Dynamics and structure of biological networks

Marseille - Luminy
February 14 - 17, 2006

Organization

Organizer: Paul Ruet.
Context: This workshop is part of Geometry of Computation 2006 (Geocal06), a special series of events in theoretical computer science organized by the GEOCAL group and taking place at the CIRM from January 30 to March 3. Geocal06 is supported by the following institutions: IML, FRUMAM, Luminy, UnivMed, Genopole, CIRM, CNRS.

Preregistration: on the Geocal06 site. Deadline: October 30, 2005.
Registration: on the Geocal06 site.

Thematic presentation

Biological networks are found at the core of all biological functions, from biochemical pathways to cell communication processes and gene regulation mechanisms. Their complexity calls for proper mathematical models and results in order to relate their structure to their dynamical properties.
In the last few years, several progresses have been made in this interdisciplinary field, e.g., the mathematical study of genetic networks, the modelisations of the structure of protein level interactions via concurrent programming languages, to quote only a few recent advances.
The workshop is intended to present and confront these lines of research, and propose possible cross-fertilisations and extensions (dynamics of metabolism, intercellular communication, stochastic aspects...). It will be an opportunity to bring together mathematicians, logicians and concurrency theorists, biologists and physicists interested in a structured approach of biological interactions.

Tentative overview of sessions

	9h - 10h30	11h - 12h30	14h - 16h30	16h30 - 18h30
Tue 14	Genetic networks	Concurrent models	Genetic networks	Concurrent models
	9h - 10h30	11h - 12h30
Wed 15	Neurobiology	Genetic networks
	9h - 10h30	11h - 12h30
Thu 16	Metabolic networks	Genetic networks
	9h - 10h30	11h - 12h30	14h - 15h30	16h - 17h30
Fri 17	Concurrent models	Concurrent models	Metabolic networks	Metabolism

Programme

Tuesday 14
9h - 9h45	Denis Thieffry	Logical modelling of genetic regulatory networks
9h45 - 10h30	Andrew Phillips	Simulating biological systems in the stochastic pi-calculus
10h30 - 11h	Coffee break
11h - 11h45	Claudine Chaouiya	Petri net modelling of biological networks
11h45 - 12h30	Volker Schmidt	Model-based analysis of keratin filament networks
12h30 - 14h	Lunch
14h - 14h45	Elisabeth Remy	On differentiation and homeostatic behaviours of discrete dynamical systems
14h45 - 15h30	Adrien Richard	Necessary conditions for multi-attractivity in discrete dynamical systems
15h30 - 16h	Coffee break
16h - 16h30	Eric Fanchon	Reachability of singular states in Thomas-Snoussi networks
16h30 - 17h	Prisacariu Cristian	Modeling MolNet systems with timed distributed pi-calculus
17h - 17h30	Jean Krivine	Reversible process algebras and self-assembly mechanisms
17h30 - 17h45	Break
17h45 - 18h30	Vincent Danos	Probabilistic model-checking bio-models
Wednesday 15
9h - 9h30	Yehezkel Ben-Ari	Oscillations physiologiques et pathologiques dans le cerveau: la belle et la bête
9h30 - 10h	Rosa Cossart	Imaging the dynamics of cortical networks
10h - 10h30	Michel Le Van Quyen	Does the brain work like the internet?
