Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V

In this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours.

A g-factor metric for k-t-GRAPPA- and PEAK-GRAPPA-based parallel imaging.

PURPOSE The aim of this work is to derive a theoretical framework for quantitative noise and temporal fidelity analysis of time-resolved k-space-based parallel imaging methods. THEORY An analytical formalism of noise distribution is derived extending the existing g-factor formulation for nontime-resolved generalized autocalibrating partially parallel acquisition (GRAPPA) to time-resolved k-space-based methods. The noise analysis considers temporal noise correlations and is further accompanied by a temporal filtering analysis. METHODS All methods are derived and presented for k-t-GRAPPA and PEAK-GRAPPA. A sliding window reconstruction and nontime-resolved GRAPPA are taken as a reference. Statistical validation is based on series of pseudoreplica images. The analysis is demonstrated on a short-axis cardiac CINE dataset. RESULTS The superior signal-to-noise performance of time-resolved over nontime-resolved parallel imaging methods at the expense of temporal frequency filtering is analytically confirmed. Further, different temporal frequency filter characteristics of k-t-GRAPPA, PEAK-GRAPPA, and sliding window are revealed. CONCLUSION The proposed analysis of noise behavior and temporal fidelity establishes a theoretical basis for a quantitative evaluation of time-resolved reconstruction methods. Therefore, the presented theory allows for comparison between time-resolved parallel imaging methods and also nontime-resolved methods. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

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RGS proteins reconstitute the rapid gating kinetics of G��γ-activated inwardly rectifying K+ channels

G protein-gated inward rectifier K+ (GIRK) channels mediate hyperpolarizing postsynaptic potentials in the nervous system and in the heart during activation of G��(i/o)-coupled receptors. In neurons and cardiac atrial cells the time course for receptor-mediated GIRK current deactivation is 20–40 times faster than that observed in heterologous systems expressing cloned receptors and GIRK channels, suggesting that an additional component(s) is required to confer the rapid kinetic properties of the native transduction pathway. We report here that heterologous expression of “regulators of G protein signaling��� (RGS proteins), along with cloned G protein-coupled receptors and GIRK channels, reconstitutes the temporal properties of the native receptor → GIRK signal transduction pathway. GIRK current waveforms evoked by agonist activation of muscarinic m2 receptors or serotonin 1A receptors were dramatically accelerated by coexpression of either RGS1, RGS3, or RGS4, but not RGS2. For the brain-expressed RGS4 isoform, neither the current amplitude nor the steady-state agonist dose-response relationship was significantly affected by RGS expression, although the agonist-independent “basal” GIRK current was suppressed by ≈40%. Because GIRK activation and deactivation kinetics are the limiting rates for the onset and termination of “slow” postsynaptic inhibitory currents in neurons and atrial cells, RGS proteins may play crucial roles in the timing of information transfer within the brain and to peripheral tissues.

Mechanism underlying bupivacaine inhibition of G protein-gated inwardly rectifying K+ channels

Local anesthetics, commonly used for treating cardiac arrhythmias, pain, and seizures, are best known for their inhibitory effects on voltage-gated Na+ channels. Cardiovascular and central nervous system toxicity are unwanted side-effects from local anesthetics that cannot be attributed to the inhibition of only Na+ channels. Here, we report that extracellular application of the membrane-permeant local anesthetic bupivacaine selectively inhibited G protein-gated inwardly rectifying K+ channels (GIRK:Kir3) but not other families of inwardly rectifying K+ channels (ROMK:Kir1 and IRK:Kir2). Bupivacaine inhibited GIRK channels within seconds of application, regardless of whether channels were activated through the muscarinic receptor or directly via coexpressed G protein G��γ subunits. Bupivacaine also inhibited alcohol-induced GIRK currents in the absence of functional pertussis toxin-sensitive G proteins. The mutated GIRK1 and GIRK2 (GIRK1/2) channels containing the high-affinity phosphatidylinositol 4,5-bisphosphate (PIP2) domain from IRK1, on the other hand, showed dramatically less inhibition with bupivacaine. Surprisingly, GIRK1/2 channels with high affinity for PIP2 were inhibited by ethanol, like IRK1 channels. We propose that membrane-permeant local anesthetics inhibit GIRK channels by antagonizing the interaction of PIP2 with the channel, which is essential for G��γ and ethanol activation of GIRK channels.

