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A Structural Perspective on the Dynamics of Biochemical Systems Sylvain Soliman

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A Structural Perspective on the Dynamics of Biochemical Systems Sylvain Soliman A structural perspective on the dynamics of biochemical systems Sylvain Soliman To cite this version: Sylvain Soliman. A structural perspective on the dynamics of biochemical systems. Bioinformatics [q-bio.QM]. Université Paris Sud - Orsay, 2016. tel-01403712 HAL Id: tel-01403712 https://tel.archives-ouvertes.fr/tel-01403712 Submitted on 7 Dec 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. HABILITATION À DIRIGER DES RECHERCHES Spécialité : Informatique par Sylvain Soliman A structural perspective on the dynamics of biochemical systems Présentée le 7 décembre 2016 devant le jury composé de : M. Vincent Danos (Rapporteur) M. Simon de Givry (Rapporteur) M. Nicolas Le Novère (Rapporteur) M. Philippe Dague M. Alain Denise M. François Fages M. Christophe Soulé H.D.R. préparée au sein de l’EPI LIFEWARE CENTRE DE RECHERCHE Inria Saclay – Île-de-France 1 rue Honoré d’Estienne d’Orves Bâtiment Alan Turing Campus de l’École Polytechnique 91120 Palaiseau Abstract In recent years Systems Biology has become a rich field of study, trying to encompass all the information that has become available thanks to the new high-throughput techniques of biologists. Fifteen years ago, a fundamental breakthrough was the publication of Kurt Kohn’s map of the cell cycle control in mammals. Its similarity with electronic circuits was crucial in both making it impossible for humans to comprehend fully, and in prompting the use of formal methods. Since then however, the networks built by biologists and modellers have continued grow- ing bigger, filled with more and more mechanistic details, especially recently acquired post- transcriptional information, but lacking most of precise kinetic data. Because analysis tech- niques providing dynamical insights mostly rely on complete kinetic information, what was challenging for the human ten years ago is now a challenge even for computers, In this manuscript we will try to give an account of our work of the last twelve years, centered around the question of model. We will define more precisely what this object is, formally, and try to handle the challenges raised by the ever growing amount of data, and corresponding size of models developed in Systems Biology. Our main focus will be the links between the structure and dynamics of those models, seen as means to use several formal methods, like Constraint Programming, to reason on their dynamics. Because of the size issue we will also discuss the question of model reduction, and the related relationships between models, formalisms and interpretations. The discrete nature of the structure underlying a model might seem opposed to the con- tinuous dynamics often associated via differential equations to that model. Nevertheless, we hope to demonstrate that the gap between those two views is quite artificial, and that recent results offer very promising perspectives to bridge it. Keywords : Systems biology, Petri nets, Constraint Programming, Abstract Interpretation, Model-Checking. Une perspective structurelle sur la dynamique des systèmes biochimiques Résumé La Biologie des Systèmes est depuis peu devenue un domaine de recherche florissant qui tente de tirer parti de toutes les informations que les techniques à haut débit des biologistes ont rendues disponibles. Il y a une quinzaine d’années, la publication de la carte du contrôle du cycle cellulaire des mammifères par Kurt Kohn a été une avancée fondamentale. Sa similarité avec un circuit électronique est cruciale dans l’impossibilité pour des humains de l’appréhender complètement mais aussi dans l’idée d’utiliser pour cela des méthodes formelles. Cependant, depuis cette carte, les réseaux construits par les biologistes et modélisateurs ont continué à croître, enrichis de détails mécanistes de plus en plus précis, en particulier des informations post-transcriptionnelles acquises récemment, mais sans données cinétiques précises. Or les méthodes d’analyse qui fournissent des informations dynamiques s’appuient principalement sur une information cinétique complète, par conséquent, ce qui était un défi pour l’humain il y a dix ans l’est devenu pour l’ordinateur aussi. Dans ce manuscrit nous allons tenter de donner une idée de notre travail des douze der- nières années, centré autour de la notion de modèle. Nous allons définir plus précisément, et formellement, cet objet, et essayer de répondre aux défis liés au foisonnement des données et à la croissance des modèles de Biologie des Systèmes. Notre approche est fondée sur les liens entre structure et dynamique d’un tel modèle, ces liens permettant d’utiliser de