10h30 - 11h	Coffee break
11h - 11h45	Marcelle Kaufman	Link between logical structure and dynamics: the example of the p53-mdm2 network
11h45 - 12h30	Etienne Farcot	A comparison of piecewise affine and discrete models of gene networks
12h30 - 14h	Lunch
Afternoon	Excursion	Good shoes for hiking in the calanques might be useful
Thursday 16
9h - 9h45	Alessandra Carbone	Detection of essential metabolic pathways
9h45 - 10h30	Julie Baussand	Distantly related proteins and proteic partners identification
10h30 - 11h	Coffee break
11h - 11h45	Arnaud Meyroneinc	Discrete time piecewise models of genetic regulatory networks
11h45 - 12h30	Samuel Bottani	L'hypothèse des motifs et la modularité des réseaux génétiques
12h30 - 14h	Lunch
Friday 17
9h - 9h45	Gordon Plotkin	Categorical structure of chemical reaction nets
9h45 - 10h30	Vincent Schächter	Investigations with constraint-based models of metabolism
10h30 - 11h	Coffee break
11h - 11h45	Cosimo Laneve	A basic calculus for molecular biology
11h45 - 12h30	François Fages	Formal languages in the biochemical abstract machine BIOCHAM
12h30 - 13h45	Lunch
13h45 - 14h15	Vincent Lacroix	Reaction motifs in metabolic networks
14h15 - 14h45	Christine Brun	Protein-protein interaction network analysis using classification methods
14h45 - 15h30	María Luz Cárdenas	Towards an understanding of life
15h30 - 16h15	Athel Cornish-Bowden	Making systems biology work
16h15 - 16h45	Coffee break
16h45 - 17h30	Christophe Soulé	A stochastic Thomas rule

Speakers: titles, abstracts and slides

Yehezkel Ben-Ari, INMED, Marseille
Title: Oscillations physiologiques et pathologiques dans le cerveau: la belle et la bête
Abstract: Les réseaux neuronaux agissent essentiellement par l'intermédiaire d'activités synchrones et oscillatoires générés par des populations de neurones regroupés en entités fonctionnelles. Ces activités qui ont des propriétés très différentes selon la nature du réseau et le type d'élément générateur (en termes de frequence notamment) permettent des fonctions intégratives très différentes comme le binding sensoriel, les capacités d'apprentissage et d'attention etc. Elles sont aussi impliquées dans des activités pathogènes et pathologiques commes les épilepsies mais aussi la maladie de Parkinson etc. La question fondamentale posée est par conséquent la nature des différences entre ces 2 patrons de décharge : est-ce la nature des neurones impliqués? le type de patron, au delà de telle fréquence ou durée, etc?
Je ferai une brève introduction à ces différents éléments en montrant les neurones générateurs et le type d'oscillations impliquées afin de permettre à Rosa Cossart et Michel Le Van Quyen de donner des exemples plus détaillés d'analyse et de fonction en relation avec le développement cérébral.
Julie Baussand, Génomique Analytique, Paris 6
Title: Distantly related proteins and proteic partners identification for biological network inference: a computational approach
Abstract: The use of hydrophobic clusters, that is groups of hydrophobic amino acids which are likely to be in contact once the protein is folded, as a structural pattern detectable from sequences to align distanly related proteins has already shown its efficiency when applied to difficult cases of proteins pairs of 15-25% sequence identity (Hung et al., 1998; Carret et al., 1999; Callebaut et al., 2005).
We present PHYBAL (Baussand et al., in preparation), for Proteins Hydrophobic Blocks Alignment, the first automatic alignment method which detects and uses hydrophobic blocks as a basic pattern to align distantly related proteins. It is based on a proteic sequence alignment method that detects hydrophobic blocks in one-dimension by a prescreening of the amino-acids sequence, and integrates the structural information in a classical alignment procedure.
Performance of the tool has been tested with a large range of gap insertion on the alignment of 8 pairs of proteins of less than 30% identity and with known structure (1 alpha+beta, 4 all alpha, 3 all beta) and confirms the accuracy of the use of hydrophobic blocks information for the alignment of distantly related proteins. Improvement for distantly related proteins detection has also been demonstrated on the Protein Data Bank. This tool is part of a larger computational system devoted to the detection of protein-protein and protein-DNA interaction sites using the combinatorics of phylogenetic trees with a distantly related proteins adaptated version of Evolutionary Trace (Lichtarge et al., 1996; Madabushi et al., 2002). We shall present how detection of proteic partners and co-evolution analysis can lead to the reconstruction of biological networks.
Samuel Bottani, Laboratoire Matières et Systèmes Complexes, Université Paris 7
Title: L'hypothèse des motifs et la modularité des réseaux génétiques (Slides)
Abstract: Les réseaux biochimiques très en vogue depuis quelques années, sont une tentative habituelle pour essayer d'assimiler le nombre de données disponibles de nos jours sur les composants biologiques moléculaires et leurs interactions. De cette représentation est né l'espoir que des connaissances utiles et des propriétés biologiques remarquables puissent être déduites directement à partir de l'étude de la structure des réseaux.
