Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Liquid fructose down-regulates liver insulin receptor substrate 2 and gluconeogeneic enzymes by modifying nutrient sensing factors in rats

High consumption of fructose-sweetened beverages has been linked to a high prevalence of chronic metabolic diseases. We have previously shown that a short course of fructose supplementation as a liquid solution induces glucose intolerance in female rats. In the present work, we characterized the fructose-driven changes in the liver and the molecular pathways involved. To this end, female rats were supplemented or not with liquid fructose (10%, w/v) for 7 or 14 days. Glucose and pyruvate tolerance tests were performed, and the expression of genes related to insulin signaling, gluconeogenesis and nutrient sensing pathways was evaluated. Fructose-supplemented rats showed increased plasma glucose excursions in glucose and pyruvate tolerance tests and reduced hepatic expression of several genes related to insulin signaling, including insulin receptor substrate 2 (IRS-2). However, the expression of key gluconeogenic enzymes, glucose-6-phosphatase and phosphoenolpyruvate carboxykinase, was reduced. These effects were caused by an inactivation of hepatic forkhead box O1 (FoxO1) due to an increase in its acetylation state driven by a reduced expression and activity of sirtuin 1 (SIRT1). Further contributing to FoxO1 inactivation, fructose consumption elevated liver expression of the spliced form of X-box-binding-protein-1 as a consequence of an increase in the activity of the mammalian target of rapamycin 1 and protein 38-mitogen activated protein kinase (p38-MAPK). Liquid fructose affects both insulin signaling (IRS-2 and FoxO1) and nutrient sensing pathways (p38-MAPK, mTOR and SIRT1), thus disrupting hepatic insulin signaling without increasing the expression of key gluconeogenic enzymes.

On the interplay between Q^2 and t dependence in exclusive diffractive production of real photons and vector mesons in ep collisions

We show how the familiar phenomenological way of combining the Q2 (photon virtuality) and t (squared momentum transfer) dependences of the scattering amplitude in Deeply Virtual Compton Scattering (DVCS) [1, 2] and Vector Meson Production (VMP) [2] processes can be understood in an off-mass-shell generalization of dual amplitudes with Mandelstam analyticity [3]. By comparing different approaches, we managed also to constrain the numerical values of the free parameters.

Gene expression profiles in rat mesenteric lymph nodes upon supplementation with Conjugated Linoleic Acid during gestation and suckling

Background Diet plays a role on the development of the immune system, and polyunsaturated fatty acids can modulate the expression of a variety of genes. Human milk contains conjugated linoleic acid (CLA), a fatty acid that seems to contribute to immune development. Indeed, recent studies carried out in our group in suckling animals have shown that the immune function is enhanced after feeding them with an 80:20 isomer mix composed of c9,t11 and t10,c12 CLA. However, little work has been done on the effects of CLA on gene expression, and even less regarding immune system development in early life. Results The expression profile of mesenteric lymph nodes from animals supplemented with CLA during gestation and suckling through dam's milk (Group A) or by oral gavage (Group B), supplemented just during suckling (Group C) and control animals (Group D) was determined with the aid of the specific GeneChip® Rat Genome 230 2.0 (Affymettrix). Bioinformatics analyses were performed using the GeneSpring GX software package v10.0.2 and lead to the identification of 89 genes differentially expressed in all three dietary approaches. Generation of a biological association network evidenced several genes, such as connective tissue growth factor (Ctgf), tissue inhibitor of metalloproteinase 1 (Timp1), galanin (Gal), synaptotagmin 1 (Syt1), growth factor receptor bound protein 2 (Grb2), actin gamma 2 (Actg2) and smooth muscle alpha actin (Acta2), as highly interconnected nodes of the resulting network. Gene underexpression was confirmed by Real-Time RT-PCR. Conclusions Ctgf, Timp1, Gal and Syt1, among others, are genes modulated by CLA supplementation that may have a role on mucosal immune responses in early life.

Gene expression profiles in rat mesenteric lymph nodes upon supplementation with Conjugated Linoleic Acid during gestation and suckling

Background Diet plays a role on the development of the immune system, and polyunsaturated fatty acids can modulate the expression of a variety of genes. Human milk contains conjugated linoleic acid (CLA), a fatty acid that seems to contribute to immune development. Indeed, recent studies carried out in our group in suckling animals have shown that the immune function is enhanced after feeding them with an 80:20 isomer mix composed of c9,t11 and t10,c12 CLA. However, little work has been done on the effects of CLA on gene expression, and even less regarding immune system development in early life. Results The expression profile of mesenteric lymph nodes from animals supplemented with CLA during gestation and suckling through dam's milk (Group A) or by oral gavage (Group B), supplemented just during suckling (Group C) and control animals (Group D) was determined with the aid of the specific GeneChip® Rat Genome 230 2.0 (Affymettrix). Bioinformatics analyses were performed using the GeneSpring GX software package v10.0.2 and lead to the identification of 89 genes differentially expressed in all three dietary approaches. Generation of a biological association network evidenced several genes, such as connective tissue growth factor (Ctgf), tissue inhibitor of metalloproteinase 1 (Timp1), galanin (Gal), synaptotagmin 1 (Syt1), growth factor receptor bound protein 2 (Grb2), actin gamma 2 (Actg2) and smooth muscle alpha actin (Acta2), as highly interconnected nodes of the resulting network. Gene underexpression was confirmed by Real-Time RT-PCR. Conclusions Ctgf, Timp1, Gal and Syt1, among others, are genes modulated by CLA supplementation that may have a role on mucosal immune responses in early life.