Cellular processes critical to sustaining physiology, including growth, division and differentiation, are carefully governed by intricate control systems. Deregulations in these systems often result in complex diseases such as cancer. Hence, it is crucial to understand the interactions between molecular players of these control systems, their emergent network dynamics, and, ultimately, the overall contribution to cellular physiology. In this dissertation, we have developed a mathematical framework to understand two such cellular systems: an early checkpoint (START) in the budding yeast cell cycle (Chapter 1), and the canonical Wnt signaling pathway involved in cell proliferation and differentiation (Chapter 2). START transition is an important decision point where the cell commits to one round DNA replication followed by cell division. Several years of experimental research have gone into uncovering molecular details of this process, but a unified understanding is yet to emerge. In chapter one, we have developed a comprehensive mathematical model of START transition that incorporates several findings including information about the phosphorylation state of key START proteins and their subcellular localization. In the second chapter, we focus on modeling the canonical Wnt signaling pathway, a cellular circuit that plays a key role in cell proliferation and differentiation. The Wnt pathway is often deregulated in colon cancers. Based on some evidence of bistability in the Wnt signaling pathway, we proposed the existence of a positive feedback loop underlying the activation and inactivation of the core protein complex of the pathway. Bistability is a common feature of biological systems that toggle between ON and OFF states because it ensures robust switching back and forth between the two states. To study and explain the behavior of this dynamical system, we developed a mathematical model. Based on experimentally determined interactions, our simple model recapitulates the observed phenomena of bimodality (bistability) and hysteresis under the effects of the physiological signal (Wnt), a Wnt-mimic (LiCl), and a stabilizer of one of the key members of core complex (IWR-1). Overall, we believe that cell biologists and molecular geneticists can benefit from our work by using our model to make novel quantitative predictions for experimental verification. / Ph. D.

abstract: Diabetes is a disease characterized by reduced insulin action and secretion, leading to elevated blood glucose. In the 1990s, studies showed that intravenous injection of fatty acids led to a sharp negative response in insulin action that subsided hours after the injection. The molecule associated with diminished insulin signalling response was a byproduct of fatty acids, diacylglycerol. This dissertation is focused on the formulation of a model built around the known mechanisms of glucose and fatty acid storage and metabolism within myocytes, as well as downstream effects of diacylglycerol on insulin action. Data from euglycemic-hyperinsulinemic clamp with fatty acid infusion studies are used to validate the qualitative behavior of the model and estimate parameters. The model closely matches clinical data and suggests a new metric to determine quantitative measurements of insulin action downregulation. Analysis and numerical simulation of the long term, piecewise smooth system of ordinary differential equations demonstrates a discontinuous bifurcation implicating nutrient excess as a driver of muscular insulin resistance. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2017

In this paper Lewontin’s notion of “quasi-independence” of characters is formalized as the assumption that a region of the phenotype space can be represented by a product space of orthogonal factors. In this picture each character corresponds to a factor of a region of the phenotype space. We consider any region of the phenotype space that has a given factorization as a “type”, i.e. as a set of phenotypes that share the same set of phenotypic characters. Using the notion of local factorizations we develop a theory of character identity based on the continuation of common factors among different regions of the phenotype space. We also consider the topological constraints on evolutionary transitions among regions with different regional factorizations, i.e. for the evolution of new types or body plans. It is shown that direct transition between different “types” is only possible if the transitional forms have all the characters that the ancestral and the derived types have and are thus compatible with the factorization of both types. Transitional forms thus have to go over a “complexity hump” where they have more quasi-independent characters than either the ancestral as well as the derived type. The only logical, but biologically unlikely, alternative is a “hopeful monster” that transforms in a single step from the ancestral type to the derived type. Topological considerations also suggest a new factor that may contribute to the evolutionary stability of “types”. It is shown that if the type is decomposable into factors which are vertex irregular (i.e. have states that are more or less preferred in a random walk), the region of phenotypes representing the type contains islands of strongly preferred states. In other words types have a statistical tendency of retaining evolutionary trajectories within their interior and thus add to the evolutionary persistence of types.

The concept of a fitness landscape arose in theoretical biology, while that of effective fitness has its origin in evolutionary computation. Both have emerged as useful conceptual tools with which to understand the dynamics of evolutionary processes, especially in the presence of complex genotype-phenotype relations. In this contribution we attempt to provide a unified discussion of these two approaches, discussing both their advantages and disadvantages in the context of some simple models. We also discuss how fitness and effective fitness change under various transformations of the configuration space of the underlying genetic model, concentrating on coarse-graining transformations and on a particular coordinate transformation that provides an appropriate basis for illuminating the structure and consequences of recombination.

