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Study of the Evolution of Symbiosis at the Metabolic Level Using Models from Game Theory and Economics Martin Wannagat

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Study of the Evolution of Symbiosis at the Metabolic Level Using Models from Game Theory and Economics Martin Wannagat Study of the evolution of symbiosis at the metabolic level using models from game theory and economics Martin Wannagat To cite this version: Martin Wannagat. Study of the evolution of symbiosis at the metabolic level using models from game theory and economics. Quantitative Methods [q-bio.QM]. Université de Lyon, 2016. English. NNT : 2016LYSE1094. tel-01394107v2 HAL Id: tel-01394107 https://hal.inria.fr/tel-01394107v2 Submitted on 22 Nov 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. No d’ordre NNT : xxx THÈSE DE DOCTORAT DE L’UNIVERSITÉ DE LYON opérée au sein de l’Université Claude Bernard Lyon 1 École Doctorale ED01 E2M2 Spécialité de doctorat : Bioinformatique Soutenue publiquement/à huis clos le 04/07/2016, par : Martin Wannagat Study of the evolution of symbiosis at the metabolic level using models from game theory and economics Devant le jury composé de : Nom Prénom, grade/qualité, établissement/entreprise Président(e) Bockmayr Alexander, Prof. Dr., Freie Universität Berlin Rapporteur Jourdan Fabien, CR1, INRA Toulouse Rapporteur Neves Ana Rute, Dr., Chr. Hansen A/S Rapporteure Charles Hubert, Prof., INSA Lyon Examinateur Andrade Ricardo, Dr., INRIA Rhône-Alpes Examinateur Sagot Marie-France, DR, LBBE, INRIA Rhône-Alpes Directrice de thèse Stougie Leen, Prof., Vrije Universiteit, CWI Amsterdam Co-directeur de thèse Marchetti-Spaccamela Alberto, Prof., Sapienza Univ. di Roma Co-directeur de thèse UNIVERSITE CLAUDE BERNARD-LYON 1 Président de l’Université M. le Professeur F. FLEURY Président du Conseil Académique M. le Professeur H. BEN HADID Vice-Président du Conseil d’Administration M. le Professeur D. REVEL Vice-président du Conseil Formation et M. le Professeur P. CHEVALIER Vie Universitaire Vice-président de la Commission Recherche M. F. VALLÉE Directeur Général des Services M. A. HELLEU COMPOSANTES SANTE Faculté de Médecin Lyon-Est - Claude Directeur: M. le Professeur J. ETIENNE Bernard Faculté de Médecine et de Maeutique Directeur: Mme la Professeure C. BURILLON Lyon Sud Charles Mérieux Faculté d’Odontologie Directeur: M. le Professeur D. BOURGEOIS Institut des Sciences Pharmaceutiques Directeur: Mme la Professeure C. VINCIGUERRA et Biologiques Institut Techniques de Réadaptation Directeur: M. le Professeur MATILLON Département de Formation et Centre de Directeur: Mme la Professeure A-M. SCHOTT Recherche en Biologie Humaine COMPOSANTES ET DEPARTEMENTS DE SCIENCES ET TECHNOLOGIE Faculté des Sciences et Technologies Directeur: M. F. De MARCHI Département Biologie Directeur: M. le Professeur F. THEVENARD Département Chimie Biochimie Directeur: Mme C. FELIX Département Génie Electrique et Directeur: M. Hassan HAMMOURI des Procédés Département Informatique Directeur: M. le Professeur S. AKKOUCHE Département Mathématiques Directeur: M. le Professeur G. TOMANOV Département Mécanique Directeur: M. le Professeur H. BEN HADID Département Physique Directeur: M. le Professeur J-C PLENET UFR Sciences et Techniques des Directeur: M. Y.VANPOULLE Activités Physiques et Sportives Observatoire des Sciences de l’Univers de Directeur: M. B. GUIDERDONI Lyon Ecole Polytechnique Universitaire de Lyon 1 Directeur: M. le Professeur E.PERRIN Ecole Supérieure de Chimie Directeur: M. G. PIGNAULT Physique Electronique Institut Universitaire de Technologie de Directeur: M. le Professeur C. VITON Lyon 1 Ecole Supérieure du Professorat et de Directeur: M. le Professeur A. MOUGNIOTTE l’Education Institut de Science Financière Directeur: M. N. LEBOISNE et d’Assurances Acknowledgements 5 TITRE en français L’étude de l’évolution de la symbiose au niveau métabolique en utilisant des modèles de la théorie des jeux et de l’économie RESUME en français Le terme symbiose recouvre tous types d’interactions entre espèces et peut être défini comme une association étroite d’espèces différentes vivant ensemble. De telles interactions impliquant des micro-organismes présentent un intérêt particulier pour l’agriculture, la santé, et les ques- tions environnementales. Tous les types d’interactions entre espèces tels que le mutualisme, le commensalisme, et la compétition, sont omniprésents dans la nature et impliquent souvent le métabolisme. La libération de métabolites par des organismes dans l’environnement permet à d’autres individus de la même espèce ou de différentes espèces de les récupérer pour leur usage propre. Dans cette thèse, nous étudions comment les