Living cells are made up of networks of interacting genes, proteins and other bio-molecules. Simple interactions between network components in forms of feedback regulations can lead to complex collective dynamics. A key task in cell biology is to gain a thorough understanding of the dynamics of intracellular systems and processes. In this thesis, a combined approach of mathematical modelling, computational simulation and analytical techniques, has been used to obtain a deeper insight into the dynamical aspects of a variety of feedback systems commonly encountered in cells. These systems range from model system with detailed available molecular knowledge to general regulatory motifs with varying network structures. Deterministic as well as stochastic modelling techniques have been employed, depending primarily on the specific questions asked. The first part of the thesis focuses on dissecting the principles behind the regulatory design of the Tryptophan Operon system in Escherichia coli. It has evolved three negative feedback loops, namely repression, attenuation and enzyme inhibition, as core regulator mechanisms to control the intracellular level of tryptophan amino acid, which is taken up for protein synthesis. Despite extensive experimental knowledge, the roles of these seemingly redundant loops remain unclear from a dynamical point of view. We aim to understand why three loops, rather than one, have evolved. Using a large-scale perturbation/response analysis through modelling and simulations and novel metrics for transient dynamics quantification, it has been revealed that the multiple negative feedback loops employed by the tryptophan operon are not redundant. In fact, they have evolved to concertedly give rise to a much more efficient, adaptive and stable system, than any single mechanism would provide. Since even the full topology of feedback interactions within a network is insufficient to determine its behavioural dynamics, other factors underlying feedback loops must be characterised to better predict system dynamics. In the second part of the thesis, we aim to derive these factors and explore how they shape system dynamics. We develop an analytical approach for stability and bifurcation analysis and apply it to class of feedback systems commonly encountered in cells. Our analysis showed that the strength and the Hill coefficient of a feedback loop play key role in determining the dynamics of the system carrying the loop. Not only that, the position of the loop was also found to be crucial in this decision. The analytical method we developed also facilitates parameter sensitivity analysis in which we investigate how the production and degradation rates affect system dynamics. We find that these rates are quite different in the way they shape up system behaviour, with the degradation rates exhibiting a more intricate manner. We demonstrated that coupled-loop systems display greater complexity and a richer repertoire of behaviours in comparison with single-loop ones. Different combinations of the feedback strengths of individual loops give rise to different dynamical regimes. The final part of the thesis aims to understand the effects of molecular noise on dynamics of specific systems, in this case the Tryptophan Operon. We developed two stochastic models for the system and compared their predictions to those given by the deterministic model. By means of simulations, we have shown that noise can induce oscillatory behaviour. On the other hand, incorporating noise in an oscillatory system can alter the characteristics of oscillation by shifting the bifurcation point of certain parameters by a substantial amount. Measurement of fluctuations reveals that that noise at the transcript level is most significant while noise at the enzyme level is smallest. This study highlights that noise should not be neglected if we want to obtain a complete understanding of the dynamic behaviour of cells.

The management and administration of legally defined marine boundaries in Australia is subject to a variety of political, legal and technical challenges. The purpose of this thesis is to address three of the technical challenges faced in the implementation of marine boundaries which cannot be dealt with by applying conventional land cadastre and land administration principles. The three challenges that are identified and addressed are (i) marine boundary delimitation and positioning uncertainty, (ii) the construction and maintenance of four dimensional marine parcels, and (iii) the modelling and management of marine boundary uncertainty metadata.

