probabilistic
representation of the genomic sequence, can be used efficiently to
discover and analyze correlations amongst initially heterogeneous and
un-relatable descriptions and genome-wide measurements. Furthermore,
this structure is usable as a support for automatically generating and
testing hypotheses for alternative gene regulatory grammars and the
evaluation of those through statistical analysis of the high-dimensional
correlations between genomic sequence, sequence annotations, and
experimental data. Finally, this structure provides a concrete and
tangible basis for attempting to infere gene regulatory networks.
- A. Bockmayr
(Slides)
Temporal constraints in the logical analysis of regulatory networks.
Starting from the logical description of gene regulatory networks
developed by R. Thomas, we present an enhanced modeling approach based
on timed automata. We obtain a refined qualitative description of the
dynamical behavior by exploiting not only information on ratios of
kinetic parameters related to synthesis and decay, but also constraints
on the time delays associated with the operations of the system. We
describe a formal framework for handling such temporal constraints using
timed automata, discuss the relationship with the original Thomas
formalism, and demonstrate the potential of this approach on some
biological examples.
- J. Carneiro
Intercellular networks: wiring and rewiring dynamics.
The immune system is a network of interacting cells, called lymphocytes. In contrast with other systems in multicellular organisms, the interaction and dynamics between lymphocytes are determined by antigen receptors that are produce by somatic recombination in precursors. Every time that a new lymphocyte is produced it maybe co-opted by the existing cell pool or simply be lost. Whether a cell is co-opted or not depends on the interactions it can make with other lymphocytes, which in turn depend on the lymphocyte's antigen receptor and state of differentiation. The questions raised are what kind of patterns develop in the lymphocyte repertoire, and how stable are these patterns. These questions are crucial to understand the immune system in health and disease. Answering these question poses new challenges for network theory and analysis.
- M. Chaves
Uncovering operational interactions in genetic networks using asynchronous boolean dynamics.
To analyze and gain intuition on the mechanisms of complex systems of large dimensions, one strategy is to simplify the model by identifying a reduced system, in the form of a smaller set of variables and interactions that still capture specific properties of the system. For large models of biological networks, the diagram of interactions is often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space.
In this context, a method will be developed for identifying the active or operational interactions responsible for a given
dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a ``reduced'' and hierarchically organized graph of transitions. The second step consists of the identification of a sub-family of logical rules to characterize the new transition
graph and diagram of interactions that remain operational in a given region of the state space.
This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between survival or programmed death.
- A. Ciliberto
How to make bistability disappear and appear again in enzmyatic reaction networks.
The cell division cycle has long been described as the alternation between two stable steady states: a mitotic state, with high CDK/CyclinB activity (the major molecular player of mitosis) and low APCCdh1 (the proteasome, responsible for CyclinB degradation), and interphase, when CDK/CyclinB activity is low and APCCdh1 high. Novak and Tyson have shown that the two states can be attributed to several antagonistic relationship that occur in the cell cycle molecular regulatory network. However, in their original model the quasi steady state approximation was not performed properly. Here we revise the NT model: we show the proper way to translate the wiring diagram into differential equations, we observe that according to the new formalism hysteresis is lost from the system, and finally we show possible mechanisms to gain bistability back.
- F. Corblin
Generalizing the discrete analyses of genetic networks using
constraints.
This work generalizes the current existing discrete approaches for
analyzing the properties of genetic networks as proposed by Thomas
using concepts that are available in constraint programming (CP).
Its goal is to allow biologists to explore the combined effects of
various types of hypotheses such as the assumed gene interactions
and the expected dynamic behavior. We have developed a constraint
program called GNBox which realizes this goal. When the data is
interpreted by a CP processor the proposed system is capable of
responding to multiple queries that encompass simulation, reverse
engineering and hybrid combination of the two without a trial-error
process but a totally automatic process. After a presentation of our
approach, we describe in details the possibilities of expression and
the functionalities of the tool among which :
combination of simulation and reverse-engineering to find specific
behaviors and coherent valuation of parameters (discrete kinetic
parameters and thresholds), addition of hypotheses about the
combination of interactions over the genes of the network, the
number of thresholds and the mutant type, relaxation of constraints
in case of incoherence (the data having contradictory effects), and
consequently suggestion of refinement of the model. We have applied
GNBox to a model of the the gap-gene system of the drosophila embryo
segmentation (collaboration with D. Thieffry). One question is to
determine a model compatible with the data of several mutants which
contains the minimal number of thresholds for each interaction. We
show how the data are modelled as constraints and that our
implementation solves efficiently the above question.
