23 resultados para Ordinary Differential Equations and Applied Dynamics

em Université de Lausanne, Switzerland


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Despite their limited proliferation capacity, regulatory T cells (T(regs)) constitute a population maintained over the entire lifetime of a human organism. The means by which T(regs) sustain a stable pool in vivo are controversial. Using a mathematical model, we address this issue by evaluating several biological scenarios of the origins and the proliferation capacity of two subsets of T(regs): precursor CD4(+)CD25(+)CD45RO(-) and mature CD4(+)CD25(+)CD45RO(+) cells. The lifelong dynamics of T(regs) are described by a set of ordinary differential equations, driven by a stochastic process representing the major immune reactions involving these cells. The model dynamics are validated using data from human donors of different ages. Analysis of the data led to the identification of two properties of the dynamics: (1) the equilibrium in the CD4(+)CD25(+)FoxP3(+)T(regs) population is maintained over both precursor and mature T(regs) pools together, and (2) the ratio between precursor and mature T(regs) is inverted in the early years of adulthood. Then, using the model, we identified three biologically relevant scenarios that have the above properties: (1) the unique source of mature T(regs) is the antigen-driven differentiation of precursors that acquire the mature profile in the periphery and the proliferation of T(regs) is essential for the development and the maintenance of the pool; there exist other sources of mature T(regs), such as (2) a homeostatic density-dependent regulation or (3) thymus- or effector-derived T(regs), and in both cases, antigen-induced proliferation is not necessary for the development of a stable pool of T(regs). This is the first time that a mathematical model built to describe the in vivo dynamics of regulatory T cells is validated using human data. The application of this model provides an invaluable tool in estimating the amount of regulatory T cells as a function of time in the blood of patients that received a solid organ transplant or are suffering from an autoimmune disease.

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As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.

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Functionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix.

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This work describes the ab initio procedure employed to build an activation model for the alpha 1b-adrenergic receptor (alpha 1b-AR). The first version of the model was progressively modified and complicated by means of a many-step iterative procedure characterized by the employment of experimental validations of the model in each upgrading step. A combined simulated (molecular dynamics) and experimental mutagenesis approach was used to determine the structural and dynamic features characterizing the inactive and active states of alpha 1b-AR. The latest version of the model has been successfully challenged with respect to its ability to interpret and predict the functional properties of a large number of mutants. The iterative approach employed to describe alpha 1b-AR activation in terms of molecular structure and dynamics allows further complications of the model to allow prediction and interpretation of an ever-increasing number of experimental data.

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Dissecting drivers of plant defence investment remains central for understanding the assemblage of communities across different habitats. There is increasing evidence that direct defence strategies against herbivores, including secondary metabolites production, differ along ecological gradients in response to variation in biotic and abiotic conditions. In contrast, intraspecific variation in indirect defences remains unexplored. Here, we investigated variation in herbivory rate, resistance to herbivores, and indirect defences in ant-attracting Vicia species along the elevation gradient of the Alps. Specifically, we compared volatile organic compounds (VOCs) and ant attraction in high and low elevation ecotypes. Consistent with adaptation to the lower herbivory conditions that we detected at higher elevations in the field, high elevation plants were visited by fewer ants and were more susceptible to herbivore attack. In parallel, constitutive volatile organic compound production and subsequent ant attraction were lower in the high elevation ecotypes. We observed an elevation-driven trade-off between constitutive and inducible production of VOCs and ant attraction along the environmental cline. At higher elevations, inducible defences increased, while constitutive defence decreased, suggesting that the high elevation ecotypes compensate for lower indirect constitutive defences only after herbivore attack. Synthesis. Overall, direct and indirect defences of plants vary along elevation gradients. Our findings show that plant allocation to defences are subject to trade-offs depending on local conditions, and point to a feedback mechanism linking local herbivore pressure, predator abundance and the defence investment of plants.

