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Modélisation Mathématique De La Dégradation Des Hydrates De Carbone Dans Le Côlon Humain Rafael Munoz Tamayo

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Modélisation Mathématique De La Dégradation Des Hydrates De Carbone Dans Le Côlon Humain Rafael Munoz Tamayo Modélisation mathématique de la dégradation des hydrates de carbone dans le côlon humain Rafael Munoz Tamayo To cite this version: Rafael Munoz Tamayo. Modélisation mathématique de la dégradation des hydrates de carbone dans le côlon humain. Mathématiques [math]. Université Paris Sud - Paris 11, 2010. Français. tel-02822888 HAL Id: tel-02822888 https://hal.inrae.fr/tel-02822888 Submitted on 6 Jun 2020 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. N° D’ORDRE THÈSE DE DOCTORAT SPECIALITE : PHYSIQUE Ecole Doctorale « Sciences et Technologies de l’Information des Télécommunications et des Systèmes » Présentée par : Rafael Muñoz-Tamayo Sujet : Modélisation Mathématique de la Dégradation des Hydrates de Carbone dans le Côlon Humain Soutenue le 22 mars 2010 devant les membres du jury : M Denis Dochain Rapporteur M Karel Keesman Rapporteur M Robbert Kleerebezem Examinateur Mme Béatrice Laroche Encadrant de thèse Mme Marion Leclerc Encadrant de thèse M Silviu-Iulian Niculescu Examinateur M Éric Walter Directeur de thèse Mathematical Modelling of Carbohydrate Degradation in the Human Colon Rafael Muñoz Tamayo Director: Éric Walter Supervisors: Béatrice Laroche Marion Leclerc Kiên Kiêu France, 2010 A Olguita y sus mariposas ¿Por qué la tierra es mi casa? ¿Por qué la noche es oscura? ¿Por qué la luna es blancura que engorda como adelgaza? ¿Por qué una estrella se enlaza con otra, como un dibujo? Y ¿por qué el escaramujo es de la rosa y del mar? Silvio Rodríguez Contents Acknowledgments 13 Context of the thesis 17 Abstract 19 Résumé 21 Notation and nomenclature 47 1 Introduction 53 2 Description of the human colon 59 2.1 Physiologyandanatomy . .. .. .. .. .. .. .. 59 2.2 Humancolonicmicrobiota . 62 2.3 Anaerobictrophicchain. 65 2.3.1 Mainfermentationpathways . 68 2.3.1.1 Embden-Meyerhoff-Parnaspathway . 68 2.3.1.2 Pyruvatemetabolism . 68 2.3.1.3 Lactateformationandutilization . 69 2.3.1.4 Hydrogenformationandutilization . 69 2.4 In vitro and in vivo modelstostudythehumancolonicecosystem . 70 2.4.1 In vitro models ........................... 71 2.4.2 In vivo models ........................... 73 9 10 CONTENTS 2.5 Conclusions................................. 74 3 Mathematical model construction 77 3.1 Knowledgebasis .............................. 77 3.1.1 Hydraulicrepresentation . 78 3.1.2 Transportphenomena. 79 3.1.3 Carbohydratedegradation . 79 3.1.4 Gaining knowledge from anaerobic digestion modelling ..... 81 3.2 Formulationofthemathematicalmodel . ... 82 3.2.1 Proximalcolonandtransversecolon . 82 3.2.2 Distalcolon............................. 86 3.3 Conclusions................................. 89 4 Handling a complex model 91 4.1 Modelsimplification ............................ 92 4.1.1 Modelstructuresimplification . 92 4.1.2 Knowledge-basedparameterreduction. .. 93 4.1.3 Modelorderreduction . 93 4.1.3.1 Singularperturbationmethod . 94 4.2 Analyzingthewholebyitsparts . 97 4.3 Parameteridentification. 98 4.3.1 Identifiability ............................ 98 4.3.1.1 Structuralidentifiability . 98 4.3.1.2 Practicalidentifiability. 99 4.3.2 Parameterestimation . 100 4.3.2.1 Maximumlikelihood . 101 4.3.2.2 Bayesian estimation: maximum a posteriori ...... 102 4.3.2.3 Optimization. 104 4.3.3 Parameteruncertainty . 104 4.4 Localsensitivityanalysis . 108 4.5 IDEAS:aMatlabtoolboxforparameterestimation . ...... 109 4.5.1 WhydevelopIDEAS? . 110 4.5.2 HowtouseIDEAS? .. .. .. .. .. .. .. 112 4.5.3 Futureextensions. 115 CONTENTS 11 4.6 Conclusions................................. 116 5 Kinetic modelling of in vitro bacterial growth experiments 119 5.1 Homoacetogenesis by the human colonic bacteria R. hydrogenotrophicus . 119 5.1.1 Experimentalsetup . 120 5.1.2 Mathematicalmodel . 120 5.1.3 Reducingthenumberofstatevariables . 123 5.1.4 Identifiabilitystudy. 129 5.1.5 Parameterestimation . 134 5.1.6 Resultsanddiscussion . 135 5.2 Lactate utilization and butyrate production by key colonic bacterial species 139 5.2.1 Mathematical model and reactions stoichiometry . ..... 140 5.2.2 Parameterestimationandmodelselection . 145 5.2.3 Resultsanddiscussion . 146 5.2.3.1 Selectingthebestmodel. 146 5.2.3.2 Reactionsstoichiometry . 148 5.2.3.3 Modellimitationsandapplications . 149 5.3 Conclusions................................. 151 6 Reducing model complexity 153 6.1 Reducingthedimensionoftheparametervector . ...... 153 6.1.1 Determination of yield factors based on stoichiometry ...... 