- A. Cornish-Bowden
(Slides)
Est-il possible de construire un modèle d'un organisme dans l'ordinateur ?
Parmi les quatre théories principales d'aujourd'hui sur l'essence de la vie, les systèmes-(M,R) (systèmes de métabolisme et de réparation) de Robert Rosen sont notables pour son insistance qu'un organisme ne peut pas avoir un modèle qu'on peut simuler dans un ordinateur. Il n'y a apparemment pas une telle interdiction pour le chémoton de Tibor Gánti, l'autopoïèse d'Humberto Maturana et de Francisco Varela, et les ensembles autocatalyiques de Stuart Kauffman, et le prétension de Rosen a attiré beaucoup d'attention récemment, avec des prétensions également fortes pour et contre sa position. Ici on décrira des efforts de modéliser un système-(M,R) simple.
- J. Demongeot
Robustesse dans les réseaux de régulation. Une approche générique.
Les réseaux de régulation biologique sont souvent étudiés au
niveau de leur dynamique (existence d'attracteurs, étude de leur
stabilité trajectorielle), mais rarement à celui de leur robustesse,
c'es-à-dire de leur capacité à résister aux perturbations exogènes,
offrant ainsi les mêmes comportements spatio-temporaux,
indépendamment d'une perte de noeuds ou d'interactions dans leur
architecture, ou bien de changements environnementaux dans leurs
conditions limites, ou encore dans leur mode de mise à jour (par
exemple, co-expression par blocs au lieu d'expression séquentielle).
Nous définissons précisément la notion générique de noeud ou arête
critique, dans le graphe d'interaction, comme étant des entités dont
la disparition provoque un changement brusque du nombre et de la
nature des attracteurs (par exemple, le passage d'un comportement
bi-stable à un unique comportement périodique) ou dans l'étendue de
leurs bassins de stabilité. Nous traiterons quelques exemples : la
régulation de la floraison, le contrôle génétique du cycle cellulaire
et la régulation de la morphogenèse des phanères.
- F. Fages
(Slides)
From reaction graphs to influence graphs and back: a theorem.
Biologists use diagrams to represent interactions between
molecular species, and on the computer, diagrammatic notations are also
more and more employed in interactive maps. These diagrams are fundamentally
of two types: reaction graphs and activation/inhibition infnluence graphs.
In this paper, we study the formal relationship between these graphs.
We consider systems of biochemical reactions with kinetic expressions,
as written in the Systems Biology Markup Language SBML, and interpreted
by a system of Ordinary Differential Equations over molecular
concentrations. We show that under a general condition of increasing
monotonicity of the kinetic expressions, and in absence of both activation
and inhibition effects between a pair of molecules, the influence graph
inferred from the stoichiometric coefficients of the reactions is identical
to the one defined by the signs of the coefficients of the Jacobian matrix.
Under these conditions, satisfied by mass action law, Michaelis-Menten and
Hill kinetics, the influence graph is thus independent of the precise
kinetic expressions, and is computable in linear time in the number of
reactions. We apply these results to Kohn’s map of the mammalian cell cycle
and to Ferrel's purely directional model of the MAPK signalling cascade
which, without any negative feedback reaction, does contain negative
circuits in its influence graph and can in fact exhibit sustained
oscillations. Finally, we propose a syntax for denoting antagonists in
reaction rules and
generalize our results to this setting.
- B. Fernandez
Symbolic dynamics of piecewise affine biological networks.
In piecewise affine dynamical systems, the dynamics can be solved formally to obtain an explicit expression of orbits in the attractor, given their symbolic code. In various situations, this expression proves to be an efficient tool to exhibit genuine orbits and to describe their variations as the parameters change.
I will present this approach in discrete time systems and will discuss two examples of models of biological networks where it allowed us to mathematically uncover the essential features of dynamics.
- J.-L. Gouzé
Stability of biological networks with high degradation rates.
We consider larges classes of biological systems having a high degradation rate. We show that, under some hypotheses, theses systems have a single equilibrium, and that this equilibrium is globally stable.
- M. Heiner
(Slides)
Time Petri nets for modelling and analysis of biochemical networks.
