Intracellular chemical messengers and neuronal function: Two examples

Two distinct classes of neurons have been examined in the nervous system of Aplysia. The membrane properties of these neurons are regulated by intracellular signalling molecules in both a short-term and a long-term fashion.^ The role of the phosphatidylinositol cycle in the control of neuronal properties was studied in a class of bursting pacemaker cells, the left upper-quadrant bursting neurons (cells L2, L3, L4, and L6) of the abdominal ganglion of Aplysia. These cells display a regular burst-firing pattern that is controlled by cyclic changes of intracellular Ca$\sp{2+}$ that occur during the bursting rhythm. The characteristic bursting pattern of these neurons occurs within a range of membrane potentials ($-35$ to $-50$ mV) called the pacemaker range. Intracellular pressure injection of inositol 1,4,5-trisphosphate (IP$\sb3$) altered the bursting rhythm of the bursting cells. Injection of IP$\sb3$ induced a brief depolarization that was followed by a long-lasting (2-15 min) hyperpolarization. When cells were voltage-clamped at potentials within the pacemaker range, injection of IP$\sb3$ generally induced a biphasic response that had a total duration of 2-15 min. An initial inward shift in holding current (I$\sb{\rm in}$), which lasted 5-120 sec, was followed by a slow outward shift in holding current (I$\sb{\rm out}$). At membrane potentials more negative than $-40$ mV, I$\sb{\rm in}$ was associated with a small and relatively voltage-independent increase in membrane conductance. I$\sb{\rm in}$ was not blocked by bath application of TTX or Co$\sp{2+}$. Although I$\sb{\rm in}$ was activated by injection of IP$\sb3$, it was not blocked by iontophoretic injection of ethyleneglycol-bis-(beta-aminoethyl ether), N, N$\sp\prime$-tetraacetic acid (EGTA) sufficient to block the Ca$\sp{2+}$-activated inward tail current (I$\sb{\rm B}$).^ Long-term (lasting at least 24 hours) effects of adenylate cyclase activation were examined in a well characterized class of mechanosensory neurons in Aplysia. The injected cells were analyzed 24 hours later by two-electrode voltage-clamp techniques. We found that K$\sp+$ currents of these cells were reduced 24 hours after injection of cAMP. The currents that were reduced by cAMP were very similar to those found to be reduced 24 hours after behavioral sensitization. These results suggest that cAMP is part of the intracellular signal that induces long-term sensitization in Aplysia. (Abstract shortened with permission of author.) ^

Studies on regulation of skeletal muscle differentiation by growth factors

Skeletal muscle differentiation involves sequential events in which proliferating undifferentiated myoblasts withdraw from the cell cycle and fuse to form multinucleated myotubes. The process of fusion is accompanied by the disappearance of proteins associated with cell proliferation and the coordinate induction of a battery of muscle-specific gene products, which includes the muscle isoenzyme of creatine kinase, nicotinic acetylcholine receptor, and contractile proteins such as alpha-actin. The molecular events associated with myogenesis are particularly amenable to experimental analysis because the events which occur in vivo can be recapitulated in vitro using established muscle cell lines. Initiation of myogenic differentiation in vitro can be achieved by removing serum from the culture medium. Myogenesis, therefore, can be considered to be regulated through a repression-type of mechanism by components in serum. The objectives of this project were to identify the components involved in regulation of myogenesis and approach the mechanism(s) whereby these components achieve their regulatory function. Initially, the effects of a series of polypeptide growth factors on myogenesis were examined. Among them TGF$\beta$ and FGF were found to be potent inhibitors of myogenic differentiation which did not affect cell proliferation. The inhibitory effects of these growth factors on differentiation requires their persistent presence in the culture medium. After myoblasts have undergone fusion, they become refractory to the inhibitory effects of TGF$\beta$, FGF, and serum. When fusion is inhibited by the presence of EGTA, a Ca$\sp{2+}$ chelator, muscle-specific genes are expressed reversibly upon removal of inhibitory growth factors. Subsequent exposure of biochemically differentiated cells to serum or TGF$\beta$ leads to down-regulation of muscle-specific genes. Stimulation with serum also leads to reentry of myocytes into the cell cycle, whereas fused myotubes are irreversibly and terminally differentiated. Measurement of levels of TGF$\beta$ receptors reveals that under non-fusing conditions, TGF$\beta$ receptor levels in biochemically differentiated myocytes remained as high as in undifferentiated myoblasts, while during terminal differentiation, TGF$\beta$ receptors decreased at least five-fold. Thus, down-regulation of TGF$\beta$ receptors is coupled to irreversible differentiation, but not reversible differentiation in the absence of fusion. The possible involvement of second messenger systems, such as cAMP and protein kinase C, in the pathway(s) by which TGF$\beta$, FGF, or serum factors transduce their signals from the cell surface to the nucleus was also examined. The results showed that myogenic differentiation is subject to negative regulation through cAMP elevation-dependent and cAMP elevation-independent pathways and that serum mitogens, TGF$\beta$ and FGF inhibit differentiation through a mechanism independent of cAMP-elevation or protein kinase C activation. ^

