The effects of meson loops in the vacuum sector of the Nambu-Jona-Lasinio model are calculated. Using the effective action formalism we take consistently all nextto-leading-order 1 Nc terms into account. This leads to a symmetry-conserving approach, in which all features of spontaneously broken chiral symmetry, such as the Goldstone theorem, the Goldberger-Treiman and the Gell-Mann-Oakes-Renner relations are preserved. Contributions to qq and F π are calculated, and are shown to be substantial, at the level of ∼ 30%, consistent with the 1 Nc expansion. The leading nonanalytic terms in the chiral expansion of qq , F π and m π have the same form as the one-loop results of chiral perturbation theory.

Control of heart rate is a complex process that integrates the function of multiple G protein-coupled receptors and ion channels. Among them, the G protein-regulated inwardly rectifying K ؉ (GIRK or K ACh ) channels of sinoatrial node and atria play a major role in beat-tobeat regulation of the heart rate. The atrial K ACh channels are heterotetrameric proteins that consist of two pore-forming subunits, GIRK1 and GIRK4. Following m 2 -muscarinic acetylcholine receptor (M2R) stimulation, K ACh channel activation is conferred by the direct binding of G protein ␤␥ subunits (G␤␥) to the channel. Here we show that atrial K ACh channels are assembled in a signaling complex with G␤␥, G protein-coupled receptor kinase, cyclic adenosine monophosphatedependent protein kinase, two protein phosphatases, PP1 and PP2A, receptor for activated C kinase 1, and actin. This complex would enable the K ACh channels to rapidly integrate ␤-adrenergic and M2R signaling in the membrane, and it provides insight into general principles governing spatial integration of different transduction pathways. Furthermore, the same complex might recruit protein kinase C (PKC) to the K ACh channel following ␣-adrenergic receptor stimulation. Our electrophysiological recordings from single atrial K ACh channels revealed a potent inhibition of G␤␥-induced channel activity by PKC, thus validating the physiological significance of the observed complex as interconnecting site where signaling molecules congregate to execute a coordinated control of membrane excitability.

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The membrane-delimited activation of muscarinic K+ channels by G protein βγ subunits plays a prominent role in the inhibitory synaptic transmission in the heart. These channels are thought to be heterotetramers comprised of two homologous subunits, GIRK1 and CIR, both members of the family of inwardly rectifying K+ channels. Here, we demonstrate that muscarinic K+ channels in neonatal rat atrial myocytes exhibit four distinct gating modes. In intact myocytes, after muscarinic receptor activation, the different gating modes were distinguished by differences in both the frequency of channel opening and the mean open time of the channel, which accounted for a 76-fold increase in channel open probability from mode 1 to mode 4. Because of the tetrameric architecture of the channel, the hypothesis that each of the four gating modes reflects binding of a different number of Gβγ subunits to the channel was tested, using recombinant Gβ1γ5. Gβ1γ5 was able to control the equilibrium between the four gating modes of the channel in a manner consistent with binding of Gβγ to four equivalent and independent sites in the protein complex. Surprisingly, however, Gβ1γ5 lacked the ability to stabilize the long open state of the channel that is responsible for the augmentation of the mean open time in modes 3 and 4 after muscarinic receptor stimulation. The modal regulation of muscarinic K+ channel gating by Gβγ provides the atrial cells with at least two major advantages: the ability to filter out small inputs from multiple membrane receptors and yet the ability to create the gradients of information necessary to control the heart rate with great precision.

We analyze the analytic structure of meson propagators in the Nambu-Jona-Lasinio model with a proper-time regulator. We show that the regulator produces unphysical complex singularities. As a result the naive use of the Wick rotation is no longer allowed. Formulas involving integration over mesonic momenta, such as meson-loop contributions or dispersion relations for meson Green's functions, cannot be written in usual forms.