In this talk, we apply established notions of time Petri nets for modelling and analysis of molecular biological systems. A crucial point of the used time concept is that it provides continuous firing durations, which can still be treated in a discrete way.
We demonstrate how to develop quantitative models of biochemical networks in a systematic manner, starting from the underlying qualitative ones. For this purpose we exploit the structural Petri net analysis technique of transition invariants, which may be interpreted as a characterization of the system?s steady state behaviour.
For the analysis of the derived quantitative model, given as time Petri net, we present analysis techniques to decide the time-dependent realisability of a transition sequence and to calculate shortest and longest time lengths.
Finally, two open problems are motivated by biochemical network examples: time-dependent boundedness and time-dependent liveness.
- M. Kaufman
From structure to dynamics: Frequency tuning in the p53-Mdm2 network.
We investigate the dynamical properties of a simple four-variable model describing the
interactions between the tumour suppressor protein p53, its main negative regulator Mdm2
and DNA damage, a model inspired by the work of Ciliberto et al. (2005). Its core consists of
an antagonist circuit between p53 and nuclear Mdm2 embedded in a 3-element negative
circuit involving p53, cytoplasmic and nuclear Mdm2. Rather than choosing a unique mode of
description, we develop an integrated approach combining a multilevel logical method with a
differential approach and stochastic simulations. We show that the essential dynamical
properties of our network are described by a small number of bifurcation scenarios that can be
interpreted in terms of the balance between the positive and negative loops of the core of the
network. These bifurcation scenarios depend on two parameters linked to post-translational
modifications of p53, the DNA-binding affinity and transcriptional activity of p53. Since
these parameters are known to be cell- and stress-type specific, we propose that different
types of cells or stresses could be characterized by different bifurcation schemes and lead to
different responses upon irradiation. Our results also account for important features of the
kinetics of the p53 response to damage that, to our knowledge, have not been addressed in
other modeling approaches. In particular, we provide an interpretation of the tuning of the
oscillation frequency that has been observed experimentally depending on the irradiation
dose, and predict that the rate of damage repair should play an important role for this
behaviour.
- R. Laubenbacher
(Slides)
The Dynamics of Conjunctive Boolean Networks.
The relationship between the properties of a dynamical system and
the structure of its defining equations has long been studied in
many contexts. This talk will present results relating to this problem for the class of
conjunctive Boolean networks, that is, Boolean networks in which
all Boolean functions are constructed with the AND operator only.
Like the class of linear Boolean networks, this class has the
advantage such networks are uniquely determined by their
dependency graph. The main results describe network
dynamics in terms of the structure of the network dependency
graph. For a given such network, all possible cycle lengths are
computed and lower and upper bounds for the number of cycles of
each length are given. The bounds are in terms of structural
features of the dependency graph of the Boolean network and its
partially ordered set of strongly connected components. For
networks with strongly connected dependency graph, the exact cycle
structure is computed.
- B. Luna Olivera
Some issues about discrete-time regulatory networks.
We consider a class of discrete-time dynamical systems on regulatory networks. These systems can be thought as a discrete-time alternative to the systems of piecewise affine differential equations and to finite state models.
We study some issues on these networks. First using a notion of determination between vertices, we define sets of dominant vertices, and we prove that in the asymptotic regime, the dynamics on a dominant set allows us to determine the state of the whole system at all times. Then we study the dynamical complexity of two-dimensional networks, which is quantity related to the proliferation of distinguishable temporal behavior. Finally, by using this modeling strategy we analyze the two-component transduction systems as module networks that regulate the integration of external information in E.coli.
- H. Matsuno
(Slides)
Hypothesis creation from the pathway simulation on hybrid Petri net.
Systems biology is a new field that aims to integrate different
levels of information to understand how biological processes function
in a cell. The experimentally coverd biological facts are usually
summarized in a picture of network composed of figures of various
shapes and sereval types of arrows reflecting the underlying biological
images. Petri net allows easy construction of a computational model
from the biological picture, further enables simulation of the model
using existing simulation tools. In this talk, we demonstrate how
a biological hypothesis can be created from the simulation on the hybrid
Petri net using circadian gene regulatory system in mammals.
- M. Maurin
Modeling of genetic regulatory network in stochastic
pi-calculus: application to the lambda-phage.
We propose a model based on the multi-valued approach of René Thomas extended by Denis Thieffry in which biological regulatory networks are represented by a graph and a set of logical parameters. In order to integrate both stochastic and temporal information in our model, we use the stochastic pi-calculus as a formal language.