Experimental dissection and characterization of the functional domains in cardiac troponin C

Contraction of vertebrate cardiac muscle is regulated by the binding of Ca$\sp{2+}$ to the troponin C (cTnC) subunit of the troponin complex. In this study, we have used site-directed mutagenesis and a variety of assay techniques to explore the functional roles of regions in cTnC, including Ca$\sp{2+}$/Mg$\sp{2+}$-binding sites III and IV, the functionally inactive site I, the N-terminal helix, the N-terminal hydrophobic pocket and the two cysteine residues with regard to their ability to form disulfide bonds. Conversion of the first Ca$\sp{2+}$ ligand from Asp to Ala inactivated sites III and IV and decreased the apparent affinity of cTnC for the thin filament. Conversion of the second ligand from Asn to Ala also inactivated these sites in the free protein but Ca$\sp{2+}$-binding was recovered upon association with troponin I and troponin T. The Ca$\sp{2+}$-concentrations required for tight thin filament-binding by proteins containing second-ligand mutations were significantly greater than that required for the wild-type protein. Mutation of site I such that the primary sequence was that of an active site with the first Ca$\sp{2+}$ ligand changed from Asp to Ala resulted in a 70% decrease in maximal Ca$\sp{2\sp+}$ dependent ATPase activity in both cardiac and fast skeletal myofibrils. Thus, the primary sequence of the inactive site I in cTnC is functionally important. Major changes in the sequence of the N-terminus had little effect on the ability of cTnC to recover maximal activity but deletion of the first nine residues resulted in a 60 to 80% decrease in maximal activity with only a minor decrease in the pCa$\sb{50}$ of activation, suggesting that the N-terminal helix must be present but that a specific sequence is not required. The formation of an inter- or intramolecular disulfide bonds caused the exposure of hydrophobic surfaces on cTnC and rendered the protein Ca$\sp{2+}$ independent. Finally, elution patterns from a hydrophobic interactions column suggest that cTnC undergoes a significant change in hydrophobicity upon Ca$\sp{2+}$ binding, the majority of which is caused by site II. These latter data show an interesting correlation between exposure of hydrophobic surfaces on and activation of cTnC. Overall, these results represent significant progress toward the elucidation of the functional roles of a variety of structural regions in cTnC. ^

Glutamate receptors expressed in {\it Xenopus\/} oocytes: Studies in function and regulation