Les astrocytes sont des cellules gliales du système nerveux central, essentielles à la formation des synapses, à la barrière hémato-encéphalique ainsi qu’au maintien de l'homéostasie. Récemment, les astrocytes ont été identifiés comme éléments clés du traitement de l'information dans le système nerveux central. Les astrocytes peuvent communiquer avec les neurones au niveau des synapses et moduler la communication neuronale en libérant des gliotransmetteurs et en absorbant des neurotransmetteurs. L’utilisation de nouvelles techniques comme la microscopie à super-résolution et les indicateurs calciques encodés génétiquement a permis de révéler une grande diversité spatio-temporelle des signaux calciques astrocytaires. La majorité de ces signaux sont observés au sein de leurs prolongements cellulaires, qui sont le site de communication entre neurones et astrocytes. Ces prolongements sont trop fins pour être observés en microscopie optique conventionnelle, de sorte que la microscopie à super-résolution et la modélisation informatique sont les seules méthodes adaptées à leur étude. Les travaux présentés dans cette thèse ont pour but d’étudier l'effet des propriétés spatiales (telles que la géométrie cellulaire, les distributions moléculaires et la diffusion) sur les signaux calciques dans les prolongements astrocytaires. Historiquement, les signaux calciques ont été modélisés à l'aide d'approches déterministes non spatiales. Ces modèles ont permis l'étude des signaux calciques à l’échelle de la cellule entière voire à l’échelle du réseau de cellules. Ces méthodes ne prennent cependant pas en compte la stochasticité inhérente aux interactions moléculaires ainsi que les effets de diffusion, qui jouent un rôle important dans les petits volumes. Cette thèse présente un modèle stochastique et spatial qui a été développé dans le but d’étudier les signaux calciques dans les prolongements fins astrocytaires. Ce travail a été réalisé en collaboration avec des expérimentateurs, qui nous ont fourni des données de microscopie électronique et à super-résolution. Ces données ont permis de valider le modèle. Les simulations du modèle suggèrent que (1) la diffusion moléculaire, fortement influencée par la concentration et la cinétique des buffers calciques endogènes et exogènes, (2) l'organisation spatiale intracellulaire des molécules, notamment le co-clustering des canaux calciques, (3) la géométrie du reticulum endoplasmique et sa localisation dans la cellule, (4) la géométrie cellulaire influencent fortement les signaux calciques et pourraient être responsables de leur grande diversité spatio-temporelle. Ces travaux contribuent à une meilleure compréhension du traitement de l’information par les astrocytes, un prérequis pour une meilleure compréhension de la communication entre les neurones et les astrocytes ainsi que de son influence sur le fonctionnement du cerveau. / Astrocytes are predominant glial cells in the central nervous system, which are essential for the formation of synapses, participate to the blood-brain barrier and maintain the metabolic, ionic and neurotransmitter homeostasis. Recently, astrocytes have emerged as key elements of information processing in the central nervous system. Astrocytes can contact neurons at synapses and modulate neuronal communication via the release of gliotransmitters and the uptake of neurotransmitters. The use of super-resolution microscopy and highly sensitive genetically encoded Ca2+ indicators (GECIs) has revealed a striking spatiotemporal diversity of Ca2+ signals in astrocytes. Most astrocytic signals occur in processes, which are the sites of neuron-astrocyte communication. Those processes are too fine to be resolved by conventional light microscopy so that super-resolution microscopy and computational modeling remain the only methodologies to study those compartments. The work presented in this thesis aims at investigating the effect of spatial properties (as e.g cellular geometry, molecular distributions and diffusion) on Ca2+ signals in those processes, which are deemed essential in such small volumes. Historically, Ca2+ signals were modeled with deterministic well-mixed approaches, which enabled the study of Ca2+ signals in astrocytic networks or whole-cell events. Those methods however ignore the stochasticity inherent to molecular interactions as well as diffusion effects, which both play important roles in small volumes. In this thesis, we present the spatially-extended stochastic model that we have developed in order to investigate Ca2+ signals in fine astrocytic processes. This work was performed in collaboration with experimentalists that performed electron as well as super-resolution microscopy. The model was validated against experimental data. Simulations of the model suggest that (1) molecular diffusion, strongly influenced by the concentration and kinetics of endogenous and exogenous buffers, (2) intracellular spatial organization of molecules, notably the co-clustering of Ca2+ channels, (3) ER geometry and localization within the cell, (4) cellular geometry strongly influence Ca2+ dynamics and can be responsible for the striking diversity of astrocytic Ca2+ signals. This work contributes to a better understanding of astrocyte Ca2+ signals, a prerequisite for understanding neuron-astrocyte communication and its influence on brain function.

