Tonic regulation of stationary asynchronous firing of a neural network

Abstract

The impact of tonic conductance upon population activity was investigated. An extra tonic transmembrane current through GABA-activated extrasynaptic GABA -receptors was found to control stationary asynchronous firing both quantitatively and qualitatively. Quantitative regulation consisted in alterating a current level of stationary population activity while qualitative regulation manifested itself in appearance of resilient asynchronous spiking in case GABA reversal potential exceeded a certain threshold. The study was based on a modified rate model after Wilson and Cowan and backed up with a computer simulation of an explicit network model.

Emergence of Relaxation Oscillations in Neurons Interacting With Non-stationary Ambient GABA

“…In absense of the second equation (Equation 5), the system reduces to a simple 1D phase line, corresponding to the case of stationary external medium. This particular case was a subject of our previous study (Adamchik and Kazantsev, 2017 ). It was shown then that introduction of tonic current did not lead to any new dynamical effects compared to the reference case, ( G = 0), characterized by a simple stable-state dynamics.…”

“…The Wang-Buzsáki interneuron (Wang and Buzsáki, 1996 ) belongs exactly to this type of neurons. In Adamchik and Kazantsev ( 2017 ), the original conductance-based model, modified in a way to account for the additional transmembrane tonic current, was reduced to the QIF neuron. The dimensionless parameter κ took the following form:…”

“…where E m , G m and k are constants listed in Table 1 . The details of the reduction can be found in Adamchik and Kazantsev ( 2017 ).…”

“…Primarily, GABA was considered to be the main inhibitory neurotransmitter in the brain until it was shown experimentally to be able to perform the bi-directional regulation of neuronal spiking activity (Song et al, 2011 ). Based on this experimental finding, a number of mathematical models describing the action of ambient GABA on the excitability properties of interneurons were suggested (Adamchik et al, 2015 ; Adamchik and Kazantsev, 2017 ). In Adamchik et al ( 2015 ), the behavior of a single interneuron embedded in the extracellular space with constant ambient GABA concentration was studied.…”

“…It was shown that depending on the parameters of tonic current, such as tonic conductance density and GABA reversal potential, the interneuron demonstrated different behavioral modes including self-oscillations. The impact of stationary GABA at the population level was studied subsequently in Adamchik and Kazantsev ( 2017 ). Specifically, it led to bistability between asynchronous firing and zero-activity state.…”