Numerical method for the 2D simulation of the respiration

International audienceIn this article we are interested in the simulation of the air flow in the bronchial tree. The model we use has already been described by Baffico, Grandmont and Maury and is based on a three part description of the respiratory tract. This model leads, after time discretization, to a Stokes system with non standard dissipative boundary conditions that cannot be easily and directly implemented in most FEM software, in particular in FreeFEM++. The objective is here to provide a new numerical method that could be implemented in any softwares. After describing the method, we illustrate it by two-dimensional simulations

A model describing the growth and the size distribution of multiple metastatic tumors

International audienceCancer is one of the greatest killers in the world, particularly in western countries. A great effort from medical research is devoted to cancer and mathematical modeling must be consider as an additional tool for the physicians and biologists to understand cancermechanisms and to determine the adapted treatments. Metastasis make all the seriousness of cancer. In 2000, Iwata et al. [9] proposed a model which describes the evolution of an untreated metastatic tumors population. We provide here a mathematical analysis of this model which brings us to the determination of a Malthusian rate characterizing the population exponential growth. We provide as well a numerical analysis of the PDE given by the model

Stepwise Development of MAIT Cells in Mouse and Human

Mucosal-associated invariant T (MAIT) cells display two evolutionarily conserved features: an invariant T cell receptor (TCR)α (iTCRα) chain and restriction by the nonpolymorphic class Ib major histocompatibility complex (MHC) molecule, MHC-related molecule 1 (MR1). MR1 expression on thymus epithelial cells is not necessary for MAIT cell development but their accumulation in the gut requires MR1 expressing B cells and commensal flora. MAIT cell development is poorly known, as these cells have not been found in the thymus so far. Herein, complementary human and mouse experiments using an anti-humanVα7.2 antibody and MAIT cell-specific iTCRα and TCRβ transgenic mice in different genetic backgrounds show that MAIT cell development is a stepwise process, with an intra-thymic selection followed by peripheral expansion. Mouse MAIT cells are selected in an MR1-dependent manner both in fetal thymic organ culture and in double iTCRα and TCRβ transgenic RAG knockout mice. In the latter mice, MAIT cells do not expand in the periphery unless B cells are added back by adoptive transfer, showing that B cells are not required for the initial thymic selection step but for the peripheral accumulation. In humans, contrary to natural killer T (NKT) cells, MAIT cells display a naïve phenotype in the thymus as well as in cord blood where they are in low numbers. After birth, MAIT cells acquire a memory phenotype and expand dramatically, up to 1%–4% of blood T cells. Finally, in contrast with NKT cells, human MAIT cell development is independent of the molecular adaptor SAP. Interestingly, mouse MAIT cells display a naïve phenotype and do not express the ZBTB16 transcription factor, which, in contrast, is expressed by NKT cells and the memory human MAIT cells found in the periphery after birth. In conclusion, MAIT cells are selected by MR1 in the thymus on a non-B non-T hematopoietic cell, and acquire a memory phenotype and expand in the periphery in a process dependent both upon B cells and the bacterial flora. Thus, their development follows a unique pattern at the crossroad of NKT and γδ T cells

Homozygous TAF8 mutation in a patient with intellectual disability results in undetectable TAF8 protein, but preserved RNA polymerase II transcription

The human general transcription factor TFIID is composed of the TATA-binding protein (TBP) and 13 TBP-associated factors (TAFs). In eukaryotic cells, TFIID is thought to nucleate RNA polymerase II (Pol II) preinitiation complex formation on all protein coding gene promoters and thus, be crucial for Pol II transcription. In a child with intellectual disability, mild microcephaly, corpus callosum agenesis and poor growth, we identified a homozygous splice-site mutation in TAF8 (NM_138572.2: c.781-1G &gt; A). Our data indicate that the patient's mutation generates a frame shift and an unstable TAF8 mutant protein with an unrelated C-terminus. The mutant TAF8 protein could not be detected in extracts from the patient's fibroblasts, indicating a loss of TAF8 function and that the mutation is most likely causative. Moreover, our immunoprecipitation and proteomic analyses show that in patient cells only partial TAF complexes exist and that the formation of the canonical TFIID is impaired. In contrast, loss of TAF8 in mouse embryonic stem cells and blastocysts leads to cell death and to a global decrease in Pol II transcription. Astonishingly however, in human TAF8 patient cells, we could not detect any cellular phenotype, significant changes in genome-wide Pol II occupancy and pre-mRNA transcription. Thus, the disorganization of the essential holo-TFIID complex did not affect global Pol II transcription in the patient's fibroblasts. Our observations further suggest that partial TAF complexes, and/or an altered TFIID containing a mutated TAF8, could support human development and thus, the absence of holo-TFIID is less deleterious for transcription than originally predicted.</p

