Dynamics of electric activities in neuron and neurons of network induced by autapses

Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.

Neurobiological theories posit that schizophrenia relates to disturbances in connectivity between brain regions. Resting-state functional magnetic resonance imaging is a powerful tool for examining functional connectivity and has revealed several canonical brain networks, including the default mode, dorsal attention, executive control, and salience networks. The purpose of this study was to examine changes in these networks in schizophrenia. 42 patients with schizophrenia and 61 healthy subjects completed a RS-fMRI scanning session. Seed-based region-of-interest correlation analysis was used to identify the default mode, dorsal attention, executive control, and salience networks. Compared to healthy subjects, individuals with schizophrenia demonstrated greater connectivity between the posterior cingulate cortex, a key hub of the default mode, and the left inferior gyrus, left middle frontal gyrus, and left middle temporal gyrus. Interestingly, these regions were more strongly connected to the executive control network in healthy control subjects. In contrast to the default mode, patients demonstrated less connectivity in the executive control and dorsal attention networks. No differences were observed in the salience network. The results indicate that resting-state networks are differentially affected in schizophrenia. The alterations are characterized by reduced segregation between the default mode and executive control networks in the prefrontal cortex and temporal lobe, and reduced connectivity in the dorsal attention and executive control networks. The changes suggest that the process of functional specialization is altered in schizophrenia. Further work is needed to determine if the alterations are related to disturbances in white matter connectivity, neurodevelopmental abnormalities, and genetic risk for schizophrenia. Copyright © 2011 Elsevier B.V. All rights reserved.

We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we find that the stability of the completely synchronous state in such networks only depends on the number of signals each neuron receives, independent of all other details of the network topology. This is in contrast with linearly coupled bursting neurons where complete synchrony strongly depends on the network structure and number of cells. Through analysis and numerics, we show that the onset of synchrony in a network with any coupling topology admitting complete synchronization is ensured by one single condition.