Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

Characterization and expression analysis of Paralichthys olivaceus voltage-dependent anion channel (VDAC) gene in response to virus infection

Voltage-dependent anion channel (VDAC, also known as mitochondrial porin) is acknowledged to play an important role in stress-induced mammalian apoptosis. In this study, Paralichthys olivaceus VDAC (PoVDAC) gene was identified as a virally induced gene from Scophthalmus Maximus Rhabdovirus (SMRV)-infected flounder embryonic cells (FEC). The full length of PoVDAC cDNA is 1380 bp with an open reading frame of 852 bp encoding a 283 amino acid protein. The deduced PoVDAC contains one alpha-helix, 13 transmembrane beta-strands and one eukaryotic mitochondrial porin signature motif. Constitutive expression of PoVDAC was confirmed in all tested tissues by real-time PCR. Further expression analysis revealed PoVDAC mRNA was upregulated by viral infection. We prepared fish antiserum against recombinant VDAC proteins and detected the PoVDAC in heart lysates from flounder as a 32 kDa band on western blot. Overexpression of PoVDAC in fish cells induced apoptosis. Immunofluoresence localization indicated that the significant distribution changes of PoVDAC have occurred in virus-induced apoptotic cells. This is the first report on the inductive expression of VDAC by viral infection, suggesting that PoVDAC might be mediated flounder antiviral immune response through induction of apoptosis. (c) 2007 Elsevier Ltd. All rights reserved.