Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions

Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

Pores in Bilayer Membranes of Amphiphilic Molecules: Coarse-Grained Molecular Dynamics Simulations Compared with Simple Mesoscopic Models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tension less membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard discs. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential

Defects in Chiral Columnar Phases: Tilt Grain Boundaries and Iterated Moire Maps

Biomolecules are often very long with a definite chirality. DNA, xanthan and poly-gamma-benzyl-glutamate (PBLG) can all form columnar crystalline phases. The chirality, however, competes with the tendency for crystalline order. For chiral polymers, there are two sorts of chirality: the first describes the usual cholesteric-like twist of the local director around a pitch axis, while the second favors the rotation of the local bond-orientational order and leads to a braiding of the polymers along an average direction. In the former case chirality can be manifested in a tilt grain boundary phase (TGB) analogous to the Renn-Lubensky phase of smectic-A liquid crystals. In the latter case we are led to a new "moire" state with twisted bond order. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In this case the polymer trajectories in the plane perpendicular to their average direction are described by iterated moire maps of remarkable complexity, reminiscent of dynamical systems.Comment: plain TeX, (33 pages), 17 figures, some uufiled and included, the remaining available at ftp://ftp.sns.ias.edu/pub/kamien/ or by request to [email protected]

Circularly polarized colour reflection from helicoidal structures in the beetle Plusiotis boucardi

Copyright © 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is the published version of an article published in New Journal of Physics Vol. 9, article 99. DOI: 10.1088/1367-2630/9/4/099A detailed optical study of the iridescent outer-shell of the beetle Plusiotis boucardi has revealed a novel microstructure which controls both the polarization and wavelength of reflected light. A previously unreported hexagonal array across the integument of the beetle exhibits highly localized regions of reflection of only red and green left-handed circularly-polarized light. Optical and transmission electron microscopy (TEM) imaging reveals the origin of this effect as an array of 'bowl-shaped' recesses on the elytra that are formed from a dual-pitch helicoidal layer. Reflectivity spectra collected from the beetle are compared to theoretical data produced using a multi-layer optics model for modelling chiral, optically anisotropic media such as cholesteric liquid crystals. Excellent agreement is obtained between data and theory produced using a model that incorporates an upper isotropic layer (of cuticular wax), followed by a short pitch (310 (± 1) nm) overlying a longer pitch (370 (±1) nm) helicoidal layer of optically anisotropic material. These layers are backed by an absorbing underlayer. Synthetic replication of this form of structure may provide a route to the fabrication of tuneable micro-mirrors for optical applications

Congenital Hypogonadotropic Hypogonadism Due to GNRH Receptor Mutations in Three Brothers Reveal Sites Affecting Conformation and Coupling

Congenital hypogonadotropic hypogonadism (CHH) is characterized by low gonadotropins and failure to progress normally through puberty. Mutations in the gene encoding the GnRH receptor (GNRHR1) result in CHH when present as compound heterozygous or homozygous inactivating mutations. This study identifies and characterizes the properties of two novel GNRHR1 mutations in a family in which three brothers display normosmic CHH while their sister was unaffected. Molecular analysis in the proband and the affected brothers revealed two novel non-synonymous missense GNRHR1 mutations, present in a compound heterozygous state, whereas their unaffected parents possessed only one inactivating mutation, demonstrating the autosomal recessive transmission in this kindred and excluding X-linked inheritance equivocally suggested by the initial pedigree analysis. The first mutation at c.845 C>G introduces an Arg substitution for the conserved Pro 282 in transmembrane domain (TMD) 6. The Pro282Arg mutant is unable to bind radiolabeled GnRH analogue. As this conserved residue is important in receptor conformation, it is likely that the mutation perturbs the binding pocket and affects trafficking to the cell surface. The second mutation at c.968 A>G introduces a Cys substitution for Tyr 323 in the functionally crucial N/DPxxY motif in TMD 7. The Tyr323Cys mutant has an increased GnRH binding affinity but reduced receptor expression at the plasma membrane and impaired G protein-coupling. Inositol phosphate accumulation assays demonstrated absent and impaired Gαq/11 signal transduction by Pro282Arg and Tyr323Cys mutants, respectively. Pretreatment with the membrane permeant GnRHR antagonist NBI-42902, which rescues cell surface expression of many GNRHR1 mutants, significantly increased the levels of radioligand binding and intracellular signaling of the Tyr323Cys mutant but not Pro282Arg. Immunocytochemistry confirmed that both mutants are present on the cell membrane albeit at low levels. Together these molecular deficiencies of the two novel GNRHR1 mutations lead to the CHH phenotype when present as a compound heterozygote