Une des propriétés les plus fréquemment citées est l'organisation modulaire des réseaux biochimiques. Selon cette vue, les réseaux seraient constitués d'un assemblage de sous-systèmes presque autonomes, associés à des fonctions bien définies. Dans ce séminaire je discuterai en particulier d'une hypothèse assez populaire de modularité de la structure à petite échelle des réseaux de régulation génétique. Selon celle-ci, il existerait des types particuliers de circuits de régulation, appelés "motifs", qui seraient les briques de construction fondamentales des réseaux et auraient été sélectionnés par l'évolution naturelle pour leurs propriétés de traitement de d'information. Dans un récent article(*) nous avons montré que ces motifs ne sont cependant pas conservés par l'évolution et qu'ils n'ont aucun rôle fonctionnel clair. Cette conclusion mets en discussion l'interprétation des réseaux biologiques et leur relation avec des fonctions biologiques complexes.
(*) Mazurie A, Bottani S, Vergassola M., "An evolutionary and functional assessment of regulatory network motifs.", Genome Biol. 2005;6(4):R35. Epub 2005 Mar 24.
Christine Brun, IBDM, Marseille
Title: Protein-protein interaction network analysis using classification methods (Slides)
Abstract: Protein-protein interaction maps are now available for at least 4 eukaryotic model organisms: the budding yeast, the worm, the fruit fly and human. These maps form large intricate networks leading to a renewed vision of the cell biology as an integrated system. However, extracting and revealing the functional information they contain depends on our ability to analyze them in detail. Indeed, although they are far from being complete, the size and the complexity of these networks (so far, between 5000 and 25000 interactions/graph edges according to the organism) make their functional analysis a difficult task.
In order to extract this information, we have developed several classification methods based on a the calculation of a distance. I will present these methods and the functional classification of the proteins resulting from their application to protein-protein interaction networks. I will also discuss the biological meaning of the results and the novel insight into cell functioning they give.
Alessandra Carbone, Génomique Analytique, Paris 6
Title: Genomic functional cores specific to different microbes and detection of essential metabolic pathways (Slides)
Abstract: The project of synthesizing a bacterial genome which can survive in the laboratory and can realize desired metabolic cycles, has been announced three years ago by Venter, Smith and Hutchison. It asks for clearing out certain basic biological mechanisms of living cells. The problem demands to search for the minimal set of genes that are essential to the life of a microbial organism. Experiments based on transposon-mediated knock-out mutagenesis realized on specific bacteria allowed to propose some minimal gene set. Independently, comparative genomics also proposed some minimal set of genes. But both these "solutions" present some intrinsic problem.
We shall present some simple mathematical ideas, that allows to predict genomic functional cores which are specific to different microbes. Within these sets, one finds many of the genes characterized with experiments and genome comparison, but also genes which might be non-orthologous or whose function might not be characterized yet. More generally, our computational approach leads to characterize essential metabolic pathways.
Claudine Chaouiya, ESIL, Marseille
Title: Petri net modelling of biological networks (Slides)
Abstract: When facing a complex interaction network, the biologist needs new means to check the coherence of tentative models with the observed dynamics, to better understand the logics of the interactions and to simulate the system behaviour for various kinds of perturbations. In this respect, Petri Nets (PNs) and their extensions constitue a promising framework for the modelling, analysis and simulation of biological networks.
I will first briefly survey the various PN based models of biological networks found in the literature, classifying them according to the targeted biological application and the PN class (standard, coloured, stochastic, hybrid, etc.). Depending on the biological question to be addressed, one has to consider different abstraction levels: the molecular level (refering to biochemical networks), the genetical level (refering to genetic networks) or the tissue level (refering to inter-cellular networks). As quantitative information is rarely available, we are mainly interested in qualitative approaches. I will focus on the qualitative modelling of metabolic pathways, and discuss to what extend a PN modelling can meet the different issues covered by the stoichiometric network analysis. Then, I will present our proposal of a PN framework for the logical modelling of gene regulatory networks, covering both coloured and standard Petri net representations.
