La construction du cerveau et de ses connexions pendant le développement reste une question ouverte dans la communauté scientifique. Des efforts fructueux ont été faits pour élucider les mécanismes de la croissance axonale, tels que la guidance axonale et les molécules de guidage. Cependant, des preuves récentes suggèrent que d'autres acteurs seraient impliqués dans la croissance des neurones in vivo. Notamment, les axones se développent dans des environnements mécaniquement contraints. Ainsi, pour bien comprendre ce processus dynamique, il faut prendre en compte les mécanismes collectifs et les interactions mécaniques au sein des populations axonales. Néanmoins, les techniques pour mesurer directement cela à partir de cerveaux vivants sont aujourd'hui insuffisantes ou lourdes à mettre en œuvre. Cette thèse résulte d'une collaboration multidisciplinaire, pour faire la lumière sur le développement axonal in vivo et les morphologies complexes des axones adultes. Notre travail a été inspiré et validé à partir d'images d'axones y individuels chez la drosophile, de type sauvage et modifiés génétiquement, que nous avons segmentés et normalisés. Nous avons d'abord proposé un cadre mathématique pour l'étude morphologique et la classification des groupes axonaux. A partir de cette analyse, nous avons émis l'hypothèse que la croissance axonale dérive d'un processus stochastique et que la variabilité et la complexité des arbres axonaux résultent de sa nature intrinsèque, ainsi que des stratégies d'élongation développées pour surmonter les contraintes mécaniques du cerveau en développement. Nous avons conçu un modèle mathématique de la croissance d'un axone isolé fondé sur des chaînes de Markov gaussiennes avec deux paramètres, représentant la rigidité axonale et l'attraction du champ cible. Nous avons estimé les paramètres de ce modèle à partir de données réelles et simulé la croissance des axones à l'échelle de populations et avec des contraintes spatiales pour tester notre hypothèse. Nous avons abordé des thèmes de mathématiques appliquées ainsi que de la biologie, et dévoilé des effets inexplorés de la croissance collective sur le développement axonal in vivo. / How the brain wires up during development remains an open question in the scientific community across disciplines. Fruitful efforts have been made to elucidate the mechanisms of axonal growth, such as pathfinding and guiding molecules. However, recent evidence suggests other actors to be involved in neuron growth in vivo. Notably, axons develop in populations and embedded in mechanically constrained environments. Thus, to fully understand this dynamic process, one must take into account collective mechanisms and mechanical interactions within the axonal populations. However, techniques to directly measure this from living brains are today lacking or heavy to implement. This thesis emerges from a multidisciplinary collaboration, to shed light on axonal development in vivo and how adult complex axonal morphologies are attained. Our work is inspired and validated from images of single wild type and mutated Drosophila y axons, which we have segmented and normalized. We first proposed a mathematical framework for the morphological study and classification of axonal groups. From this analysis we hypothesized that axon growth derives from a stochastic process, and that the variability and complexity of axonal trees result from its intrinsic nature, as well as from elongation strategies developed to overcome the mechanical constraints of the developing brain. We designed a mathematical model of single axon growth based on Gaussian Markov Chains with two parameters, accounting for axon rigidity and attraction to the target field. We estimated the model parameters from data, and simulated the growing axons embedded in spatially constraint populations to test our hypothesis. We dealt with themes from applied mathematics as well as from biology, and unveiled unexplored effects of collective growth on axonal development in vivo.

Kieselalgen (Diatomee) sind eukaryotische einzellige Algen die hochspezifische Proteine (sogenannte Silaffine) erzeugen, um ‘nanopatterned’ Silica-Zellwände herzustellen. Diese Proteine zeigen geringe oder gar keine Homologie innerhalb der Diatomeen Gattung und sind ausgiebig (extensiv) posttranslatorisch modifiziert. Zum Unterschied zu konventioneller Modifikation (z.B. Phosphorylierung und Glykosylierung) weisen Lysinreste von Silaffinen einige Polyaminketten mit sehr heterogenen molekularen Strukturen auf. Diese Modifikationen sind spezifisch für Kieselalgen und spielen somit hypothetisch eine Rolle in der Biosilica-Synthese. Allerdings sind Lysin Polyamin Modifikationen, modifizierte Proteine und modifizierte Stellen kaum charakterisiert. Um diese Frage zu beantworten entwickelten wir eine Methode Polyamine zu quantifizieren und die Position von Polyamin-Modifikationen in engverwandte Proteine zu identifizieren (in morphologisch unterschiedliche Diatomeen Thalassiosira pseudonana, T. oceanica und Cyclotella cryptica). Wir zeigten, dass das Gesamtmuster von Polyaminender phylogenetischen Nähe dieser Kieselalgenarten folgt und dass diese Polyaminmodifikationen an Konsensusstellen sogar in Proteinen auftraten, die keine Sequenzähnlichkeit zeigten.:CONTENTS Summary Zusammenfassung List of figures List of tables Abbreviations 1 Introduction 1.1 Diatoms 1.2 Diatom biosilica 1.2.1 Biosilicification in nature 1.2.2 Diatom biosilica structure and cell cycle 1.2.3 The cell biology of biosilica morphogenesis 1.3 The role of polyamine PTMs in diatom biosilicification 1.3.1 Identifying biomolecules associated with diatom biosilica 1.3.2 PTM complexity of biosilica-associated proteins 1.3.3 Lysine ε-polyamine PTMs in biosilica-associated proteins 1.4 Mass spectrometry in PTM discovery 1.4.1 Modification-specific proteomics 1.4.2 Analysis of polyamine-modified lysines by MS 1.4.3 Fractionation of proteins and peptides prior to MS 1.4.4 MS/MS analysis in modification-specific proteomics 1.4.5 Bioinformatics tools for modification-specific proteomics 1.5 Rationale of the thesis 2 Aim of the thesis 3 Results and discussion 3.1 A method for analysis of ε-polyamine PTMs 3.1.1 Establishing a method to analyse ε-polyamines 3.1.2 Method applicability for lysine PTM profiling 