On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given. (c) 2007 Elsevier Ltd. All rights reserved.

Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order

The spectral theory for linear autonomous neutral functional differential equations (FDE) yields explicit formulas for the large time behaviour of solutions. Our results are based on resolvent computations and Dunford calculus, applied to establish explicit formulas for the large time behaviour of solutions of FDE. We investigate in detail a class of two-dimensional systems of FDE. (C) 2009 Elsevier Inc. All rights reserved.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

Averaging for retarded functional differential equations

We consider retarded functional differential equations in the setting of Kurzweil-Henstock integrable functions and we state an averaging result for these equations. Our result generalizes previous ones. (C) 2011 Elsevier Inc. All rights reserved.

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system With impulses is considered. (c) 2008 Elsevier Ltd. All rights reserved.

STABILITY FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations are obtained by means of the correspondence of this class of equations with GODEs.

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

Differential regulation of the renin-angiotensin system by nicotine in WKY and SHR glia

Given that (1) the renin-angiotensin system (RAS) is compartmentalized within the central nervous system in neurons and glia (2) the major source of brain angiotensinogen is the glial cells, (3) the importance of RAS in the central control of blood pressure, and (4) nicotine increases the probability of development of hypertension associated to genetic predisposition; the objective of the present study was to evaluate the effects of nicotine on the RAS in cultured glial cells from the brainstem and hypothalamus of Wistar Kyoto (WKY) and spontaneously hypertensive (SHR) rats. Ligand binding, real-time PCR and western blotting assays were used to compare the expression of angiotensinogen, angiotensin converting enzyme, angiotensin converting enzyme 2 and angiotensin II type1 receptors. We demonstrate, for the first time, that there are significant differences in the basal levels of RAS components between WKY and SHR rats in glia from 1-day-old rats. We also observed that nicotine is able to modulate the renin-angiotensin system in glial cells from the brainstem and hypothalamus and that the SHR responses were more pronounced than WKY ones. The present data suggest that nicotine effects on the RAS might collaborate to the development of neurogenic hypertension in SHR through modulation of glial cells.

Differential regulation of FGF-2 in neurons and reactive astrocytes of axotomized rat hypoglossal nucleus. A possible therapeutic target for neuroprotection in peripheral nerve pathology

Despite the favorable treatment of cranial nerve neuropathology in adulthood, some cases are resistant to therapy leading to permanent functional impairments In many cases, suitable treatment is problematic as the therapeutic target remains unknown Basic fibroblast growth factor (bFGF, FGF 2) is involved in neuronal maintenance and wound repair following nervous system lesions It is one of few neurotrophic molecules acting in autocrine, paracrine and intracrine fashions depending upon specific circumstances Peripheral cranial somatic motor neurons, i e hypoglossal (XII) neurons, may offer a unique opportunity to study cellular FGF 2 mechanisms as the molecule is present in the cytoplasm of neurons and in the nuclei of astrocytes of the central nervous system FGF-2 may trigger differential actions during development, maintenance and lesion of XII neurons because axotomy of those cells leads to cell death during neonatal ages, but not in adult life Moreover, the modulatory effects of astroglial FGF 2 and the Ca+2 binding protein S100 beta have been postulated in paracrine mechanisms after neuronal lesions In our study, adult Wistar rats received a unilateral crush or transection (with amputation of stumps) of XII nerve, and were sacrificed after 72 h or 11 days Brains were processed for immunohistochemical localization of neurofilaments (NF), with or without counterstaining for Nissl substance, ghat fibrillary acidic protein (GFAP, as a marker of astrocytes), S100 beta and FGF-2 The number of Nissl positive neurons of axotomized XII nucleus did not differ from controls The NF immunoreactivity increased in the perikarya and decreased in the neuropil of axotomized XII neurons 11 days after nerve crush or transection An astrocytic reaction was seen in the ipsilateral XII nucleus of the crushed or transected animals 72 h and 11 days after the surgery The nerve lesions did not change the number of FGF-2 neurons in the ipsilateral XII nucleus, however, the nerve transection increased the number of FGF-2 ghat profiles by 72 h and 11 days Microdensitometric image analysis revealed a short lasting decrease in the intensity of FGF 2 immunoreactivity in axotomized XII neurons by 72 h after nerve crush or transection and also an elevation of FGF-2 in the ipsilateral of ghat nuclei by 72h and 11 days after the two lesions S100 beta decreased in astrocytes of 11-day transected XII nucleus The two-color immunoperoxidase for the simultaneous detection of the GFAP/FGF-2 indicated FGF-2 upregulation in the nuclei of reactive astrocytes of the lesioned XII nucleus Astroglial FGF-2 may exert paracrine trophic actions in mature axotomized XII neurons and might represent a therapeutic target for neuroprotection in peripheral nerve pathology (C) 2009 Elsevier GmbH All rights reserved

