Modélisation algébrique de la dynamique multi-échelles des réseaux de régulation biologique

Representing and analyzing large biological regulatory networks arethe two main challenges of the understanding of the livingmachinery. The work we expose here focuses on discrete modeling,usually composed of graphs and sets of parameters, and especiallyon a previously developed framework called Process Hitting, whichallows to give an atomistic representation of some components andtheir combined dynamics. In this thesis, we propose several newframeworks that consist of alternatives to the Process Hitting. Theirhigher expressivity permits to integrate discrete constraints intomodels based on the knowledge of reaction durations orsynchronicity relationships. We also propose a new method toanalyze the dynamics of such models by abstract interpretationwhich allows to answer reachability questions and is well-suited tolarge-scale models (made of hundreds of components, andpotentially more). This method relies on an approximation of thedynamics that avoids the combinatorial explosion usually inherent tosuch analyses, thus answering in in tenths of a second at the priceof being sometimes inconclusive. At last, we discuss the formalbonds between the different formalisms developed in this thesis andthe link with some other widespread discrete modelings. Wepropose several translations from and to these other modelings, inorder to benefit from the high power of modeling and analysis ofthese different frameworks.La représentation et l’analyse des grands réseaux de régulationbiologique sont les deux défis majeurs dans la compréhension desmécanismes du vivant. Le travail exposé dans cette thèse seconcentre sur les modèles discrets, souvent représentés sous laforme de graphes et d’ensembles de paramètres. Il s’inspirenotamment d’un formalisme préalablement développé, appeléFrappes de Processus, qui repose sur une représentation atomiqued’un ensemble de composants et de leur dynamique. Nousproposons dans cette thèse plusieurs représentations alternatives àce formalisme, qui possèdent une plus grande expressivité. Cesreprésentations sont adaptées à l’intégration de contraintesdiscrètes dans les modèles provenant de durées relatives ou derelations de synchronisme entre certaines réactions. Nousproposons par ailleurs une méthode d’analyse de la dynamique parinterprétation abstraite qui permet de répondre à des questionsd’atteignabilité. Cette méthode est spécifiquement adaptée à l’étudedes modèles de grande taille, pouvant contenir plusieurs centainesde composants, et potentiellement davantage. Elle repose en effetsur une approximation de la dynamique qui évite ainsi l’explosioncombinatoire inhérente à ce type d’analyse, permettant de répondreen quelques dixièmes de secondes au prix d’être parfois nonconclusive. Enfin, nous traçons des liens formels entre les différentsformalismes développés dans cette thèse, ainsi qu’avec plusieursautres modélisations discrètes répandues. Nous permettons ainsi àun modèle de jouir des capacités de représentation et d’analyse deplusieurs formalismes à la fois

Modélisation algébrique de la dynamique multi-échelles des réseaux de régulation biologique

Representing and analyzing large biological regulatory networks arethe two main challenges of the understanding of the livingmachinery. The work we expose here focuses on discrete modeling,usually composed of graphs and sets of parameters, and especiallyon a previously developed framework called Process Hitting, whichallows to give an atomistic representation of some components andtheir combined dynamics. In this thesis, we propose several newframeworks that consist of alternatives to the Process Hitting. Theirhigher expressivity permits to integrate discrete constraints intomodels based on the knowledge of reaction durations orsynchronicity relationships. We also propose a new method toanalyze the dynamics of such models by abstract interpretationwhich allows to answer reachability questions and is well-suited tolarge-scale models (made of hundreds of components, andpotentially more). This method relies on an approximation of thedynamics that avoids the combinatorial explosion usually inherent tosuch analyses, thus answering in in tenths of a second at the priceof being sometimes inconclusive. At last, we discuss the formalbonds between the different formalisms developed in this thesis andthe link with some other widespread discrete modelings. Wepropose several translations from and to these other modelings, inorder to benefit from the high power of modeling and analysis ofthese different frameworks.La représentation et l’analyse des grands réseaux de régulationbiologique sont les deux défis majeurs dans la compréhension desmécanismes du vivant. Le travail exposé dans cette thèse seconcentre sur les modèles discrets, souvent représentés sous laforme de graphes et d’ensembles de paramètres. Il s’inspirenotamment d’un formalisme préalablement développé, appeléFrappes de Processus, qui repose sur une représentation atomiqued’un ensemble de composants et de leur dynamique. Nousproposons dans cette thèse plusieurs représentations alternatives àce formalisme, qui possèdent une plus grande expressivité. Cesreprésentations sont adaptées à l’intégration de contraintesdiscrètes dans les modèles provenant de durées relatives ou derelations de synchronisme entre certaines réactions. Nousproposons par ailleurs une méthode d’analyse de la dynamique parinterprétation abstraite qui permet de répondre à des questionsd’atteignabilité. Cette méthode est spécifiquement adaptée à l’étudedes modèles de grande taille, pouvant contenir plusieurs centainesde composants, et potentiellement davantage. Elle repose en effetsur une approximation de la dynamique qui évite ainsi l’explosioncombinatoire inhérente à ce type d’analyse, permettant de répondreen quelques dixièmes de secondes au prix d’être parfois nonconclusive. Enfin, nous traçons des liens formels entre les différentsformalismes développés dans cette thèse, ainsi qu’avec plusieursautres modélisations discrètes répandues. Nous permettons ainsi àun modèle de jouir des capacités de représentation et d’analyse deplusieurs formalismes à la fois

