Reducibility and contractivity of Runge-Kutta methods revisited

The exact relation between a Cooper-like reducibility concept and the reducibilities introduced by Hundsdorfer, Spijker and by Dahlquist and Jeltsch is given. A shifted Runge-Kutta scheme and a transplanted differential equation is introduced in such a fashion that the input/output relation remains unchanged under these transformations. This gives a technique to prove stability and contractivity results. This is demonstrated on the example of contractivity disk

On curl-preserving finite volume discretizations for shallow water equations

The preservation of intrinsic or inherent constraints, like divergence-conditions, has gained increasing interest in numerical simulations of various physical evolution equations. In Torrilhon and Fey, SIAM J. Numer. Anal. (42/4) 2004, a general framework is presented how to incorporate the preservation of a discrete constraint into upwind finite volume methods. This paper applies this framework to the wave equation system and the system of shallow water equations. For the wave equation a curl-preservation for the momentum variable is present and easily identified. The preservation in case of the shallow water system is more involved due to the presence of convection. It leads to the vorticity evolution as generalized curl-constraint. The mechanisms of vorticity generation are discussed. For the numerical discretization special curl-preserving flux distributions are discussed and their incorporation into a finite volume scheme described. This leads to numerical discretizations which are exactly curl-preserving for a specific class of discrete curl-operators. The numerical experiments for the wave equation show a significant improvement of the new method against classical schemes. The extension of the curl-free numerical discretization to the shallow water case is possible after isolating the pressure flux. Simulation examples demonstrate the influence of the modification. The vortex structure is more clearly resolve

Downregulation of muscarinic- and 5-HT1B-mediated modulation of [3H]acetylcholine release in hippocampal slices of rats with fimbria-fornix lesions and intrahippocampal grafts of septal origin

Adult Long-Evans female rats sustained electrolytic fimbria-fornix lesions and, two weeks later, received intrahippocampal suspension grafts of fetal septal tissue. Sham-operated and lesion-only rats served as controls. Between 6.5 and 8 months after grafting, both the [3H]choline accumulation and the electrically evoked [3H]acetylcholine ([3H]ACh) release were assessed in hippocampal slices. The release of [3H]ACh was measured in presence of atropine (muscarinic antagonist, 1 microM), physostigmine (acetylcholinesterase inhibitor, 0.1 microM), oxotremorine (muscarinic agonist, 0.01 microM-10 microM), mecamylamine (nicotinic antagonist, 10 microM), methiothepin (mixed 5-HT1/5-HT2 antagonist, 10 microM), 8-OH-DPAT (5-HT1A agonist, 1 microM), 2-methyl-serotonin (5-HT3 agonist, 1 microM) and CP 93129 (5-HT1B agonist, 0.1 microM-100 microM), or without any drug application as a control. In lesion-only rats, the specific accumulation of [3H]choline was reduced to 46% of normal and the release of [3H]ACh to 32% (nCi) and 43% (% of tissue tritium content). In the grafted rats, these parameters were significantly increased to 63%, 98% and 116% of control, respectively. Physostigmine reduced the evoked [3H]ACh release and was significantly more effective in grafted (-70%) than in sham-operated (-56%) or lesion-only (-54%) rats. When physostigmine was superfused throughout, mecamylamine had no effect. Conversely, atropine induced a significant increase of [3H]ACh release in all groups, but this increase was significantly larger in sham-operated rats (+209%) than in the other groups (lesioned: +80%; grafted: +117%). Oxotremorine dose-dependently decreased the [3H]ACh release, but in lesion-only rats, this effect was significantly lower than in sham-operated rats. Whatever group was considered, 8-OH-DPAT, methiothepin and 2-methyl-serotonin failed to induce any significant effect on [3H]ACh release. In contrast, CP 93129 dose-dependently decreased [3H]ACh release. This effect was significantly weaker in grafted rats than in the rats of the two other groups. Our data confirm that cholinergic terminals in the intact hippocampus possess inhibitory muscarinic autoreceptors and serotonin heteroreceptors of the 5-HT1B subtype. They also show that both types of receptors are still operative in the cholinergic terminals which survived the lesions and in the grafted cholinergic neurons. However, the muscarinic receptors in both lesioned and grafted rats, as well as the 5-HT1B receptors in grafted rats show a sensitivity which seems to be downregulated in comparison to that found in sham-operated rats. In the grafted rats, both types of downregulations might contribute to (or reflect) an increased cholinergic function that results from a reduction of the inhibitory tonus which ACh and serotonin exert at the level of the cholinergic terminal

Modulation of electrically evoked acetylcholine release in cultured rat septal neurones