3.1.3 Profiling of lysine PTMs in silaffin-3 3.2 Profiling lysine PTMs in biosilica extracts 3.2.1 Lysine PTM profile and characteristic fragments 3.2.2 Elucidation of phosphopolyamine structures 3.2.3 LysinePTMprofilesofAFSMextracts 3.2.4 Comparison of AFIM and AFSM profiles in T. pseudonana 3.2.5 Phylogenetic relationship across three diatom species 3.3 PTM localization and discovery of consensus motifs 3.3.1 Multiple protease strategy for mapping lysine PTMs 3.3.2 Selection of deprotection technique 3.3.3 Mapping lysine PTMs on tpSil3 using iterative search strategy 3.3.4 Deconvolution of raw MS/MS spectra 3.3.5 PTM mapping by polyamine-specific fragments 3.3.6 Identification of consensus motifs harboring lysine PTMs 4 Conclusions and Outlook 5.1 Synthesis of polyamine standards 5.2 Isolation of biosilica-associated proteins 5.3 Expression of tpSil3 from synthetic gene 5.4 HCl hydrolysis 5.5 AQC-derivatization of amino acids and polyamines 5.6 LC-MS/MS analysis of QAC-derivatives 5.7 Amino acid measurement using UV-detection 5.8 Direct infusion MS/MS analysis 5.9 Acetylation of phosphopolyamines 5.10 31P-NMR measurements 5.11 Deglycosylation with TFMS 5.12 Treatment with HF·pyridine soluble complex 5.13 Anhydrous HF-treatment 5.14 Protein analysis by GeLC-MS/MS 5.15 Proteomics data processing A Appendix B Bibliography Acknowledgments Publications Declaration / Erklärung / Diatoms are eukaryotic unicellular algae that employ highly specialized proteins called silaffins for making nanopatterned silica-based cell walls. These proteins share little or no homology across diatom species and are extensively post-translationally modified. Apart from conventional modifications (e. g., phosphorylation and glycosylation) lysine residues of silaffins bear polyamine chains with highly heterogeneous molecular structure. The latter appear to be specific for silicifying organisms and therefore hypothesized to play a key role in biosilica synthesis. However, polyamine modifications of lysines, modified proteins, and modification sites remain poorly characterized. To address these questions, we developed a method to quantify polyamines and identify sites of polyamine modifications in proteins from phylogenetically closely related, yet morphologically distinct diatoms Thalassiosira pseudonana, T. oceanica, and Cyclotella cryptica. We demonstrated that the overall pattern of polyamines followed the phylogenetic proximity across these diatom species and showed that polyamine modifications occurred at consensus sites even in proteins showing no sequence similarity.:CONTENTS Summary Zusammenfassung List of figures List of tables Abbreviations 1 Introduction 1.1 Diatoms 1.2 Diatom biosilica 1.2.1 Biosilicification in nature 1.2.2 Diatom biosilica structure and cell cycle 1.2.3 The cell biology of biosilica morphogenesis 1.3 The role of polyamine PTMs in diatom biosilicification 1.3.1 Identifying biomolecules associated with diatom biosilica 1.3.2 PTM complexity of biosilica-associated proteins 1.3.3 Lysine ε-polyamine PTMs in biosilica-associated proteins 1.4 Mass spectrometry in PTM discovery 1.4.1 Modification-specific proteomics 1.4.2 Analysis of polyamine-modified lysines by MS 1.4.3 Fractionation of proteins and peptides prior to MS 1.4.4 MS/MS analysis in modification-specific proteomics 1.4.5 Bioinformatics tools for modification-specific proteomics 1.5 Rationale of the thesis 2 Aim of the thesis 3 Results and discussion 3.1 A method for analysis of ε-polyamine PTMs 3.1.1 Establishing a method to analyse ε-polyamines 3.1.2 Method applicability for lysine PTM profiling 3.1.3 Profiling of lysine PTMs in silaffin-3 3.2 Profiling lysine PTMs in biosilica extracts 3.2.1 Lysine PTM profile and characteristic fragments 3.2.2 Elucidation of phosphopolyamine structures 3.2.3 LysinePTMprofilesofAFSMextracts 3.2.4 Comparison of AFIM and AFSM profiles in T. pseudonana 3.2.5 Phylogenetic relationship across three diatom species 3.3 PTM localization and discovery of consensus motifs 3.3.1 Multiple protease strategy for mapping lysine PTMs 3.3.2 Selection of deprotection technique 3.3.3 Mapping lysine PTMs on tpSil3 using iterative search strategy 3.3.4 Deconvolution of raw MS/MS spectra 3.3.5 PTM mapping by polyamine-specific fragments 3.3.6 Identification of consensus motifs harboring lysine PTMs 4 Conclusions and Outlook 5.1 Synthesis of polyamine standards 5.2 Isolation of biosilica-associated proteins 5.3 Expression of tpSil3 from synthetic gene 5.4 HCl hydrolysis 5.5 AQC-derivatization of amino acids and polyamines 5.6 LC-MS/MS analysis of QAC-derivatives 5.7 Amino acid measurement using UV-detection 5.8 Direct infusion MS/MS analysis 5.9 Acetylation of phosphopolyamines 5.10 31P-NMR measurements 5.11 Deglycosylation with TFMS 5.12 Treatment with HF·pyridine soluble complex 5.13 Anhydrous HF-treatment 5.14 Protein analysis by GeLC-MS/MS 5.15 Proteomics data processing A Appendix B Bibliography Acknowledgments Publications Declaration / Erklärung

of the thesis The presented work explores the function and regulation of intracellular signaling that utilizes phospholipase D (PLD) and phosphatidic acid (PA), especially in the context of cellular morphogenesis of plants. PLDs cleave membrane phospholipids to phosphatidic acid, which has important biophysical and signaling role in many contexts, such as stress response, regulation of cytoskeletal dynamics and vesicular transport. Vesicular transport is essential in focused tip growth of plant pollen tubes and root hairs. Part of the work deals with NADPH oxidases, that are an emerging counterpart of PLD/PA signaling. Tobacco pollen tubes served as the main experimental model, as it enables assessing of changes in secretory pathway after pharmacological or genetic treatments. A technique utilizing antisense oligonucleotides was used for selective knock-down of PLD isoforms, NADPH oxidase and newly studied family of lipid phosphate phosphatases (LPPs) in pollen tubes. This enabled to assess functions of individual isoforms. For studying of selected gene families, various bioinformatic tool were utilized, such as dendrogram construction, analysis of available expression data and creating of virtual proteome. These tools together enabled to select potentially important genes for further experimental...

