Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices

A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable representation of the Hamiltonian, and the Toeplitz property of the asymptotic part of the obtained {\it infinite} matrix is used. Thus, the problem is reduced to the inversion of a {\it finite} matrix

Epileptogenesis in the developing brain: what can we learn from animal models?

Knowledge of the processes by which epilepsy is generated (epileptogenesis) is incomplete and has been a topic of major research efforts. Animal models can inform us about these processes. We focus on the distinguishing features of epileptogenesis in the developing brain and model prolonged febrile seizures (FS) that are associated with human temporal lobe epilepsy. In the animal model of FS, epileptogenesis occurs in approximately 35% of rats. Unlike the majority of acquired epileptogeneses in adults, this process early in life (in the febrile seizures model as well as in several others) does not require "damage" (cell death). Rather, epileptogenesis early in life involves molecular mechanisms including seizure-evoked, long-lasting alterations of the expression of receptors and ion channels. Whereas transient changes in gene expression programs are common after early-life seizures, enduring effects, such as found after experimental FS, are associated with epileptogenesis. The ability of FS to generate long-lasting molecular changes and epilepsy suggests that mechanisms, including cytokine activation that are intrinsic to FS generation, may play a role also in the epileptogenic consequences of these seizures

Febrile seizures: an appropriate-aged model suitable for long-term studies.

Seizures induced by fever are the most prevalent age-specific seizures in infants and young children. Whether they result in long-term sequelae such as neuronal loss and temporal lobe epilepsy is controversial. Prospective studies of human febrile seizures have found no adverse effects on the developing brain. However, adults with temporal lobe epilepsy and associated limbic cell loss frequently have a history of prolonged febrile seizures in early life. These critical issues may be resolved using appropriate animal models. Published models of hyperthermic seizures have used 'adolescent' and older rats, have yielded a low percentage of animals with actual seizures, or have suffered from a high mortality, rendering them unsuitable for long-term studies. This article describes the establishment of a model of febrile seizures using the infant rat. Hyperthermia was induced by a regulated stream of mildly heated air, and the seizures were determined by both behavioral and electroencephalographic (EEG) criteria. Stereotyped seizures were generated in 93.6% of 10-11-day-old rats. EEG correlates of these seizures were not evident in cortical recordings, but were clearly present in depth recordings from the amygdala and hippocampus. Prolonged febrile seizures could be induced without burns, yielding a low mortality (11%) and long-term survival. In summary, in infant rat paradigm of EEG-confirmed, hyperthermia-induced seizures which is suitable for long-term studies is described. This model should be highly valuable for studying the mechanisms and sequelae of febrile seizures

Competitive random sequential adsorption of point and fixed-sized particles: analytical results

We study the kinetics of competitive random sequential adsorption (RSA) of particles of binary mixture of points and fixed-sized particles within the mean-field approach. The present work is a generalization of the random car parking problem in the sense that it considers the case when either a car of fixed size is parked with probability q or the parking space is partitioned into two smaller spaces with probability (1-q) at each time event. This allows an interesting interplay between the classical RSA problem at one extreme (q=1), and the kinetics of fragmentation processes at the other extreme (q=0). We present exact analytical results for coverage for a whole range of q values, and physical explanations are given for different aspects of the problem. In addition, a comprehensive account of the scaling theory, emphasizing on dimensional analysis, is presented, and the exact expression for the scaling function and exponents are obtained.Comment: 7 pages, latex, 3 figure

Spatial and temporal evolution of neuronal activation, stress and injury in lithium-pilocarpine seizures in adult rats.