We focus on the lambda-phage example in its most relevant model, that is with four genes and we are currently processing a statistical analysis to determine the exact role of the ratio of evolution rates for the choice between lytic and lysogenic cycles. The capacity of inferring properties on the system thanks to the model is a major advantage: it reinforces the relevance of our choice to introduce the temporality into the formalism of René Thomas.
- A. Naldi
(Slides)
Réduction de graphes de régulation logiques preservant les comportements essentiels.
La complexité croissante des réseaux de régulation complique l'analyse de leur dynamique. Nous définissons une méthode de réduction pour les modèles logiques multi-valués. Partant d'un modèle détaillé, notre méthode permet de déterminer un modèle réduit en itérant le "masquage" de composants de régulation. Cette construction de modèles réduits préserve un certain nombre de propriétés dynamiques du modèle d'origine. En particulier, les états stables et attracteurs complexes sont conservés. Plus généralement, nous étudions les relations entre la configuration d'attracteurs du modèle d'origine et celle du modèle réduit, ainsi que la question de l'atteignabilité des attracteurs.
- L. Paulevé
(Slides)
Temporal parameters within pi-calculus modeling of gene regulatory networks.
Pi-calculus is a concurrent processes algebra used in many computer science
fields to model complex parallel computer systems. Among different variants, the
stochastic Pi-calculus is well suitable for modeling biological processes.
Stochastic Pi-calculus associates interaction and delay rates to every
reaction. These temporal parameters will determine the probabilities of all
the reactions in the system and their duration.
By using computer science modeling and verification techniques, our first goal
is to design an automated verification method of the global system behavior for
a given set of temporal parameters. It will require a formal specification of
global systems dynamics and algorithms to check the match with a stochastic
Pi-calculus program. This work will permit to infer the values of the
temporal parameters.
We will present a modeling for gene regulatory networks using stochastic pi-
calculus and first algorithms for the temporal parameters inference given
stabilities and trajectories probabilities specifications.
- M. Pedicini
(Slides)
Implementation of a regulatory gene network to simulate the TH1/2 differentiation in an agent-based model of hypersensitivity reactions.
An unbalanced differentiation of T helper cells from precursor type TH0 to the TH1 or TH2 phenotype in immune responses often leads to a pathological condition. In general, immune reactions biased toward TH1 responses may result in auto-immune diseases, while enhanced TH2 responses may cause allergic reactions. The aim of this work is to integrate a gene network of the TH differentiation in an agent-based model of the hyper-sensitivity reaction. The implementation of such a system introduces a second level of description beyond the mesoscopic level of the inter-cellular interaction of the agent-based model. The intra-cellular level consists in the cell internal dynamics of gene activation and transcription. The gene regulatory network includes genes-relatedmolecules that have been found to be involved in the differentiation process in TH cells.
Results: The simulator reproduces the hallmarks of an IgE-mediated hypersensitive reaction and provides an example of how to combine the mesoscopic level description of immune cells with the microscopic gene-level dynamics.
- A. Richard
(Slides)
Circuits positifs et négatifs dans les systèmes dynamiques
discrets modélisant les réseaux de gènes.
On s'intéresse à l'influence des circuits positifs et négatifs dans
les systèmes dynamiques discrets asynchrones introduits par René
Thomas pour modéliser le comportement des réseaux de gènes.
Ces systèmes sont décrits par les itérations asynchrones d'une
application F qui opère sur un espace des états fini X égale au
produit cartésien de n intervalles finis d'entiers. Dans un premier
temps, on visualise ces itérations sous la forme d'un graphe orienté
sur X appelé graphe de transition asynchrone de F. Les attracteurs du
système sont alors définis comme les plus petit sous-ensembles de X
sans transition sortante. Les attracteurs de cardinalité 1 sont les
points fixes de F et correspondent aux états stable du systèmes; les
autres contiennent des cycles et sont dits cycliques. Dans un second
temps, on introduit une matrice Jacobienne pour F adaptée au contexte
asynchrone. Comme dans le cas continu et le cas booléen, on peut alors
associer à chaque état du système un graphe d'interactions local défini
à partir des signes des entrées de la Jacobienne évaluée à cet état.