The amino acid glutamate is the primary excitatory neurotransmitter for the CNS and is responsible for the majority of fast synaptic transmission. Glutamate receptors have been shown to be involved in multiple forms of synaptic plasticity such as LTP, LTD, and the formation of specific synaptic connections during development. In addition to contributing to the plasticity of the CNS, glutamate receptors also are involved in, at least in part, various pathological conditions such as epilepsy, ischemic damage due to stroke, and Huntington's chorea. The regulation of glutamate receptors, particularly the ionotropic NMDA and AMPA/KA receptors is therefore of great interest. In this body of work, glutamate receptor function and regulation by kinase activity was examined using the Xenopus oocyte which is a convenient and faithful expression system for exogenous proteins. Glutamate receptor responses were measured using the two-electrode voltage clamp technique in oocytes injected with rat total forebrain RNA. NMDA elicited currents that were glycine-dependent, subject to block by Mg$\sp{2+}$ in a voltage-dependent manner and sensitive to the specific NMDA antagonist APV in a manner consistent with those types of responses found in neural tissue. Similarly, KA-evoked currents were sensitive to the specific AMPA/KA antagonist CNQX and exhibited current voltage relationships consistent with the calcium permeable type II KA receptors found in the hippocampus. There is evidence to indicate that NMDA and AMPA/KA receptors are regulated by protein kinase A (PKA). We explored this by examining the effects of activators of PKA (forskolin, 1-isobutyl-3-methylxanthine (IBMX) and 8-Br-cAMP) on NMDA and KA currents in the oocyte. In buffer where Ca$\sp{2+}$ was replaced by 2 mM Ba$\sp{2+},$ forskolin plus IBMX and 8-Br-cAMP augmented currents due to NMDA application but not KA. This augmentation was abolished by pretreating the oocytes in the kinase inhibitor K252A. The use of chloride channel blockers resulted in attenuation of this effect indicating that Ba$\sp{2+}$ influx through the NMDA channel was activating the endogenous calcium-activated chloride current and that the cAMP mediated augmentation was at the level of the chloride channel and not the NMDA channel. This was confirmed by (1) the finding that 8-Br-cAMP increased chloride currents elicited via calcium channel activation while having no effect on the calcium channels themselves and (2) the fact that lowering the Ba$\sp{2+}$ concentration to 200 $\mu$M abolished the augmentation NMDA currents by 8-Br-cAMP. Thus PKA does not appear to modulate ionotropic glutamate receptors in our preparation. Another kinase also implicated in the regulation of NMDA receptors, calcium/phospholipid-dependent protein kinase (PKC), was examined for its effects on the NMDA receptor under low Ba$\sp{2+}$ (200 $\mu$M) conditions. Phorbol esters, activators of PKC, induced a robust potentiation of NMDA currents that was blockable by the kinase inhibitor K252A. Furthermore activation of metabotropic receptors by the selective agonist trans-ACPD, also potentiated NMDA albeit more modestly. These results indicate that neither NMDA nor KA-activated glutamate receptors are modulated by PKA in Xenopus oocytes whereas NMDA receptors appear to be augmented by PKC. Furthermore, the endogenous chloride current of the oocyte was found to be responsive to Ba$\sp{2+}$ and in addition is enhanced by PKA. Both of these latter findings are novel. In conclusion, the Xenopus oocyte is a useful expression system for the analysis of ligand-gated channel activity and the regulation of those channels by phosphorylation. ^

Mechanistic studies of mouse skin tumor promotion by chrysarobin

Since the anthrone chrysarobin oxidizes and generates free radicals, investigations were conducted to assess a possible role for free radicals or reactive oxygen species (ROS) in skin tumor promotion by chrysarobin. Epidermal glutathione levels were not noticeably altered by chrysarobin, nor did a glutathione-depleting agent enhance promotion by chrysarobin. Multiple applications of chrysarobin increased lipid peroxide levels in mouse epidermis two-fold as compared with controls. The antioxidant $\alpha$-tocopherol and the lipoxygenase inhibitor nordihydroguaiaretic acid both inhibited production of lipid peroxides by chrysarobin. The antioxidants $\alpha$-tocopherol acetate and ascorbyl palmitate effectively inhibited promotion and promoter-related effects induced by chrysarobin. Since prooxidant states can lead to increases in intracellular Ca$\sp{2+}$, the effect of two Ca$\sp{2+}$ antagonists, verapamil and TMB-8, on chrysarobin-induced promotion and promoter-related effects were investigated. Both Ca$\sp{2+}$ antagonists inhibited promotion and promoter-related effects induced by chrysarobin, suggesting a possible role for intracellular Ca$\sp{2+}$ alterations in chrysarobin-tumor promotion. Since radical generating compounds are reported to possess the ability to enhance progression of papillomas to squamous cell carcinomas (SCCs), the effects of chrysarobin on papilloma development were tested. Growth kinetics and regression of papillomas generated with limited promotion with chrysarobin were similar to what was reported for the nonradical generating promoter 12-O-tetradecanoylphorbol-13-acetate (TPA) (Aldaz et al., 1991). To test the chrysarobin's ability to enhance progression of pre-existing papillomas to SCCs, tumors were generated by initiation with dimethylbenz (a) anthracene and promotion with TPA. Then mice were treated with chrysarobin, TPA or acetone for 45 weeks. When mice treated with chrysarobin were compared to mice treated continually with TPA with similar numbers of papillomas, the number of papillomas that progressed to SCCs was similar, suggesting that papilloma burden influences the progression of papillomas to SCCs, rather than radical production. In summary, the present study suggests that chrysarobin produces oxidative stress in mouse epidermis as indicated by the generation of lipid peroxides. Antioxidants inhibited production of lipid peroxides and tumor promotion by chrysarobin. Collectively, these data suggest a role for free radicals or ROS in tumor promotion by chrysarobin. ^

