Influence of firing mechanisms on gain modulation

We studied the impact of a dynamical threshold on the f-I curve-the relationship between the input and the firing rate of a neuron-in the presence of background synaptic inputs. First, we found that, while the leaky integrate-and-fire model cannot reproduce the f-I curve of a cortical neuron, the leaky integrate-and-fire model with dynamical threshold can reproduce it very well. Second, we found that the dynamical threshold modulates the onset and the asymptotic behavior of the f-I curve. These results suggest that a cortical neuron has an adaptation mechanism and that the dynamical threshold has some significance for the computational properties of a neuron.Comment: 7 pages, 4 figures, conference proceeding

Boundary-crossing identities for diffusions having the time-inversion property

We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family

The Euler-Maruyama approximation for the absorption time of the CEV diffusion

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme

Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron

We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure

GABAergic Neuron Deficit As An Idiopathic Generalized Epilepsy Mechanism: The Role Of BRD2 Haploinsufficiency In Juvenile Myoclonic Epilepsy

Idiopathic generalized epilepsy (IGE) syndromes represent about 30% of all epilepsies. They have strong, but elusive, genetic components and sex-specific seizure expression. Multiple linkage and population association studies have connected the bromodomain-containing gene BRD2 to forms of IGE. In mice, a null mutation at the homologous Brd2 locus results in embryonic lethality while heterozygous Brd2+/− mice are viable and overtly normal. However, using the flurothyl model, we now show, that compared to the Brd2+/+ littermates, Brd2+/− males have a decreased clonic, and females a decreased tonic-clonic, seizure threshold. Additionally, long-term EEG/video recordings captured spontaneous seizures in three out of five recorded Brd2+/− female mice. Anatomical analysis of specific regions of the brain further revealed significant differences in Brd2+/− vs +/+ mice. Specifically, there were decreases in the numbers of GABAergic (parvalbumin- or GAD67-immunopositive) neurons along the basal ganglia pathway, i.e., in the neocortex and striatum of Brd2+/− mice, compared to Brd2+/+ mice. There were also fewer GABAergic neurons in the substantia nigra reticulata (SNR), yet there was a minor, possibly compensatory increase in the GABA producing enzyme GAD67 in these SNR cells. Further, GAD67 expression in the superior colliculus and ventral medial thalamic nucleus, the main SNR outputs, was significantly decreased in Brd2+/− mice, further supporting GABA downregulation. Our data show that the non-channel-encoding, developmentally critical Brd2 gene is associated with i) sex-specific increases in seizure susceptibility, ii) the development of spontaneous seizures, and iii) seizure-related anatomical changes in the GABA system, supporting BRD2's involvement in human IGE

Historical introduction

The Laboratory of Neurophysiology of Memory started its existence in 1954 by systematic research into spreading depression of EEG activity of laboratory rodents and by the use of this remarkable phenomenon as a functional ablation method in behavioral research. Its main contributions were in the study of memory formation and consolidation, interhemispheric transfer, motor learning, conditioned taste aversion and spatial orientation and navigation. In the last five years it concentrated on navigation of rats in multiple reference frames, on electrophysiological evidence for the role of hippocampal place cells support of behavior in such dissociated frames, on the analysis of idiothetic and allothetic forms of navigation and on the mathematical methods allowing assessment of the contribution of goal directed locomotion to place cell activity. The methods used in spatial memory research in rats were used for examination of human subjects in a laboratory equipped with a tracking system for humans in the hospital Homolka. Animal models of Alzheimer disease were studied in transgenic mice with the human gene for the beta amyloid precursor protein. Key words Spreading EEG depression • Spatial memory • Place cells • Hippocampus • Alzheimer’s diseas