Subject of the dissertation is a probability analysis on creation of embankment subsoil filtration deformations. Out of the broad topic of filtration deformations, the dissertation is focused at initiation of the process. At this phase, the overlying layers downstream of levee get uplifted, and eventually get breached. The process of downstream subsoil failure probability estimation is formulated using mathematical and statistical modelling. Within the scope of parametrical study the suggested method is applied onto a test environment. Results of the probability estimation are compared with results obtained using Limit state design method. The results of stochastic modelling can be used for improvement of Limit state design method precision.

Uganda is using a strategy called treatment as prevention where as many individuals as possible that are infected with HIV receive treatment. As a result, the number of newly infected individuals has decreased significantly. However, there is a discussion about a potential problem regarding transmitted drug resistance. This work aims to investigate if this in fact will be a problem in the future, and to estimate the costs for different scenarios. Through developing a population-based mathematical model that describes transmission dynamics of HIV in Uganda, stochastic simulations are made for different conditions. Through analysing our simulations, we can see that Uganda may have to change their approach to HIV treatment. / För att minska smittoriskerna av HIV nyttjar Uganda en strategi som syftar till att behandla så många smittade personer som möjligt. Detta har lett till en signifikant minskning av antalet smittade personer. Det har dock uppstått en diskussion angående om läkemedels-resistent smitta kan komma att utgöra ett problem. Detta arbete syftar till att undersöka om detta kan utgöra ett problem i framtiden samt till att uppskatta de kostnader som kan uppstå i olika typer av scenarion. Under olika förutsättningar genomförs stokastiska simuleringar med hjälp av en matematisk populationsmodell framtagen för att beskriva spridningen av HIV i Uganda. Genom att analysera resultaten från olika simuleringar dras slutsatsen att Uganda kan behöva omvärdera sitt tillvägagångssätt gällande behandling av HIV.

La fusion thermonucléaire est l'une des candidates favorites a la production d'énergie au courant de ce siècle. Parmi les défi que nous pose cette discipline, on note la turbulence au bord des machine de fusion et l'interaction plasma paroi. En effet nous avons montre que les fluctuations turbulentes affectent le transport des particules neutres et le rayonnement qui leur est associe. En particulier, sont affectes les neutres lents (dont le libre parcours moyen est de l'ordre de la longueur de corrélation des fluctuations), comme les molécules et les atomes d´impuretés pulvérises a la parois. Cette conclusion nous a conduit a inclure ces fluctuations dans le code de transport EIRENE utilise pour le dimensionnement de la machine ITER. Il a aussi été montre qu'en moyenne les fluctuations favorisent la pénétration des neutres dans le plasma. / Edge plasma of tokamaks manifests high level of fluctuations amplitude (>50%). It has been demonstrated that such a fluctuations affect significantly the transport of neutral particles, and in particular the slow particles as molecules and sputtered impurities. That is their penetration depth in the plasma is enhanced in the average. Then turbulent fluctuations are now implemented in the monte carlo transport code EIRENE used for the design of ITER.

In spite of remarkable progress in molecular biology, our understanding of the dynamics and functions of intra- and inter-cellular biological networks has been hampered by their complexity. Kinetics modelling, an important type of mathematical modelling, provides a rigorous and reliable way to reveal the complexity of biological networks. In this thesis, two genetic regulatory networks have been investigated via kinetic models. In the first part of the study, a model is developed to represent the transcriptional regulatory network essential for the circadian rhythms in Drosophila. The model incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not used to describe the regulation of genes, instead the explicit reactions of binding and unbinding processes of transcription factors to promoters are modelled. The model is described by a set of ordinary differential equations and the parameters are estimated from the in vitro experimental data of the clocks' components. The simulation results show that the model reproduces sustained circadian oscillations in mRNA and protein concentrations that are in agreement with experimental observations. It also simulates the entrainment by light-dark cycles, the disappearance of the rhythmicity in constant light and the shape of phase response curves resembling that of experimental results. The model is robust over a wide range of parameter variations. In addition, the simulated E-box mutation, perS and perL mutants are similar to that observed in the experiments. The deficiency between the simulated mRNA levels and experimental observations in per01, tim01 and clkJrk mutants suggests some differences in the model from reality. Finally, a possible function of VRI/PDP1 loops is proposed to increase the robustness of the clock. In the second part of the study, the sources of intrinsic noise and the influence of extrinsic noise are investigated on an intracellular viral infection system. The contribution of the intrinsic noise from each reaction is measured by means of a special form of stochastic differential equation, the chemical Langevin equation. The intrinsic noise of the system is the linear sum of the noise in each of the reactions. The intrinsic noise arises mainly from the degradation of mRNA and the transcription processes. Then, the effects of extrinsic noise are studied by means of a general form of stochastic differential equation. It is found that the noise of the viral components grows logarithmically with increasing noise intensities. The system is most susceptible to noise in the virus assembly process. A high level of noise in this process can even inhibit the replication of the viruses. In summary, the success of this thesis demonstrates the usefulness of models for interpreting experimental data, developing hypotheses, as well as for understanding the design principles of genetic regulatory networks.