These methodological aspects will be illustrated by the modelling of the regulation of the Tryptophan biosynthesis in E. Coli, which encompasses a mixed metabolic/genetic network.
Athel Cornish-Bowden, CNRS-BIP, Marseille
Title: Making systems biology work (Slides)
Abstract: The field known as systems biology has grown in a few years from almost nothing. As currently practised, however, its underlying philosophy remains as resolutely reductionist as anything that preceded it, and until it incorporates a genuinely systemic view of biology it will be little more than a new name for an old approach applied on a massively increased scale. In mathematical terms, the fundamental problem is to understand how living organisms escape the infinite regress implicit in a description of metabolism, as a process that creates and maintains itself. Some authors have claimed that the solution to this problem proposed by Robert Rosen is mathematically invalid, but we believe we have shown otherwise. In any case, even if the solution turns out to be invalid the problem itself is real, and will not go away simply by virtue of not being addressed. It will need to be solved before any real progress towards creating artificial organisms can be made.
Rosa Cossart, INMED, Marseille
Title: Imaging the dynamics of cortical networks (Slides)
Abstract:
María Luz Cárdenas, BIP-IBSM-CNRS, Marseille
Title: Towards an understanding of life (Slides)
Abstract: Since the rise of molecular biology, few biologists have shown much interest in how life is defined, and the pioneering work of Robert Rosen has been largely ignored. However, if the promise of systems biology to revolutionize biotechnology is ever to be realized it will be necessary to incorporate the idea of metabolic circularity: metabolism makes metabolism, which makes metabolism, which... At the simplest level this means that it is not enough to consider metabolism as a series of reactions between metabolites catalysed by enzymes that are treated as given: enzymes are not given; they are themselves products of the same metabolism that they catalyse, and they are maintained by processes that are also products of the same mechanism, which are likewise maintained by other processes, and so, in principle, ad infinitum. So there is a problem of infinite regress that needs to be addressed.
Vincent Danos, PPS, Paris
Title: Probabilistic model-checking bio-models
Abstract:
François Fages, INRIA, Rocquencourt
Title: Formal languages in the Biochemical Abstract Machine BIOCHAM (Slides)
Abstract: With the advent of formal languages for modeling biological systems, the design of automated reasoning tools to assist the biologist becomes possible. The biochemical abstract machine BIOCHAM software environment offers a rule-based language to model bio-molecular interactions and a powerful temporal logic based language to formalize the biological properties of the system. Building on these two formal languages, machine learning techniques can be used to infer new molecular interaction rules from temporal properties, or to estimate kinetic parameter values, in order to semi-automatically correct or complete models from observed biological properties of the system. In this article we describe the formal languages of BIOCHAM and illustrate, on a simple cell cycle control model, the use of the machine learning system.
Eric Fanchon, Institut de Biologie Structurale, Grenoble
Title: Reachability of singular states in Thomas-Snoussi networks (Slides)
Abstract: The "asynchronous multivalued logic networks" proposed by R. Thomas, E. H. Snoussi and colleagues (1) can be viewed as a discrete abstraction of a special class of Piecewise-Affine Differential Equations (PADEs). This formalism allows a qualitative analysis of the dynamical behavior of such systems. The influence graph associated to the PADE system defines the architecture of the network and the parameters characterize the strength of the (non-linear) interactions. Recently, this formalism has been extended by de Jong et al. (2) to take into account the so-called 'singular states' and the 'sliding modes'. Singular states are states of reduced dimensionality located at thresholds or intersection of thresholds, and sliding modes are trajectories that slide along a threshold. As the introduction of singular states increases considerably the size of the computational problem, a natural question is whether it is really necessary to introduce them. I will present a generalization of a theorem of E. Snoussi giving a necessary condition for a singular state to contain a sliding mode (persistent state). This establishes a relation between topological characteristics of the influence graph and characteristics of some states. Based on this, I will show that a simple analysis of the topology of the influence graph allows to identify the set of singular states which are reachable from a regular domain. We can thus introduce selectively the fraction of singular states which are really needed to describe the dynamics of the network.