Glutamine-Expanded Ataxin-7 Alters TFTC/STAGA Recruitment and Chromatin Structure Leading to Photoreceptor Dysfunction

Spinocerebellar ataxia type 7 (SCA7) is one of several inherited neurodegenerative disorders caused by a polyglutamine (polyQ) expansion, but it is the only one in which the retina is affected. Increasing evidence suggests that transcriptional alterations contribute to polyQ pathogenesis, although the mechanism is unclear. We previously demonstrated that theSCA7 gene product, ataxin-7 (ATXN7), is a subunit of the GCN5 histone acetyltransferase–containing coactivator complexes TFTC/STAGA. We show here that TFTC/STAGA complexes purified from SCA7 mice have normal TRRAP, GCN5, TAF12, and SPT3 levels and that their histone or nucleosomal acetylation activities are unaffected. However, rod photoreceptors from SCA7 mouse models showed severe chromatin decondensation. In agreement, polyQ-expanded ataxin-7 induced histone H3 hyperacetylation, resulting from an increased recruitment of TFTC/STAGA to specific promoters. Surprisingly, hyperacetylated genes were transcriptionally down-regulated, and expression analysis revealed that nearly all rod-specific genes were affected, leading to visual impairment in SCA7 mice. In conclusion, we describe here a set of events accounting for SCA7 pathogenesis in the retina, in which polyQ-expanded ATXN7 deregulated TFTC/STAGA recruitment to a subset of genes specifically expressed in rod photoreceptors, leading to chromatin alterations and consequent progressive loss of rod photoreceptor function

Modelisation, mathematical analysis and numerical simulation of problems coming from biology

Cette thèse est consacrée à l’étude de quatre problèmes issus de la biologie. Le premier concerne la modélisation d’une population de métastases. Le modèle abouti a une équation de McKendrick-Von Foerster : une équation de conservation munie d’un terme au bord non–local. Nous montrons l’existence d’une unique solution et étudions son comportement asymptotique à l’aide de la notion d’entropie relative généralisée. L’étude numérique utilise le schéma WENO. Le deuxième concerne la modélisation de la respiration. Nous étudions la simulation des flux d’air dans l’appareil respiratoire à l’aide d’un modèle multi–échelle. Le système obtenu possède des conditions aux bords dissipatives non–usuelles. La méthode numérique employée est une méthode de décomposition qui permet de réduire le problème à la résolution de problèmes de Stokes avec conditions aux bords de type Dirichlet–Neumann classiques. Puis nous proposons un modèle pour les échanges gazeux montrant l’hétérogénéité de l’absorption de l’oxygène le long de l’arbre bronchique. La troisième partie concerne la cascade MAPK dans des ovocytes de Xénopes. La modélisation amène à une équation de type KPP. Après une étude mathématique montrant l’existence d’un front d’onde, nous réalisons une étude numérique fine du système. Enfin, nous étudions le système de Patlak–Keller–Segel 1D après explosion. Après une étude mathématique permettant de décrire le système après explosion à l’aide d’une mesure de défaut, nous donnons un schéma numérique adoptant le point de vue du transport optimal et permettant de simuler le système après explosion.We investigate four models coming from biological contexts. The first one concerns a model describing the growth of a population of tumors. This model leads to a McKendrick–Von Foerster equation : a conservation law with a non–local boundary condition. We prove the existence and unicity of a solution, then we study, using the general relative entropy, its asymptotic behavior. We provide numerical simulations using WENO scheme. The second part concerns the modelisation of the respiration. First we study the air flux in the bronchial tree using a mulstiscale model. The system present non–usual dissipative boundary conditions. The numerical scheme we use is based on a decomposition idea that reduce the system to the resolution of Stokes problems with standard Dirichlet–Neumann conditions. Then, we propose a model concerning the gas exchanges bringing to light the heterogeneity of the absorption of oxygen along the bronchial tree. The third part concerns the MAPK cascade in Xenopus oocytes. The modelisation leads to an equation of KPP type. A mathematical study shows the existence of travelling waves. Then we provide a detailed numerical study of the system. Finally, the last part, concerns the system of Patlak–Keller–Segel 1D after blow–up. The mathematical study provide a description of the system after blow–up, based on the notion of default meausure. Then we propose a numerical scheme, adopting the optimal transport viewpoint and allowing to simulate the system after blow–up