Decapentaplegic (Dpp), a member of the TGF-[Beta] superfamily, acts as a morphogen to direct cell differentiation, determine cell fate and promote cell survival and proliferation in Drosophila wing development. To investigate the role of Dpp in Drosophila wing development, three aspects of the patterning role of Dpp have been analyzed. First, I investigated the cellular responses to Dpp signaling by a loss of function strategy. The consequences of lacking Dpp signal transduction on cell morphology and tissue integrity were analyzed. Second, I investigated whether Dpp signaling is down-stream of Hh signaling to maintain the normal cell segregation at the A/P boundary by clonal analysis. Third, I investigated whether cross talk among the Hh, Dpp and Wg signaling pathways exists and what its relevance for wing patterning is. To investigate the role of Dpp in Drosophila wing development, the general strategies are to look at the phenotypes of loss-of-function and gain-of-function. Mutant clones lacking Dpp signal transduction by knock down Dpp receptor Thick veins (Tkv) do not survive in wing blade due to JNK dependent apoptosis. To get larger mutant clones for analysis, JNK pathway was inhibited by knock down bsk (encodes JNK) in mutant clones lacking Dpp signaling using FLP-FRT system. Clones double mutant for tkv and bsk did not undergo apoptosis, but recovered at very low frequencies compared to sibling clones. Here, I showed that the low recovery of tkv bsk double mutant clones are due to the extrusion of mutant cells. The extrusion of tkv bsk double mutant cells correlated with changes in the actin cytoskeleton and a dramatic loss of the apical microtubule web normally present in these cells. These results suggest that Dpp signaling is required for cell morphogenesis in Drosophila wing development. We propose that Dpp acts as a survival factor in the wing disc epithelium by orchestrating proper cytoskeletal organization and maintaining normal cell-cell contact. Drosophila wing is subdivided into anterior (A) and posterior (P) compartments. This developing into adjacent compartments is crucial for the patterning of Drosophila wing. Previous study has shown that Hedgehog (Hh) signaling is required in A cells to maintain the A/P boundary and is sufficient to specify A type cell sorting. A previous study has in addition implicated the signaling molecule Decapentaplegic (Dpp) in maintaining the A/P boundary. However, this study did not address whether and in which cells, A and/or P, Dpp signal transduction was required to maintain this boundary. Here, I have analyzed the role of components of the Dpp signal transduction pathway and the relation of Dpp and Hh signaling in maintaining the A/P boundary by clonal analysis. I showed that Dpp signaling mediated by the Dpp target gene, T-box protein Optomotor-blind (Omb), is required in A cells, but not in P cells, to maintain the normal position of the A/P boundary. During patterning formation, it is essential for cells to receive precise positional information to pattern the tissue. It has been proposed for a long time that different signaling pathways such as Hedgehog (Hh), Dpp and Wingless (Wg) signaling pathways provide positional information for tissue patterning in an integrated manner. Recently, evidence of interactions between Hh and Dpp as well as Wg and Hh signaling pathways has been reported in Drosophila wing. Here, I have identified additional interactions among Hh, Dpp and Notch/Wg signaling. We propose that the selector gene engrailed, Hh and Dpp signaling interact with each other to regulate target genes expression and thus to pattern the wing along the A/P axis. Further more, I showed that Dpp signaling is also participating in the patterning along the D/V axis by interaction with the selector gene apterous and Notch/Wg signaling.

Les cellules dans la nature se développent dans un large éventail de formes, suivant divers modèles de croissance. Malgré l'importance de ces processus fondamentaux, la façon dont les cellules régulent leur croissance et leur morphogenèse est encore mal comprise. Dans cette thèse, j'ai exploré ces aspects, avec une approche principalement biomécanique, en concentrant mes investigations sur des cellules à paroi à croissance de pointe et en exploitant en particulier la levure fissipare Schyzosaccharomyces pombe. J'ai d'abord développé de nouvelles méthodes pour mesurer les paramètres mécaniques clés de la paroi cellulaire in vivo et à grande échelle, ce qui a permis les premières observations de la dynamique des parois cellulaires. Ceci a révélé que la paroi cellulaire est plus souple et très variable au niveau des pôles de croissance, et presque stable et plus rigide dans les sites non cultivés. Au cours de l'allongement, il existe une interaction entre la mécanique des parois et la croissance cellulaire, dont le contrôle actif permet l'expansion cellulaire tout en préservant l'intégrité des cellules. De plus, j'ai observé qu'il existe une forte corrélation entre la mécanique des parois cellulaires et la morphologie cellulaire, et des perturbations des propriétés de la paroi affectent directement l'établissement et la maintenance de la forme. Ensemble, mes résultats montrent que la régulation de la paroi est fondamentale dans la détermination de la dynamique cellulaire dans les cellules à parois épaissies. Globalement, cela suggère que l'observation dynamique de la mécanique de surface cellulaire est essentielle pour une compréhension complète des processus multifactoriels et complexes comme la croissance et la morphogenèse. / Cells in nature develop in a wide range of forms, following diverse growth patterns. Despite the importance of these fundamental processes, how cells regulate their growth and morphogenesis is still poorly understood. In this thesis, I explored these processes, focusing my investigations on tip growing walled cells and in particular, by exploiting the fission yeast Schyzosaccharomyces pombe, adopting a mainly biomechanical approach. To this aim, I first developed novel methods to measure key cell wall mechanical parameters in vivo and in large scale, which allowed the very first observations of cell wall dynamics. This revealed that the cell wall is softer and highly variable at growing poles, and almost stable and stiffer at non-growing sites. During elongation, there is an interplay between wall mechanics and cell growth, whose active control allows cell expansion while preserving cell integrity. In addition, I observed that there is a strong correlation between cell wall mechanics and cell morphology, and ectopic perturbations of wall properties directly affect shape establishment and maintenance. Together my results show that the regulation of wall mechanics is fundamental in the determination of cell dynamics in tip growing walled cells. Moreover, this suggests that dynamic observation of cell surface mechanics is crucial for a complete understanding of multifactorial and complex processes as growth and morphogenesis.

