A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Disruption of embryonic blood-CSF barrier in chick embryos reveals the actual importance of this barrier to control E-CSF composition and homeostasis in early brain development

In vertebrates, early brain development takes place at the expanded anterior end of the neural tube. After closure of the anterior neuropore, the brain wall forms a physiologically sealed cavity that encloses embryonic cerebrospinal fluid (E-CSF), a complex and protein-rich fluid that is initially composed of trapped amniotic fluid. E-CSF has several crucial roles in brain anlagen development. Recently, we reported the presence of transient blood-CSF barrier located in the brain stem lateral to the ventral midline, at the mesencephalon and prosencephalon level, in chick and rat embryos by transporting proteins, water, ions and glucose in a selective manner via transcellular routes. To test the actual relevance of the control of E-CSF composition and homeostasis on early brain development by this embryonic blood-CSF barrier, we block the activity of this barrier by treating the embryos with 6-aminonicotinamide gliotoxin (6-AN). We demonstrate that 6-AN treatment in chick embryos blocks protein transport across the embryonic blood-CSF barrier, and that the disruption of the barrier properties is due to the cease transcellular caveolae transport, as detected by CAV-1 expression cease. We also show that the lack of protein transport across the embryonic blood-CSF barrier influences neuroepithelial cell survival, proliferation and neurogenesis, as monitored by neurepithelial progenitor cells survival, proliferation and neurogenesis. The blockage of embryonic blood-CSF transport also disrupts water influx to the E-CSF, as revealed by an abnormal increase in brain anlagen volume. These experiments contribute to delineate the actual extent of this blood-CSF embryonic barrier controlling E-CSF composition and homeostasis and the actual important of this control for early brain development, as well as to elucidate the mechanism by which proteins and water are transported thought transcellular routes across the neuroectoderm, reinforcing the crucial role of E-CSF for brain development.

The embryonic blood-CSF barrier has molecular elements for specific glucose transport and for the general transport of molecules via transcellular routes.

In vertebrates, early brain development takes place at the expanded anterior end of the neural tube, which is filled with embryonic cerebrospinal fluid (E-CSF). We have recently identified a transient blood-CSF barrier that forms between embryonic days E3 and E4 in chick embryos and that is responsible for the transport of proteins and control of E-CSF homeostasis, including osmolarity. Here we examined the presence of glucose transporter GLUT-1 as well the presence of caveolae-structural protein Caveolin1 (CAV-1) in the embryonic blood-CSF barrier which may be involved in the transport of glucose and of proteins, water and ions respectively across the neuroectoderm. In this paper we demonstrate the presence of GLUT-1 and CAV-1 in endothelial cells of blood vessels as well as in adjacent neuroectodermal cells, located in the embryonic blood-CSF barrier. In blood vessels, these proteins were detected as early as E4 in chick embryos and E12.7 in rat embryos, i.e. the point at which the embryonic blood-CSF barrier acquires this function. In the neuroectoderm of the embryonic blood-CSF barrier, GLUT-1 was also detected at E4 and E12.7 respectively, and CAV-1 was detected shortly thereafter in both experimental models. These experiments contribute to delineating the extent to which the blood-CSF embryonic barrier controls E-CSF composition and homeostasis during early stages of brain development in avians and mammals. Our results suggest the regulation of glucose transport to the E-CSF by means of GLUT-1 and also suggest a mechanism by which proteins are transported via transcellular routes across the neuroectoderm, thus reinforcing the crucial role of E-CSF in brain development.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