The electrically evoked release of acetylcholine and its modulation via auto- and heteroreceptors were studied in primary cell cultures prepared from embryonic rat septum (ED 17). Cultures were grown for 1, 2 or 3 weeks on circular, poly D-lysine-coated glass coverslips. They developed a dense network of non-neuronal and neuronal cells, only some of which were immunopositive for choline acetyltransferase. To measure acetylcholine release, the cells on the coverslips were pre-incubated with [3H]choline (0.1 micromol/L), superfused with modified Krebs-Henseleit buffer at 25 degrees C and electrically stimulated twice for 2 min (S1, S2; 3 Hz, 0.5 ms, 90-100 mA). The electrically evoked overflow of [3H] from the cells consisted of approximately 80% of authentic [3H]Ach, was largely Ca2+-dependent and tetrodotoxin sensitive, and hence represents an action potential-evoked, exocytotic release of acetylcholine. Using pairs of selective agonists and antagonist added before S2, muscarinic autoreceptors, as well as inhibitory adenosine A1- and opioid mu-receptors, could be detected, whereas delta-opioid receptors were not found. Evoked [3H] overflow from cultures grown for 1 week, although Ca2+ dependent and tetrodotoxin sensitive, was insensitive to the muscarinic agonist oxotremorine, whereas the effect of oxotremorine on cells grown for 3 weeks was even more pronounced than that in 2-week-old cultures. In conclusion, similar to observations on rat septal tissue in vivo, acetylcholine release from septal cholinergic neurones grown in vitro is inhibited via muscarinic, adenosine A1 and mu-opioid receptors. This in vitro model may prove useful in the exploration of regulatory mechanisms underlying the expression of release modulating receptors on septal cholinergic neurones

Intrahippocampal grafts containing cholinergic and serotonergic fetal neurons ameliorate spatial reference but not working memory in rats with fimbria-fornix/cingular bundle lesions

Three-month-old Long-Evans female rats sustained aspirative lesions of the dorsal septohippocampal pathways and, 2 weeks later, received intrahippocampal suspension grafts containing cells from the mesencephalic raphe, cells from the medial septum and the diagonal band of Broca, or a mixture of both. Lesion-only and sham-operated rats were used as controls. All rats were tested for locomotor activity 1 week, 3 and 5 months after lesion surgery, for spatial working memory in a radial maze from 5 to 9 months, and for reference and working memory in a water tank during the 9th month after lesioning. Determination of hippocampal concentration of acetylcholine, noradrenaline, and serotonin was made after completion of behavioral testing. Compared to sham-operated rats, all rats with lesions, whether grafted or not, exhibited increased levels of locomotor activity and made more errors in the radial maze. The lesioned rats were also impaired in the probe trial (30 first seconds) of the water-tank test made according to a protocol requiring intact reference memory capabilities. While rats with septal or raphe grafts were also impaired, the rats with co-grafts showed performances not significantly different from those of sham-operated rats. With a protocol requiring intact working memory capabilities, all lesioned rats, whether grafted or not, were impaired in the water-tank test. In the dorsal hippocampus of lesion-only rats, the concentration of acetylcholine and serotonin was significantly reduced. In rats with septal grafts or co-grafts, the concentration of acetylcholine was close to normal, as was that of serotonin in rats with raphe grafts or co-grafts. These results confirm previous findings showing that co-grafts enabled the neurochemical properties of single grafts to be combined. Data from the water-tank test suggest that cholinergic and serotonergic hippocampal reinnervations by fetal cell grafts may induce partial recovery of spatial reference, but not working memory capabilities in rats

Modulation of 5-hydroxytryptamine release in hippocampal slices of rats: Effects of fimbria-fornix lesions on 5-HT1b-autoreceptor and α2-heteroreceptor function

Fimbria-fornix lesions disrupt important parts of serotonergic and noradrenergic hippocampal afferents and elicit sprouting of sympathetic fibers from the superior cervical ganglion. Since 5-hydroxytryptamine (5-HT) release in the hippocampus is modulated by 5-HT1B auto- and alpha2-heteroreceptors, we investigated whether such lesions may alter these presynaptic mechanisms. Hippocampal slices of sham-operated (SHAM) and fimbria-fornix-lesioned (LES) rats (14 months after surgery) were preincubated with [3H]5-HT, superfused continuously, and stimulated electrically using two stimulation conditions: either (a) 360 pulses 3 Hz, or (b) 20 pulses 100 Hz (2 ms, 28 mA, 4 V/chamber). The amount of [3H]5-HT taken up by slices from LES rats was significantly reduced, whereas the evoked 5-HT release (in percent of tissue-3H) was unchanged compared to that of SHAM rats. The 5-HT1B agonist CP 93,129 or the alpha2-agonist UK 14,304 reduced the evoked 5-HT release more potently in slices from LES rats, but only using stimulation condition (a), which permits inhibition by endogenously released transmitters. In LES rats, the facilitatory effect of the 5-HT antagonist metitepine was weaker, whereas that of the alpha2-antagonist idazoxane was more pronounced than in SHAM rats. In LES rats, hippocampal 5-HT content was reduced to about 45% of SHAM levels, whereas that of noradrenaline was increased by about 30% (high-performance liquid chromatography). We conclude: (1) despite LES-induced changes in tissue levels of endogenous ligands, there is no down- or upregulation of 5-HT1B-autoreceptors or alpha2-heteroreceptors on serotonergic neurons in the denervated rat hippocampus. (2) The reduced endogenous autoinhibition (by 5-HT) seems to be compensated for by an increased heteroinhibition (by noradrenaline)

