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.

Postprandial enrichment of triacylglycerol-rich lipoproteins with omega-3 fatty acids: lack of an interaction with apolipoprotein E genotype?

Background: We have previously demonstrated that carrying the apolipoprotein (apo) E epsilon 4 (E4+) genotype disrupts omega-3 fatty acids (n − 3 PUFA) metabolism. Here we hypothesise that the postprandial clearance of n − 3 PUFA from the circulation is faster in E4+ compared to non-carriers (E4−). The objective of the study was to investigate the fasted and postprandial fatty acid (FA) profile of triacylglycerol-rich lipoprotein (TRL) fractions: Sf >400 (predominately chylomicron CM), Sf 60 − 400 (VLDL1), and Sf 20 − 60 (VLDL2) according to APOE genotype. Methods: Postprandial TRL fractions were obtained in 11 E4+ (ε3/ε4) and 12 E4− (ε3/ε3) male from the SATgenε study following high saturated fat diet + 3.45 g/d of docosahexaenoic acid (DHA) for 8-wk. Blood samples were taken at fasting and 5-h after consuming a test-meal representative of the dietary intervention. FA were characterized by gas chromatography. Results: At fasting, there was a 2-fold higher ratio of eicosapentaenoic acid (EPA) to arachidonic acid (P = 0.046) as well as a trend towards higher relative% of EPA (P=0.063) in theSf >400 fraction of E4+. Total n − 3 PUFA in the Sf 60 − 400 and Sf 20 − 60 fractions were not APOE genotype dependant. At 5 h, there was a trend towards a time × genotype interaction (P=0.081) for EPA in theSf >400 fraction. When sub-groups were form based on the level of EPA at baseline within the Sf >400 fraction, postprandial EPA (%) was significantly reduced only in the high-EPA group. EPA at baseline significantly predicted the postprandial response in EPA only in E4+ subjects (R2 = 0.816). Conclusion: Despite the DHA supplement contain very low levels of EPA, E4+ subjects with high EPA at fasting potentially have disrupted postprandial n − 3 PUFA metabolism after receiving a high-dose of DHA. Trial registration: Registered at clinicaltrials.gov/show/NCT01544855.

Endothelin-1 and fibroblast growth factors stimulate the mitogen-activated protein kinase signaling cascade in cardiac myocytes. The potential role of the cascade in the integration of two signaling pathways leading to myocyte hypertrophy.

Maximally effective concentrations of endothelin-1 (ET-1), acidic FGF (aFGF), or 12-O-tetradecanoylphorbol-13-acetate (TPA) activated mitogen-activated protein kinase (MAPK) by 3-4-fold in crude extracts of myocytes cultured from neonatal rat heart ventricles. Maximal activation was achieved after 5 min. Thereafter, MAPK activity stimulated by ET-1 or aFGF declined to control values within 1-2 h, whereas activation by TPA was more sustained. Two peaks of MAPK activity (a 42- and a 44-kDa MAPK) were resolved in cells exposed to ET-1 or aFGF by fast protein liquid chromatography on a Mono Q column. One major and one minor peak of MAPK kinase (MAPKK) was stimulated by ET-1 or aFGF. Cardiac myocytes expressed protein kinase C (PKC)-alpha, -delta, -epsilon and -zeta as shown immunoblotting. Exposure to 1 microM TPA for 24 h down-regulated PKC-alpha, -delta, and -epsilon, but not PKC-zeta. This maneuver wholly abolished the activation of MAPK on re-exposure to TPA but did not affect the response to aFGF. The effect of ET-1 was partially down-regulated. ET-1 stimulated phospho[3H]inositide hydrolysis 18-fold, whereas aFGF stimulated by only 30%. Agonists which initially utilize dissimilar signaling pathways may therefore converge at the level of MAPKK/MAPK and this may be relevant to the hypertrophic response of the heart.

Differential activation of protein kinase C isoforms by endothelin-1 and phenylephrine and subsequent stimulation of p42 and p44 mitogen-activated protein kinases in ventricular myocytes cultured from neonatal rat hearts.

