Pas de résumé en français / Malaria is a devastating global health problem that affected 219 million people and caused 660,000 deaths in 2010. Inaccurate estimation of the level of infection may have adverse clinical and therapeutic implications for patients, and for epidemiological endpoint measurements. The level of infection, expressed as the parasite density (PD), is classically defined as the number of asexual parasites relative to a microliter of blood. Microscopy of Giemsa-stained thick blood smears (TBSs) is the gold standard for parasite enumeration. Parasites are counted in a predetermined number of high-power fields (HPFs) or against a fixed number of leukocytes. PD estimation methods usually involve threshold values; either the number of leukocytes counted or the number of HPFs read. Most of these methods assume that (1) the distribution of the thickness of the TBS, and hence the distribution of parasites and leukocytes within the TBS, is homogeneous; and that (2) parasites and leukocytes are evenly distributed in TBSs, and thus can be modeled through a Poisson-distribution. The violation of these assumptions commonly results in overdispersion. Firstly, we studied the statistical properties (mean error, coefficient of variation, false negative rates) of PD estimators of commonly used threshold-based counting techniques and assessed the influence of the thresholds on the cost-effectiveness of these methods. Secondly, we constituted and published the first dataset on parasite and leukocyte counts per HPF. Two sources of overdispersion in data were investigated: latent heterogeneity and spatial dependence. We accounted for unobserved heterogeneity in data by considering more flexible models that allow for overdispersion. Of particular interest were the negative binomial model (NB) and mixture models. The dependent structure in data was modeled with hidden Markov models (HMMs). We found evidence that assumptions (1) and (2) are inconsistent with parasite and leukocyte distributions. The NB-HMM is the closest model to the unknown distribution that generates the data. Finally, we devised a reduced reading procedure of the PD that aims to a better operational optimization and a practical assessing of the heterogeneity in the distribution of parasites and leukocytes in TBSs. A patent application process has been launched and a prototype development of the counter is in process.

Malaria is a devastating global health problem that affected 219 million people and caused 660,000 deaths in 2010. Inaccurate estimation of the level of infection may have adverse clinical and therapeutic implications for patients, and for epidemiological endpoint measurements. The level of infection, expressed as the parasite density (PD), is classically defined as the number of asexual parasites relative to a microliter of blood. Microscopy of Giemsa-stained thick blood smears (TBSs) is the gold standard for parasite enumeration. Parasites are counted in a predetermined number of high-power fields (HPFs) or against a fixed number of leukocytes. PD estimation methods usually involve threshold values; either the number of leukocytes counted or the number of HPFs read. Most of these methods assume that (1) the distribution of the thickness of the TBS, and hence the distribution of parasites and leukocytes within the TBS, is homogeneous; and that (2) parasites and leukocytes are evenly distributed in TBSs, and thus can be modeled through a Poisson-distribution. The violation of these assumptions commonly results in overdispersion. Firstly, we studied the statistical properties (mean error, coefficient of variation, false negative rates) of PD estimators of commonly used threshold-based counting techniques and assessed the influence of the thresholds on the cost-effectiveness of these methods. Secondly, we constituted and published the first dataset on parasite and leukocyte counts per HPF. Two sources of overdispersion in data were investigated: latent heterogeneity and spatial dependence. We accounted for unobserved heterogeneity in data by considering more flexible models that allow for overdispersion. Of particular interest were the negative binomial model (NB) and mixture models. The dependent structure in data was modeled with hidden Markov models (HMMs). We found evidence that assumptions (1) and (2) are inconsistent with parasite and leukocyte distributions. The NB-HMM is the closest model to the unknown distribution that generates the data. Finally, we devised a reduced reading procedure of the PD that aims to a better operational optimization and a practical assessing of the heterogeneity in the distribution of parasites and leukocytes in TBSs. A patent application process has been launched and a prototype development of the counter is in process.