(1) E. H. Snoussi, Dyn. Stab. Sys., 4, 189 (1989); E. H. Snoussi & R. Thomas, Bull. Math. Biol., 55, 973, (1993); R. Thomas and M. Kaufman, Chaos, 11, 180-195 (2001).
(2) H. de Jong, J.-L. Gouze, C. Hernandez, M. Page, T. Sari, and J. Geiselmann, Bull. Math. Biol., 66, 301-340 (2004).
Etienne Farcot, INRIA, Sophia-Antipolis
Title: A comparison of mathematical models of gene networks: piecewise affine systems and discrete systems (Slides)
Abstract: Different kinds of models have been proposed in the last decades to model the dynamics of gene regulatory networks. Among these, piecewise affine differential equations and discrete (both in space and time) dynamical systems represent two largely used and studied classes. These two classes share many features, and have been compared in several manner in the past. In this talk we propose a comparison in terms of symbolic dynamics. We show in particular that discrete systems can be described as a superset of a symbolic representation of piecewise affine systems. For a large class of systems, the subset of admissible trajectories has a strictly lower topological entropy than the whole superset, i.e. the former form a neglictible set in the limit of infinite time.
Marcelle Kaufman, Université libre, Bruxelles
Title: Link between logical structure and dynamics: The example of the p53-mdm2 network
Abstract: Protein p53 is a transcriptional regulator of a large number of genes involved notably in growth arrest, DNA repair, apoptosis and cellular senescence. It therefore plays an essential role in the control of the proliferation of abnormal cells. The level of this key tumor suppressor protein is tightly regulated by the ubiquitin ligase mdm2 through a negative feedback circuit. This negative circuit prevents the permanent presence of high p53 levels that would be lethal for the cells. Normally, the p53-mdm2 network is "off" (low p53 levels) and it is activated only when cells are stressed or damaged, for example by ionizing radiations, aberrant growth signals or drugs. In particular, the DNA damage resulting from ionizing radiations leads to an increase in the level of active p53, which in turn activates the damage repair process, thereby preventing the proliferation of genetically unstable cells.
To model the dynamics of the p53-mdm2-DNA damage network upon irradiation we used a combined logical and differential approach. The logical description provides a powerful way to analyze influence diagrams and unveil all the dynamical potentialities of a network. It also highlights the link between the structure of a regulatory network and its dynamical properties. The differential approach allows one to incorporate details and provides more quantitative information on the evolution dynamics. This strategy allowed us to capture the rich variety of behavior to be expected for the p53-mdm2 network and to reproduce several features of the experimental data for single cells and cell populations. It also allowed us to account for the observed variability between different cells and between different cell types.
Jean Krivine, INRIA, Rocquencourt
Title: Reversible process algebras and self-assembly mechanisms (Slides)
Abstract: Formal languages have been used succesfully to describe biomolecular reactions. Among them, process algebras such as pi-calculus, ambients or CCS offer an interesting one-to-one correspondence with molecular interactions. Without any constraints on what a "formal molecule" can do, one can drift from the original one-to-one interpretation to an "encoding" of biological systems that has interesting properties to study but that is no longer a model of those systems. In particular, when engaged in a complex transaction, a computer process can acquire exclusive usage of resources to avoid unwanted behavior such as deadlocks. However, at the biological level complicate "protocols", such as gene activation/inhibition, occur without comparable "intelligent" mechanisms. Proteins and molecules simply engage blind interactions and chemical exchanges to reach a desired form. In this talk, we will see that using a process calculus that implements reversible interactions, it becomes possible to avoid the "intelligent" mechanisms and to stick to the biological intuition. The key idea is that most interactions are reversible (this allow breaking unstable complexes) while some are not (thus modelling stability). We will see that, through a careful causality analysis of the chain of reversible interactions that lead to stable patterns, it becomes possible to describe the apparently "intelligent" global behavior of highly unsynchronized systems.