The translocation of protein kinase C (PKC) isoforms PKC-alpha, PKC-delta, PKC-epsilon, and PKC-zeta from soluble to particulate fractions was studied in ventricular cardiomyocytes cultured from neonatal rats. Endothelin-1 (ET-1) caused a rapid ETA receptor-mediated translocation of PKC-delta and PKC-epsilon (complete in 0.5-1 min). By 3-5 min, both isoforms were returning to the soluble fraction, but a greater proportion of PKC-epsilon remained associated with the particulate fraction. The EC50 of translocation for PKC-delta was 11-15 nM ET-1 whereas that for PKC-epsilon was 1.4-1.7 nM. Phenylephrine caused a rapid translocation of PKC-epsilon (EC50 = 0.9 microM) but the proportion lost from the soluble fraction was less than with ET-1. Translocation of PKC-delta was barely detectable with phenylephrine. Neither agonist caused any consistent translocation of PKC-alpha or PKC-zeta. Activation of p42 and p44 mitogen-activated protein kinase (MAPK) by ET-1 or phenylephrine followed more slowly (complete in 3-5 min). Phosphorylation of p42-MAPK occurred simultaneously with its activation. The proportion of the total p42-MAPK pool phosphorylated in response to ET-1 (50%) was greater than with phenylephrine (20%). In addition to activation of MAPK, an unidentified p85 protein kinase was activated by ET-1 in the soluble fraction whereas an unidentified p58 protein kinase was activated in the particulate fraction.

Expression of protein kinase C isoforms during cardiac ventricular development.

The expression of protein kinase C (PKC) isoforms (PKC-alpha, PKC-beta 1, PKC-delta, PKC-epsilon, and PKC-zeta) was studied by immunoblotting in whole ventricles of rat hearts during postnatal development (1-26 days) and in the adult. PKC-alpha, PKC-beta 1, PKC-delta, PKC-epsilon, and PKC-zeta were detected in ventricles of 1-day-old rats, although PKC-alpha and PKC-beta 1 were only barely detectable. All isoforms were rapidly downregulated during development, with abundances relative to total protein declining in the adult to < 25% of 1-day-old values. PKC-beta 1 was not detectable in adult ventricles. The specific activity of PKC was also downregulated. The rat ventricular myocyte becomes amitotic soon after birth but continues to grow, increasing its protein content 40- to 50-fold between the neonate and the 300-g adult. An important question is thus whether the amount of PKC per myocyte is downregulated. With the use of isolated cells, immunoblotting showed that the contents per myocyte of PKC-alpha and PKC-epsilon increased approximately 10-fold between the neonatal and adult stages. In rat ventricles, the rank of association with the particulate fraction was PKC-delta > PKC-epsilon > PKC-zeta. Association of these isoforms with the particulate fraction was less in the adult than in the neonate. In primary cultures of ventricular myocytes prepared from neonatal rat hearts, 1 microM 12-O-tetradecanoylphorbol-13-acetate (TPA) elicited translocation of PKC-alpha, PKC-delta, and PKC-epsilon from the soluble to the particulate fraction in < 1 min, after which time no further translocation was observed. Prolonged exposure (16 h) of myocytes to 1 microM TPA caused essentially complete downregulation of these isoforms, although downregulation of PKC-epsilon was slower than for PKC-delta. In contrast, PKC-zeta was neither translocated nor downregulated by 1 microM TPA. Immunoblotting of human ventricular samples also revealed downregulation of PKC relative to total protein during fetal/postnatal development.

Stimulation of phosphatidylinositol hydrolysis, protein kinase C translocation, and mitogen-activated protein kinase activity by bradykinin in rat ventricular myocytes: dissociation from the hypertrophic response.

In ventricular myocytes cultured from neonatal rat hearts, bradykinin (BK), kallidin or BK(1-8) [(Des-Arg9)BK] stimulated PtdinsP2 hydrolysis by 3-4-fold. EC50 values were 6 nM (BK), 2 nM (kallidin), and 14 microM [BK(1-8)]. BK or kallidin stimulated the rapid (less than 30 s) translocation of more than 80% of the novel protein kinase C (PKC) isoforms nPKC-delta and nPKC-epsilon from the soluble to the particulate fraction. EC50 values for nPKC-delta translocation by BK or kallidin were 10 and 2 nM respectively. EC50 values for nPKC-epsilon translocation by BK or kallidin were 2 and 0.6 nM respectively. EC50 values for the translocation of nPKC-delta and nPKC-epsilon by BK(1-8) were more than 5 microM. The classical PKC, cPKC-alpha, and the atypical PKC, nPKC-zeta, did not translocate. BK caused activation and phosphorylation of p42-mitogen-activated protein kinase (MAPK) (maximal at 3-5 min, 30-35% of p42-MAPK phosphorylated). p44-MAPK was similarly activated. EC50 values for p42/p44-MAPK activation by BK were less than 1 nM whereas values for BK(1-8) were more than 10 microM. The order of potency [BK approximately equal to kallidin > BK (1-8)] for the stimulation of PtdInsP2 hydrolysis, nPKC-delta and nPKC-epsilon translocation, and p42/p44-MAPK activities suggests involvement of the B2 BK receptor subtype. In addition, stimulation of all three processes by BK was inhibited by the B2BK receptor-selective antagonist HOE140 but not by the B1-selective antagonist Leu8BK(1-8). Exposure of cells to phorbol 12-myristate 13-acetate for 24 h inhibited subsequent activation of p42/p44-MAPK by BK suggesting participation of nPKC (and possibly cPKC) isoforms in the activation process. Thus, like hypertrophic agents such as endothelin-1 (ET-1) and phenylephrine (PE), BK activates PtdInsP2 hydrolysis, translocates nPKC-delta, and nPKC-epsilon, and activates p42/p44-MAPK. However, in comparison with ET-1 and PE, BK was only weakly hypertrophic as assessed by cell morphology and patterns of gene expression. This difference could not be attributed to dissimilarities between the duration of activation of p42/p44-MAPK by BK or ET-1. Thus activation of these signalling pathways alone may be insufficient to induce a powerful hypertrophic response.