Constraint Identification Using Modified Hoare Logic on Hybrid Models of Gene Networks

We present a new hybrid Hoare logic dedicated for a class of linear hybrid automata well suited to model gene regulatory networks. These automata rely on Thomas\u27 discrete framework in which qualitative parameters have been replaced by continuous parameters called celerities. The identification of these parameters remains one of the keypoints of the modelling process, and is difficult especially because the modelling framework is based on a continuous time. We introduce Hoare triples which handle biological traces and pre/post-conditions. Observed chronometrical biological traces play the role of an imperative program for classical Hoare logic and our hybrid Hoare logic, defined by inference rules, is proved to be sound. Furthermore, we present a weakest precondition calculus (a la Dijkstra) which leads to constraints on dynamical parameters. Finally, we illustrate our "constraints generator" with a simplified circadian clock model describing the rhythmicity of cells in mammals on a 24-hour period

Abducing Biological Regulatory Networks from Process Hitting models

International audienceThe Process Hitting (PH) is a recently introduced framework to model concurrent processes. It is notably suitable to model Biological Regulatory Networks (BRNs) with partial knowledge of cooperations by defining the most permissive dynamics. On the other hand, the qualitative modeling of BRNs has been widely addressed using René Thomas' formalism. Given a PH model of a BRN, we first tackle the inference of the underlying Interaction Graph between components. Then the inference of corresponding Thomas' models is provided by inferring some parameters and abducing the compatible parametrizations

Exhaustive analysis of dynamical properties of Biological Regulatory Networks with Answer Set Programming

International audienceThe combination of numerous simple influences between the components of a Biological Regulatory Network (BRN) often leads to behaviors that cannot be grasped intuitively. They thus call for the development of proper mathematical methods to delineate their dynamical properties. As a consequence , formal methods and computer tools for the modeling and simulation of BRNs become essential. Our recently introduced discrete formalism called the Process Hitting (PH), a restriction of synchronous automata networks, is notably suitable to such study. In this paper, we propose a new logical approach to perform model-checking of dynamical properties of BRNs modeled in PH. Our work here focuses on state reachability properties on the one hand, and on the identification of fixed points on the other hand. The originality of our model-checking approach relies in the exhaustive enumeration of all possible simulations verifying the dynamical properties thanks to the use of Answer Set Programming

Identification of Biological Regulatory Networks from Process Hitting models

International audienceQualitative formalisms offer a well-established alternative to the more tradi-tionally used differential equation models of Biological Regulatory Networks (BRNs). These formalisms led to numerous theoretical works and practical tools to understand emerging behaviors. The analysis of the dynamics of very large models is however a rather hard problem, which led us to previously in-troduce the Process Hitting framework (PH), which is a particular class of non-deterministic asynchronous automata network (or safe Petri nets). Its major advantage lies in the efficiency of several static analyses recently designed to assess dynamical properties, making it possible to tackle very large models. In this paper, we address the formal identification of qualitative models of BRNs from PH models. First, the inference of the Interaction Graph from a PH model summarizes the signed influences between the components that are effective for the dynamics. Second, we provide the inference of all René-Thomas models of BRNs that are compatible with a given PH. As the PH allows the specification of nondeterministic interactions between components, our inference emphasizes the ability of PH to deal with large BRNs with incomplete knowledge on interactions, where Thomas's approach fails because of the combinatorics of parameters. The inference of corresponding Thomas models is implemented using An-swer Set Programming, which allows in particular an efficient enumeration of (possibly numerous) compatible parametrizations

The Hoare-fol Tool

This document presents the tool named "Application of Hoare Logic and Dijkstra's Weakest Proposition Calculus to Biological Regulatory Networks Using Path Programs with Branching First-Order Logic Operators" or Hoare-fol for short. This tool consists in an implementation of the theoretical work developed in [Bernot et al., 2019] and contains the following features: (1) computation of the weakest precondition of a Hoare triple, (2) simplification of this weakest precondition using De Morgan laws and partial knowledge on the initial state, and (3) translation into Answer Set Programming to allow a solving of all compatible solutions

The Hoare-fol Tool

This document presents the tool named "Application of Hoare Logic and Dijkstra's Weakest Proposition Calculus to Biological Regulatory Networks Using Path Programs with Branching First-Order Logic Operators" or Hoare-fol for short. This tool consists in an implementation of the theoretical work developed in [Bernot et al., 2019] and contains the following features: (1) computation of the weakest precondition of a Hoare triple, (2) simplification of this weakest precondition using De Morgan laws and partial knowledge on the initial state, and (3) translation into Answer Set Programming to allow a solving of all compatible solutions