Differential expression of connexins during histogenesis of the chick retina

Gap junction (GJ) channels couple adjacent cells, allowing transfer of second messengers, ions, and molecules up to 1 kDa. These channels are composed by a multigene family of integral membrane proteins called connexins (Cx). In the retina, besides being essential circuit element in the visual processing, GJ channels also play important roles during its development. Herein, we analyzed Cx43, Cx45, Cx50, and Cx56 expression during chick retinal histogenesis. Cx exhibited distinct expression profiles during retinal development, except for Cx56, whose expression was not detected. Cx43 immunolabeling was observed at early development, in the transition of ventricular zone and pigmented epithelium. Later, Cx43 was seen in the outer plexiform and ganglion cell layers, and afterwards also in the inner plexiform layer. We observed remarkable changes in the phosphorylation status of this protein, which indicated modifications in functional properties of this Cx during retinal histogenesis. By contrast, Cx45 showed stable gene expression levels throughout development and ubiquitous immunoreactivity in progenitor cells. From later embryonic development, Cx45 was mainly observed in the inner retina, and it was expressed by glial cells and neurons. In turn, Cx50 was virtually absent in the chick retina at initial embryonic phases. Combination of PCR, immunohistochemistry and Western blot indicated that this Cx was present in differentiated cells, arising in parallel with the formation of the visual circuitry. Characterization of Cx expression in the developing chick retina indicated particular roles for these proteins and revealed similarities and differences when compared to other species. (C) 2008 Wiley Periodicals, Inc.

Differential response of AMPA and NMDA glutamate receptors of Purkinje cells to aging of the chicken cerebellum

Aging can lead to cognitive, affective, learning, memory and motor deficits. Since the cerebellum and glutamatergic neurotransmission are involved in several of those functions, the present work aimed at studying the expression of AMPA and NMDA glutamate receptor subunits in the chick cerebellum during aging. Young (30 days old) and aged (ca. 4 years old) chickens (Gallus gallus) were used in order to evaluate the expression of GluR1, GluR2/3 and NR1 subunits. The cerebella of young and aged chickens were subjected to immunohistochemical and immunoblotting techniques. Numbers of GluR1, GluR2/3 and NR1-positive cells and optical density of the immunoblotting data were analyzed and submitted to statistical analysis using ANOVA and the Bonferroni post hoc test. Mean density of Purkinje cells stained for Giemsa, GluR1, GluR2/3 and NR1 in the cerebellum all showed a statistically significant decrease in aged animals when compared to the young animals (Giemsa, P < 0.01; GluRs and NR1, P < 0.03). However, the ratio of GluR1 and GluR2/3-positive Purkinje cells in relation the total number of Purkinje cells found in each time point decreased with aging (ca. 10%), whereas the ratio of NR1-positive cells increased (ca. 9%). The immunoblotting data showed a significant decrease of GluR1 (ca. 66%) and GluR2/3 (ca. 55%) protein expression with aging, but did not reveal changes for NR1. Our data suggest that aging can lead to differential changes in the pattern of expression of glutamate receptor subunits, which can underlie at least part of the cognitive and motor disorders found in aged animals. (c) 2010 Elsevier Ireland Ltd. All rights reserved.