La morphogenèse cellulaire représente l’ensemble des évènements qui dictent la forme et la structure d’une cellule. Ces changements morphologiques sont importants pour de nombreux mécanismes vitaux, comme le développement embryonnaire, la réaction inflammatoire ou encore la cicatrisation. Pour cela, la morphogénèse cellulaire dépend principalement du remodelage du cytosquelette cellulaire qui, une fois associé à la membrane plasmique, forme l’armature de la cellule. L’ezrine, la radixine et la moésine appartiennent à la famille de protéines ERM et lient la membrane plasmique au cytosquelette d’actine et aux microtubules. De ce fait, les protéines ERM sont impliquées dans différents processus fondamentaux nécessitant un remodelage du cortex cellulaire tels que la mitose et la migration. Dans un contexte pathologique, la surexpression et/ou la sur-activation des protéines ERM corrèlent avec un haut potentiel métastatique et un pauvre pronostic chez les patients. Une meilleure compréhension de la régulation de ces trois protéines pourrait ainsi aider au développement de nouvelles solutions thérapeutiques. L’objectif de mon doctorat portait sur l’identification et la caractérisation de nouvelles voies de signalisation régulant les protéines ERM. Dans un premier temps (i), j’ai participé au développement et la caractérisation de sondes BRET2 permettant de suivre l’activité de chaque protéine ERM en temps réel. Ces sondes BRET2 sont d’ailleurs compatibles avec des études à grande échelle ce qui nous permettra de réaliser des cribles génomiques et chimiques dans le but d’identifier, respectivement, de nouveaux régulateurs et inhibiteurs pharmacologiques des protéines ERM. Ensuite (ii), grâce aux sondes BRET2, nous avons identifié les microtubules en tant que nouveaux régulateurs négatifs des protéines ERM. Nous avons alors montré que la dépolymérisation des microtubules d’interphase à l’entrée en mitose participe à l’activation des protéines ERM et à l’arrondissement cellulaire. Enfin (iii), nous avons montré que le récepteur couplé aux protéines G TPα régule l’activité des protéines ERM dans des cellules de cancer du sein triple négatif. Cette régulation est d’ailleurs importante pour la motilité de ces cellules. Pour conclure, en plus d’avoir développé de nouveaux outils utiles pour des études à grande échelle, mon travail de doctorat a permis de mettre en lumière deux nouvelles voies de signalisation régulant les protéines ERM au cours de la mitose et la migration cellulaire. Sans compter l’apport de nouvelles informations sur un aspect fondamental, mon travail a apporté de nouvelles pistes de réflexion quant aux rôles des protéines ERM dans le développement des métastases. / Cell morphogenesis represents the set of events that dictate the shape and structure of a cell. These morphological changes are important for many vital mechanisms such as embryonic development, inflammatory response, or wound healing. Cell morphogenesis depends mainly on the remodeling of the cell cytoskeleton which forms the framework of the cell when associated with the plasma membrane. Ezrin, radixin and moesin belong to the ERM family and crosslink the plasma membrane to the actin cytoskeleton and microtubules. Therefore, ERMs are involved in various fundamental processes requiring remodeling of the cell cortex such as mitosis and migration. In a pathological context, overexpression and/or overactivation of ERMs correlate with high metastatic potential and poor prognosis in patients. Thus, a better understanding of the regulation of these three proteins could help in the development of new therapeutic solutions. The aim of my PhD work was to identify and characterize novel signaling pathways regulating ERMs. In a first step (i), I participated in the development and characterization of BRET2 biosensors allowing to follow the activity of each ERM protein in real time. These BRET2 biosensors are compatible with large-scale studies which will allow us to perform genomic and chemical screens to identify, respectively, new upstream regulators and pharmacological inhibitors of ERMs. Secondly (ii), based on BRET2-chemical screen, we identified microtubules as new negative regulators of ERMs. We then showed that depolymerization of interphase microtubules at mitosis entry triggers ERM activation and cell rounding. Finally (iii), we showed that the G protein-coupled receptor TPα regulates the activity of ERMs in triple negative breast cancer cells. This regulation is important for the motility of these cells. To conclude, in addition to having developed new tools useful for large-scale studies, my PhD work has uncovered two new signaling pathways regulating ERMs during mitosis and cell motility. In addition to providing new information on a fundamental aspect, my work has provided new insights into the roles of ERMs in the development of metastasis.

No description available.