Transmission properties of high barrier coated paperboard packages

High barrier materiaaleilla pyritään pidentämään pakattujen elintarvikkeiden hyllyikää. Barrierin tärkein tehtävä on elintarvikkeen suojaaminen hapelta ja kosteudelta. Alumiinin käyttöä barriermateriaalina pyritään vähentämään korvaamalla alumiini polymeereillä, jotka täyttävät elintarvikkeiden asettamat korkeat säilyvyysvaatimukset. Etyylivinyylialkoholin (EVOH) hapenläpäisevyys on kuivissa olosuhteissa alhaisin kaupallisista muovilaaduista. EVOH tarjoaa myös erinomaisen suojan muita kaasuja, rasvoja, hajuja ja aromeja vastaan ja sitä on helppo prosessoida. Polyamideilla on erinomainen kaasutiiveys sekä hyvä lujuus ja sitkeys. Eri muovilaatuja sekoittamalla voidaan vähentää hapenläpäisyä ja parantaa prosessointia. Polyolefiineja käytetään yleisesti päällystysmateriaaleina, koska ne suojaavat tuotetta erinomaisesti kosteudelta. Hapenläpäisyllä tarkoitetaan hapen kulkeutumista materiaalin läpi joko permeaation kautta tai reikien ja vuotojen läpi. Kaasun permeoitumiseen materiaalin läpi vaikuttavat materiaalin vapaa tilavuus, kiteisyysaste, orientaatio, substituointi, suhteellinen kosteus, lämpötila, barrierkerroksen paksuus, paine-ero ja permeoituvan molekyylin ominaisuudet. Kokeellisessa osassa analysoitiin ja vertailtiin kartonkipohjaisia mehutölkkejä, joissa käytettävät high barrier materiaalit olivat EVOH ja PA. Kartonkipohjaisia alumiinitölkkejä käytettiin referenssinä. Pakkausten hapenläpäisevyysmittauksissa saatiin samasta näytteestä toistettavia tuloksia, vaikka vuotomittauksissa saadut tulokset eivät olleet vertailukelpoisia hapenläpäisytulosten kanssa. Tölkkien valmistus vaikutti oleellisesti pakkausten tiiveysominaisuuksiin. Hapenläpäisy vuotojen ja reikien läpi oli merkittävämpää kuin hapenläpäisy materiaalin läpi. Pakkausten tiiveysominaisuuksia analysoitiin mittaamalla appelsiinimehun askorbiini-happopitoisuus. Askorbiinihapon hajoaminen mitattiin koetölkkeihin pakatusta appelsiinimehusta, ja lämpötilan, valon ja hapen vaikutusta askorbiinihapon hajoamiseen tutkittiin 12 viikon ajan. Lämpötilalla oli suurin vaikutus askorbiinihapon hajoamiseen huolimatta käytetystä pakkausmateriaalista.

Reliable computation of robust response tori on the verge of breakdown

We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.

Endoscopic epiglottopexy using Lichtenberger's needle carrier to avoid breakdown of repair.

Severe type III laryngomalacia LM is represented by a retroflexed epiglottis that touches the posterior pharyngeal wall and obstructs the laryngeal inlet. Endoscopic epiglottopexy is advised in such cases wherein pexy sutures are passed between the epiglottis and base of tongue. Using conventional needle carriers, it is difficult to pass such sutures that go deep enough into the tongue base. Such a pexy is prone to a break down. We describe a novel technique of placing these glossoepiglottic sutures using the Lichtenberger's needle carrier. We used this technique in three patients with excellent results and report no complications. We propose to use this technique in cases of epiglottic prolapse seen in severe LM and certain hypotonic conditions.

Role of an LRR receptor-like kinase in the establishment of a functional root endodermal barrier

