4,291 research outputs found

    Generic Morse-Smale property for the parabolic equation on the circle

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    In this paper, we show that, for scalar reaction-diffusion equations ut=uxx+f(x,u,ux)u_t=u_{xx}+f(x,u,u_x) on the circle S1S^1, the Morse-Smale property is generic with respect to the non-linearity ff. In \cite{CR}, Czaja and Rocha have proved that any connecting orbit, which connects two hyperbolic periodic orbits, is transverse and that there does not exist any homoclinic orbit, connecting a hyperbolic periodic orbit to itself. In \cite{JR}, we have shown that, generically with respect to the non-linearity ff, all the equilibria and periodic orbits are hyperbolic. Here we complete these results by showing that any connecting orbit between two hyperbolic equilibria with distinct Morse indices or between a hyperbolic equilibrium and a hyperbolic periodic orbit is automatically transverse. We also show that, generically with respect to ff, there does not exist any connection between equilibria with the same Morse index. The above properties, together with the existence of a compact global attractor and the Poincar\'e-Bendixson property, allow us to deduce that, generically with respect to ff, the non-wandering set consists in a finite number of hyperbolic equilibria and periodic orbits . The main tools in the proofs include the lap number property, exponential dichotomies and the Sard-Smale theorem. The proofs also require a careful analysis of the asymptotic behavior of solutions of the linearized equations along the connecting orbits

    Discovery and Development of Small Molecule Allosteric Modulators of Glycoprotein Hormone Receptors

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    Glycoprotein hormones, follicle-stimulating hormone (FSH), luteinizing hormone (LH), and thyroid stimulating hormone (TSH) are heterodimeric proteins with a common subunit and hormone-specific subunit. These hormones are dominant regulators of reproduction and metabolic processes. Receptors for the glycoprotein hormones belong to the family of G-protein coupled receptors (GPCR). FSH receptor (FSHR) and LH receptor (LHR) are primarily expressed in somatic cells in ovary and testis to promote egg and sperm production in women & men respectively. TSH receptor (TSHR) is expressed in thyroid cells and regulates the secretion of T3 & T4. Glycoprotein hormones bind to the large extracellular domain of the receptor and cause a conformational change in the receptor that leads to activation of more than one intracellular signaling pathway. Several small molecules have been described to activate/inhibit glycoprotein hormone receptors through allosteric sites of the receptor. Small molecule allosteric modulators have the potential to be administered orally to patients thus improving the convenience of treatment. It has been a challenge to develop a small molecule allosteric agonist for glycoprotein hormones that can mimic the agonistic effects of the large natural ligand to activate similar signaling pathways. However, in the past few years, there have been several promising reports describing distinct chemical series with improved potency in preclinical models. In parallel, proposal of new structural model for FSH receptor and in silico docking studies of small molecule ligands to glycoprotein hormone receptors provide a giant leap on the understanding of the mechanism of action of the natural ligands and new chemical entities on the receptors. This review will focus on the current status of small molecule allosteric modulators of glycoprotein hormone receptors, their effects on common signaling pathways in cells, their utility for clinical application as demonstrated in preclinical models, and use of these molecules as novel tools to dissect the molecular signaling pathways of these receptors

    Review of the literature concerning the yellow plant and animal pigments.

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    Cover title.Digitized 2007 AES.Includes bibliographical references (pages 334-336)

    Chemical and physiological relations of pigments of milk fat to the carotin and xanthophylls of green plants.

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    Cover title.Digitized 2007 AES.Includes bibliographical references (page 387)

    Yellow pigments of blood serum, carotin and xanthophylls during digestion, the pigments of human milk fat.

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    Cover title.Digitized 2007 AES.Includes bibliographical references (page 439)

    Pigments of the body fat corpus luteum and skin secretions of the cow.

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    Cover title.Digitized 2007 AES.Includes bibliographical references (page 411)
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