The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear equations is constructed in the form of an expansion over particle clusters whose evolution is described by the corresponding order cumulant (semi-invariant) of evolution operators for the von Neumann equations. For the initial data from the space of sequences of trace class operators the existence of a strong and a weak solution of the Cauchy problem is proved. We discuss the relationships of this solution both with the $s$-particle statistical operators, which are solutions of the BBGKY hierarchy, and with the $s$-particle correlation operators of quantum systems.Comment: 26 page

Scattering theory on graphs

We consider the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure

Kirchhoff's Rule for Quantum Wires

In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with $n$ channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy $E>0$ is explicitly given in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory. Finally we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs only use known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitean symplectic forms.Comment: 40 page

Src Dependent Pancreatic Acinar Injury Can Be Initiated Independent of an Increase in Cytosolic Calcium

Several deleterious intra-acinar phenomena are simultaneously triggered on initiating acute pancreatitis. These culminate in acinar injury or inflammatory mediator generation in vitro and parenchymal damage in vivo. Supraphysiologic caerulein is one such initiator which simultaneously activates numerous signaling pathways including non-receptor tyrosine kinases such as of the Src family. It also causes a sustained increase in cytosolic calcium- a player thought to be crucial in regulating deleterious phenomena. We have shown Src to be involved in caerulein induced actin remodeling, and caerulein induced changes in the Golgi and post-Golgi trafficking to be involved in trypsinogen activation, which initiates acinar cell injury. However, it remains unclear whether an increase in cytosolic calcium is necessary to initiate acinar injury or if injury can be initiated at basal cytosolic calcium levels by an alternate pathway. To study the interplay between tyrosine kinase signaling and calcium, we treated mouse pancreatic acinar cells with the tyrosine phosphatase inhibitor pervanadate. We studied the effect of the clinically used Src inhibitor Dasatinib (BMS-354825) on pervanadate or caerulein induced changes in Src activation, trypsinogen activation, cell injury, upstream cytosolic calcium, actin and Golgi morphology. Pervanadate, like supraphysiologic caerulein, induced Src activation, redistribution of the F-actin from its normal location in the sub-apical area to the basolateral areas, and caused antegrade fragmentation of the Golgi. These changes, like those induced by supraphysiologic caerulein, were associated with trypsinogen activation and acinar injury, all of which were prevented by Dasatinib. Interestingly, however, pervanadate did not cause an increase in cytosolic calcium, and the caerulein induced increase in cytosolic calcium was not affected by Dasatinib. These findings suggest that intra-acinar deleterious phenomena may be initiated independent of an increase in cytosolic calcium. Other players resulting in acinar injury along with the Src family of tyrosine kinases remain to be explored. © 2013 Mishra et al

Contribution of NADPH Oxidase to Membrane CD38 Internalization and Activation in Coronary Arterial Myocytes

The CD38-ADP-ribosylcyclase-mediated Ca2+ signaling pathway importantly contributes to the vasomotor response in different arteries. Although there is evidence indicating that the activation of CD38-ADP-ribosylcyclase is associated with CD38 internalization, the molecular mechanism mediating CD38 internalization and consequent activation in response to a variety of physiological and pathological stimuli remains poorly understood. Recent studies have shown that CD38 may sense redox signals and is thereby activated to produce cellular response and that the NADPH oxidase isoform, NOX1, is a major resource to produce superoxide (O2·−) in coronary arterial myocytes (CAMs) in response to muscarinic receptor agonist, which uses CD38-ADP-ribosylcyclase signaling pathway to exert its action in these CAMs. These findings led us hypothesize that NOX1-derived O2·− serves in an autocrine fashion to enhance CD38 internalization, leading to redox activation of CD38-ADP-ribosylcyclase activity in mouse CAMs. To test this hypothesis, confocal microscopy, flow cytometry and a membrane protein biotinylation assay were used in the present study. We first demonstrated that CD38 internalization induced by endothelin-1 (ET-1) was inhibited by silencing of NOX1 gene, but not NOX4 gene. Correspondingly, NOX1 gene silencing abolished ET-1-induced O2·− production and increased CD38-ADP-ribosylcyclase activity in CAMs, while activation of NOX1 by overexpression of Rac1 or Vav2 or administration of exogenous O2·−significantly increased CD38 internalization in CAMs. Lastly, ET-1 was found to markedly increase membrane raft clustering as shown by increased colocalization of cholera toxin-B with CD38 and NOX1. Taken together, these results provide direct evidence that Rac1-NOX1-dependent O2·− production mediates CD38 internalization in CAMs, which may represent an important mechanism linking receptor activation with CD38 activity in these cells