Submitted by Eunice Novais (enovais@uepg.br) on 2018-09-03T20:15:34Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Pedro J Miranda.pdf: 2542145 bytes, checksum: bb9638f5d6706faee0cb0ad113f1d1de (MD5) / Made available in DSpace on 2018-09-03T20:15:34Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Pedro J Miranda.pdf: 2542145 bytes, checksum: bb9638f5d6706faee0cb0ad113f1d1de (MD5) Previous issue date: 2018-08-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese tem por principal objetivo formalizar e modelar a emergência e a Lei de Proporcionalidade Intrínseca (LPI). Ambos os conceitos são trabalhados e precisados metafisicamente e, então, matematizados. Tal formalização matemática é realizada por meio da Teoria de Categorias utilizando constructos, functores underlying e a categoria dos conjuntos. A Lei de Proporcionalidade Intrínseca é o conjunto das operações internas e suas propriedades que estão nos objetos de um constructo que compõe uma emergência. A aplicação direta desse resultado ocorre em sistemas biológicos concebidos como todos substanciais vivos. A decomposição de um sistema biológico de diversos modos suscita uma aplicação deste modelo: como é possível que diferentes decomposições de um mesmo sistema gerem categorias com propriedades tão diferentes? Esse fenômeno é modelado e explicado pela aplicação direta da emergência e da LPI. Essa aplicação é mediada por meio de Biologia Relacional concebida pelo biólogo matemático Robert Rosen. Além disso, construímos neste trabalho uma Teoria de Nocautes e a aplicamos em um estudo de caso ecológico. / This thesis has as main aim the formalization and the modeling of the emergence and of the Intrinsic Proportionality Law (IPL). Both concepts are initially worked and metaphysically specified for then, in a second moment, be turned into a mathematical concept. Such mathematical formalization is made by means of Category Theory, utilizing constructs, underlying functors and the category of sets. The Intrinsic Proportionality Law is a set of operations and its properties that are within objects of a construct that composes an emergence. The direct application of this result is made on biological systems conceived as living substantial wholes. The decomposition of such a system, by several ways, evokes an application: how is it possible that different decompositions of the same system generate categories with different properties? This phenomenon is modeled and explained by the direct application of emergence and IPL. Such application is mediated by means of Relational Biology, which was conceived by the mathematical biologist Robert Rosen. Additionally, we also built in this work a Knockout Theory and applied it in an ecological study case.

One of the most unforgiving processes in nature is that of Muller's ratchet, a seemingly irreversible accumulation of deleterious mutations that all organisms have to deal with or face extinction. The most obvious way to avoid fitness collapse is recombination, though asexual populations usually do not have the luxury of recombining freely.  With the aid of computational and mathematical models, we have studied other situations where this threat is averted and the organism can survive the ratchet. The results show that a ratchet where all mutations have the same deleterious fitness effect is very effectively stalled for large effects. However, if mutations are allowed to have a broad range of effects, the fitness-loss rate can be substantial even with the same mean effect as the one-type ratchet, but we have  identified parameter regions where even the broad-range effects are effectively stopped. The fitness-loss from a ratchet is very sensitive to the mutation rate and a mutation that increases the mutation rate (mutator) can easily start an otherwise stalled ratchet. Large effect mutators are heavily counter-selected, but smaller mutators can spread in the population. They can be stopped by reversals (antimutators), but even if the mutation rate is equilibrated in this way, there will be large fluctuations in mutation rate and even larger in the fitness-loss rate due to the feedback amplification in their coupling.    Another way of preventing the ratchet is by reversal of the deleterious mutations themselves through back-mutations or compensatory mutations. The rate required to stop the ratchet using only back-mutations before the fitness collapses is very large. A detailed comparison between the deleterious mutations in the ratchet and in a sexual population was made and the difference was found to be greatest for large populations with large genomes. There are obviously many ways to survive the ratchet, but even more ways to drive a species to extinction by enhancing and speeding up the ratchet. By modelling and testing the ratchet for numerous different situations, we show the effects of some of these threats and benefits.