Effects of grafts containing cholinergic and/or serotonergic neurons on cholinergic, serotonergic and noradrenergic markers in the denervated rat hippocampus

Long-Evans female rats sustained aspirative lesions of the septohippocampal pathways and, 2 weeks later, received intrahippocampal suspension grafts prepared from the regions including either the medial septum and the diagonal band of Broca (group S), or the mesencephalic raphe (group R), or from both these regions together (group S + R). Sham-operated (group SHAM) and lesion-only (group LES) rats were used as controls. Six months after grafting, high affinity synaptosomal uptake of choline (HACU) and serotonin (HASU), choline acetyltransferase (ChAT) activity and, using HPLC, the content of serotonin ([5-HT]), 5-hydroxyindolacetic acid ([5-HIAA]) and noradrenaline ([NA]) were determined in three rostro-caudal segments of the hippocampus (designated hereafter as the dorsal, the 'middle' and the ventral segments). In all three segments of the dorsal hippocampus, septohippocampal lesions decreased HACU, ChAT activity, HASU and [5-HT]; [5-HIAA] was decreased only in the middle and ventral hippocampal segments. The lesions also resulted in an above normal increase of [NA]. Septal grafts increased HACU and ChAT in the three hippocampal regions, had no effect on serotonergic markers and attenuated the lesion-induced increase of [NA] in only the dorsal and middle hippocampal segments. Raphe grafts increased HASU, [5-HT] and [5-HIAA] in the dorsal and middle hippocampal segments, had no effects on cholinergic markers and did not affect the lesion-induced increase of [NA]. Co-grafts increased HACU, ChAT activity, HASU, [5-HT] and [5-HIAA], and attenuated the lesion-induced increase in [NA]. These data demonstrate that grafts of fetal neurons placed into the denervated hippocampus may induce a neurochemical recovery which depends upon the anatomical origin of the grafted cells. They also show that co-grafting allows to combine the neurochemical properties of two fetal brain regions grafted separately. Furthermore, our findings suggest that graft-derived cholinergic reinnervation of the hippocampus prevents the lesion-induced increase of noradrenaline concentration which is likely to result from sympathetic sprouting. Thus, our data confirm the results of a previous experiment carried out at a post-grafting delay of 10-11 months, and show that the graft-induced effects reported previously are already massively present by 6 months after surgery

The effects of intrahippocampal raphe and/or septal grafts in rats with fimbria-fornix lesions depend on the origin of the grafted tissue and the behavioural task used

Long-Evans female rats sustained electrolytic lesions of the fimbria and the dorsal fornix and, two weeks later, received intrahippocampal suspension grafts of fetal tissue. The grafts were prepared from regions including either the medial septum and the diagonal band of Broca (septal grafts), or the mesencephalic raphe (raphe grafts), or from both these regions together (co-grafts). All rats were submitted to a series of behavioural tests (home cage and open-field locomotion, spontaneous alternation, radial-arm maze and Morris water maze performance) run over two periods after grafting (one to nine weeks and 20-35 weeks). Two weeks after completion of behavioural testing, histological (acetylcholinesterase and Cresyl Violet staining) and/or neurochemical (choline acetyltransferase activity, high-affinity synaptosomal uptake of choline and serotonin, noradrenaline, serotonin and 5-hydroxyindolacetic acid concentrations) verifications were performed on the hippocampus. Compared to sham-operated rats, lesion-only rats exhibited hyperactivity which was transient in a familiar environment (home cage) and lasting in an unfamiliar one (open field), decreased rates of spontaneous T-maze alternation, and impaired memory performance in both the radial-arm maze and the Morris water maze. These rats also showed decreased cholinergic and serotonergic markers with a maximal depletion in the septal two-thirds of the hippocampus. Noradrenaline concentration tended to be increased in the dorsal third of the hippocampus, but was not modified in the other two-thirds. While septal grafts specifically increased the cholinergic markers and raphe grafts the serotonergic ones, neither of these grafts produced a lasting effect on any behavioural variable. Conversely, the co-grafts, which increased both the cholinergic and serotonergic markers in the septal two-thirds of the hippocampus, completely normalized the Morris water maze probe trial performance, but failed to affect any of the other behavioural variables. Our present results confirm that grafts of fetal neurons injected into the denervated hippocampus may induce a neurochemical recovery that depends on the anatomical origin of the grafted cells, and that co-grafting two fetal brain regions allows the combination of their individual neurochemical properties. Furthermore, our results show that these neurochemical effects of the co-grafts may be involved in the recovery of behavioural function observed in the water maze. However, somewhat paradoxically, those effects appear inefficient for inducing any recovery in other behavioural tasks, even in the radial-arm maze; which is assumed to measure similar spatial functions