Ras signaling in tumor necrosis factor-induced apoptosis

Tumor necrosis factor (TNF)-induced apoptosis is important in immunologic cytotoxicity, autoimmunity, sepsis, normal embryonic development, and wound healing. TNF exerts cytotoxicity on many types of tumor cells but not on normal cells. The molecular events leading to cell death triggered by TNF are still poorly understood. We found that enforced expression of an activated H-ras oncogene converted the non-tumorigenic TNF-resistant C3H 10T1/2 fibroblasts into tumorigenic cells (10TEJ) that also became very sensitive to TNF-induced apoptosis. This finding suggested that the oncogenic form of H-Ras, in which the p21 is locked in the GTP-bound form, could play a role in TNF-induced apoptosis of these cells. To investigate whether Ras activation is an obligatory step in TNF-induced apoptosis, we introduced two different molecular antagonists of Ras, namely the Rap1A tumor suppressor gene or the dominant-negative rasN17 gene, into H-ras transformed 10TEJ cells. Expression of either Rap1A or RasN17 in 10TEJ cells resulted in abrogation of TNF-induced apoptosis. Similar results were obtained by expression of either Ras antagonist in L929 cells, a fibroblast cell line that is sensitive to TNF-induced apoptosis but does not have a ras mutation. The effects of Rap-1A and RasN17 appear to be specific to TNF, since cytotoxicity induced by doxorubicin and thapsigargin are unaffected. Additionally, constitutive apoptosis sensitivity in isolated nuclei, as measured by activation of Ca$\sp{2+}$-dependent endogenous endonuclease, is not affected by Rap-1A or RasN17. Moreover, TNF treatment of L929 cells increased Ras-bound GTP, indicating that Ras activation is triggered by TNF. Thus, Ras activation is required for TNF-induced apoptosis in mouse cells. ^

The electrophysiology of glomerular mesangial cells

Glomerular mesangial cells (MC) are renal vascular cells that regulate the surface area of glomerular capillaries and thus, partly control glomerular filtration rate. Clarification of the signal transduction pathways and ionic mechanisms modulating MC tone are critical to understanding the physiology and pathophysiology of these cells, and the integrative role these cells play in fluid and electrolyte homeostasis. The patch clamp technique and an assay of cell concentration were used to electrophysiologically and pharmacologically analyze the ion channels of the plasmalemmal of human glomerular MC maintained in tissue culture. Moreover, the signal transduction pathways modulating channels involved in relaxation were investigated. Three distinct K$\sp+$-selective channels were identified: two low conductance channels (9 and 65pS) maintained MC at rest, while a larger conductance (206pS) K$\sp+$ channel was quiescent at rest. This latter channel was pharmacologically and biophysically similar to the large, Ca$\sp{2+}$-activated K$\sp+$ channel (BK$\rm\sb{Ca}$) identified in smooth muscle. BK$\rm\sb{Ca}$ played an essential role in relaxation of MC. In cell-attached patches, the open probability (P$\rm\sb{o}$) of BK$\rm\sb{Ca}$ increased from a basal level of $<$0.05 to 0.22 in response to AII (100nM)-induced mobilization of cytosolic Ca$\sp{2+}$. Activation in response to contractile signals (membrane depolarization and Ca$\sp{2+}$ mobilization) suggests that BK$\rm\sb{Ca}$ acts as a low gain feedback regulator of contraction. Atrial natriuretic factor (ANF; 1.0$\mu$M) and nitroprusside (NP; 0.1mM), via the second messenger, cGMP, increase the feedback gain of BK$\rm\sb{Ca}$. In cell-attached patches bathed with physiological saline, these agents transiently activated BK$\rm\sb{Ca}$ from a basal $\rm P\sb{o}<0.05$ to peak responses near 0.50. As membrane potential hyperpolarizes towards $\rm E\sb{K}$ (2-3 minutes), BK$\rm\sb{Ca}$ inactivates. Upon depolarizing V$\rm\sb{m}$ with 140 mM KCl, db-cGMP (10$\mu$M) activated BK$\rm\sb{Ca}$ to a sustained P$\rm\sb{o}$ = 0.51. Addition of AII in the presence of cGMP further increased P$\rm\sb{o}$ to 0.82. Activation of BK$\rm\sb{Ca}$ by cGMP occured via an endogenous cGMP-dependent protein kinase (PKG): in excised, inside-out patches, PKG in the presence of Mg-ATP (0.1mM) and cGMP increased P$\rm\sb{o}$ from 0.07 to 0.39. In contrast, neither PKC nor PKA influenced BK$\rm\sb{Ca}$. Endogenous okadaic acid-sensitive protein phosphatase suppressed BK$\rm\sb{Ca}$ activity. Binning the change in P$\rm\sb{o}\ (\Delta P\sb{o}$) of BK$\rm\sb{Ca}$ in response to PKG (n = 69) established two distinct populations of channels: one that responded ($\cong$67%, $\rm\Delta P\sb{o} = 0.45 \pm 0.03$) and one that was unresponsive ($\Delta\rm P\sb{o} = 0.00 \pm 0.01$) to PKG. Activation of BK$\rm\sb{Ca}$ by PKG resulted from a decrease in the Ca$\sp{2+}$- and voltage-activation thresholds independent of sensitivities. In conclusion, mesangial BK$\rm\sb{Ca}$ channels sense both electrical and chemical signals of contraction and act as feedback regulators by repolarizing the plasma membrane. ANF and NO, via cGMP, stimulate endogenous PKG, which subsequently decreases the activation threshold of BK$\rm\sb{Ca}$ to increase the gain of this feedback regulatory signal. ^