Vincent Lacroix, BAOBAB, HELIX-INRIA et Université Claude Bernard, Lyon
Title: Reaction motifs in metabolic networks
Abstract: The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. We start by surveying existing definitions of both modules and motifs, and then introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif. After introducing a formal framework motivated by biological considerations and an algorithm for searching for all occurrences of a reaction motif in a network, we discuss some initial applications to the study of pathway evolution of metabolic networks.
Joint work with Marie-France Sagot, BAOBAB Team, HELIX-INRIA and University Claude Bernard, Lyon. Have contributed also to this work: Cristina Gomes Fernandes (Computer Science Dept., University of São Paulo, Brazil), Anne Morgat (Fondation Rhône-Alpes Futur, France and Swiss Institute of Bioinformatics, Geneva, Switzerland) and Alain Viari (HELIX-INRIA, France).
Cosimo Laneve, Università di Bologna
Title: A basic calculus for molecular biology (Slides)
Abstract: A basic language for describing proteins and membranes, the biok-calccalculus, is introduced. Bonds are represented by means of shared names. Interactions are modeled at the domain level. Protein-protein interactions have to be at most binary; membrane-membrane interactions have to be quaternary. We show that any version of brane calculus can be computed in our calculus with a comparable behaviour in the bisimulation sense.
Michel Le Van Quyen, INSERM, Paris
Title: Does the brain work like the internet?
Abstract: Neuronal networks are extremely complex, including a huge morphological and modecular diversity of cellular constituents, but are capable to coordinate and integrate distributed celllar activities into large synchronous ensembles. In particular, synchronized oscillations occur throughout the neocortex and hippocampus in vivo and have been proposed to constitute a basic mechanism for various forms of integrative operations of the brain. Furthermore, various diseases of the nervous system, most notably the epilepsies, are characterised by even unique forms of network oscillations. One of the main challenge of modern neuroscience is to understand how these dynamic oscillations are related to the wiring structure of the anatomical connectivity. In my talk, I will suggest that a mathematically definable wiring topology known as "small-world" or scale-free networks can help understand to how these coherent oscillations can easily emerge from cellular interactions. These network topologies have a strong "in-homogeneity"-many nodes had few connections and a very few nodes connected with many others. These "super-connected" nodes act as hubs, providing the networks with fast transmission of information, compatible with an axonal wiring economy. Interestingly, these network structures are close to other found in technological, biological and social systems, such as the internet. Therefore, techniques to optimize one kind of network could potentially be applied to another. This could have important implications in neurosciences, notably opening perspectives for new therapeutic interventions in epilepsy.
Arnaud Meyroneinc, CPT, Marseille
Title: Discrete time piecewise models of genetic regulatory networks: single cell and population dynamics (Slides)
Abstract: We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise and contracting mappings whose variables represent gene expression levels. When compared to other models of regulatory networks, these models have an additional parameter which is identified as quantifying interaction delays. In spite of their simplicity, their dynamics presents a rich variety of behaviours. This phenomenology is not limited to piecewise models but extends to smooth nonlinear discrete time models of regulatory networks. After a short review of the general properties of the dynamics of such type of models we shall concentrate on a specific biological question: the allelic exclusion in the recombination mechanism of the Tbeta chains during the maturation of the T cells of the immune system. This example shows the relevance of considering a model of the histories of single cells followed by the analysis of the dynamics of populations of such cells.
Andrew Phillips, Microsoft, Cambridge
Title: Simulating biological systems in the stochastic pi-calculus (Slides)
Abstract: This talk presents a programming language for designing and simulating computer models of biological systems. The language is based on a mathematical formalism known as the pi-calculus, and the simulation algorithm is based on standard kinetic theory of physical chemistry. The language will first be presented using a simple graphical notation, and will subsequently be used to model and simulate a number of intriguing biological systems. The main benefit of the language is its ability to model large systems incrementally, by composing simpler models of subsystems in an intuitive way. The language also facilitates mathematical reasoning of system models, which in future could help provide insight into some of the fundamental properties of biological systems.