Inhibition of function in Xenopus oocytes of the inwardly rectifying G-protein-activated atrial K channel (GIRK1) by overexpression of a membrane-attached form of the C-terminal tail.

Coexpression in Xenopus oocytes of the inwardly rectifying guanine nucleotide binding (G)-protein-gated K channel GIRK1 with a myristoylated modification of the (putative) cytosolic C-terminal tail [GIRK1 aa 183-501 fused in-frame to aa 1-15 of p60src and denoted src+ (183-501)] leads to a high degree of inhibition of the inward G-protein-gated K+ current. The nonmyristoylated segment, src- (183-501), is not active. Although some interference with assembly is not precluded, the evidence indicates that the main mechanism of inhibition is interference with functional activation of the channel by G proteins. In part, the tail functions as a blocking particle similar to a "Shaker ball"; it may also function by competing for the available supply of free G beta gamma liberated by hormone activation of a seven-helix receptor. The non-G-protein-gated weak inward rectifier ROMK1 is less effectively inhibited, and a Shaker K channel was not inhibited. Immunological assays show the presence of a high concentration of src+ (183-501) in the plasma membrane and the absence of any membrane forms for the nonmyristoylated segment.

Evidence that neuronal G-protein-gated inwardly rectifying K+ channels are activated by G beta gamma subunits and function as heteromultimers.

Guanine nucleotide-binding proteins (G proteins) activate K+ conductances in cardiac atrial cells to slow heart rate and in neurons to decrease excitability. cDNAs encoding three isoforms of a G-protein-coupled, inwardly rectifying K+ channel (GIRK) have recently been cloned from cardiac (GIRK1/Kir 3.1) and brain cDNA libraries (GIRK2/Kir 3.2 and GIRK3/Kir 3.3). Here we report that GIRK2 but not GIRK3 can be activated by G protein subunits G beta 1 and G gamma 2 in Xenopus oocytes. Furthermore, when either GIRK3 or GIRK2 was coexpressed with GIRK1 and activated either by muscarinic receptors or by G beta gamma subunits, G-protein-mediated inward currents were increased by 5- to 40-fold. The single-channel conductance for GIRK1 plus GIRK2 coexpression was intermediate between those for GIRK1 alone and for GIRK2 alone, and voltage-jump kinetics for the coexpressed channels displayed new kinetic properties. On the other hand, coexpression of GIRK3 with GIRK2 suppressed the GIRK2 alone response. These studies suggest that formation of heteromultimers involving the several GIRKs is an important mechanism for generating diversity in expression level and function of neurotransmitter-coupled, inward rectifier K+ channels.

Time factors of differentially preserved wood in two calcitic concretions in Pennsylvanian black shale from Indiana / Bertram G. Woodland -- and Catherine K. Richardson --.

v.33:no.10(1975)

String quartet no. 14 (1) in G major, K 387. [music] /

Mode of access: Internet.

The life of General Sir Edward Bruce Hamley, K.C B., K.C.M.G. ;

Mode of access: Internet.

Weltgeschichte in gemeinverständlicher Darstellung, in Verbindung mit G. Bourgin, E. Ciccotti, E. Hanslik, S. Hellmann, K. Kaser, E.G. Klauber, E. Kohn, J. Kromayer und A. von Rosthorn,

Mode of access: Internet.

Supplementary despatches and memoranda of Field Marshal Arthur, duke of Wellington, K. G.

Titles vary: v. 5 has title, "Civil correspondence and memoranda"; v. 6-15 have title, "Supplementary despatches. Correspondence and memoranda. "