nombreuses méthodes formelles, comme par exemple la programmation par contraintes, pour raisonner sur la dynamique de ces objets. Le problème de la taille nous amènera par ailleurs à envisa- ger les questions de réduction de modèle, mais aussi de liens entre modèles, formalismes et interprétations. La nature discrète de la structure qui sous-tend un modèle peut sembler opposée à la continuité de la dynamique qui lui est souvent associée via des équations différentielles. Ce- pendant nous espérons démontrer que cette séparation est essentiellement artificielle, et que les résultats récents offrent des perspectives prometteuses de la réduire. Mots-clefs : Biologie des systèmes, réseaux de Petri, Programmation par Contraintes, Inter- prétation Abstraite, Model-Checking. As an adolescent I aspired to lasting fame, I craved factual certainty, and I thirsted for a meaningful vision of human life - so I became a scientist. This is like becoming an archbishop so you can meet girls. Remerciements M. Cartmill Je tiens d’abord à remercier l’équipe Lifeware, et même l’ancienne équipe Contraintes, dont les membres ont depuis des années contribué à mon travail, que ce soit à travers des publications communes, des séminaires de groupe ou même des discussions à table ou en pause café. L’ambiance agréable dont je profite n’est pas étrangère au plaisir renouvelé que j’ai d’aller travailler le matin. Même les anciens membres sont pour certains devenus des amis, ce qui montre leur incroyable capacité à supporter mon humour, mes références musicales des années 80 et ma manière de parler trop fort. Merci en particulier à François qui a su accepter mes particularités (comment ça je n’aime pas voyager ?) tout en ne cessant de me pousser dans la direction la meilleure pour moi. Je remercie aussi ma famille, notamment mes parents qui sans bien savoir ce qu’est une HDR n’en ont pas moins été encourageants depuis bien longtemps. Mes amis hors du monde académique qui ne comprennent rien à mon travail mais continuent à feindre l’admiration, dans l’espoir secret que je pourrai prochainement réparer leur imprimante défectueuse. Enfin mon épouse, Lisa, qui, malgré des moments difficiles, n’a jamais varié dans son soutien inébranlable ; c’est à elle que je dédie ce mémoire. iii Contents 1 Introduction 1 1.1 Context – Systems Biology and Modelling . 2 1.1.1 What is a model? . 3 1.1.2 Simple Biocham Modelling Language . 3 1.1.3 A picture is worth one thousand words . 4 1.1.4 Size is a growing issue . 5 1.1.5 From qualitative to quantitative . 6 1.2 Preliminaries - Reaction models as bipartite graphs . 6 1.2.1 Boolean and bounded views . 7 1.2.2 Continuous and Stochastic views . 8 1.2.3 Petri nets . 8 2 Dynamical Analysis Based on Structural Properties 11 2.1 Context . 11 2.2 Place and Transition Invariants . 12 2.2.1 Computing invariants with Constraint Programming . 13 2.2.2 Finding steady states corresponding to steady fluxes . 23 2.3 Siphons and Traps . 33 2.4 Circuit-based Conditions for Multistationarity . 62 3 Structural and Dynamical Model Reduction 79 3.1 Context . 79 3.2 Subgraph Epimorphisms . 80 3.2.1 A Graphical Method for Reducing and Relating Models . 81 3.2.2 On the Subgraph Epimorphism Problem . 89 3.3 A Constraint Solving Approach to Tropical Equilibration . 105 v vi 4 One Structure, a Hierarchy of Semantics 117 4.1 Abstraction and Type Inference . 118 4.1.1 Abstract Interpretation and Types for Systems Biology . 118 4.1.2 From Reaction Models to Influence Graphs and Back: A Theorem 138 4.2 Relating ODE Systems and Reaction Models . 152 4.2.1 Inferring Reaction Systems from ODEs . 152 4.2.2 A Unique Transformation from ODEs to Reaction Networks . 168 Conclusion 175 Bibliography 176 Research is the process of going up alleys to see if they are blind. Marston Bates Chapter 1 Introduction Summary 1.1 Context – Systems Biology and Modelling . 2 1.1.1 What is a model? . 3 1.1.2 Simple Biocham Modelling Language . 3 1.1.3 A picture is worth one thousand words . 4 1.1.4 Size is a growing issue . 5 1.1.5 From qualitative to quantitative . 6 1.2 Preliminaries - Reaction models as bipartite graphs . 6 1.2.1 Boolean and bounded views . 7 1.2.2 Continuous and Stochastic views . 8 1.2.3 Petri nets . 8 I would first like to point out that most of the work presented in this thesishas already been published. Furthermore, it is usually common work with several of my colleagues, François Fages my former Ph.D. advisor and leader of the team, but also Ph.D. students and interns that spent some time in the LIFEWARE team and also researchers from other institutions. I thus decided to compile these results, not as a compendium of novel research, or as a proof of the amount of work I did by myself, but rather with the aim to share a perspective upon this emerging body of work.
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