On établit ensuite certaines relations entre les graphe d'interactions
locaux associés à F et les attracteurs du graphe de transition
asynchrone de F. On commence par une version discrète de la première
conjecture de Thomas: Si le graphe de transition asynchrone contient
plusieurs attracteurs, alors il existe un graphe d'interactions local
contenant un circuit positif. On généralise ensuite ce résultat en
établissant une borne supérieure sur le nombre d'attracteurs qui ne
dépend que de la topologie des circuits positifs présent dans les
graphes d'interactions locaux. On présente finalement une version
discrète de la seconde conjecture de Thomas: Si le graphe de
transition asynchrone contient un attracteur cyclique alors l'union
des graphes d'interactions associés aux états de l'attracteur contient
un circuit négatif.
- V. Schächter
Systematic refinement of a global metabolic model of
Acinetobacter baylyi using gene essentialities.
Gene essentiality screens can be used to significantly upgrade our knowledge on the
metabolism of a given species. Genome-scale metabolic models can predict reactions
essentiality by analyzing the capabilities of the underlying reaction network in a simulated
environment : the relationship between these two types of essentialities is encoded in a genereaction
correspondence. Previous work has shown that the identification of inconsistencies
between experimental and predicted phenotypes can guide the expert search for model
corrections. We introduce here a method, AutoGPR, that automatically corrects the genereaction
correspondence in global metabolic models, by reasoning on a suitable model
representation together with the set of experimental facts. This refinement strategy was
applied to an initial metabolic model reconstruction of Acinetobacter baylyi ADP1, a recently
sequenced soil bacterium for which a genome-wide single-gene knock-out library was
phenotyped on several growth media. Two rounds of refinement yield a significant set of
model corrections and new annotations, showing that large-scale genetics data can be used to
rapidly and systematically obtain an accurate metabolic model of a recently sequenced
bacterium.
- H. Siebert
(Slides)
Feedback Circuits and Attractors of Boolean Regulatory Networks.
In the well-known formalism of R. Thomas the structure of a biological
regulatory network is represented by an interaction graph. The possible
dynamical behaviors corresponding to the interaction graph and a set of
discrete parameters can also be represented by a directed graph.
Recently, there have been several results clarifying the relation
between motifs in the network structure and motifs in the dynamics of
the network. In this talk, we focus on a converse of the so-called
Thomas Conjectures which show the necessity of the existence of positive
resp. negative feedback circuits in the interaction graph for the
existence of multiple resp. cyclic attractors in the graph capturing the
dynamics.
- C. Soulé
(Groupe de travail "Règles de Thomas")
- R. Thomas
Itération ciblée selon la nature du point fixe recherché.
Le concept de multistationnarité est devenu essentiel à la compréhension de la différenciation cellulaire . Aussi les biologistes théoriciens sont-ils de plus en plus fréquemment confrontés à l'étude de systèmes d'équations différentielles (non linéaires) doués d'états stationnaires multiples. Ces états stationnaires, définis comme les racines réelles du système d'équations d'état stationnaire, sont identifiés en pratique comme points fixes de processus d'itération. De nombreuses méthodes ont été développées pour assurer ou améliorer la convergence du processus d'itération. Cet exposé décrit un algorithme qui assure et s'il y a lieu, accélère, la convergence de l'itération vers un point fixe correspondant à un type choisi (col, noeud ou foyer stable ou instable) d'état stationnaire.
- F. Alves,
- J. Aracena,
- V. Baldazzi,
- G. Batt,
- A. Benecke,
- A. Bockmayr,
- J. Carneiro,
- C. Chaouiya,
- M. Chaves,
- A. Ciliberto,
- J.-P. Comet,
- F. Corblin,
- A. Cornish-Bowden,
- A. Crumière,
- J. Demongeot,
- F. Fages,
- E. Farcot,
- A. Fauré,
- B. Fernandez,
- J.-L. Gouzé,
- M. Heiner,
- M. Kaufman,
- R. Laubenbacher,
- B. Luna Olivera,
- M. Magnin,
- H. Matsuno,
- M. Maurin,
- T. Merle,
- P. Monteiro,
- A. Naldi,
- M. Noual,
- L. Paulevé,
- M. Pedicini,
- E. Remy,
- A. Richard,
- P. Ruet,
- V. Schächter,
- S. Sené,
- H. Siebert,
- H. E. Snoussi,
- C. Soulé,
- D. Thieffry,
- R. Thomas.