Characterization of calcium signaling mechanisms in osteoblasts

Bone remodeling is controlled by the osteoclast, which resorbs bone, and the osteoblast, which synthesizes and secretes proteins that are eventually mineralized into bone. Ca$\sp{2+}$ homeostasis and signaling contribute to the function of nearly all cell types, and understanding both in the osteoblast is of importance given its secretory properties and interaction with osteoclasts. This study was undertaken to identify and investigate the physiology of the Ca$\sp{2+}$ signaling mechanisms present in osteoblasts. The Ca$\sp{2+}$ pumps, stores and channels present in osteoblasts were studied. RT-PCR cloning revealed that osteoblast-like cells express PMCA1b, an alternatively spliced transcript of the plasma membrane Ca$\sp{2+}$-ATPase. The PMCA1b isoform contains a consensus phosphorylation site for cAMP-dependent protein kinase A and a modified calmodulin binding domain. The regulation of osteoblast function by agents that act via cAMP-mediated pathways may involve alterations in the activity of the plasma membrane Ca$\sp{2+}$-ATPase.^ Calcium release from intracellular stores is a signaling mechanism used universally by cells responding to hormones and growth factors, and the compartmentalization and regulated release of calcium is cell-type specific. Fura-2 was employed to monitor intracellular Ca$\sp{2+}$. Thapsigargin and 2,5,-di-(tert-butyl)-1,4-benzohydroquinone (tBuHQ), two inhibitors of endoplasmic reticulum Ca$\sp{2+}$-ATPase activity, both emptied a single intracellular calcium pool which was released in response to either ATP or thrombin, identifying it as the inositol 1,4,5-trisphosphate-sensitive calcium store. The Ca$\sp{2+}$ storage system present in osteoblasts is typical of a non-excitable cell type, despite these cells sharing characteristics of excitable cells such as voltage-sensitive Ca$\sp{2+}$ channels (VSCCs).^ VSCCs are important cell surface regulators of membrane permeability to Ca$\sp{2+}$. In non-excitable cells VSCCs act as cellular transducers of stimulus-secretion coupling, activators of intracellular proteins, and in control of cell growth and differentiation. Functional VSCCs have been shown to exist in osteoblasts, however, no molecular cloning has been reported. To obtain information concerning the molecular identity of the osteoblastic VSCC, we used an RT-PCR regional amplification approach. Sequencing of the products indicated that osteoblasts express at least two isoforms of the L-type VSCC, $\alpha 1\sb{\rm C-a}$ and the $\alpha 1\sb{\rm C-d}$, which share regions of identity to the $\alpha \sb{\rm 1C}$ isoform first identified in cardiac myocytes. The ability of $1,25(\rm OH)\sb2D\sb3$ and structural analogs to modulate expression of Ca$\sp{2+}$ channel mRNA was then investigated. Cells were cultured for 48 hr in the presence of $1,25(\rm OH)\sb2D\sb3$ or vitamin D analogs, and the levels of mRNA encoding VSCC $\alpha \sb{\rm 1C}$ were quantitated using a competitive RT-PCR assay. It was found that $1,25(\rm OH)\sb2D\sb3$ and analog BT reduced steady state levels of $\alpha \sb{\rm 1C}$ mRNA. Conversely, analog AT did not alter steady state levels of Ca$\sp{2+}$ channel mRNA. Since it has been shown previously that analog BT, but not AT, binds and activates the nuclear vitamin D receptor, these findings suggest that the down regulation of channel mRNA involves the nuclear receptor for $1,25(\rm OH)\sb2D\sb3$. ^