The endodermis is a highly conserved cell layer present in the root of all vascular plants, except Lycophytes. This tissue layer establishes a protective diffusion barrier surrounding the vasculature and is expected to prevent passive, uncontrolled flow of nutrients through the root. This barrier property is achieved by the production of Casparian strips (CS), a localized cell wall impregnation of lignin in the anticlinal walls of each endodermal cell, forming a belt-like structure sealing the extracellular space. The CS act as a selective barrier between the external cell layers and the vascular cylinder and are thought to be important in many aspects of root function. For instance, selective nutrient uptake and sequestration from the soil, resistance to different abiotic and biotic stresses are expected to involve functional CS. Although discovered 150 years ago, nothing was known about the genes involved in CS establishment until recently. The use of the model plant Arabidopsis thaliana together with both reverse and forward genetic approaches led to the discovery of an increasing number of genes involved in different steps of CS formation during the last few years. One of these genes encodes SCHENGEN3 (SGN3), a leucine-rich repeat receptor-like kinase (LRR-RLK). SGN3 was discovered first by reverse genetic due to its endodermis-enriched expression, and the corresponding mutant displays strong endodermal permeability of the apoplastic tracer Propidium Iodide (PI) indicative of defective CS. One aim of this thesis is to study the role of SGN3 at the molecular level in order to understand its involvement in establishing an impermeable CS. The endodermal permeability of sgn3 is shown to be the result of incorrect localization of key proteins involved in CS establishment (the "Casparian strip domain proteins", CASPs), leading to non-functional CS interrupted by discontinuities. CASPs localize in the plasma membrane domain subjacent to the CS, named the Casparian Strip membrane Domain (CSD). The CSD discontinuities in sgn3 together with SGN3 localization in close proximity to the CASPs lead to the assumption that SGN3 is involved in the formation of a continuous CSD. In addition, SGN3 might have a second role, acting as a kinase reporting CSD integrity leading to lignin and suberin production in CSD/CS defective plants. Up to now, sgn3 is the strongest and most specific CS mutant available, displaying tracer penetration along the whole length of the seedling root. For this reason, this mutant is well suited in order to characterize the physiological behaviour of CS affected plants. Due to the lack of such mutants in the past, it was not possible to test the presumed functions of CS by using plants lacking this structure. We decided to use sgn3 for this purpose. Surprisingly, sgn3 overall growth is only slightly affected. Nevertheless, processes expected to rely on functional CS, such as water transport through the root, nutrient homeostasis, salt tolerance and resistance to an excess of some nutrients are altered in this mutant. On the other hand, homeostasis for most elements and drought tolerance are not affected in sgn3. It is surprising to observe that homeostatic defects are specific, with a decrease in potassium and an increase in magnesium levels. It indicates a backup system, set up by the plant in order to counteract free diffusion of nutrients into the stele. For instance, potassium shortage in sgn3 upregulates the transcription of potassium influx transport proteins and genes known to be induced by potassium starvation. Moreover, sgn3 mutant is hypersensitive to low potassium conditions. Hopefully, these results about SGN3 will help our understanding of CS establishment at the molecular level. In addition, physiological experiments using sgn3 should give us a framework for future experiments and help us to understand the different roles of CS and their involvement during nutrient radial transport through the root. -- L'endoderme est un tissu présent dans les racines de toutes les plantes vasculaires à l'exception des Lycophytes. Ce tissu établit une barrière protectrice entourant les tissus vasculaires dans le but d'éviter la diffusion passive et incontrôlée des nutriments au travers de la racine. Cette propriété de barrière provient de la production des cadres de Caspary, une imprégnation localisée de lignine des parties anticlinales de la paroi de chaque cellule d'endoderme. Cela donne naissance à un anneau/cadre qui rend étanche l'espace extracellulaire. Les cadres de Caspary agissent comme une barrière sélective entre les couches externes de la racine et le cylindre central et sont supposés être importants dans beaucoup d'aspects du fonctionnement de la racine. Par exemple, l'absorption sélective de nutriments et leur séquestration à partir du sol ainsi que la résistance contre différents stress abiotiques et biotiques sont supposés impliquer des cadres de Caspary fonctionnels. Bien que découverts il y a 150 ans, rien n'était connu concernant les gènes impliqués dans Ja formation des cadres de Caspary jusqu'à récemment. Durant ces dernière années, l'utilisation de la plante modèle Arabidopsis thaliana ainsi que des approches de génétique inverse et classique ont permis la découverte d'un nombre croissant de gènes impliqués à différentes