Dépliages et interprétation abstraite pour réseaux de régulation biologiques paramétrés

The analysis of dynamics of biological regulatory networks, notably signalling and gene regulatory networks, faces the uncertainty of the exact computational model. Indeed, most of the knowledge available concerns the existence of (possibly indirect) interactions between biological entities (species), e.g. proteins, RNAs, genes, etc. The details on how different regulators of a same target cooperate, and even more so on consistent rates for those interactions, however, are rarely available. In this regard, qualitative modelling approaches in the form of discrete regulatory networks, such as Boolean and Thomas networks, offer an appropriate level of abstraction for the biological regulatory network dynamics. As discrete regulatory networks are based on an influence graph, they require few additional parameters compared to classical quantitative models. Nevertheless, determining the discrete parameters is a well known challenge, and a major bottleneck for providing robust predictions from computational models.The influence graph of a regulatory network establishes dependencies for the evolution of each specie, specified by the directed edges of the graph. The dependencies alone, however, do not suffice to specify the logical function governing the evolution of a specie. Instead the logical functions associated to each specie, constrained by the influence graph, are encoded within the parameters of a discrete regulatory network. The space of admissible logical functions is then represented by a parametric regulatory network. On the one hand, parametric regulatory networks can be used for identification of parameter values for which the resulting discrete regulatory network satisfies given (dynamical) properties. Parameter identification of regulatory networks can thus be seen as a particular instance of model synthesis, in the constrained setting of the underlying influence graph. On the other hand, parametric regulatory networks may be analysed as a stand-alone model, for making predictions that are robust with respect to variability in the network.The analysis of parametric regulatory network dynamics is hampered by dual combinatorial explosion, of the state space and of the parameter space. In this thesis, we develop novel methods of parametric regulatory network analysis, in the form of specialised semantics, aimed at alleviating the combinatorial explosion. First, we introduce abstract interpretation for the set of admissible parameter evaluations (parametrisations).The abstraction allows us to represent any set of parametrisations by a constant size encoding, at the cost of a conservative over-approximation. Second, we lift partial order semantics in the form of unfolding from Petri nets to parametric regulatory networks. The influence graphs of biological regulatory networks tend to be relatively sparse, allowing for a lot of concurrency. This can be harnessed by partial order reduction methods to produce concise state space representations.The two approaches are aimed at tackling both aspects of the dual combinatorial explosion and are introduced in a compatible manner, allowing one to employ them simultaneously. Such application is supported by a prototype implementation used to conduct experiments on various parametric regulatory networks. We further consider refinements of the methods, such as an on-the-run model reduction method lifted to parametric regulatory networks from automata networks.L'analyse de la dynamique des réseaux de régulation biologique, notamment des réseaux de signalisation et de régulation génique, fait face à l'incertitude du modèle de calcul exact. En effet, la plupart des connaissances disponibles concernent l'existence d'interactions (éventuellement indirectes) entre des entités biologiques (espèces), par ex. protéines, ARN, gènes, etc. Les détails sur la manière dont les différents régulateurs d'une même cible coopèrent, et plus encore sur les taux cohérents pour ces interactions, sont cependant rarement disponibles. A cet égard, des approches de modélisation qualitative sous forme de réseaux de régulation discrets, tels que les réseaux booléens et Thomas, offrir un niveau d'abstraction approprié pour la dynamique du réseau de régulation biologique. Les réseaux de régulation discrets étant basés sur un graphe d'influence, ils nécessitent peu de paramètres supplémentaires par rapport aux modèles quantitatifs classiques. Néanmoins, la détermination des paramètres discrets est un défi bien connu et un goulot d'étranglement majeur pour fournir des prédictions robustes à partir de modèles informatiques.Le graphe d'influence d'un réseau de régulation établit des dépendances pour l'évolution de chaque espèce, spécifiées par les arêtes dirigées du graphe. Les dépendances seules, cependant, ne suffisent pas pour spécifier la fonction logique régissant l'évolution d'une espèce. Au lieu de cela, les fonctions logiques associées à chaque espèce, contraintes par le graphe d'influence, sont codées dans les paramètres d'un réseau de régulation discret. L'espace des fonctions logiques admissibles est alors représenté par un réseau de régulation paramétrique. D'une part, les réseaux de régulation paramétriques peuvent être utilisés pour l'identification de valeurs de paramètres pour lesquelles le réseau de régulation discret résultant satisfait des propriétés (dynamiques) données. L'identification des paramètres des réseaux de régulation peut ainsi être vue comme un exemple particulier de synthèse de modèle, dans le cadre contraint du graphe d'influence sous-jacent. D'autre part, les réseaux de régulation paramétriques peuvent être analysés comme un modèle autonome, pour faire des prédictions robustes vis-à-vis de la variabilité du réseau.L'analyse de la dynamique du réseau de régulation paramétrique est entravée par la double explosion combinatoire, de l'espace d'états et de l'espace des paramètres. Dans cette thèse, nous développons de nouvelles méthodes d'analyse de réseau de régulation paramétrique, sous forme de sémantique spécialisée, visant à atténuer l'explosion combinatoire. Tout d'abord, nous introduisons une interprétation abstraite de l'ensemble des évaluations de paramètres admissibles (paramétrisations). L'abstraction permet de représenter n'importe quel ensemble de paramétrisations par un encodage de taille constante, au prix d'une sur-approximation conservatrice. Deuxièmement, nous élevons la sémantique d'ordre partiel sous la forme d'un déploiement des réseaux de Petri vers des réseaux de régulation paramétriques. Les graphiques d'influence des réseaux de régulation biologique ont tendance à être relativement clairsemés, ce qui permet une grande concurrence. Cela peut être exploité par des méthodes de réduction d'ordre partiel pour produire des représentations d'espace d'état concises.Les deux approches visent à aborder les deux aspects de la double explosion combinatoire et sont introduites de manière compatible, ce qui permet de les utiliser simultanément. Une telle application est soutenue par une implémentation prototype utilisée pour mener des expériences sur divers réseaux de régulation paramétriques. Nous considérons en outre des raffinements des méthodes, comme une méthode de réduction de modèle à la volée portée aux réseaux de régulation paramétriques à partir de réseaux d'automates