L’évaluation expérimentale des mécanismes de l’initiation, de la propagation, et de la fin des crises d’épilepsie est un problème complexe. Cette thèse consiste en le développement d’un modèle de réseau de neurones aux caractéristiques biologiques pertinentes à la compréhension des mécanismes de genèse et de propagation de crises d’épilepsie. Nous démontrons que les décharges de type pointes ondes peuvent être générées par les neurones inhibiteurs seuls, tandis que les décharges rapides sont dues en grande partie aux neurones excitateurs. Nous concluons que les variations lentes d’excitabilité globale du système, dues aux fluctuations du milieu extracellulaire, et les interactions électro-tonique par jonctions communicantes sont les facteurs favorisant la genèse de crise localement, tandis qu’à plus large échelle spatiale les communications synaptiques excitatrices et le couplage extracellulaire qui participe davantage à la propagation des crises d’une région du cerveau à une autre. / This thesis consists in the development of a network model of spiking neurons and the systematic investigation of conditions under which the network displays the emergent dynamic behaviors known from the Epileptor, a well-investigated abstract model of epileptic neural activity. We find that exogenous fluctuations from extracellular environment and electro-tonic couplings between neurons play an essential role in seizure genesis. We demonstrate that spike-waves discharges, including interictal spikes, can be generated primarily by inhibitory neurons only, whereas excitatory neurons are responsible for the fast discharges during the wave part. We draw the conclusion that slow variations of global excitability, due to exogenous fluctuations from extracellular environment, and gap junction communication push the system into paroxysmal regimes locally, and excitatory synaptic and extracellular couplings participate in seizure spread globally across brain regions.

Wolbachien sind weitverbreitete bakterielle Symbionten von Arthropoden. Sie werden überwiegend durch maternale Vererbung übertragen, können aber auch horizontal von Art zu Art übertragen werden. Wolbachien sind berüchtigt dafür, die Wirtsreproduktion zu manipulieren, können aber auch Mutualismen mit ihren Wirten evolvieren. In dieser Arbeit untersuche ich, welche Rolle horizontale Transmission und mutualistische Effekte bei der Wolbachien-Pandemie unter Arthropoden spielen. Zunächst schätze ich, dass Millionen Arthropodenarten mit Wolbachien infiziert sind. Um diese erstaunliche Verbreitung zu verstehen, entwickele ich ein Modell zur horizontalen zwischenartlichen Transmission von Wolbachien, das auf epidemiologischer und Netzwerk-Theorie aufbaut. Die Ergebnisse weisen auf die Bedeutung von horizontaler Transmission über große phylogenetische Distanzen hin. Da eine erfolgreiche Transmission wahrscheinlich durch symbionteninduzierte Wirtsvorteile begünstigt wird, betrachte ich dann umfassend und kritisch Wolbachien-Arthropoden-Mutualismen und finde diese in vielfältigen Kontexten, aber nur begrenzt Hinweise auf Wolbachien-induzierten Wirtsschutz. Mithilfe eines populationsgenetischen Modells untersuche ich dann den Einfluss von Wirtsvorteilen auf die Infektionsdynamik von Wolbachien. Erstmalig leite ich Invasionsbedingungen und Gleichgewichtsfrequenzen für Wolbachien-Doppelinfektionen her. Die Ergebnisse bestätigen, dass Wirtsvorteile die Invasion von Wolbachien in neue Wirte erheblich erleichtern. Schließlich untersuche ich die Wechselwirkungen zwischen einer Wolbachien-Infektion und dem Immunsystem des Wirtes, wobei ein Schwerpunkt auf reaktiven Sauerstoffspezies liegt. Ich schlage eine Hypothese vor, die unterschiedliche Immunantworten in neuen und ko-evolvierten Assoziationen erklärt. Insgesamt sprechen die Ergebnisse dieser Arbeit für einen wesentlichen Anteil von horizontaler Transmission und mutualistischen Effekten an der Wolbachien-Pandemie in Arthropoden. / Wolbachia are widespread bacterial symbionts of arthropods. They are transmitted predominantly via maternal inheritance, but are also able to move between different species (horizontal transmission). Wolbachia are notorious for selfishly interfering with host reproduction, but they can also evolve mutualistic associations with their hosts. In this thesis, we analyze the role of horizontal transmission and mutualistic effects in the Wolbachia pandemic among arthropods. First, we derive an estimate of the number of Wolbachia-infected arthropod species and find that millions of species are infected. In order to explain this striking distribution, we develop a model of Wolbachia horizontal transmission between species, building on epidemiological theory and network theory. Our findings point to the importance of transmission over large phylogenetic distances. Given that successful horizontal transmission is likely to be facilitated by symbiont-induced host benefits, we then perform a comprehensive review of Wolbachia-arthropod mutualisms and find that these occur in diverse contexts, although the evidence of Wolbachia-induced host protection in nature is limited so far. By means of a population genetic model, we then analyze the influence of host benefits on the infection dynamics of Wolbachia. For the first time, we derive invasion conditions and equilibrium frequencies for Wolbachia double infections. Our results corroborate that host benefits substantially facilitate invasion of Wolbachia into novel hosts. Finally, we examine the interactions between Wolbachia infection and the host immune system, with a focus on reactive oxygen species. We propose a hypothesis that explains differential immune responses in novel and coevolved associations. Taken together, the findings presented in this thesis argue for a significant involvement of horizontal transmission and mutualistic effects in the Wolbachia pandemic among arthropods.