Das Studium von Transportmechanismen in komplexen Organismen stellt eine zentrale Herausforderung dar, nicht nur in medizinischen und biologischen Disziplinen, sondern auch zunehmend in der Physik und Netzwerktheorie. Insbesondere sind bionisch inspirierte Designprinzipien zunehmend relevant, da sie zuverlässige Lösungsansätze zu verschiedenen theoretischen und technischen Problemen bieten. Herausstechend sind dabei vaskuläre Netzwerke in Säugetieren, deren Entwicklung auffällig stark auf Selbstorganisation beruhen und die korrekte Verteilung von Sauerstoff, Wasser, Blut oder Ähnlichem erlaubt. Dies wird erreicht durch ein komplexes biochemisches Signalsystem, welches an makroskopische Stimulationen, wie z. B. Reibung und Stress, gekoppelt ist. Die Morphogenese solcher Flussnetzwerke ist allerdings noch anderen Restriktionen unterworfen, da diese räumlich eingebettete Objekte darstellen. Sie sind als solche signifikant beschränkter in ihrer Skalierbarkeitund Dynamik. Diese Dissertation addressiert daher relevante Fragestellungen zur Charakterisierung von Netzwerken und der Morphogenesesimulationen von drei-dimensional eingebetteten Netzwerken Die Schlüsselmechanismen auf die wir uns hier konzentrieren sind Flussfluktuationen, Interaktionen zwischen Paarstrukturen und die Aufnahme von Nährstoffen. Zu Beginn zeigen wir, wie sich konventionelle Ansätze zu Flussfluktuationen als allgemeine Einparametermodelle darstellen lassen. Wir demonstrieren damit den kontinuierlichen Übergang zu zunehmend vernetzten Strukturen und indizieren Topologieabhängigkeiten der Plexus in Anbetracht dieses Übergangs. Darauf aufbauend formulieren wir ein neues Adaptationsmodell für ineinander verwobene Gefäßnetzwerke wie sie auch in der Leber, Bauchspeicheldrüse oder Niere vorkommen. Wir diskutieren anhand dieser Strukturen lokale Wechselwirkungen von dreidimensionalen Netzwerken. Dadurch können wir zeigen, dass repulsiv gekoppelte Netzwerke fluktuationsinduzierte Vernetzungen auflösen und attraktive Kopplungen einen neuen Mechanismus zur Erzeugung eben jener darstellen. Als nächstes verallgemeinern wir die Murray Regel für solch komplexe Wechselwirkungen und Fluktuationen. Die daraus abgeleiteten Relationen nutzen wir zur Regression der Modellparameter und testen diese an den Gefäßnetzwerken der Leber. Weiterhin verallgemeinern wir konventionelle Transportmodelle für die Nährstoffaufnahme in beliebigem Gewebe und testen diese in Morphogenesemodellen gegen die bekannten Ansätze zur Dissipationsminimierung. Hier zeigen sich komplexe Übergänge zwischen vernetzten Strukturen und unkonventionelles Phasenverhalten. Allerdings indizieren die Ergebnisse Widersprüche zu echten Kapillargefäßen und wir vermuten Adaptationsmethoden ohne Gefäßgrößenänderung als wahrscheinlicheren Mechanismus. Im Ausblick schlagen wir auf unseren Ergebnissen aufbauende Folgemodelle vor, welche die Modellierung komplexer Transportprozesse zwischen verschränkten Gefäßnetzwerken zum Ziel haben.:Introduction 1 1.1 Complex networks in biology . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Flow networks in mammals . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Network morphogenesis . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Modelling flow network adaptation . . . . . . . . . . . . . . . . 8 1.2.2 Metrics for biological flow networks . . . . . . . . . . . . . . . . 11 Scaling in spatial networks . . . . . . . . . . . . . . . . . . . . . 12 Redundancy of flow networks . . . . . . . . . . . . . . . . . . . 13 1.3 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3.1 Spatial embedding in metabolic costs models . . . . . . . . . . . 16 1.3.2 Characterizing three-dimensional reticulated networks . . . . . . 17 1.3.3 Optimal design for metabolite uptake . . . . . . . . . . . . . . . 20 2 Theory and Methods 23 2.1 Basic principles and mathematics . . . . . . . . . . . . . . . . . . . . 23 2.1.1 Mathematical basics . . . . . . . . . . . . . . . . . . . . . . . . 23 Linear equation systems . . . . . . . . . . . . . . . . . . . . . 23 Dynamical systems and optimization . . . . . . . . . . . . . . 25 Graph theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1.2 Basic hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . 30 Momentum and mass balance . . . . . . . . . . . . . . . . . . . 30 Diffusion-Advection . . . . . . . . . . . . . . . . . . . . . . . . . 31 Flow in a thin channel . . . . . . . . . . . . . . . . . . . . . . . 32 2.1.3 Kirchhoff networks . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Complex transport problems . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.1 Taylor dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.2 Flow-driven pruning . . . . . . . . . . . . . . . . . . . . . . . . 38 Metabolic cost functions . . . . . . . . . . . . . . . . . . . . . . 38 Adaptation and topological transitions . . . . . . . . . . . . . . 40 3 Results 43 3.1 On single network adaptation with fluctuating flow patterns . . . . . . 43 3.1.1 Incorporating flow fluctuations: Noisy, uncorrelated sink patterns 44 3.1.2 Fluctuation induced nullity transitions . . . . . . . . . . . . . . 48 3.1.3 Finite size effects and topological saturation limits . . . . . . . 52 3.2 On geometric coupling between intertwined networks . . . . . . . . . . 55 3.2.1 Power law model of interacting multilayer networks . . . . . . . 55 3.2.2 Adaptation dynamics of intertwined vessel systems . . . . . . . 57 x 3.2.3 Repulsive coupling induced nullity breakdown . . . . . . . . . . 59 3.2.4 Attractive coupling induced nullity onset . . . . . . . . . . . . 66 3.3 On generalizing and applying geometric laws to complex transport networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3.1 Generalizing Murray’s law for complex flow networks . . . . . . 73 Murray’s law for fluctuating flows . . . . . . . . . . . . . . . . . 74 Murray’s Law for extended metabolic costs models . . . . . . . 77 3.3.2 Interpolating model parameters for intertwined networks . . . . 78 Testing ideal Kirchhoff networks . . . . . . . . . . . . . . . . . . 79 3.3.3 Identifying geometrical fingerprints in the liver lobule . . . . . . 85 3.4 On the optimization of metabolite uptake in complex flow networks . . 91 3.4.1 Metabolite transport in thin channel systems . . . . . . . . . . . 