Les communautés végétales constituent des systèmes complexes au sein desquels de nombreuses espèces, pouvant présenter une large variété de traits fonctionnels, interagissent entre elles et avec leur environnement. En raison de la quantité et de la diversité de ces interactions les mécanismes qui gouvernent les dynamiques des ces communautés sont encore mal connus. Les approches basées sur la modélisation permettent de relier de manière mécaniste les processus gouvernant les dynamiques des individus ou des populations aux dynamiques des communautés qu'ils forment. L'objectif de cette thèse était de développer de telles approches et de les mettre en oeuvre pour étudier les mécanismes sous-jacents aux dynamiques des communautés. Nous avons ainsi développés deux approches de modélisation. La première s'appuie sur un cadre de modélisation stochastique permettant de relier les dynamiques de populations aux dynamiques des communautés en tenant compte des interactions intra- et interspécifiques et de l'impact des variations environnementale et démographique. Cette approche peut-être aisément appliquée à des systèmes réels et permet de caractériser les populations végétales à l'aide d'un petit nombre de paramètres démographiques. Cependant nos travaux suggèrent qu'il n'existe pas de relation simple entre ces paramètres et les traits fonctionnels des espèces, qui gouvernent pourtant leur réponse aux facteurs externes. La seconde approche a été développée pour dépasser cette limite et s'appuie sur le modèle individu-centré Nemossos qui représente de manière explicite le lien entre le fonctionnement des individus et les dynamiques de la communauté qu'ils forment. Afin d'assurer un grand potentiel d'application à Nemossos, nous avons apportés une grande attention au compromis entre réalisme et coût de paramétrisation. Nemossos a ainsi pu être entièrement paramétré à partir de valeur de traits issues de la littérature , son réalisme a été démontré, et il a été utilisé pour mener des expériences de simulations numériques sur l'importance de la variabilité temporelle des conditions environnementales pour la coexistence d'espèces fonctionnellement différentes. La complémentarité des deux approches nous a permis de proposer des éléments de réponse à divers questions fondamentales de l'écologie des communautés incluant le rôle de la compétition dans les dynamiques des communautés, l'effet du filtrage environnementale sur leur composition fonctionnel ou encore les mécanismes favorisant la coexistence des espèces végétales. Ici ces approches ont été utilisées séparément mais leur couplage peut offrir des perspectives intéressantes telles que l'étude du lien entre le fonctionnement des plantes et les dynamiques des populations. Par ailleurs chacune des approches peut être utilisée dans une grande variété d'expériences de simulation susceptible d'améliorer notre compréhension des mécanismes gouvernant les communautés végétales. / Plant communities are complex systems in which multiple species differing by their functional attributes interact with their environment and with each other. Because of the number and the diversity of these interactions the mechanisms that drive the dynamics of theses communities are still poorly understood. Modelling approaches enable to link in a mechanistic fashion the process driving individual plant or population dynamics to the resulting community dynamics. This PhD thesis aims at developing such approaches and to use them to investigate the mechanisms underlying community dynamics. We therefore developed two modelling approaches. The first one is based on a stochastic modelling framework allowing to link the population dynamics to the community dynamics whilst taking account of intra- and interspecific interactions as well as environmental and demographic variations. This approach is easily applicable to real systems and enables to describe the properties of plant population through a small number of demographic parameters. However our work suggests that there is no simple relationship between these parameters and plant functional traits, while they are known to drive their response to extrinsic factors. The second approach has been developed to overcome this limitation and rely on the individual-based model Nemossos that explicitly describes the link between plant functioning and community dynamics. In order to ensure that Nemossos has a large application potential, a strong emphasis has been placed on the tradeoff between realism and parametrization cost. Nemossos has then been successfully parameterized from trait values found in the literature, its realism has been demonstrated and it has been used to investigate the importance of temporal environmental variability for the coexistence of functionally differing species. The complementarity of the two approaches allows us to explore various fundamental questions of community ecology including the impact of competitive interactions on community dynamics, the effect of environmental filtering on their functional composition, or the mechanisms favoring the coexistence of plant species. In this work, the two approaches have been used separately but their coupling might offer interesting perspectives such as the investigation of the relationships between plant functioning and population dynamics. Moreover each of the approaches might be used to run various simulation experiments likely to improve our understanding of mechanisms underlying community dynamics.