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A new metabolite profiling approach combined with an ultrarapid sample preparation procedure was used to study the temporal and spatial dynamics of the wound-induced accumulation of jasmonic acid (JA) and its oxygenated derivatives in Arabidopsis thaliana. In addition to well known jasmonates, including hydroxyjasmonates (HOJAs), jasmonoyl-isoleucine (JA-Ile), and its 12-hydroxy derivative (12-HOJA-Ile), a new wound-induced dicarboxyjasmonate, 12-carboxyjasmonoyl-l-isoleucine (12-HOOCJA-Ile) was discovered. HOJAs and 12-HOOCJA-Ile were enriched in the midveins of wounded leaves, strongly differentiating them from the other jasmonate metabolites studied. The polarity of these oxylipins at physiological pH correlated with their appearance in midveins. When the time points of accumulation of different jasmonates were determined, JA levels were found to increase within 2-5 min of wounding. Remarkably, these changes occurred throughout the plant and were not restricted to wounded leaves. The speed of the stimulus leading to JA accumulation in leaves distal to a wound is at least 3 cm/min. The data give new insights into the spatial and temporal accumulation of jasmonates and have implications in the understanding of long-distance wound signaling in plants.

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Neurofilament (NF) proteins consist of three subunits of different molecular weights defined as NF-H, NF-M, and NF-L. They are typical structures of the neuronal cytoskeleton. Their immunocytochemical distribution during postnatal development of cat cerebellum was studied with several monoclonal and polyclonal antibodies against phosphorylated or unmodified sites. Expression and distribution of the triplet neurofilament proteins changed with maturation. Afferent mossy and climbing fibers in the medullary layer contained NF-M and NF-L already at birth, whereas NF-H appeared later. Within the first three postnatal weeks, all three subunits appeared in mossy and climbing fibers in the internal granular and molecular layers and in the axons of Purkinje cells. Axons of local circuit neurons such as basket cells expressed these proteins at the end of the first month, whereas parallel fibers expressed them last, at the beginning of the third postnatal month. Differential localization was especially observed for NF-H. Depending on phosphorylation, NF-H proteins were found in different axon types in climbing, mossy, and basket fibers or additionally in parallel fibers. A nonphosphorylated NF-H subunit was exclusively located in some Purkinje cells at early developmental stages and in some smaller interneurons later. A novel finding is the presence of a phosphorylation site in the NF-H subunit that is localized in dendrites of Purkinje cells but not in axons. Expression and phosphorylation of the NF-H subunit, especially, is cell-type specific and possibly involved in the adult-type stabilization of the axonal and dendritic cytoskeleton.

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Genomic islands are DNA elements acquired by horizontal gene transfer that are common to a large number of bacterial genomes, which can contribute specific adaptive functions, e.g. virulence, metabolic capacities or antibiotic resistances. Some genomic islands are still self-transferable and display an intricate life-style, reminiscent of both bacteriophages and conjugative plasmids. Here we studied the dynamical process of genomic island excision and intracellular reintegration using the integrative and conjugative element ICEclc from Pseudomonas knackmussii B13 as model. By using self-transfer of ICEclc from strain B13 to Pseudomonas putida and Cupriavidus necator as recipients, we show that ICEclc can target a number of different tRNA(Gly) genes in a bacterial genome, but only those which carry the GCC anticodon. Two conditional traps were designed for ICEclc based on the attR sequence, and we could show that ICEclc will insert with different frequencies in such traps producing brightly fluorescent cells. Starting from clonal primary transconjugants we demonstrate that ICEclc is excising and reintegrating at detectable frequencies, even in the absence of recipient. Recombination site analysis provided evidence to explain the characteristics of a larger number of genomic island insertions observed in a variety of strains, including Bordetella petri, Pseudomonas aeruginosa and Burkholderia.

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Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.

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The OLS estimator of the intergenerational earnings correlation is biased towards zero, while the instrumental variables estimator is biased upwards. The first of these results arises because of measurement error, while the latter rests on the presumption that the education of the parent family is an invalid instrument. We propose a panel data framework for quantifying the asymptotic biases of these estimators, as well as a mis-specification test for the IV estimator. [Author]

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Objectives: To characterize the modifications of gene expression of adenosine receptors (AR), TRPC channels, HIF-1α and iNOS during the early cardiogenesis in response to chronic hypoxia exposure. Methods: 4-day-old chick embryos were subjected in ovo to 6H, 12H and 24H of hypoxia (10% O2). The mRNA expression was quantified by RT-qPCR. Results: The targeted genes were found to be expressed at mRNA level with a differential expression pattern within the heart. Hypoxia has no significant effect on mRNA expression of ARs, TRPCs channels and iNOS within the heart. By contrast, HIF-1α mRNA expression shows a tendency to be down-regulated by hypoxia. Conclusion: These results suggest that an intrauterine oxygen lack does not significantly affect expression of genes involved in adenosine signaling and in calcium handling by store operated channels (TRPC).