91 On single channel solutions . . . . . . . . . . . . . . . . . . . . 91 On detailed absorption rate models . . . . . . . . . . . . . . . . 93 On linear network solutions . . . . . . . . . . . . . . . . . . . . 96 On the uptake in spanning tree and reticulated networks . . . . 97 3.4.2 Optimizing metabolite uptake in shear-stress driven systems . . 100 Link-wise supply-demand model . . . . . . . . . . . . . . . . . . 101 Volume-wise supply-demand model . . . . . . . . . . . . . . . . 110 4 Discussion and Outlook 119 4.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.3.1 Metabolite transport in the liver lobule . . . . . . . . . . . . . . 124 Expansion of the Ostrenko model . . . . . . . . . . . . . . . . . 124 Complex multi transport probems in biology . . . . . . . . . . . 127 4.3.2 Absorption rate optimization and microscopic elimination models 128 Appendix A More on coupled intertwined networks 131 A.1 Coupling of Diamond lattices . . . . . . . . . . . . . . . . . . . . . . . 131 A.1.1 Repulsive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 131 A.1.2 Attractive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.2 Coupling of Laves Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.2.1 Repulsive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.2.2 Attractive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 136 B More on metabolite uptake adaptation 139 B.1 Deriving dynamical systems from demand-supply relationships . . . . . 139 B.2 Microscopic uptake models . . . . . . . . . . . . . . . . . . . . . . . . . 142 B.2.1 Detailed uptake estimation in single layer systems . . . . . . . . 142 B.2.2 Detailed uptake estimation in liver sinusoids . . . . . . . . . . . 143 B.3 Metabolite uptake in three-dimensional plexi . . . . . . . . . . . . . . . 145 B.3.1 Link-wise demand adaptation . . . . . . . . . . . . . . . . . . . 145 B.3.2 Volume-wise demand adaptation . . . . . . . . . . . . . . . . . . 150 Bibliography 155 / Understanding the transport of fluid in complex organisms has proven to be a key challenge not only in the medical and biological sciences, but in physics and network theory as well. This is even more so as biologically-inspired design principles have been increasing in popularity, reliably generating solutions to common theoretical and technical problems. On that note, vascular networks in mammalian organs display a magnificent level of self-organization, allowing them to develop and mature, yet miraculously orchestrate the correct transport of oxygen, water, blood etc. This is achieved by a dedicated biochemical feedback system, which is coupled to macroscopic stimuli, such as mechanical stresses. Another important constraint for the morphogenesis of flow networks is their environment, as these networks are spatially embedded. They are therefore exposed to significant constraints with regards to their scalability and dynamical behavior, which are not yet well understood. This thesis addresses the current challenges of network characterization and morphogenesis modeling for three-dimensional embedded networks. In order to derive proper maturation mechanisms, we propose a set of toy models for the creation of non-planar, entangled and reticulated networks. The key mechanisms we focus on in this thesis are flow fluctuation, coupling of pairing structures and metabolite uptake. We show that in accordance with previous theoretical approaches, fluctuation induced nullity can be formulated as a single parameter problem. We demonstrate that the reticulation transition follows a logarithmic law and find plexi with certain topologies to have limited nullity transitions, rendering such plexi intrinsically wasteful in terms of fluctuation generated reticulation. Moreover, we formulate a new coupling model for entangled adapting networks as an approach for vasculature found in the liver lobules, pancreas, kidneys etc. We discuss a model based on local, distance-dependent interactions between pairs of three-dimensional network skeletons. In doing so we find unprecedented delay and breakdown of the fluctuation induced nullity transition for repulsive interactions. In addition we find a new nullity transition emerging for attractive coupling. Next, we study how flow fluctuations and complex metabolic costs can be incorporated into Murray’s Law. Utilizing this law for interpolation, we are able to derive order of magnitude estimation for the parameters in liver networks, suggesting fluctuation driven adaptation to be the dominant factor. We also conclude that attractive coupling is a reasonable mechanism to account for the maintenance of entangled structures. We test optimal metabolite uptake in Kirchhoff networks by evaluating the impact of solute uptake driven dynamics relative to wall-shear stress driven adaptation. Here, we find that a nullity transition emerges in case of a dominant metabolite uptake machinery. In addition to that, we find re-entrant behavior in case of high absorption rates and discover a complex interaction between shear-stress generation and feedback. Nevertheless, we conclude that metabolite uptake optimization is not likely to occur due to radial adaptation alone. We suggest areas for further studies, which should consider absorption rate variation in order to account for realistic uptake profiles. In our outlook, we suggest a complex morphogenesis model for intertwined networks based on the results of this thesis.:Introduction 1 1.1 Complex networks in biology . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Flow networks in mammals . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Network morphogenesis . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Modelling flow network adaptation . . . . . . . . . . . . . . . . 8 1.2.2 Metrics for biological flow networks . . . . . . . . . . . . . . . . 11 Scaling in spatial networks . . . . . . . . . . . . . . . . . . . . . 12 Redundancy of flow networks . . . . . . . . . . . . . . . . . . . 13 1.3 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3.1 Spatial embedding in metabolic costs models . . . . . . . . . . . 16 1.3.2 Characterizing three-dimensional reticulated networks . . . . . . 17 1.3.3 Optimal design for metabolite uptake . . . . . . . . . . . . . . . 