étapes de la formation de cette structure. Un des ces gènes code pour SCHENGEN3 (SGN3), un récepteur kinase "leucine-rich repeat receptor-like kinase" (LRR-RLK). SGN3 a été découvert en premier par génétique inverse grâce à son expression enrichie dans l'endoderme. Les cadres de Caspary ne sont pas fonctionnels dans le mutant correspondant, ce qui est visible à cause de la perméabilité de l'endoderme au traceur apoplastique Propidium Iodide (PI). Un des objectifs de cette thèse est d'étudier la fonction de SGN3 au niveau moléculaire dans le but de comprendre son rôle dans la formation des cadres de Caspary. J'ai pu démontrer que la perméabilité de l'endoderme du mutant sgn3 est le résultat de la localisation incorrecte de protéines impliquées dans la formation des cadres de Caspary, les "Casparian strip domain proteins" (CASPs). Cela induit des cadres de Caspary non fonctionnels, contenant de nombreuses interruptions. Les CASPs sont localisés à la membrane plasmique dans un domaine sous-jacent les cadres de Caspary appelé Casparian Strip membrane Domain (CSD). Les interruptions du CSD dans le mutant sgn3, ainsi que la localisation de SGN3 à proximité des CASPs nous font penser à un rôle de SGN3 dans l'élaboration d'un CSD ininterrompu. De plus, SGN3 pourrait avoir un second rôle, agissant en tant que kinase reportant l'intégrité du CSD et induisant la production de lignine et de subérine dans des plantes contenant des cadres de Caspary non fonctionnels. Jusqu'à ce jour, sgn3 est le mutant en notre possession le plus fort et le plus spécifique, ayant un endoderme perméable tout le long de la racine. Pour cette raison, ce mutant est adéquat dans le but de caractériser la physiologie de plantes ayant des cadres de Caspary affectés. De manière surprenante, la croissance de sgn3 est seulement peu affectée. Néanmoins, des processus censés nécessiter des cadres de Caspary fonctionnels, comme le transport de l'eau au travers de la racine, l'homéostasie des nutriments, la tolérance au sel et la résistance à l'excès de certains nutriments sont altérés dans ce mutant. Malgré tout, l'homéostasie de la plupart des nutriments ainsi que la résistance au stress hydrique ne sont pas affectés dans sgn3. De manière surprenante, les altérations de l'ionome de sgn3 sont spécifiques, avec une diminution de potassium et un excès de magnésium. Cela implique un système de compensation établi par la plante dans le but d'éviter la diffusion passive des nutriments en direction du cylindre central. Par exemple, le manque de potassium dans sgn3 augmente la transcription de transporteurs permettant l'absorption de cet élément. De plus, des gènes connus pour être induits en cas de carence en potassium sont surexprimés dans sgn3 et la croissance de ce mutant est sévèrement affectée dans un substrat pauvre en potassium. Ces résultats concernant SGN3 vont, espérons-le, aider à la compréhension du processus de formation des cadres de Caspary au niveau moléculaire. De plus, les expériences de physiologie utilisant sgn3 présentées dans cette thèse devraient nous donner une base pour des expériences futures et nous permettre de comprendre mieux le rôle des cadres de Caspary, et plus particulièrement leur implication dans le transport radial des nutriments au travers de la racine. -- Les plantes terrestres sont des organismes puisant l'eau et les nutriments dont elles ont besoin pour leur croissance dans le sol grâce à leurs racines. De par leur immobilité, elles doivent s'adapter à des sols contenant des quantités variables de nutriments et il leur est crucial de sélectionner ce dont elles ont besoin afin de ne pas s'intoxiquer. Cette sélection est faite grâce à un filtre formé d'un tissu racinaire interne appelé endoderme. L'endoderme fabrique une barrière imperméable entourant chaque cellule appelée "cadre de Caspary". Ces cadres de Caspary empêchent le libre passage des nutriments, permettant un contrôle précis de leur passage. De plus, ils sont censés permettre de résister contre différents stress environnementaux comme la sécheresse, la salinité du sol ou l'excès de nutriments. Bien que découverts il y a 150 ans, rien n'était connu concernant les gènes impliqués dans la formation des cadres de Caspary jusqu'à récemment. Durant ces dernière années, l'utilisation de la plante modèle Arabidopsis thaliana a permis la découverte d'un nombre croissant de gènes impliqués à différentes étapes de la formation de cette structure. Un de ces gènes code pour SCHENGEN3 (SGN3), un récepteur kinase "leucine-rich repeat receptor-like kinase" (LRR- RLK). Nous montrons dans cette étude que le gène SGN3 est impliqué dans la formation des cadres de Caspary, et que le mutant correspondant sgn3 a des cadres de Caspary interrompus. Ces interruptions rendent l'endoderme perméable, l'empêchant de bloquer le passage des molécules depuis le sol vers le centre de la racine. En utilisant ce mutant, nous avons pu caractériser la physiologie de plantes ayant des cadres de Caspary affectés. Cela a permis de découvrir que le transport de l'eau au travers de la racine était affecté dans le mutant sgn3. De plus, l'accumulation de certains éléments dans les feuilles de ce mutant est altérée. Nous avons également pu montrer une sensibilité de ce mutant à un excès de sel ou de certains nutriments comme le fer et le manganèse.