interactions entre espèces façon- nent l’environnement. Nous examinons les questions de (i) quels sont les besoins minimaux en éléments nutritifs pour établir la croissance, et (ii) quels métabolites peuvent être échangés entre un organisme et son environnement. L’énumération de tous les ensembles minimaux stoechiométriques de précurseurs et de tous les ensembles minimaux de métabolites échangés, en utilisant des modèles complets de réseaux métaboliques, fournit un meilleur aperçu des in- teractions entre les espèces. Dans un environnement spatialement homogène, les métabolites qui sont libérés dans un tel environnement sont partagés par tous les individus. Le problème qui se pose alors est de savoir comment les tricheurs, les individus qui profitent des métabo- lites libérés sans contribuer au bien public, peuvent être exclus de la population. Ceci et d’autres configurations ont déjà été modélisées avec des approches de la théorie des jeux et de l’économie. Nous examinons comment les concepts d’ensembles minimaux de précurseurs stoechiométriques et d’ensembles minimaux de composés échangés peuvent être introduits dans ces modèles. MOTS-CLEFS en français symbiose; métabolisme; modélisation des réseaux métaboliques; énumeration; ensembles min- imaux de précurseurs; ensembles minimaux de fabriques; ensembles minimaux de métabolites échangés; théorie des jeux; économie Title in english Study of the evolution of symbiosis at the metabolic level using models from game theory and economics Abstract in english Symbiosis, a term that brings all types of species interaction under one banner, is defined as a close association of different species living together. Species interactions that comprise microorganisms are of particular interest for agriculture, health, and environmental issues. All kinds of species interactions such as mutualism, commensalism, and competition, are omnipresent in nature and occur often at the metabolic level. Organisms release metabolites to the environment which are then taken up by other individuals of the same or of different species. In this thesis, we study how species interactions shape the environment. We examine the questions of (i) what are the minimal nutrient requirements to sustain growth, and (ii) which metabolites can be exchanged between an organism and its environment. Enumerating all minimal stoichiometric precursor sets, and all minimal sets of exchanged metabolites, using metabolic network models, provide a better insight into species interactions. In a spatially homogeneous environment, the metabolites that are released to such an environment are shared by all individuals. The problem that then arises is how cheaters, individuals that profit from the released metabolites without contributing to the public good, can be prevented 8 from the population. This and other configurations were already modeled with approaches from game theory and economics. We examine how the concepts of minimal stoichiometric precursor sets and minimal sets of exchanged compounds can be introduced into such models. Keywords in english symbyosis; metabolism; metabolic network modeling; enumeration; minimal stoichiometric precursor sets; minimal stoichiometric factories; minimal sets of exchanged compounds; game theory; economics Contents Introduction 11 1 Biological Concepts 15 1.1 Symbiosis ...................................... 15 1.2 Metabolic Network ................................. 17 2 Mathematical Concepts 21 2.1 Metabolic Network modeling ........................... 23 2.1.1 Weighted Directed Hypergraph ...................... 23 2.1.2 Constraint-based models .......................... 23 2.2 Game Theory .................................... 26 2.2.1 Non-Cooperative Game Theory ...................... 27 2.2.2 Cooperative Game Theory ......................... 35 2.3 Economic Models .................................. 38 2.3.1 Comparative advantage .......................... 38 2.3.2 General equilibrium theory ........................ 39 3 Minimal Precursor Sets 43 3.1 Introduction ..................................... 43 3.2 Definitions and Properties ............................. 46 3.3 Complexity ..................................... 51 3.4 Relation to previous work ............................. 53 3.5 Enumerating precursor sets via MILP ...................... 54 3.5.1 Enumeration of minimal SPS ....................... 54 3.5.2 MILP constraints for MD − SPS ..................... 55 3.6 Results and Discussion ............................... 56 3.6.1 Comparison between Sasita and Eker et al.’s approach ........ 56 3.6.2 Comparison between Sasita and combinatorial approach ....... 56 3.6.3 Enumerating
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