20 2 Theory and Methods 23 2.1 Basic principles and mathematics . . . . . . . . . . . . . . . . . . . . 23 2.1.1 Mathematical basics . . . . . . . . . . . . . . . . . . . . . . . . 23 Linear equation systems . . . . . . . . . . . . . . . . . . . . . 23 Dynamical systems and optimization . . . . . . . . . . . . . . 25 Graph theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1.2 Basic hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . 30 Momentum and mass balance . . . . . . . . . . . . . . . . . . . 30 Diffusion-Advection . . . . . . . . . . . . . . . . . . . . . . . . . 31 Flow in a thin channel . . . . . . . . . . . . . . . . . . . . . . . 32 2.1.3 Kirchhoff networks . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Complex transport problems . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.1 Taylor dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.2 Flow-driven pruning . . . . . . . . . . . . . . . . . . . . . . . . 38 Metabolic cost functions . . . . . . . . . . . . . . . . . . . . . . 38 Adaptation and topological transitions . . . . . . . . . . . . . . 40 3 Results 43 3.1 On single network adaptation with fluctuating flow patterns . . . . . . 43 3.1.1 Incorporating flow fluctuations: Noisy, uncorrelated sink patterns 44 3.1.2 Fluctuation induced nullity transitions . . . . . . . . . . . . . . 48 3.1.3 Finite size effects and topological saturation limits . . . . . . . 52 3.2 On geometric coupling between intertwined networks . . . . . . . . . . 55 3.2.1 Power law model of interacting multilayer networks . . . . . . . 55 3.2.2 Adaptation dynamics of intertwined vessel systems . . . . . . . 57 x 3.2.3 Repulsive coupling induced nullity breakdown . . . . . . . . . . 59 3.2.4 Attractive coupling induced nullity onset . . . . . . . . . . . . 66 3.3 On generalizing and applying geometric laws to complex transport networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3.1 Generalizing Murray’s law for complex flow networks . . . . . . 73 Murray’s law for fluctuating flows . . . . . . . . . . . . . . . . . 74 Murray’s Law for extended metabolic costs models . . . . . . . 77 3.3.2 Interpolating model parameters for intertwined networks . . . . 78 Testing ideal Kirchhoff networks . . . . . . . . . . . . . . . . . . 79 3.3.3 Identifying geometrical fingerprints in the liver lobule . . . . . . 85 3.4 On the optimization of metabolite uptake in complex flow networks . . 91 3.4.1 Metabolite transport in thin channel systems . . . . . . . . . . . 91 On single channel solutions . . . . . . . . . . . . . . . . . . . . 91 On detailed absorption rate models . . . . . . . . . . . . . . . . 93 On linear network solutions . . . . . . . . . . . . . . . . . . . . 96 On the uptake in spanning tree and reticulated networks . . . . 97 3.4.2 Optimizing metabolite uptake in shear-stress driven systems . . 100 Link-wise supply-demand model . . . . . . . . . . . . . . . . . . 101 Volume-wise supply-demand model . . . . . . . . . . . . . . . . 110 4 Discussion and Outlook 119 4.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.3.1 Metabolite transport in the liver lobule . . . . . . . . . . . . . . 124 Expansion of the Ostrenko model . . . . . . . . . . . . . . . . . 124 Complex multi transport probems in biology . . . . . . . . . . . 127 4.3.2 Absorption rate optimization and microscopic elimination models 128 Appendix A More on coupled intertwined networks 131 A.1 Coupling of Diamond lattices . . . . . . . . . . . . . . . . . . . . . . . 131 A.1.1 Repulsive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 131 A.1.2 Attractive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.2 Coupling of Laves Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.2.1 Repulsive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.2.2 Attractive coupling . . . . . . . . . . . . . . . . . . . . . . . . . 136 B More on metabolite uptake adaptation 139 B.1 Deriving dynamical systems from demand-supply relationships . . . . . 139 B.2 Microscopic uptake models . . . . . . . . . . . . . . . . . . . . . . . . . 142 B.2.1 Detailed uptake estimation in single layer systems . . . . . . . . 142 B.2.2 Detailed uptake estimation in liver sinusoids . . . . . . . . . . . 143 B.3 Metabolite uptake in three-dimensional plexi . . . . . . . . . . . . . . . 145 B.3.1 Link-wise demand adaptation . . . . . . . . . . . . . . . . . . . 145 B.3.2 Volume-wise demand adaptation . . . . . . . . . . . . . . . . . . 150 Bibliography 155

[pt] O objetivo geral da presente Tese é analisar a morfogênese do sistema de drenagem do rio Paraíba do Sul e reconhecer os processos envolvidos na sua evolução. Para tanto, foram utilizados os seguintes procedimentos metodológicos: (i) revisão bibliográfica sobre a temática; (ii) construção de um banco de dados temáticos georreferenciados; (iii) análise morfológica e morfométricas dos sistemas de drenagem e do relevo; (iv) processamento de dados em ambiente SIG e análise dos resultados. Ao analisar a morfologia dos sistemas de drenagem na bacia hidrográfica do rio Paraíba do Sul foram identificadas zonas de convergência de drenagem ao longo da calha principal do rio, estando associadas aos grábens originados pelo tectonismo cenozoico que atingiu o planalto sudeste, sendo eles: Taubaté, Resende, Volta Redonda, Três Rios e Itaocara. Além disso, percebeu-se a ocorrência de gorges (gargantas) próximos às zonas de convergência de drenagem, o que sugere a formação de paleodivisores ao longo da bacia. Foram extraídos perfis normalizados de afluentes de drenagem que indicam que rios distantes da foz do rio Paraíba do Sul apresentam índices de concavidades elevados, indicando maior ajuste ao nível de base. Os mapas Seppômen indicam a formação de depressões topográficas ao longo do Planalto Sudeste, situados nos grábens e nas zonas de convergência de drenagem. A análise de perfis topográficos ao longo do divisor da Mantiqueira indica maior dissecação na porção nordeste e menor dissecação na porção sul, esta característica é corroborada pelos valores de chi (χ) que indicam um divisor mais próximo do equilíbrio na porção norte enquanto o divisor na porção sul está submetido à processos de migração e recuo. Com a análise dos resultados, pode-se dizer