Dans ce mémoire, nous présentons l’utilisation de techniques de model-checking pour l’inférence de paramètres de réseaux de régulation génétique (GRN) et l’analyse formelle d’une voie de signalisation. Le coeur du mémoire est décrit dans la première partie, dans laquelle nous proposons une approche pour inférer les paramètres biologiques régissant les dynamiques de modèles discrets de GRN. Les GRN sont encodés sous la forme d’un méta-modèle, appelé GRN paramétré, de telle façon qu’une instance de paramètres définit un modèle discret du GRN initial. Sous réserve que les propriétés biologiques d’intérêt s’expriment sous la forme de formules LTL, les techniques de model-checking LTL sont combinées à celles d’exécution symbolique et de résolution de contraintes afin de sélectionner les modèles satisfaisant ces propriétés. L’enjeu est de contourner l’explosion combinatoire en terme de taille et de nombre de modèles discrets. Nous avons implémenté notre méthode en Java, dans un outil appelé SPuTNIk. La seconde partie décrit une collaboration avec des neuropédiatres, qui ont pour objectif de comprendre l’apparition du phénotype protecteur ou toxique des microglies (un type de macrophage du cerveau) chez les prématurés. Cette partie exploite un autre versant du model-checking, celui du modelchecking statistique, afin d’étudier un type de réseau biologique particulier : la voie de signalisation Wnt/β-caténine, qui permet la transmission d’un signal de l’extérieur à l’intérieur des cellules via une cascade de réactions biochimiques. Nous présentons ici l’apport du model-checker stochastique COSMOS, utilisant la logique stochastique à automate hybride (HASL), un formalisme très expressif nous permettant une analyse formelle sophistiquée des dynamiques de la voie Wnt/β-caténine, modélisée sous la forme d’un processus stochastique à événements discrets. / In this thesis, we present the use of model checking techniques for inference of parameters of Gene Regulatory Networks (GRNs) and formal analysis of a signalling pathway. In the first and main part, we provide an approach to infer biological parameters governing the dynamics of discrete models of GRNs. GRNs are encoded in the form of a meta-model, called Parametric GRN, such that a parameter instance defines a discrete model of the original GRN. Provided that targeted biological properties are expressed in the form of LTL formulas, LTL model-checking techniques are combined with symbolic execution and constraint solving techniques to select discrete models satisfying these properties. The challenge is to prevent combinatorial explosion in terms of size and number of discrete models. Our method is implemented in Java, in a tool called SPuTNIk. The second part describes a work performed in collaboration with child neurologists, who aim to understand the occurrence of toxic or protective phenotype of microglia (a type of macrophage in the brain) in the case of preemies. We use an other type of model-checking, the statistical model-checking, to study a particular type of biological network: the Wnt/β- catenin pathway that transmits an external signal into the cells via a cascade of biochemical reactions. Here we present the benefit of the stochastic model checker COSMOS, using the Hybrid Automata Stochastic Logic (HASL), that is an very expressive formalism allowing a sophisticated formal analysis of the dynamics of the Wnt/β-catenin pathway, modelled as a discrete event stochastic process.