Abstract. We prove the instability of large classes of steady states of the two-dimensional Euler equation. For an odd shear flow, beginning with the Rayleigh equation, we define a family of operators depending on some positive parameter. Then we use infinite determinants to keep track of the signs of the eigenvalues of these operators. The existence of purely growing modes follows from a continuation argument. Employing a new analysis of neutral modes together with a rigorous justification of Tollmien's classical method, we obtain a sharp condition for linear and hence nonlinear instability of a general class of bounded shear flows. We obtain similar results for bounded rotating flows and unbounded shear flows.

—Ischemia induces apoptosis as well as necrosis of cardiac myocytes. We recently reported the cloning of a cDNA that encodes an apoptotic inhibitor, ARC, that is expressed predominantly in cardiac and skeletal muscle. In the present study, we examined the ability of ARC to protect rat embryonic heart–derived H9c2 cells from apoptosis induced by hypoxia, a component of ischemia. We found that H9c2 cells express ARC and that exposure to hypoxia substantially reduces ARC expression while inducing apoptosis. Transfected H9c2 cells in which cytosolic ARC protein levels remain elevated during hypoxia were significantly more resistant to hypoxia-induced apoptosis than parental H9c2 cells or H9c2 cells transfected with a control vector. Loss of endogenous ARC in the cytosol of H9c2 cells was associated with translocation of ARC from the cytosol to intracellular membranes, release of cytochrome c from the mitochondria, activation of caspase-3, poly(ADP-ribose)polymerase (PARP) cleavage, and DNA fragmentation. All of these events were inhibited in H9c2 cells overexpressing ARC when compared with control cells. In contrast, caspase inhibitors prevented PARP cleavage but not cytochrome c release, suggesting that exogenously expressed ARC acts upstream of caspase activation in this model of apoptosis. These results demonstrate that ARC can protect heart myogenic H9c2 cells from hypoxia-induced apoptosis, and that ARC prevents cytochrome c release by acting upstream of caspase activation, perhaps at the mitochondrial level. The full text of this article is available at http://www.circresaha.org.

The discovery that 15-deoxy-Delta12,14-prostaglandin J2 (15d-PGJ2) is a ligand for the gamma-isoform of peroxisome proliferator-activated receptor (PPAR) suggests nuclear signaling by prostaglandins. Studies were undertaken to determine the nephron localization of PPAR isoforms and their heterodimer partners, retinoid X receptors (RXR), and to evaluate the function of this system in the kidney. PPARalpha mRNA, determined by RT-PCR, was found predominately in cortex and further localized to proximal convoluted tubule (PCT); PPARgamma was abundant in renal inner medulla, localized to inner medullary collecting duct (IMCD) and renal medullary interstitial cells (RMIC); PPARbeta, the ubiquitous form of PPAR, was abundant in all nephron segments examined. RXRalpha was localized to PCT and IMCD, whereas RXRbeta was expressed in almost all nephron segments examined. mRNA expression of acyl-CoA synthase (ACS), a known PPAR target gene, was stimulated in renal cortex of rats fed with fenofibrate, but the expression was not significantly altered in either cortex or inner medulla of rats fed with troglitazone. In cultured RMIC cells, both troglitazone and 15d-PGJ2 significantly inhibited cell proliferation and dramatically altered cell shape by induction of cell process formation. We conclude that PPAR and RXR isoforms are expressed in a nephron segment-specific manner, suggesting distinct functions, with PPARalpha being involved in energy metabolism through regulating ACS in PCT and with PPARgamma being involved in modulating RMIC growth and differentiation.