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Calcium (Ca2+) ist ein in eukaryotischen Zellen allgegenwärtiger sekundärer Botenstoff. Durch Inositoltrisphosphat (IP3) ausgelöste Ca2+-Signale von IP3-Rezeptoren (IP3Rs) sind eines der universellsten Zell Signalübertragungssysteme. Ca2+ Signale sind fundamental stochastisch. Dennoch hat sich die Modellierung dieser Ca2+-Signale bisher stark auf deterministische Ansätze mit gewöhnlichen Differentialgleichungen gestützt. Diese wurden als Ratengleichungen etabliert und beruhen auf räumlich gemitteltem Ca2+ Werten. Diese Ansätze vernachlässigen Rauschen und Zufall. In dieser Dissertation präsentieren wir ein stochastisches Modell zur Erzeugung von Ca2+ Spikes in Form einer linearen Zustands-Kette. Die Anzahl offener Cluster ist die Zustandsvariable und Erholung von negativem Feedback wird berücksichtigt. Wir identifizieren einen Ca2+ Spike mit dem ersten Erreichen eines kritischen Zustands und sein Interspike Intervall mit der first-passage time (FPT) zu diesem Zustand. Dafür entwickeln wir einen allgemeinen mathematischen Rahmen zur analytischen Berechnung von FPTs auf solch einer Kette. Wir finden z.B. einen allgemein verringerten CV, der ein deutliches Minimum in Abhängigkeit der Zustandskettenlänge N aufweist. Dies nennen wir resonante Länge. Danach ergänzen wir positives Feedback und wenden das Modell auf verschiedene Zelltypen an. Es erfasst alle verfügbaren allgemeinen Beobachtungen zu Ca2+ Signalvorgängen. Es erlaubt uns Einblicke in den Zusammenhang von Agonistenstärke und Puffraten. Auch werden einzelne Ca2+ Spikes in Purkinje Neuronen, welche eine Rolle für Lernen und Erinnerung spielen, als stochastisches reaction-diffusion Model in einer 3D Dornenfortsatz Geometrie modelliert. Ataxia, eine Krankheit, die zum Verlust der Feinmotorik führt, wird auf defekte IP3R zurückgeführt, die abnormale Ca2+ Spikes erzeugen. Dieser Zustand wird ebenfalls untersucht und es wird ein Weg zur Wiederherstellung normaler Ca2+ Spikes vorgeschlagen. / Calcium (Ca2+) is a ubiquitous 2nd messenger molecule in all eukaryotic cells. Inositol trisphosphate (IP3)-induced Ca2+ signalling via IP3 receptors (IP3Rs) is one of the most universal signalling systems used by cells to transmit information. Ca2+ signalling is noisy and a fundamentally stochastic system. Yet, modelling of IP3-induced Ca2+ signalling has relied heavily on deterministic approaches with ordinary differential equations in the past, established as rate equations using spatially averaged Ca2+. These approaches neglect the defining features of Ca2+ signalling, noise and fluctuations. In this thesis, we propose a stochastic model of Ca2+ spike generation in terms of a linear state chain with the number of open clusters as its state variable, also including recovery from negative feedback. We identify a Ca2+ spike with reaching a critical state for the first time, and its interspike interval with the first passage time to that state. To this end, a general mathematical framework for analytically computing first-passage times of such a linear chain is developed first. A substantially reduced CV with a pronounced minimum, dependent on the chain length N, termed resonant length, are found. Positive feedback is then included into the model, and it is applied directly to various cell types. The model is fundamentally stochastic and successfully captures all available general observations on Ca2+ signalling. Also, we specifically study single Ca2+ spikes in spines of Purkinje neurons, assumed to be important for motor learning and memory, using MCell to simulate a reaction-diffusion system in a complex 3D Purkinje spine geometry. The model successfully reproduces experimentally findings on properties of Ca2+ spikes. Ataxia, a pathological condition resulting in, e.g., a loss of fine motor control, assumed to be caused by malfunctioning IP3Rs, is modelled and a possible way of recovery is suggested.

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