Microtubule Associated Protein 1b (MAP1B) Is a Marker of the Microtubular Cytoskeleton in Podocytes but Is Not Essential for the Function of the Kidney Filtration Barrier in Mice.

Podocytes are essential for the function of the kidney glomerular filter. A highly differentiated cytoskeleton is requisite for their integrity. Although much knowledge has been gained on the organization of cortical actin networks in podocyte's foot processes, less is known about the molecular organization of the microtubular cytoskeleton in primary processes and the cell body. To gain an insight into the organization of the microtubular cytoskeleton of the podocyte, we systematically analyzed the expression of microtubule associated proteins (Maps), a family of microtubules interacting proteins with known functions as regulator, scaffold and guidance proteins. We identified microtubule associated protein 1b (MAP1B) to be specifically enriched in podocytes in human and rodent kidney. Using immunogold labeling in electron microscopy, we were able to demonstrate an enrichment of MAP1B in primary processes. A similar association of MAP1B with the microtubule cytoskeleton was detected in cultured podocytes. Subcellular distribution of MAP1B HC and LC1 was analyzed using a double fluorescent reporter MAP1B fusion protein. Subsequently we analyzed mice constitutively depleted of MAP1B. Interestingly, MAP1B KO was not associated with any functional or structural alterations pointing towards a redundancy of MAP proteins in podocytes. In summary, we established MAP1B as a specific marker protein of the podocyte microtubular cytoskeleton.

Cyclosporine A kinetics in brain cell cultures and its potential of crossing the blood-brain barrier.

There is an increasing need to develop improved systems for predicting the safety of xenobiotics. However, to move beyond hazard identification the available concentration of the test compounds needs to be incorporated. In this study cyclosporine A (CsA) was used as a model compound to assess the kinetic profiles in two rodent brain cell cultures after single and repeated exposures. CsA induced-cyclophilin B (Cyp-B) secretion was also determined as CsA-specific pharmacodynamic endpoint. Since CsA is a potent p-glycoprotein substrate, the ability of this compound to cross the blood-brain barrier (BBB) was also investigated using an in vitro bovine model with repeated exposures up to 14days. Finally, CsA uptake mechanisms were studied using a parallel artificial membrane assay (PAMPA) in combination with a Caco-2 model. Kinetic results indicate a low intracellular CsA uptake, with no marked bioaccumulation or biotransformation. In addition, only low CsA amounts crossed the BBB. PAMPA and Caco-2 experiments revealed that CsA is mostly trapped to lipophilic compartments and exits the cell apically via active transport. Thus, although CsA is unlikely to enter the brain at cytotoxic concentrations, it may cause alterations in electrical activity and is likely to increase the CNS concentration of other compounds by occupying the BBBs extrusion capacity. Such an integrated testing system, incorporating BBB, brain culture models and kinetics could be applied for assessing neurotoxicity potential of compounds.