Regulation of phospholipases C and D in rat ventricular myocytes: stimulation by endothelin-1, bradykinin and phenylephrine.

The physiological activator of protein kinase C (PKC), diacylglycerol, is formed by hydrolysis of phosphoinositides (PI) by phospholipase C (PLC) or phosphatidylcholine by phospholipase D (PLD). We have measured activation of these phospholipases by endothelin-1 (ET-1), bradykinin (BK), or phenylephrine (PE) in ventricular myocytes cultured from neonatal rat. The stimulation of PI hydrolysis after 10 min by 0.1 microM ET-1 (about 12-fold) was much greater than for BK or PE (each about four-fold), and did not correlate with translocation of nPKC delta or nPKC epsilon (Clerk A. Bogoyevitch MA. Andersson MB. Sugden PH, 1994. J Biol Chem 269: 32848-32857: Clerk A, Gillespie-Brown J, Fuller SJ, Sugden PH, 1996. Biochem J 317: 109-118). However, ET-1 and BK stimulated a similar rapid increase in [3H]InsP, formation (< 30 s), which was much greater than that seen with PE. This early phase correlated with PKC translocation. Acute or chronic exposure to 12-O-tetradecanoylphorbol-13-acetate (TPA) or treatment with Ro-31-8220 showed that the stimulation of PI hydrolysis by PE, but not ET-1 or BK, was inhibited by activation of PKC. Furthermore, ET-1 and BK heterologously desensitized the stimulation of PI hydrolysis by PE, ET-1 or BK homologously uncoupled their own receptors from [3H]InsP3 formation, but there was no evidence of heterologous desensitization with these two agonists. Anomalously, chronic exposure to TPA increased the stimulation of PI hydrolysis by BK, but this probably resulted from an increase in BK receptor density. PLD was also rapidly activated by TPA. ET-1, BK or PE. Experiments with Ro-31-8220 showed that the stimulation of PLD by ET-1 and BK was mediated through activation of PKC. We discuss the characteristics of the activation of PI hydrolysis and PLD by ET-1, BK, and PE with respect to the translocation of PKC.

PKC-dependent activation of p46/p54 JNKs during ischemic preconditioning in conscious rabbits.

A conscious rabbit model was used to study the effect of ischemic preconditioning (PC) on stress-activated kinases [c-Jun NH(2)-terminal kinases (JNKs) and p38 mitogen-activated protein kinase (MAPK)] in an environment free of surgical trauma and attending external stress. Ischemic PC (6 cycles of 4-min ischemia/4-min reperfusion) induced significant activation of protein kinase C (PKC)-epsilon in the particulate fraction, which was associated with activation of p46 JNK in the nuclear fraction and p54 JNK in the cytosolic fraction; all of these changes were completely abolised by the PKC inhibitor chelerythrine. Selective enhancement of PKC-epsilon activity in adult rabbit cardiac myocytes resulted in enhanced activity of p46/p54 JNKs, providing direct in vitro evidence that PKC-epsilon is coupled to both kinases. Studies in rabbits showed that the activation of p46 JNK occurred during ischemia, whereas that of p54 JNK occurred after reperfusion. A single 4-min period of ischemia induced a robust activation of the p38 MAPK cascade, which, however, was attenuated after 5 min of reperfusion and disappeared after six cycles of 4-min ischemia/reperfusion. Overexpression of PKC-epsilon in cardiac myocytes failed to increase the p38 MAPK activity. These results demonstrate that ischemic PC activates p46 and p54 JNKs via a PKC-epsilon-dependent signaling pathway and that there are important differences between p46 and p54 JNKs with respect to the subcellular compartment (cytosolic vs. nuclear) and the mechanism (ischemia vs. reperfusion) of their activation after ischemic PC.