GLP-1 Inhibits and Adrenaline Stimulates Glucagon Release by Differential Modulation of N- and L-Type Ca(2+) Channel-Dependent Exocytosis

Glucagon secretion is inhibited by glucagon-like peptide-1 (GLP-1) and stimulated by adrenaline. These opposing effects on glucagon secretion are mimicked by low (1-10 nM) and high (10 mu M) concentrations of forskolin, respectively. The expression of GLP-1 receptors in a cells is <0.2% of that in beta cells. The GLP-1-induced suppression of glucagon secretion is PKA dependent, is glucose independent, and does not involve paracrine effects mediated by insulin or somatostatin. GLP-1 is without much effect on a cell electrical activity but selectively inhibits N-type Ca(2+) channels and exocytosis. Adrenaline stimulates a cell electrical activity, increases [Ca(2+)] enhances L-type Ca(2+) channel activity, and accelerates exocytosis. The stimulatory effect is partially PKA independent and reduced in Epac2-deficient islets. We propose that GLP-1 inhibits glucagon secretion by PKA-dependent inhibition of the N-type Ca(2+) channels via a small increase in intracellular cAMP ([cAMP]). Adrenaline stimulates L-type Ca(2+) channel-dependent exocytosis by activation of the low-affinity cAMP sensor Epac2 via a large increase in [cAMP],.

Differential effects of formaldehyde exposure on the cell influx and vascular permeability in a rat model of allergic lung inflammation

Exposure to air pollutants such as formaldehyde (FA) leads to inflammation, oxidative stress and immune-modulation in the airways and is associated with airway inflammatory disorders such as asthma. The purpose of our study was to investigate the effects of exposure to FA on the allergic lung inflammation. The hypothesized link between reactive oxygen species and the effects of FA was also studied. To do so, male Wistar rats were exposed to FA inhalation (1%, 90 min daily) for 3 days. and subsequently sensitized with ovalbumin (OVA)-alum by subcutaneous route One week later the rats received another OVA-alum injection by the same route (booster). Two weeks later the rats were challenged with aerosolized OVA. The OVA challenge of rats upon FA exposure induced an elevated release of LTB(4). TXB(2), IL-1 beta, IL-6 and VEGF in lung cells, increased phagocytosis and lung vascular permeability, whereas the cell recruitment into lung was reduced. FA inhalation induced the oxidative burst and the nitration of proteins in the lung Vitamins C, E and apocynin reduced the levels of LTB(4) in BAL-cultured cells of the FA and FA/OVA groups, but Increased the cell influx into the lung of the FA/OVA rats. In OVA-challenged rats, the exposure to FA was associated to a reduced lung endothelial cells expression of intercellular cell adhesion molecule 1 (ICAM-1) In conclusion, our findings suggest that FA down regulate the cellular migration into the lungs after an allergic challenge and increase the ability of resident lung cells likely macrophages to generate inflammatory mediators, explaining the increased lung vascular permeability Our data are indicative that the actions of FA involve mechanisms related to endothelium-leukocyte interactions and oxidative stress, as far as the deleterious effects of this air pollutant on airways are concerned. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

Differential effects of neuromuscular blockers on twitches and tetani in the isolated rat muscle: a multiple comparison study using simultaneous confidence intervals

In the present work a comparative quantitative evaluation of the differential effects of neuromuscular blockers on twitches and tetani was performed, encompassing: atracurium, cisatracurium, mivacurium, pancuronium, rocuronium and vecuronium. The sciatic nerve-extensor digitorum longus muscle of the rat was used, in vitro. Twitches were evoked at 0.1 Hz and tetani at 50 Hz. The differential effects of the studied compounds on twitches and tetani were statistically compared using simultaneous confidence intervals for the ratios between mean IC(50) for the block of twitches and mean IC(50) for the block of tetani. The results of ratios of mean IC(50) together with their corresponding 95% simultaneous confidence intervals were: vecuronium: 2.5 (1.8-3.5); mivacurium: 3.8 (3.0-4.9); pancuronium: 3.9 (2.0-7.6); rocuronium: 6.1 (3.8-9.9); atracurium: 9.0 (6.4-12.6); cisatracurium: 13.1 (6.0-28.4). Using the criteria that neuromuscular blockers displaying disjunct confidence intervals for the ratios of mean IC(50) differ statistically with regard to differential effects on twitches and tetani, significant differences in ratios of IC(50) were detected in the following cases: vecuronium vs. rocuronium, vs. atracurium and vs. cisatracurium and mivacurium vs: cisatracurium and vs. atracurium. The results show that the magnitude of the differential effects of neuromuscular blockers on twitches and tetani, as evaluated in the present work in the form of ratios of mean IC(50), does not depend on the chemical structure (comparing steroidal and isoquinolinic compounds), but seems to depend on differential pre- and post-synaptic effects of the compounds. It is also suggested that the greater the ability of a compound to block twitches and tetani in a differential manner, the safer is the compound from the clinical anesthesiology viewpoint.