The Hidden Sexuality of Alexandrium Minutum: An Example of Overlooked Sex in Dinoflagellates

Dinoflagellates are haploid eukaryotic microalgae in which rapid proliferation causes dense blooms, with harmful health and economic effects to humans. The proliferation mode is mainly asexual, as the sexual cycle is believed to be rare and restricted to stressful environmental conditions. However, sexuality is key to explaining the recurrence of many dinoflagellate blooms because in many species the fate of the planktonic zygotes (planozygotes) is the formation of resistant cysts in the seabed (encystment). Nevertheless, recent research has shown that individually isolated planozygotes in the lab can enter other routes besides encystment, a behavior of which the relevance has not been explored at the population level. In this study, using imaging flow cytometry, cell sorting, and Fluorescence In Situ Hybridization (FISH), we followed DNA content and nuclear changes in a population of the toxic dinoflagellate Alexandrium minutum that was induced to encystment. Our results first show that planozygotes behave like a population with an “encystment-independent” division cycle, which is light-controlled and follows the same Light:Dark (L:D) pattern as the cycle governing the haploid mitosis. Resting cyst formation was the fate of just a small fraction of the planozygotes formed and was restricted to a period of strongly limited nutrient conditions. The diploid-haploid turnover between L:D cycles was consistent with two-step meiosis. However, the diel and morphological division pattern of the planozygote division also suggests mitosis, which would imply that this species is not haplontic, as previously considered, but biphasic, because individuals could undergo mitotic divisions in both the sexual (diploid) and the asexual (haploid) phases. We also report incomplete genome duplication processes. Our work calls for a reconsideration of the dogma of rare sex in dinoflagellates.Versión del edito

Familial Glucocorticoid Receptor Haploinsufficiency by Non-Sense Mediated mRNA Decay, Adrenal Hyperplasia and Apparent Mineralocorticoid Excess

Primary glucocorticoid resistance (OMIM 138040) is a rare hereditary disease that causes a generalized partial insensitivity to glucocorticoid action, due to genetic alterations of the glucocorticoid receptor (GR). Investigation of adrenal incidentalomas led to the discovery of a family (eight affected individuals spanning three generations), prone to cortisol resistance, bilateral adrenal hyperplasia, arterial hypertension and hypokalemia. This phenotype exacerbated over time, cosegregates with the first heterozygous nonsense mutation p.R469[R,X] reported to date for the GR, replacing an arginine (CGA) by a stop (TGA) at amino-acid 469 in the second zinc finger of the DNA-binding domain of the receptor. In vitro, this mutation leads to a truncated 50-kDa GR lacking hormone and DNA binding capacity, devoid of hormone-dependent nuclear translocation and transactivation properties. In the proband's fibroblasts, we provided evidence for the lack of expression of the defective allele in vivo. The absence of detectable mutated GR mRNA was accompanied by a 50% reduction in wild type GR transcript and protein. This reduced GR expression leads to a significantly below-normal induction of glucocorticoid-induced target genes, FKBP5 in fibroblasts. We demonstrated that the molecular mechanisms of glucocorticoid signaling dysfunction involved GR haploinsufficiency due to the selective degradation of the mutated GR transcript through a nonsense-mediated mRNA Decay that was experimentally validated on emetine-treated propositus' fibroblasts. GR haploinsufficiency leads to hypertension due to illicit occupation of renal mineralocorticoid receptor by elevated cortisol rather than to increased mineralocorticoid production reported in primary glucocorticoid resistance. Indeed, apparent mineralocorticoid excess was demonstrated by a decrease in urinary tetrahydrocortisone-tetrahydrocortisol ratio in affected patients, revealing reduced glucocorticoid degradation by renal activity of the 11β-hydroxysteroid dehydrogenase type 2, a GR regulated gene. We propose thus that GR haploinsufficiency compromises glucocorticoid sensitivity and may represent a novel genetic cause of subclinical hypercortisolism, incidentally revealed bilateral adrenal hyperplasia and mineralocorticoid-independent hypertension