Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Phosphorylation of CLEC-2 is dependent on lipid rafts, actin polymerization, secondary mediators, and Rac

The C-type lectin-like receptor 2 (CLEC-2) activates platelets through Src and Syk tyrosine kinases via a single cytoplasmic YxxL motif known as a hem immunoreceptor tyrosine-based activation motif (hemITAM). Here, we demonstrate using sucrose gradient ultracentrifugation and methyl-beta-cyclodextrin treatment that CLEC-2 translocates to lipid rafts upon ligand engagement and that translocation is essential for hemITAM phosphorylation and signal initiation. HemITAM phosphorylation, but not translocation, is also critically dependent on actin polymerization, Rac1 activation, and release of ADP and thromboxane A(2) (TxA(2)). The role of ADP and TxA(2) in mediating phosphorylation is dependent on ligand engagement and rac activation but is independent of platelet aggregation. In contrast, tyrosine phosphorylation of the GPVI-FcRgamma-chain ITAM, which has 2 YxxL motifs, is independent of actin polymerization and secondary mediators. These results reveal a unique series of proximal events in CLEC-2 phosphorylation involving actin polymerization, secondary mediators, and Rac activation.

The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Phenylephrine promotes phosphorylation of Bad in cardiac myocytes through the extracellular signal-regulated kinases 1/2 and protein kinase A.

Studies in non-cardiomyocytic cells have shown that phosphorylation of the Bcl-2 family protein Bad on Ser-112, Ser-136 and Ser-155 decreases its pro-apoptotic activity. Both phenylephrine (100 microM) and the cell membrane-permeating cAMP analog, 8-(4-chlorophenylthio)-cAMP (100 microM), protected against 2-deoxy-D-glucose-induced apoptosis in neonatal rat cardiac myocytes as assessed by terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling (TUNEL). In cardiac myocytes, phenylephrine primarily stimulates the alpha-adrenoceptor, but, at high concentrations (100 microM), it also increases the activity of the cAMP-dependent protein kinase, protein kinase A (PKA) through the beta-adrenoceptor. Phenylephrine (100 microM) promoted rapid phosphorylation of Bad(Ser-112) and Bad(Ser-155), though we were unable to detect phosphorylation of Bad(Ser-136). Phosphorylation of Bad(Ser-112) was antagonized by either prazosin or propranolol, indicating that this phosphorylation required stimulation of both alpha(1)- and beta-adrenoceptors. Phosphorylation of Bad(Ser-155) was antagonized only by propranolol and was thus mediated through the beta-adrenoceptor. Inhibitor studies and partial purification of candidate kinases by fast protein liquid chromatography showed that the p90 ribosomal S6 kinases, p90RSK2/3 [which are activated by the extracellular signal-regulated kinases 1 and 2 (ERK1/2)] directly phosphorylated Bad(Ser-112), whereas the PKA catalytic subunit directly phosphorylated Bad(Ser-155). However, efficient phosphorylation of Bad(Ser-112) also required PKA activity. These data suggest that, although p90RSK2/3 phosphorylate Bad(Ser-112) directly, phosphorylation of this site is enhanced by phosphorylation of Bad(Ser-155). These phosphorylations potentially diminish the pro-apoptotic activity of Bad and contribute to the cytoprotective effects of phenylephrine and 8-(4-chlorophenylthio)-cAMP.

Differential crosstalk between estrogen receptor (ER) alpha and ER beta and the thyroid hormone receptor isoforms results in flexible regulation of the consensus ERE

Crosstalk between nuclear receptors is important for conversion of external and internal stimuli to a physiologically meaningful response by cells. Previous studies from this laboratory have demonstrated crosstalk between the estrogen (ER) and thyroid hormone receptors (TR) on two estrogen responsive physiological promoters, the preproenkephalin and oxytocin receptor gene promoter. Since ERa and ERb are isoforms possessing overlapping and distinct transactivation properties, we hypothesized that the interaction of ERa and b with the various TR isoforms would not be equivalent. To explore this hypothesis, the consensus estrogen response element (ERE)derived from the Xenopus vitellogenin gene is used to investigate the differences in interaction between ERa and b isoforms and the different TR isoforms in fibroblast cells. Both the ER isoforms transactivate from the consensus ERE, though ERa transactivates to a greater extent than ERb. Although neither of the TRb isoforms have an effect on ERa transactivation from the consensus ERE, the liganded TRa1 inhibits the ERa transactivation from the consensus ERE. In contrast, the liganded TRa1 facilitates ERb-mediated transactivation. The crosstalk between the TRb isoforms with the ERa isoform, on the consensus ERE, is different from that with the ERb isoform. The use of a TRa1 mutant, which is unable to bind DNA, abolishes the ability of the TRa1 isoform to interact with either of the ER isoforms. These differences in nuclear receptor crosstalk reveal an important functional difference between isoforms, which provides a novel mechanism for neuroendocrine integration.