172,039 research outputs found

    Green-Kubo Formula for Weakly Coupled Systems with Noise

    No full text
    We study the Green-Kubo (GK) formula κ(ε, ς) for the heat conductivity of an infinite chain of d-dimensional finite systems (cells) coupled by a smooth nearest neighbor potential εV . The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength ς. Noting that κ(ε, ς) exists and is finite whenever ς > 0, we are interested in what happens when the strength of the noise ς → 0. For this, we start in this work by formally expanding κ(ε, ς) in a power series in ε, κ(ε, ς) = ε 2 P n≥2 ε n−2κn(ς) and investigating the (formal) equations satisfied by κn(ς). We show in particular that κ2(ς) is well defined when no pinning potential is present, and coincides formally with the heat conductivity obtained in the weak coupling (van Hove) limit, where time is rescaled as ε −2 t, for the cases where the latter has been established [24, 12]. For one-dimensional systems, we investigate κ2(ς) as ς → 0 in three cases: the disordered harmonic chain, the rotor chain and a chain of strongly anharmonic oscillators. Moreover, we formally identify κ2(ς) with the conductivity obtained by having the chain between two reservoirs at

    Vagus nerve stimulation induces cell proliferation and changes in neuronal morphology in the rat hippocampus

    No full text
    Purpose of study: Vagus nerve stimulation (VNS) is used to treat pharmacotherapy-resistant epilepsy. Observations of mood elevation during VNS therapy for epilepsy suggested that such treatment might also show efficacy for refractory major depression. The molecular mechanism(s) underlying its therapeutic action remains unclear, however. By using a rat model of VNS we previously showed that acute VNS increases the gene expression of growth factors in the rat brain as well as the release of norepinephrine. We have now examined the effects of chronic VNS on hippocampal cell proliferation as well as on the expression of DCX and BDNF in rat brain and whether such effects might be associated with behavioral changes similar to those induced by chronic antidepressant drugs. Methods: Male Sprague-Dawley rats were used and a VNS therapy stimulator (Cyberonics, Houston, TX) was implanted. Cell proliferation in the hippocampus of rats subjected to acute (3h) or chronic (1 month) VNS was examined by injection of bromodeoxyuridine (BrdU) and immunohistochemistry. Expression of doublecortin (DCX) and brain-derived neurotrophic factor (BDNF) was evaluated by immunofluorescence staining. Behavioral effects were studied in the forced swim and elevated plus- maze tests. Results: Acute VNS induced an increase in the number of BrdU+ cells in the dentate gyrus that was apparent 24 h (2200±159; P < 0.05) and 3 weeks (2448±129; P < 0.01) after treatment compared with that apparent in sham-operated controls (1760±74). It also induced long- lasting increases in the amount of DCX immunoreactivity (+39%; P < 0.05) and in the number of DCX+ neurons (+57%; P<0.01). Neither the number of BrdU+ cells nor the amount of DCX immunoreactivity was increased 3 weeks after the cessation of chronic VNS. Moreover, VNS induced long-lasting increases in the amount of BDNF immunoreactivity and the number of BDNF+ cells (+104% and +40% respectively; P < 0.001). VNS also affected the dendritic complexity of DCX+ neurons in the hippocampus. Nevertheless, in contrast to chronic imipramine, chronic VNS had no effect on the behavior ofratsintheforcedswimorelevatedplus-mazetests. Conclusions: In the hippocampus VNS induced cell proliferation and persistent changes in morphology ofDCX+ neurons. These effects were accompanied by a robust increase in the expression of BDNF, which may play an important role in consolidating the changes in neuronal connections as suggested by the increased complexity of the dendritic arborization. Thus, some of the effects of chronic VNS appear to be similar to those induced by chronic treatment with antidepressant drugs but do not correlate with corresponding behavioral changes. Although further clinical and experimental studies are necessary to better understand the mechanisms of VNS, our results show that the promotion of neurogenesis and the expression of growth factors are rapidly induced by VNS differently from antidepressant. Whether such early newly generated neurons contribute to existing or de novo networks that might mediate antiepileptic or antidepressant effects remains to be determined

    EFFECTS OF WITHDRAWAL OF LOW ETHANOL CONCENTRATIONS ON GABA(A) RECEPTOR GENE EXPRESSION IN RAT CEREBELLAR GRANULE NEURONS IN CULTURE

    No full text
    One of the most likely targets of ethanol (EtOH) in the central nervous system (CNS) is the GABAA receptor (GABAAR). While the effects of EtOH have been the subject of study on most common CNS GABAAR composition, many other subunit combinations have only recently been tested for their EtOH responses. The a4b2d GABAARs are very sensitive to alcohol, with a concentration of 1 mM EtOH signifcantly enhancing GABAergic currents. Moreover, a6 and a4, when combined with b3 and d-containing subunits were associated with EtOH enhancement of function. Nevertheless, other studies were not able to obtain functional effects of low (1–30 mM) concentrations of EtOH. A plethora of studies both ‘‘in vivo’’ and ‘‘in vitro’’ show that chronic EtOH and EtOH withdrawal, can modify the gene expression of the GABAAR, but in these studies large concentrations of EtOH (50–200 mM) were used. A key question is whether GABAAR gene expression can be altered also by lower concentrations (e.g., 1–50 mM) of EtOH. In order to address this question we here used rat cerebellar granule cells in culture chronically treated with EtOH (1–100 mM). We then measured the GABAAR gene expression by RNase protection assay in two experimental conditions: After chronic EtOH (5 days) or its withdrawal (3 hours). Our results demonstrated that the only subunit affected by chronic EtOH treatment was the c2, the mRNA of which resulted decreased ()20%; p < 0.01) only at concentrations of 50 mM or higher. Neither low nor high concentrations of EtOH were able to change the gene expression of the other subunits of the GABAAR (a1, a4, a6 and d). On the contrary, EtOH withdrawal at the lowest concentration (1 mM) significantly decreased the abundance of the a1, a6 and d subunits ()36; )26 and )16% respectively; p < 0.05), but did not change the a4 subunit mRNA abundance. Similar results were observed using 10 mM EtOH for a1, a6 and d subunits ()37; )38 and 22% respectively; p < 0.05). The a4 subunit was up-regulated only by withdrawal of 100 mM EtOH (+31%; p < 0.01). This is the first report showing that low concentrations of EtOH, such as 1 mM, can modify GABAAR gene expression. These effects were subunit specific and more evident after withdrawal, suggesting that even such low EtOH concentrations when removed may disrupt neuronal excitability controlled by GABAAR; nevertheless, the key question of whether specific GABAAR subunits are more selectively sensitive to low EtOH remains still unanswered
    corecore