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Summary The present thesis work focused on the ecology of benthic invertebrates in the proglacial floodplain of the Rhone in the Swiss Alps. The main glacial Rhone River and a smaller glacial tributary, the Mutt River, joined and entered a braiding multi-thread area. A first part concentrated on the disruption of the longitudinal patterns of environmental conditions and benthic invertebrate fauna in the Rhone by its tributary the Mutt. The Mutt had less harsh environmental conditions, higher taxonomic richness and more abundant zoobenthos compared to the Rhone upstream of the confluence. Although the habitat conditions in the main stream were little modified by the tributary, the fauna was richer and more diverse below the confluence. Colonisation from the Mutt induced the occurrence of faunal elements uncommon of glacial streams in the upper Rhone, where water temperature remains below 4°C. Although the glacial Rhone dominated the system with regard to hydrology and certain environmental conditions, the Mutt tributary has to be seen as the faunal driver of the system. The second part of the study concerned the spatio-temporal differentiation of the habitats and the benthic communities along and across the flood plain. No longitudinal differentiation was found. The spatial transversal differentiation of three habitat types with different environmental characteristics was successfully reflected in the spatial variability of benthic assemblages. This typology separated marginal sites of the flood plain, left bank sites under the influence of the Mutt, and the right bank sites under the influence of the Rh6ne. Faunistic spatial differences were emphasized by the quantitative structure of the fauna, richness, abundances and Simpson index of diversity. Seasonal environmental variability was positively related with Simpson index of diversity and the total richness per site. Low flow conditions were the most favourable season for the fauna and November was characterized by low spatial environmental heterogeneity, high spatial heterogeneity of faunal assemblage, maximum taxonomic richness, a particular taxonomic composition, highest abundances, as well as the highest primary food resources. The third part studied the egg development of three species of Ephemeroptera in the laboratory at 1.5 to 7°C and the ecological implications in the field. Species revealed very contrasting development strategies. Baetis alpinus has a synchronous and efficient egg development, which is faster in warmer habitats, enabling it to exploit short periods of favourable conditions in the floodplain. Ecdyonurus picteti has a very long development time slightly decreasing in warmer conditions. The high degree of individual variation suggests a genetic determination of the degree-days demand. Combined with the glacial local conditions, this strategy leads to an extreme delay of hatching and allows it to develop in very unpredictable habitats. Rhithrogena nivata is the second cold adapted species in Ephemeroptera. The incubation duration is long and success largely depends on the timing of hatching and the discharge conditions. This species is able to exploit extremely unstable and cold habitats where other species are limited by low water temperatures. The fourth part dealt with larval development in different habitats of the floodplain. Addition of data on egg development allowed the description of the life histories of the species from oviposition until emergence. Rhithrogena nivata and loyolaea generally have a two-year development, with the first winter passed as eggs and the second one as larvae. Development of Ecdyonurus picteti is difficult to document but appears to be efficient in a harsh and unpredictable environment. Baetis alpinus was studied separately in four habitats of the floodplain system with contrasting thermal regimes. Differences in success and duration of larval development and in growth rates are emphasised. Subvention mechanisms between habitats by migration of young or grown larvae were demonstrated. Development success and persistence of the populations in the system were thus increased. Emergence was synchronised to the detriment of the optimisation of the adult's size and fecundity. These very different development strategies induce a spatial and temporal distribution in the use of food resources and ecological niches. The last part of this work aimed at the synthesis of the characteristics and the ecological features of three distinct compartments of the system that are the upper Rhone, the Mutt and the floodplain. Their particular role as well as their inter-dependence concerning the structure and the dynamics of the benthic communities was emphasised. Résumé Ce travail de thèse est consacré à l'écologie des invertébrés benthiques dans la zone alluviale proglaciaire du Rhône dans les Alpes suisses. Le