154 6.2 Reducingthedimensionofthestatevector . ..... 158 6.3 Conclusions................................. 160 7 The mathematical model as a virtual experimental platform 163 7.1 Adynamicandspatialpicture . 164 7.2 Whatistheimpactofdietaryfiber?. 171 7.3 Whatistheroleofthemucus? . 173 7.4 Modellimitations .............................. 173 7.5 Conclusions................................. 175 8 Animal rodents inoculated with a minimal human colonic microbiota: an ongoing experimental work 177 8.1 Selectionofaminimalfunctionalmicrobiota . ...... 178 12 CONTENTS 8.2 Conclusions................................. 182 9 Concluding remarks and perspectives 183 Publications 189 Appendix 191 A Numerical values of the model parameters 193 Bibliography 197 Acknowledgments * Remerciements * Agradecimientos Je tiens tout d’abord à remercier les équipes de recherche qui ont fait que mon travail soit possible. Ils sont : l’Unité d’Ecologie et Physiologie du système Digestif (UEPSD), département MIcrobiologie et Chaîne Alimentaire (MICA), l’unité Mathématiques et In- formatique Appliquées (MIA), département MIA de l’Institut national de la recherche agronomique (INRA), ainsi que le Laboratoire des Signaux et Systèmes (L2S) et le projet AlimIntest. Merci pour m’avoir pourvu des excellentes conditions de travail. Naturellement, ce chapitre est consacré à dire merci, mais pas un merci comme ce qu’on utilise tous les jours. Non, moi je veux dire un merci avec un chapeau à tous les gens qui m’on soutenu dans ce projet. Donc, je veux dire Merci\. Je me sens très honoré d’avoir été encadré par Béatrice Laroche, Marion Leclerc et Éric Walter. Nous avons formé une équipe de travail intéressante, où j’ai pu étendre mon hori- zon de connaissance et personnel. Je leur dois quelques changements dans ma façon de penser, et ça je l’apprécie vraiment. Merci à eux pour avoir eu aussi l’intérêt et le temps de me connaître, pour l’indépendance et la confiance. Béatrice, je te remercie pour l’enthousiasme que tu as mis dans ce projet, pour ta pa- tience à m’expliquer tant des choses sur l’univers de la théorie de systèmes. Merci pour le temps partagé dans lequel nous avons discuté d’autres choses que des équations. Il a été très important et réconfortant de pouvoir compter toujours sur ton soutien personnel 13 14 Acknowledgments et ton amitié. Marion, je te remercie pour ton attitude critique et open minded, pour voir plus loin de l’écran, pour tes idées éloignées de la ligne standard, pour chercher des justifications et des arguments biologiques aux équations. Merci pour toutes les discussions au sujet de métabolisme bactérien. Merci pour ton amitié, pour les échanges musicaux et pour ton intérêt à me faire connaître la culture française. Éric, travailler et partager avec toi a été une expérience très enrichissante. J’ai été tou- jours impressionné par ta curiosité et ta connaissance de multiples sujets et ton sens de l’humour. Je te remercie pour ton exigence, tes appels au monde factuel, tes critiques et ton rigueur. Merci de m’avoir appris à analyser ma thèse au-delà de son contexte spéci- fique. Je voudrais remercier spécialement Jean-Philippe Steyer (LBE-INRA-Narbonne). Merci Jean-Phi pour avoir ouvert cette porte pour moi. Je te remercie sincèrement pour ton aide et accompagnement, ton soutien et ta confiance. Merci d’avoir toujours eu l’intérêt de discuter de mon travail et aussi pour le diffuser dans la communauté scientifique de la digestion anaérobie. Ces lignes sont vraiment insuffisantes. J’ai eu de la chance de faire partie de plusieurs équipes de recherche. Chacun d’entre elles m’as apporté une diversité des choses.Je voudrais remercier tout l’ensemble de l’UEPSD, dirigé par Joël Doré pour son accueil. Merci pour enrichir ma connaissance en biologie. C’était un plaisir de partager avec vous ce temps, où j’ai appris de vous plus que ce que vous pouvez imaginer. Joël, je te remercie pour toutes les discussions et les innombrables réponses à mes questions. Je veux remercier Hervé Blottière pour les discussions autour des AGCC. Merci aux gens avec qui j’ai partagé au jour le jour, Patou, Laure, Antonella, Karine, Omar, Stan, Julien (merci pour nos discussions sur ton noyau). Je veux remercier Florence, Fabienne et Charlène, qui m’ont expliqué les détails sur les expériences in vivo. Je tiens à remercier l’unité MIA, dirigée par Alain Trubuil. Merci pour les bons mo- ments autour du café du matin. Je remercie Kiên Kiêu, qui a été toujours disponible à discuter et m’aider. Merci pour l’échange d’idées. Alain, je te remercie pour ton intérêt Acknowledgments 15 sur mon sujet et ta disposition à discuter. Éric et Fabrice, merci
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