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The development of post-genomic technologies has led to a paradigm shift in the way we study genetic regulatory networks (GRNs) - the underlying systems which mediate cell function. To complement this, the focus is on devising scalable, unambiguous and automated formal techniques for holistically modelling and analysing these complex systems. Quantitative approaches offer one possible solution, but do not appear to be commensurate with currently available data. This motivates qualitative approaches such as Boolean networks (BNs) , which abstractly model the system without requiring such a high level of data completeness. Qualitative approaches enable fundamental dynamical properties to be studied, and are well-suited to initial investigations. However, strengthened formal techniques and tool support are required if they are to meet the demands of the biological community. This thesis aims to investigate, develop and evaluate the application of Petri nets (PNs) for qualitatively modelling and analysing GRNs. PNs are well-established in the field of computer science, and enjoy a number of attractive benefits, such a wide range of techniques and tools, which make them ideal for studying biological systems. We take an existing qualitative PN approach for modelling GRNs based on BNs, and extend it to more general models based on multi-valued networks (MVNs). Importantly, we develop tool support to automate model construction. We illustrate our approach with two detailed case studies on Boolean models for carbon stress in Escherichia coli and sporulation in Bacillus subtilis, and then consider a multi-valued model of the former. These case studies explore the analysis power of PN s by exploiting a range of techniques and tools. A number of behavioural differences are identified between the two E. coli models which lead us to question their formal relationship. We investigate this by proposing a framework for reasoning about the behaviour of MVNs at different levels of abstraction. We develop tool support for practical models, and show a number of important results which motivate the need for multi-valued modelling. Asynchronous BN s can be seen to be more biologically realistic than their synchronous counterparts. However, they have the drawback of capturing behaviour which is unrealisable in practice. We propose a novel approach for refining such behaviour using signal transition graphs, a PN formalism from asynchronous circuit design. We automate our approach, and demonstrate it using a BN of the lysis-lysogeny switch in phage A. Our results show that a more realistic asynchronous model can be derived which preserves the stochastic switch.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A diversity-aware computational framework for systems biology

L'abstract è presente nell'allegato / the abstract is in the attachmen

Simulating bacterial transcription and translation in a stochastic pi-calculus

International audienceStochastic simulation of genetic networks based on models in the stochastic pi-calculus is a promising recent approach. This paper contributes an extensible model of the central mechanisms of gene ex- pression i.e. transcription and translation, at the prototypical instance of bacteria. We reach extensibility through object-oriented abstractions, that are expressible in a stochastic π-calculus with pattern guarded inputs. We illustrate our generic model by simulating the effect of translational bursting in bacterial gene expression