MaReBio
Organisation
Thematics
Programme
Speakers
Participants

Discrete models of biological networks : from structure to dynamics
Modèles discrets de réseaux biologiques : de la structure à la dynamique

CIRM (Marseille Luminy)
November 3 - 7, 2008

Organisation

Organising committee. C. Chaouiya, E. Remy, P. Ruet.
Scientific committee. A. Cornish-Bowden, J. Demongeot, J.-L. Gouzé, M. Kaufman, C. Soulé, D. Thieffry.

The meeting will take place at the CIRM, and is organised by the members of the ANR project MaReBio (Mathematics of Biological Networks), which is a young researchers programme (ANR-05-JCJC-0126-01) started in November 2005.

The meeting is supported by the following institutions: ANR, IML, CIRM, Conseil Général des Bouches-du-Rhône, Ville de Marseille, BioMAGNet.

Thematic presentation

Most biological processes are controoled by biological networks implying different kinds of molecular interactions. The increase of molecular and genetic analyses, together with the large-scale experiments of functional genomics, enabled the identification of interaction networks controlling key biological proccesses such as the cell cycle or various developmental processes. The complexity of these networks calls for mathematical and computational tools, directed towards an analysis of the structure and the dynamics of these networks. This analysis, building upon biological data, should enable us to confirm the topology of interactions, or to revise their definition by offering hypothetical new molecular agents or new interactions.

The thematics of the meeting focusses more specifically on the link (already precisely stated in some cases) between the structural properties of the interaction network and induced dynamical properties. In particular, it is important to identify the type of attractors of such dynamical systems (e.g., stable states or cyclic attractors). The role of regulatory circuits in particular is well-known by modellers. The goal is therefore to present the state of the art and perspectives of research in this field. With a particular attention to discrete models, but connections with known results for continuous (differential for instance) models will certainly be fruitful.

Our objective is therefore to offer a state of the art on an essential thematics in the field of modelising and analysing biological networks, identify research perspectives and reinforce the connections between active researchers in the field. To this end, we shall encourage the participation of mathematicians and bioinformaticians which are experts in the field, and open the meeting with an enlarged call for contributions so as to initiate new possible collaborations.

During the whole week, time will be kept for discussion, in the spirit of a workshop. Participation and formation of students and young researchers are one of the main objectives of the meeting, in particular during working groups.
Description of thematics:

• Discrete modelisations of genetic networks (logic models, automata....).
• Concurrent processes (Petri nets, pi-calculi,...).
• From continuous to qualitative models (piece-linear differential equations, discrete equations,...).
• Regulatory circuits : dynamic and biological roles (Thomas rules).
• Composition and modularity of networks.

Call for submissions. Young researchers (PhD students of Postdocs) who wished to participate and give an oral presentation of their work in an area related to the workshop thematics have been invited to submit an abstract (maximum 2 pages, pdf format) to:

ruet at iml.univ-mrs.fr

before September 1st, 2008. Authors were informed of the decision, acceptance or rejection, before October 1st, 2008.

Preliminary programme

Monday 3
11h15 - 11h45		Welcoming introduction at the "annexe" of CIRM (rooms 1-2)
11h45 - 12h30	M. Kaufman	From structure to dynamics: Frequency tuning in the p53-Mdm2 network
12h30 - 14h	Lunch
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	Coffee
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
Tuesday 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	Coffee
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	Lunch
Afternoon	Working groups	Inverse ingeneering (R. Laubenbacher), Formal methods (F. Fages)
Wednesday 5
9h - 9h45	R. Thomas	Targeted iteration according to the nature of steady states
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	Coffee
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	Lunch
Afernoon	Free
Thursday 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	Reducing logical regulatory graphs yet keeping essential behaviours
10h35 - 10h55	Coffee
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	Lunch
Afternoon	Working groups	Thomas' rules (C. Soulé), Networks of networks (J. Carneiro)
Friday 7
9h45 - 10h30	A. Cornish-Bowden	Is it possible to construct a model of a living organism in the computer?
10h30 - 10h55	Coffee
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	Robustness in regulatory networks. A generic approach
12h30 - 14h	Lunch

Speakers

• 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)
  Is it possible to construct a model of a living organism in the computer? Among the four principal current theories of the nature of life the (M,R)-systems (metabolism-repair systems) of Robert Rosen are noteworthy for his insistence that a living organism cannot have a computer-simulable model. There seems to be no such prohibition for the chemoton of Tibor Gánti, the autopoiesis of Humberto Maturana and Francisco Varela, or the autocatalytic sets of Stuart Kauffman, and Rosen's claim has recently attracted a great deal of controversy, with equally strong claims made both for and against his position. Efforts to construct a computer model of a simple (M,R)- system will be presented.
• J. Demongeot
  Robustness in regulatory networks. A generic approach. The biological regulatory networks are often studied on their dynamical side (existence of attractors, study of their trajectory stability) but rarely on their robustness, that is their ability to resist to external perturbations, then offering the same spatio-temporal patterns independently of the loss of nodes or edges in their interaction architecture, or of the change in their environmental boundary conditions, or more of their mode of updating (e.g. co-expression versus sequential expression in genetic networks). We will define precisely the generic notion of critical node or edge in the interaction graph whose disappearance can cause dramatic changes in the number and type of attractors (e.g. passage from a bistable behavior to a unique periodic regime) or in the range of their basins of stability. We will treat some examples: flowering regulation, cell cycle genetic control and feather morphogenesis metabolic driving.
• 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)
  Reducing logical regulatory graphs yet keeping essential behaviours. The increasing complexity of regulatory networks complicates their dynamical analysis. Here, we define a reduction method for multi-valued logical models. Starting with a detailed model, our method enables the computation of a reduced model by iteratively "hiding" regulatory components. This construction of reduced models ensures the preservation of a number of dynamical properties of the original model. In particular, stable states and more complex attractors are conserved. More generally, we address the question of the relationship between the attractor configuration of the original model and that of the reduced model, along with the issue of attractor reachability.
• 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 (Working groug "Thomas' rules")
  
• R. Thomas
  Targeted iteration according to the nature of steady states. Multistationarity has become an essential concept for the understanding of cell differentiation. As a result, theoretical biologists have more and more frequently to determine the steady state values, often multiple, of systems of nonlinear differential equations. These are defined as the real roots of the steady state equations, and identified in practice as fixed points of iterative processes. A number of methods have been developed in order to permit or improve convergence. Here, we describe a simple algorithm that ensures and, if required, accelerates, convergence towards a fixed point of the iteration process that corresponds to a pre-determined type of steady state (e.g. saddle point, stable or unstable node or focus, ?) of the differential system.

Participants

• 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.