The two-pore channel TPCN2 mediates NAADP-dependent Ca2+-release from lysosomal stores

Second messenger-induced Ca2+-release from intracellular stores plays a key role in a multitude of physiological processes. In addition to 1,4,5-inositol trisphosphate (IP3), Ca2+, and cyclic ADP ribose (cADPR) that trigger Ca2+-release from the endoplasmatic reticulum (ER), nicotinic acid adenine dinucleotide phosphate (NAADP) has been identified as a cellular metabolite that mediates Ca2+-release from lysosomal stores. While NAADP-induced Ca2+-release has been found in many tissues and cell types, the molecular identity of the channel(s) conferring this release remained elusive so far. Here, we show that TPCN2, a novel member of the two-pore cation channel family, displays the basic properties of native NAADP-dependent Ca2+-release channels. TPCN2 transcripts are widely expressed in the body and encode a lysosomal protein forming homomers. TPCN2 mediates intracellular Ca2+-release after activation with low-nanomolar concentrations of NAADP while it is desensitized by micromolar concentrations of this second messenger and is insensitive to the NAADP analog nicotinamide adenine dinucleotide phosphate (NADP). Furthermore, TPCN2-mediated Ca2+-release is almost completely abolished when the capacity of lysosomes for storing Ca2+ is pharmacologically blocked. By contrast, TPCN2-specific Ca2+-release is unaffected by emptying ER-based Ca2+ stores. In conclusion, these findings indicate that TPCN2 is a major component of the long-sought lysosomal NAADP-dependent Ca2+-release channel

Nanomolar oxytocin synergizes with weak electrical afferent stimulation to activate the locomotor CPG of the rat spinal cord in vitro.

Synergizing the effect of afferent fibre stimulation with pharmacological interventions is a desirable goal to trigger spinal locomotor activity, especially after injury. Thus, to better understand the mechanisms to optimize this process, we studied the role of the neuropeptide oxytocin (previously shown to stimulate locomotor networks) on network and motoneuron properties using the isolated neonatal rat spinal cord. On motoneurons oxytocin (1 nM-1 \u3bcM) generated sporadic bursts with superimposed firing and dose-dependent depolarization. No desensitization was observed despite repeated applications. Tetrodotoxin completely blocked the effects of oxytocin, demonstrating the network origin of the responses. Recording motoneuron pool activity from lumbar ventral roots showed oxytocin mediated depolarization with synchronous bursts, and depression of reflex responses in a stimulus and peptide-concentration dependent fashion. Disinhibited bursting caused by strychnine and bicuculline was accelerated by oxytocin whose action was blocked by the oxytocin antagonist atosiban. Fictive locomotion appeared when subthreshold concentrations of NMDA plus 5HT were coapplied with oxytocin, an effect prevented after 24 h incubation with the inhibitor of 5HT synthesis, PCPA. When fictive locomotion was fully manifested, oxytocin did not change periodicity, although cycle amplitude became smaller. A novel protocol of electrical stimulation based on noisy waveforms and applied to one dorsal root evoked stereotypic fictive locomotion. Whenever the stimulus intensity was subthreshold, low doses of oxytocin triggered fictive locomotion although oxytocin per se did not affect primary afferent depolarization evoked by dorsal root pulses. Among the several functional targets for the action of oxytocin at lumbar spinal cord level, the present results highlight how small concentrations of this peptide could bring spinal networks to threshold for fictive locomotion in combination with other protocols, and delineate the use of oxytocin to strengthen the efficiency of electrical stimulation to activate locomotor circuits

The Endoplasmic Reticulum Stress Response in Neuroprogressive Diseases: Emerging Pathophysiological Role and Translational Implications

The endoplasmic reticulum (ER) is the main cellular organelle involved in protein synthesis, assembly and secretion. Accumulating evidence shows that across several neurodegenerative and neuroprogressive diseases, ER stress ensues, which is accompanied by over-activation of the unfolded protein response (UPR). Although the UPR could initially serve adaptive purposes in conditions associated with higher cellular demands and after exposure to a range of pathophysiological insults, over time the UPR may become detrimental, thus contributing to neuroprogression. Herein, we propose that immune-inflammatory, neuro-oxidative, neuro-nitrosative, as well as mitochondrial pathways may reciprocally interact with aberrations in UPR pathways. Furthermore, ER stress may contribute to a deregulation in calcium homoeostasis. The common denominator of these pathways is a decrease in neuronal resilience, synaptic dysfunction and even cell death. This review also discusses how mechanisms related to ER stress could be explored as a source for novel therapeutic targets for neurodegenerative and neuroprogressive diseases. The design of randomised controlled trials testing compounds that target aberrant UPR-related pathways within the emerging framework of precision psychiatry is warranted