Long-term synaptic facilitation of tail sensorimotor connections in {\it Aplysia\/}

Long-term sensitization in Aplysia is a well studied model for the examination of the cellular and molecules mechanisms of long-term memory. Several lines of evidence suggest long-term sensitization is mediated at least partially by long-term synaptic facilitation between the sensory and motor neurons. The sensitization training and one of its analogues, serotonin (5-HT), can induce long-term facilitation. In this study, another analogue to long-term sensitization training has been developed. Stimulation of peripheral nerves of pleural-pedal ganglia preparation induced long-term facilitation at both 24 hr and 48 hr. This is the first report that long-term facilitation in Aplysia persists for more than 24 hr, which is consistent with the observation that long-term sensitization lasts for more than one day. Thus, the data support the hypothesis that long-term facilitation is an important mechanism for long-term sensitization.^ One of the major differences between short-term and long-term facilitation is that long-term facilitation requires protein synthesis. Therefore, the effects of anisomycin, a protein synthesis inhibitor, on long-term facilitation was examined. Long-term facilitation induced by nerve stimulation was inhibited by 2 $\mu$M anisomycin, which inhibits $\sim$90% of protein synthesis. Nevertheless, at higher concentration (20 $\mu$M), anisomycin induced long-term facilitation by itself, which raises an interesting question about the function of anisomycin other than protein synthesis inhibition.^ Since protein synthesis is critical for long-term facilitation, a major goal is to identify and functionally characterize the molecules whose mRNA levels are altered during the formation of long-term facilitation. Behavioral training or its analogues (nerve stimulation and 5-HT) increases the level of mRNA of calmodulin (CaM). Thus, the role of Ca$\sp{2+}$-CaM-dependent protein kinase II (CaMKII), a major substrate of CaM, in long-term facilitation induced by nerve stimulation was examined. KN-62, a specific CaMKII inhibitor, did not block either the induction or the maintenance of long-term facilitation induced by nerve stimulation. These data indicate that CaMKII may not be involved in long-term facilitation. Another protein whose mRNA level of a molecule was increased by the behavioral training and the treatment of 5-HT is Aplysia tolloid/BMP-1-like protein 1 (apTBL-1). Tolloid in Drosophila and BMP-1 in human tissues are believed to be secreted as a metalloprotease to activate TGF-$\beta.$ Thus, the long-term effects of recombinant human TGF-$\beta1$ on synaptic strength were examined. Treatment of ganglia with TGF-$\beta1$ produced long-term facilitation, but not short-term or intermediate-term facilitation ($\le$4 hr). In addition, TGF-$\beta1$ and 5-HT were not additive in producing long-term facilitation, which indicates an interaction between two cascades. Moreover, 5-HT-induced facilitation (at both 24 hr and 48 hr) and nerve stimulation-induced facilitation (at 24 hr) were inhibited by TGF-$\beta$ sRII, a TGF-$\beta$ inhibitor. These results suggest that TGF-$\beta$ is part of the cascade of events underlying long-term sensitization, and also indicate that a signaling molecule used in development may also have functions in adult neuronal plasticity. ^

Otsar leshon ha-Ḳodesh Hoc Est, Thesavrvs Lingvae Sanctae : Sic Enim Inscribere placuit lexicon hoc Hebraicum ...

Autore reuerendo patre Sancte Pagnino Lucensi ... antistite

Heisenberg symmetry and hypermultiplet manifolds

We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg U (1). We finally discuss the realization of the latter by gauging appropriate Sp(2, 4) generators in N = 2 conformal supergravity.

Complectens Partem Alteram Voluminis XXXI.

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Additamenta ad Tractatum de Sacrificiis

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Eusebii Onomasticon cum latina interpretatione S. Hieronymi

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De Republica Hebraeorum, commentario illustratus opera Constantini l'Empereur ab Oppijck

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