Rhône, torrent glaciaire principal, reçoit les eaux de la Mutt, affluent glaciaire secondaire, puis pénètre dans une zone de tressage formée de plusieurs bras. La première partie de l'étude se concentre sur la disruption par la Mutt des processus longitudinaux, tant environnementaux que faunistiques, existants dans le Rhône. Les conditions environnementales régnant dans la Mutt sont moins rudes, la richesse taxonomique plus élevée et le zoobenthos plus abondant que dans le Rhône en amont de la confluence. Bien que les conditions environnementales dans le torrent principal soient peu modifiées par l'affluent, la faune s'avère être plus riche et plus diversifiée en aval de la confluence. La colonisation depuis la Mutt permet l'occurrence de taxons inhabituels dans le Rhône en amont de la confluence, où la température de l'eau se maintient en dessous de 4°C. Bien que le Rhône, torrent glaciaire principal, domine le système du point de vu de l'hydrologie et de certains paramètres environnementaux, l'affluent Mutt doit être considéré comme l'élément structurant la faune dans le système. La deuxième partie concerne la différentiation spatiale et temporelle des habitats et des communautés benthiques à travers la plaine alluviale. Aucune différentiation longitudinale n'a été mise en évidence. La différentiation transversale de trois types d'habitats sur la base des caractéristiques environnementales a été confirmée par la variabilité spatiale de la faune. Cette typologie sépare les sites marginaux de la plaine alluviale, ceux sous l'influence de la Mutt (en rive gauche) et ceux sous l'influence du Rhône amont (en rive droite). Les différences spatiales de la faune sont mises en évidence par la structure quantitative de la faune, la richesse, les abondances et l'indice de diversité de Simpson. La variabilité saisonnière du milieu est positivement liée avec l'indice de diversité de Simpson et la richesse totale par site. L'étiage correspond à la période la plus favorable pour la faune et novembre réunit des conditions de faible hétérogénéité spatiale du milieu, de forte hétérogénéité spatiale de la faune, une richesse taxonomique maximale, une composition faunistique particulière, les abondances ainsi que les ressources primaires les plus élevées. La troisième partie est consacrée à l'étude du développement des oeufs de trois espèces d'Ephémères au laboratoire à des températures de 1.5 à 7°C, ainsi qu'aux implications écologiques sur le terrain. Ces espèces présentent des stratégies de développement très contrastées. Baetis alpinus a un développement synchrone et efficace, plus rapide en milieu plus chaud et lui permettant d'exploiter les courtes périodes de conditions favorables. Ecdyonurus picteti présente une durée de développement très longue, diminuant légèrement dans des conditions plus chaudes. L'importante variation interindividuelle suggère un déterminisme génétique de la durée de développement. Cette stratégie, associée aux conditions locales, conduit à un décalage extrême des éclosions et permet à l'espèce de se développer dans des habitats imprévisibles. Rhithrogena nivata est la seconde espèce d'Ephémères présentant une adaptation au froid. L'incubation des oeufs est longue et son succès dépend de la période des éclosions et des conditions hydrologiques. Cette espèce est capable d'exploiter des habitats extrêmement instables et froids, où la température est facteur limitant pour d'autres espèces. La quatrième partie traite du développement larvaire dans différents habitats de la plaine alluviale. Le développement complet est décrit pour les espèces étudiées de la ponte jusqu'à l'émergence. Rhithrogena nivata et loyolaea atteignent généralement le stade adulte en deux ans, le premier hiver étant passé sous forme d'oeuf et le second sous forme de larve. Le développement de Ecdyonurus picteti est difficile à documenter, mais s'avère cependant efficace dans un environnement rude et imprévisible. Baetis alpinus a été étudié séparément dans quatre habitats de la plaine ayant des régimes thermiques contrastés. La réussite et la durée du développement embryonnaire ainsi que les taux de croissance y sont variables. Des mécanismes de subvention entre habitats sont possibles par la migration de larves juvéniles ou plus développées, augmentant ainsi la réussite du développement et le maintien des populations dans le système. L'émergence devient synchrone, au détriment de l'optimisation de la taille et de la fécondité des adultes. Ces stratégies très différentes induisent une distribution spatiale et temporelle dans l'usage des ressources et des niches écologiques. La dernière partie synthétise les caractéristiques écologiques des trois compartiments du système que sont le Rhône amont, la Mutt et la zone alluviale. Leurs rôles particuliers et leurs interdépendances du point de vue de la structure et de la dynamique des communautés benthiques sont mis en avant.