Cristian Prisacariu, Institute of Computer Science, Romanian Academy
Title: Modeling MolNet Systems with Timed Distributed pi-calculus (Slides)
Abstract: In this work we first present a brief introduction to the new modeling framework Timed Distributed pi-calculus (TDpi). It is based on the pi-calculus and combines the resource access restrictions imposed by a typing system with time constraints and time coordination aspects. TDpi is intended to model distributed systems with time and resource constraints and coordination problems. The presentation focuses on the modeling of a MolNet system with the new calculus. MolNet is a tool for simulating behavior of molecular networks. It has a component based client-server architecture with a mathematical foundation on Dynamic Structure Discrete Event Systems formalism in order to simulate the continuous changes in a molecular network. A MolNet system is designed as a distributed system with a server coordinating communications between system components. Discussion about further work involves the verifier for models described in TDpi and its integration within the simulation tool.
Gordon Plotkin, Edinburgh
Title: Categorical structure of chemical reaction nets
Abstract:
Elisabeth Remy, IML, Marseille
Title: On differentiation and homeostatic behaviours of discrete dynamical systems (Slides)
Abstract: Genetic regulatory networks are usually represented by signed directed graphs. We study rules proposed by the biologist R. Thomas and relating the structure of such graphs with some typical properties of its dynamics. More precisely, he states that the presence of positive (resp. negative) circuit is a necessary condition for the occurence of multiple stable states, i.e., differentiation (resp. of stables oscillations, i.e., homeostasis). We present here these results, and an extention to a more general form of differentiation, in a discrete formalism, so called "the logical formalism". Joint work with P. Ruet.
Adrien Richard, Université d'Evry, Laboratoire de Méthodes Informatiques
Title: Necessary conditions for multi-attractivity in discrete dynamical systems (Slides)
Abstract: We discuss properties on dynamical systems that have been observed by R. Thomas in the course of his analysis of genetic regulatory networks. The logical structure of these networks are often represented by interaction graphs i.e. graphs whose nodes represent genes and edges their interactions. Furthermore, each interaction is labelled with a sign (which is positive for an activation and negative for an inhibition). R. Thomas conjectured that the presence of a positive circuit (i.e. a circuit containing an even number of inhibitions) in an interaction graph is a necessary condition for the dynamics of the corresponding genetic network to contain several fixed points. We prove this conjecture in a general discrete framework by using an approach similar to the one used by E. Remy et al. and Soulé. We model genetic networks by discrete dynamical systems i.e. by maps from a finite dimensional discrete vector space to itself. Given such a map F and two point a and b, we define the (local) interaction graph G(a,b) giving the part of the (global) interaction graph which plays a role at point a when point b is taken as reference point (we use for that a generalization of the discrete Jacobian matrices defined for Boolean dynamical systems). Then, we prove that if a and b are two distinct fixed points of F then there exists a point c such that G(c,a) has a positive circuit. Moreover, by focusing on the asynchronous dynamics that R. Thomas attaches to F, we prove that positive circuits are necessary for the coexistence not only of fixed points but also of more complex attractors including attractive cycles.
Volker Schmidt, Université d'Ulm, Allemagne
Title: Model-Based Analysis of Keratin Filament Networks in Scanning Electron Microscopy Images of Cancer Cells (Slides)
Abstract: The keratin filament network is an important part of the cytoskeleton in epithelial cells. It is involved in the regulation of shape and viscoelasticity of the cells. In-vitro studies indicated that geometrical network characteristics, such as filament cross-link density, determine the biophysical properties of the filament network. Scanning electron microscopy images of filaments were processed by a skeletonisation algorithm based on morphological operators to obtain a graph structure which represents individual filaments as well as their connections. This method was applied to investigate the effects of the so-called transforming growth factor alpha (TGF-alpha) on the morphology of keratin networks in pancreatic cancer cells. By estimating geometrical network characteristics, like the length and orientation distributions of the keratin filaments, and by fitting random tessellation models, a significant alteration of keratin network morphology could be detected in response to TGF-alpha.
References M. Beil, H. Braxmeier, F. Fleischer, V. Schmidt, P. Walther (2005) Quantitative Analysis of Keratin Filament Networks in Scanning Electron Microscopy Images of Cancer Cells. Journal of Microscopy (to appear) M. Beil, S. Eckel, F. Fleischer, H. Schmidt, V. Schmidt, P. Walther (2005) Fitting of Random Tessellation Models to Cytoskeleton Network Data. Journal of Theoretical Biology (to appear) C. Gloaguen, F. Fleischer, H. Schmidt, V. Schmidt (2005) Fitting of Stochastic Telecommunication Network Models via Distance Measures and Monte-Carlo Tests. Telecommunication Systems (to appear).
