Generalized coherent and squeezed states based on the h(1)⊗su(2)h(1) \otimes su(2) algebra

States which minimize the Schr\"odinger--Robertson uncertainty relation are constructed as eigenstates of an operator which is a element of the h(1) \oplus \su(2) algebra. The relations with supercoherent and supersqueezed states of the supersymmetric harmonic oscillator are given. Moreover, we are able to compute gneneral Hamiltonians which behave like the harmonic oscillator Hamiltonian or are related to the Jaynes--Cummings Hamiltonian.Comment: 42 pages, 10 figure

Invariant vector fields and the prolongation method for supersymmetric quantum systems

The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a constant magnetic field are reviewed from the point of view of the vector field prolongation method. Generators of supersymmetries are then introduced so that we get Lie superalgebras of symmetries and supersymmetries. This approach does not require the introduction of Grassmann valued differential equations but a specific matrix realization and the concept of dynamical symmetry. The Jaynes-Cummings model and supersymmetric generalizations are then studied. We show how it is closely related to the preceding models. Lie algebras of symmetries and supersymmetries are also obtained.Comment: 37 pages, 7 table

Coherent and squeezed states of quantum Heisenberg algebras

Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give rise to new classes of deformed coherent and squeezed states. They are parametrized by deformed algebra parameters and suitable redefinitions of them as paragrassmann numbers. Some properties of these deformed states also are analyzed.Comment: 32 pages, 3 figure

EphA4 activation of c-Abl mediates synaptic loss and LTP blockade caused by amyloid-β oligomers.

The early stages of Alzheimer's disease are characterised by impaired synaptic plasticity and synapse loss. Here, we show that amyloid-β oligomers (AβOs) activate the c-Abl kinase in dendritic spines of cultured hippocampal neurons and that c-Abl kinase activity is required for AβOs-induced synaptic loss. We also show that the EphA4 receptor tyrosine kinase is upstream of c-Abl activation by AβOs. EphA4 tyrosine phosphorylation (activation) is increased in cultured neurons and synaptoneurosomes exposed to AβOs, and in Alzheimer-transgenic mice brain. We do not detect c-Abl activation in EphA4-knockout neurons exposed to AβOs. More interestingly, we demonstrate EphA4/c-Abl activation is a key-signalling event that mediates the synaptic damage induced by AβOs. According to this results, the EphA4 antagonistic peptide KYL and c-Abl inhibitor STI prevented i) dendritic spine reduction, ii) the blocking of LTP induction and iii) neuronal apoptosis caused by AβOs. Moreover, EphA4-/- neurons or sh-EphA4-transfected neurons showed reduced synaptotoxicity by AβOs. Our results are consistent with EphA4 being a novel receptor that mediates synaptic damage induced by AβOs. EphA4/c-Abl signalling could be a relevant pathway involved in the early cognitive decline observed in Alzheimer's disease patients

Cholinergic abnormalities, endosomal alterations and up-regulation of nerve growth factor signaling in Niemann-Pick Type C Disease

Background: Neurotrophins and their receptors regulate several aspects of the developing and mature nervous system, including neuronal morphology and survival. Neurotrophin receptors are active in signaling endosomes, which are organelles that propagate neurotrophin signaling along neuronal processes. Defects in the Npc1 gene are associated with the accumulation of cholesterol and lipids in late endosomes and lysosomes, leading to neurodegeneration and Niemann-Pick type C (NPC) disease. The aim of this work was to assess whether the endosomal and lysosomal alterations observed in NPC disease disrupt neurotrophin signaling. As models, we used i) NPC1-deficient mice to evaluate the central cholinergic septo-hippocampal pathway and its response to nerve growth factor (NGF) after axotomy and ii) PC12 cells treated with U18666A, a pharmacological cellular model of NPC, stimulated with NGF. Results: NPC1-deficient cholinergic cells respond to NGF after axotomy and exhibit increased levels o

Cholinergic Abnormalities, Endosomal Alterations and Up-Regulation of Nerve Growth Factor Signaling in Niemann-Pick Type C Disease

Abstract Background Neurotrophins and their receptors regulate several aspects of the developing and mature nervous system, including neuronal morphology and survival. Neurotrophin receptors are active in signaling endosomes, which are organelles that propagate neurotrophin signaling along neuronal processes. Defects in the Npc1 gene are associated with the accumulation of cholesterol and lipids in late endosomes and lysosomes, leading to neurodegeneration and Niemann-Pick type C (NPC) disease. The aim of this work was to assess whether the endosomal and lysosomal alterations observed in NPC disease disrupt neurotrophin signaling. As models, we used i) NPC1-deficient mice to evaluate the central cholinergic septo-hippocampal pathway and its response to nerve growth factor (NGF) after axotomy and ii) PC12 cells treated with U18666A, a pharmacological cellular model of NPC, stimulated with NGF. Results NPC1-deficient cholinergic cells respond to NGF after axotomy and exhibit increased levels of choline acetyl transferase (ChAT), whose gene is under the control of NGF signaling, compared to wild type cholinergic neurons. This finding was correlated with increased ChAT and phosphorylated Akt in basal forebrain homogenates. In addition, we found that cholinergic neurons from NPC1-deficient mice had disrupted neuronal morphology, suggesting early signs of neurodegeneration. Consistently, PC12 cells treated with U18666A presented a clear NPC cellular phenotype with a prominent endocytic dysfunction that includes an increased size of TrkA-containing endosomes and reduced recycling of the receptor. This result correlates with increased sensitivity to NGF, and, in particular, with up-regulation of the Akt and PLC-γ signaling pathways, increased neurite extension, increased phosphorylation of tau protein and cell death when PC12 cells are differentiated and treated with U18666A. Conclusions Our results suggest that the NPC cellular phenotype causes neuronal dysfunction through the abnormal up-regulation of survival pathways, which causes the perturbation of signaling cascades and anomalous phosphorylation of the cytoskeleton.</p

PPAR-mediated mitochondrial dynamics modulation.

<p>We have previously proposed a direct link between antioxidant PPARs activity and Wnt signaling pathway <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064019#pone.0064019-Itoh1" target="_blank">[19]</a>. Based on our present results we hypothesize that PPARs are able to modulate mitochondrial dynamics trough different cellular mechanisms. Complementary to the Wnt signaling pathway (<i>FZD</i>, frizzled; <i>LRP 5/6</i>, low density lipoprotein receptor-related protein; <i>DVL</i>, disheveled; <i>βcat</i>, β-catenin), PPARs might act inducing directly the expression of several mitochondrial-related proteins (<i>UCP</i>, uncoupled protein; <i>DRP1</i>, dynamin related protein 1; <i>Mfn</i>, mitofusin; <i>mtTFA</i>, mitochondrial transcription factor). Additionally, the PPARs-mediated calcium balance might also offer another control point for mitochondrial dynamics modulation (<i>VDCC</i>, voltage dependent calcium channels; <i>NMDAR</i>, NMDA receptor; <i>VGCC</i>, voltage-gated calcium channels; <i>PKC</i>, protein kinase C).</p