This thesis explores the role of collective cell migration and self-organisation in the development of the embryo and in vitro tissue formation through mathematical and computational approaches. We consider how population heterogeneity, microenvironmental signals and cell-cell interactions facilitate cells to collectively organise and navigate, with the aim to work towards uncovering general rules and principles, rather than delving into the microscopic molecular details. To ensure the biological relevance of our results, we collaborate closely with experimental biologists working on two model systems. First, to understand how neural crest cells obtain directionality, maintain persistence and specialise during their migration, we use computational simulations in parallel with imaging of chick embryos under genetic and surgical perturbations. We show how only a few cells adopting a leader state that enables them to read out chemical signals can lead a population of cells in a follower state over long distances in the embryo. Furthermore, we devise and test an improved mechanism of how cells dynamically switch between leader and follower states in the presence of a chemoattractant gradient. Our computational work guides the choice of new experiments, aids in their interpretation and probes hypotheses in ways the experiments can not. Secondly, to study the self-organisation of mouse skin cells in vitro, we draw on aggregation processes and scaling theory. Dermal and epidermal cells, after being dissociated and mixed, can reconstitute functional (transplantable and hair-growing) skin in culture. Using kinetic aggregation models and scaling analysis we show that the initial clustering of epidermal cells can be described by Smoluchowski coagulation, consistent with the dynamics of the "clustering clusters" universality class. Then, we investigate a potential mechanism for the size-regulation of cell aggregates during the later stages of the skin reconstitution process. Our analysis shows the extent to which this tissue formation follows a single physical process and when the transition to different dynamics occurs, which may be triggered by cellular biochemical changes.

Les systèmes reproducteurs déterminent comment le matériel génétique est transmis d’une génération à la suivante […]. Les espèces qui combinent de la reproduction sexuée et asexuée/clonale sont très répandues [… mais] l’effet de leur système reproducteur sur leur évolution reste énigmatique et discuté.L’objectif de cette thèse est de modéliser la dynamique des fréquences génotypiques d’une population avec une combinaison de reproduction sexuée et/ou clonale dans des cycles de vie principalement diploïdes [. … Un] modèle du type chaine de Markov avec temps et états discrets sert de base mathématique pour décrire [leurs] changements […] au cours du temps.Les résultats montrent que la reproduction partiellement asexuée peut en effet modifier la dynamique de la diversité génomique par rapport à une reproduction strictement sexuée ou strictement asexuée. […] L’histoire démographique a un rôle important pour les organismes partiellement clonaux et doit être prise en compte dans toute analyse […].Cette thèse fait des recommandations pour la collecte des données et une hypothèse de base pour l’interprétation des données de génétique/génomique […]. Ces résultats ont des retombées dans plusieurs domaines, allant de la recherche fondamentale […] à des applications en agriculture […], pêche […] et protection de la nature […]. / Reproductive systems determine how genetic material is passed from one generation to the next, making them an important factor for evolution. Organisms that combine sexual and asexual/clonal reproduction are very widespread [… yet] the effects of their reproductive system on their evolution are still controversial and poorly understood.The aim of this thesis was to model the dynamics of genotype frequencies under combined sexual/clonal reproduction in dominantly diploid life cycles [. … A] state and time discrete Markov chain model served as the mathematical basis to describe [their] changes […] through time.The results demonstrate that partial clonality may indeed change the dynamics of genomic diversity compared to either exclusively sexual or exclusively clonal populations. […] Time has a crucial role in partially clonal populations and needs to be taken into account in any analysis of their genomic diversity.This thesis provides recommendations for data collection and a null hypothesis for the interpretation of population genetic/genomic data […]. Moreover, it includes new methods for the analysis of genotype-based population genetic Markov chain models. These results have a high potential relevance in several areas, ranging from basic research […] to applications in agriculture […], fisheries […] and nature conservation […].