que o sistema fluvial da Bacia Hidrográfica do rio Paraíba do Sul possui uma complexa história evolutiva, herdada pela interação de esforços tectônicos e processos geomorfológicos sobre o relevo. Sua paleodrenagem era formada por sistemas fluviais endorreicos que convergiam na direção das depressões do relevo formadas com a consolidação do Rift Continental do Sudeste do Brasil. Esta afirmação é comprovada por três evidências: (i) a ocorrência de drenagens inversas ao canal principal do rio Paraíba do Sul; (ii) Perfis de drenagens muito ajustados ao nível de base distantes da foz; (iii) a formação de zonas topográficas deprimidas interrompidas por elevações observados no mapa Seppômen. A evolução do sistema de drenagem da área de estudo se deu por meio de erosão remontante a partir de capturas fluviais sobre o planalto sudeste brasileiro. Estes mecanismos de erosão remontante e capturas fluviais dissecaram os paleodivisores e criaram vagas erosivas que incorporaram, uma a uma, os sistemas fluviais endorreicos do RCSB ao Oceano Atlântico. O sistema de capturas e o pulso erosivo do rio Paraíba do Sul atingiu o divisor da Serra da Mantiqueira inicialmente a norte, através do rio Pomba, e avançou sobre o planalto sudeste incorporando sistemas de drenagem endorréicos por meio de capturas de drenagem até configurar o sistema de drenagem atual. / [en] The main objective of this Thesis is to analyze the morphogenesis of the Paraíba do Sul River drainage system and to recognize the processes involved in its evolution. For that, the following methodological procedures were used: (i) bibliographic review about the theme; (ii) construction of a georeferenced thematic database; (iii) morphological and morphometric analysis of drainage and relief systems; (iv) data processing in a GIS environment and analysis of results. Analyzing the morphology of the drainage systems in the Paraíba do Sul river basin, drainage convergence zones were identified along the main river channel, being associated with the grays originated by the cenozoic tectonism that reached the southeast plateau, being: Taubaté, Resende, Volta Redonda, Três Rios and Itaocara. The occurrence of gorges (gorges) near the drainage convergence zones was noticed, which suggests the formation of paleodividers along the basin. Standardized profiles of drainage tributaries were extracted, indicating that rivers distant from the mouth of the Paraíba do Sul River have high concavity indexes, indicating greater adjustment at the base level. Seppômen maps indicate the formation of topographic depressions along the Southeast Plateau, located on the slopes and in the drainage convergence zones. These depressions occur at the Cenozoic grabens along the southeast plateau. Analysis of topographic profiles along the divider of Mantiqueira indicates greater dissection in the northeast portion and lesser dissection in the southern portion, this characteristic is corroborated by the chi (χ) values that indicate a divider closer to balance in the northern portion while the divider in the southern portion is submitted to migration and retreat processes. With the analysis of the results, it can be said that the river system of the Paraíba do Sul River Basin has a complex evolutionary history, inherited by the interaction of tectonic efforts and geomorphological processes on the relief. Its paleodrainage was formed by endorheic river systems that converged in the direction of the relief depressions formed with the consolidation of the Continental Rift of Southeast Brazil. This statement is supported by three evidences: (i) occurrence of reverse drains to the main channel of the Paraíba do Sul River; (ii) Drainage profiles very adjusted to the base level far from the mouth; (iii) formation of depressed topographic zones interrupted by elevations observed in the Seppômen map. The evolution of the drainage system in the study area was achieved through eroding erosion from river catches over the southeastern Brazilian plateau. Mechanisms of remounting erosion and river catches dissected the paleodividers and created erosive waves that incorporated, one by one, the RCSB s endorheic river systems into the Atlantic Ocean. The capture system and the erosive pulse of the Paraíba do Sul River reached the Serra da Mantiqueira divider initially to the north, through the Pomba River, and advanced over the southeast plateau incorporating endorheic drainage systems by means of drainage catches until the system was configured. current drainage.

Collective cell migration is a defining feature of many morphogenetic processes. Diseases such as congenital heart diseases and cancer arise due to mis-regulation of collective migratory behaviour and animal models have played a pivotal role in dissecting the molecular mechanisms which underlie this process. During embryonic heart development, cardiac precursors undergo a stage of collective migration in both vertebrates and invertebrates. We developed a paradigm to quantitatively assess collective cell migration of cardiac precursors in live embryos of Drosophila, which is the simplest genetic model organism with a heart. Therefore, we studied processes which are commonly observed in most collective cell migration models such as guidance signalling and extracellular matrix remodelling. Our results demonstrate that leading edge of migrating cardioblasts is highly active and that this behaviour is regulated by guidance cues, Slit and Netrin and their respective receptors Robo/Robo2 and Frazzled/Uncoordinated5. These molecules cooperatively promote leading edge motility and epithelial characteristics of the cardioblasts. Next, we determined that matrix restructuring around the cardioblasts requires proteases Mmp1 and Mmp2, which are members of the highly conserved Matrix Metalloproteinase family. We demonstrate that Mmp1 and Mmp2 have distinct roles during lumen formation, however, both Mmp1 and Mmp2 are required for collective motility of the cardioblast leading edge. Hence, we propose that embryonic heart development in Drosophila is an effective and amenable model of collective cell migration which can be applied to discover unique mechanisms which coordinate cell movement in groups. / Thesis / Doctor of Philosophy (PhD)