Modélisation, analyse mathématique et simulation numérique de problèmes issus de la biologie

Cette thèse est consacrée à l étude de quatre problèmes issus de la biologie. Le premier concerne la modélisation d une population de métastases. Le modèle abouti a une équation de McKendrick-Von Foerster : une équation de conservation munie d un terme au bord non local. Nous montrons l existence d une unique solution et étudions son comportement asymptotique à l aide de la notion d entropie relative généralisée. L étude numérique utilise le schéma WENO. Le deuxième concerne la modélisation de la respiration. Nous étudions la simulation des flux d air dans l appareil respiratoire à l aide d un modèle multi échelle. Le système obtenu possède des conditions aux bords dissipatives non usuelles. La méthode numérique employée est une méthode de décomposition qui permet de réduire le problème à la résolution de problèmes de Stokes avec conditions aux bords de type Dirichlet Neumann classiques. Puis nous proposons un modèle pour les échanges gazeux montrant l hétérogénéité de l absorption de l oxygène le long de l arbre bronchique. La troisième partie concerne la cascade MAPK dans des ovocytes de Xénopes. La modélisation amène à une équation de type KPP. Après une étude mathématique montrant l existence d un front d onde, nous réalisons une étude numérique fine du système. Enfin, nous étudions le système de Patlak Keller Segel 1D après explosion. Après une étude mathématique permettant de décrire le système après explosion à l aide d une mesure de défaut, nous donnons un schéma numérique adoptant le point de vue du transport optimal et permettant de simuler le système après explosion.We investigate four models coming from biological contexts. The first one concerns a model describing the growth of a population of tumors. This model leads to a McKendrick Von Foerster equation : a conservation law with a non local boundary condition. We prove the existence and unicity of a solution, then we study, using the general relative entropy, its asymptotic behavior. We provide numerical simulations using WENO scheme. The second part concerns the modelisation of the respiration. First we study the air flux in the bronchial tree using a mulstiscale model. The system present non usual dissipative boundary conditions. The numerical scheme we use is based on a decomposition idea that reduce the system to the resolution of Stokes problems with standard Dirichlet Neumann conditions. Then, we propose a model concerning the gas exchanges bringing to light the heterogeneity of the absorption of oxygen along the bronchial tree. The third part concerns the MAPK cascade in Xenopus oocytes. The modelisation leads to an equation of KPP type. A mathematical study shows the existence of travelling waves. Then we provide a detailed numerical study of the system. Finally, the last part, concerns the system of Patlak Keller Segel 1D after blow up. The mathematical study provide a description of the system after blow up, based on the notion of default meausure. Then we propose a numerical scheme, adopting the optimal transport viewpoint and allowing to simulate the system after blow up.LILLE1-Bib. Electronique (590099901) / SudocSudocFranceF

Understanding the Physiological Requirements of the Mountain Bike Cross-Country Olympic Race Format

International audienceObjectives: To evaluate the physiological requirements imposed by the current mountain biking Cross-Country Olympic (XCO) format. Methods: Sixteen Cross-Country cyclists competing at national or international level participated in this study. All participants completed a simulated and a real official race on a cycling-accredited race track. Oxygen consumption ((V) over dotO(2)) and heart rate (HR) values expressed as %(V) over dotO(2max) and %HRmax, respectively, were divided into three physiological intensity zones. The first zone (Z1) was the physiological region below VT1, the second zone (Z2) corresponded to a region between VT1 and VT2, and the third zone (Z3) was located between VT2 and VO2max . For power output, an additional fourth zone was considered above maximal aerobic power (MAP). Results: When competing in the current XCO format, 37.0 +/- 17.9% of the race is performed above the second ventilatory threshold at a mean intensity of 87% (V) over dotO(2max) and 25% of the race was spent above MAP. This contribution varied between laps, with a very high intensity during the first lap and more aerobic subsequent laps. The durations of most of the periods beyond MAP oscillated between 5 and 30 s. Between these short, repeated bursts, low-intensity periods of exercise were recorded. Conclusion: The current XCO race format is an acyclical and intermittent exercise comparable to high-intensity team sports. Moreover, our results highlight the relevance of (V) over dotO(2) values when analyzing XCO performance, they should be combined with commonly used HR and/or power output data