In order to follow the spatial and temporal evolution of neuronal damage, cellular activation and stress responses subsequent to lithium-pilocarpine seizures of various durations in the adult rat, we analyzed the expression of Fos protein and local cerebral glucose utilization as markers of cellular activation, HSP72 immunoreactivity and acid fuchsin staining as indicators of cellular stress and injury, and Cresyl violet staining for the assessment of neuronal damage. The expression of Fos appeared very early, 2-30 min after the onset of polyspikes and intensified during the following 4 h. Fos immunoreactivity was especially high in the hippocampus, cerebral cortex, amygdala and anterior olfactory nuclei. Local cerebral glucose utilization measured during the second hour of seizures was largely increased (350-580%) over control levels in cortical areas, amygdala, dentate gyrus, caudate nucleus and mediodorsal thalamus. HSP72 immunoreactivity never appeared earlier than 40-50 min after the onset of polyspikes, and was most prominent in hippocampal CA3 area, cerebral cortex (except the piriform cortex) and anterior olfactory nuclei. Acid fuchsin staining was maximal in the piriform cortex and the polymorphic layer of the dentate gyrus. Staining was moderate in the sensorimotor cortex and the amygdala. Neuronal damage was extensive in the piriform and entorhinal cortices, the hippocampal CA3 area and the polymorphic layer of the dentate gyrus, basal amygdala, mediodorsal thalamus and anterior olfactory nuclei. In conclusion, the present study shows that brain regions with the highest expression of Fos and the largest metabolic activation were also highly stained with acid fuchsin and most heavily damaged. Conversely, there is no clear relationship between HSP72 expression, cellular activation and neuronal damage

Hyperpolarization activated cyclic-nucleotide gated (HCN) channels in developing neuronal networks.

Developing neuronal networks evolve continuously, requiring that neurons modulate both their intrinsic properties and their responses to incoming synaptic signals. Emerging evidence supports roles for the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels in this neuronal plasticity. HCN channels seem particularly suited for fine-tuning neuronal properties and responses because of their remarkably large and variable repertoire of functions, enabling integration of a wide range of cellular signals. Here, we discuss the involvement of HCN channels in cortical and hippocampal network maturation, and consider potential roles of developmental HCN channel dysregulation in brain disorders such as epilepsy

Hippocampal neuroplasticity induced by early-life stress: functional and molecular aspects.

Whereas genetic factors contribute crucially to brain function, early-life events, including stress, exert long-lasting influence on neuronal function. Here, we focus on the hippocampus as the target of these early-life events because of its crucial role in learning and memory. Using a novel immature-rodent model, we describe the deleterious consequences of chronic early-life 'psychological' stress on hippocampus-dependent cognitive tasks. We review the cellular mechanisms involved and discuss the roles of stress-mediating molecules, including corticotropin releasing hormone, in the process by which stress impacts the structure and function of hippocampal neurons

Hippocampal neurogenesis is not enhanced by lifelong reduction of glucocorticoid levels.

Neurogenesis of dentate gyrus granule cells is generally considered to be negatively regulated by glucocorticoids. We tested the hypothesis that exposure to low plasma corticosteroid levels starting in the early postnatal period enhances granule cell proliferation rate during adulthood. Rat pups were adrenalectomized (ADX) on postnatal day 10 and were then "clamped" throughout life at low corticosterone levels via oral supplementation. Neurogenesis was determined using BrdU immunochemistry at 3 and 12 months in clamped rats as compared with age-matched, sham-operated controls. Rate of neurogenesis did not differ between the groups at either 3 or 12 months. It was significantly lower in 12-month-old compared with 3-month-old rats, despite the presence of an age-dependent increase of plasma corticosterone only in the sham-ADX rats. Granule cell layer volume, granule cell density, and granule cell degeneration (determined using apoptotic markers) were indistinguishable in the two groups, further supporting the comparable rate of neurogenesis under differing chronic glucocorticoid levels. In addition, whereas acute deprivation of plasma glucocorticoids (adrenalectomy) in adult rats evoked a burst of granule cell neurogenesis, complete elimination of these hormones (by stopping hormone supplementation) in adult, early-life ADX/clamped rats did not. These data do not support a simple inverse relationship between chronic plasma glucocorticoid levels and granule cell neurogenesis. Specifically, chronic modulation of glucocorticoid levels commencing early in life evokes additional, adaptive, and compensatory mechanisms that contribute to the regulation of granule cell proliferation