Vincent Schächter, Genoscope, Evry
Title: Investigations with constraint-based models of metabolism: 1) reconstructing a global metabolic model of Acinetobacter ADP1 and 2) studying the variability of flux-coupling patterns across environments
Abstract: The availability of complete genomes, of the first metabolomics datasets, and the rise in expectations toward the explanatory and predictive powers of biological network models has given a new impulse to the study of metabolism, thought by many to be a well-understood field a few years ago. One important aim is metabolic reconstruction : comparative methods confirm that procaryote metabolism, in particular, exhibits huge variability, and there are significant gaps in our knowledge of the best known network of metabolic reactions, that of E.coli. Another aim is to better understand the global metabolic behaviour of a (bacterial) cell, seen as a biochemical transformation machine interacting with its environment. Classical models based on sets of differential equations have limited applicability here, both because of the rarity of experimentally determined kinetic parameters, and because of the size of the networks involved.
Constraint-based modeling of metabolism is a semi-formal framework dedicated to the modelling of metabolic processes at steady state, i.e. a global state of the metabolic network is defined as a distribution of fluxes within the network reactions. It emerged in the 90s as a radical simplification of kinetic models and was developed to allow tractable modelling of genome-scale metabolic networks. During the last 4 years, it has been applied successfully to a variety of reconstruction, structural analyses and predictive tasks on large metabolic networks in bacteria and yeast, yielding non-trivial biological insights.
The steady-state hypothesis positions the framework at a level of detail intermediate between description of static network structure and representation of network dynamics. The focus, rather than being on fully instantiated descriptions of the systems behavior, is on sets of such descriptions, i.e. sets of flux distributions compatible with a set of constraints representing the current knowledge on the structure of the network, on thermodynamic and kinetic parameters, and on input/output relationships of the network with its environment. This solution set can be refined incrementally as new constraints are added, ensuring some robustness in structural analyses and metabolic behaviour predictions with respect to modifications of the model.
These models, albeit based on very strong simplifying assumptions, can be used to predict with a reasonable degree of accuracy a number of qualitative observables. They also provide a basis for interpretation of additional experimental information (e.g. metabolic fluxes, metabolic concentrations) as these become available, as well as for the design of more detailed models. They may also be used for theoretical investigations into the plasticity and evolution of metabolic function.
We will start by introducing the steady-state metabolic flux modeling framework and its constraint-based version. We will then focus on two applications of the framework. The first applications fits within the context of the Metabolic Thesaurus project, an experimental effort aimed at understanding the metabolism of, Acinetobacter ADP1 (a versatile, highly competent, strictly aerobic, gram-negative soil bacterium with biodegradative capabilities) using large-scale phenotypic and biochemical data. We will describe the reconstruction of a global metabolic model of Acinetobacter ADP1, up to a point where good agreement was reached between model predictions and a significant set of experimental data on single-deletion mutant growth phenotypes.
The second project is a theoretical study on the variability of flux-coupling patterns across a large set of simulated metabolic environments. Flux-coupling relationships correspond to pairs of reactions for which the value of the flux in one reaction constrains the value of the flux in the other reaction, over the entire set of flux distributions. We will present the approach and preliminary results.
Christophe Soulé, IHES, Bures-sur-Yvette
Title: A stochastic Thomas rule (Slides)
Abstract:
Denis Thieffry, IBDM, Marseille
Title: Logical modelling of genetic regulatory networks (Slides)
Abstract: A proper understanding of the mechanisms controlling gene expression requires the integration of molecular and genetic data into full fledge mathematical models. This contribution focuses on a multi-level, logical approach, which enables a flexible qualitative modelling of complex regulatory networks. This approach encompasses the development of a dedicated software suite (GIN-sim), and will be illustrated by applications to pattern formation and cell differentiation in the fly Drosophila melanogaster.