PubMed · 4319332
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V L Dunin-Barkovskiĭ. [Variations in the activity level in simple closed neuron chains].. https://pubmed.ncbi.nlm.nih.gov/4319332/
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We numerically study the subharmonic response of a heterogeneous pool of neurons to a pair of independent inputs. The neurons are stimulated with periodic pulse trains of frequencies f(1)=2 Hz and f(2)=3 Hz, and with inharmonic pulses whose frequencies f(1) and f(2) are equally shifted an amount Delta f. When both inputs are subthreshold, we find that the neurons respond at a frequency equal to f(2)-f(1) in the harmonic situation (Delta f=0), that increases linearly with Delta f in the inharmonic case. Thus the neurons detect a frequency not present in the input; this effect is termed "ghost resonance". When one of the inputs is slightly suprathreshold the ghost resonance persists, but responses related with the frequency of the suprathreshold input also emerge. This behavior must be taken into account in experimental studies of signal integration and coincidence detection by neuronal pools.
In a series of recent papers, Bonciocat et al., have shown that the faradaic current density of an electrode redox reactions occurring with combined limitations, of charge transfer and nonstationary linear, semi-infinite diffusion, is the solution of an integral equation of Volterra type. This integral equation has been transformed to describe the transport of ions through the interface between two immiscible electrolytic solutions. According to Goldman, Hodkin, Katz theory, the rest potential of a biological membrane is determined by the maintenance of different concentrations of the ions Na+, K+ and Cl-, in the two aqueous solutions separated by the membrane. Using the integral equations (of Volterra type) for the ionic current densities iNa, iK, iCl, and applying the open circuit condition (i.e., iNa + iK + iCl = 0), the potential differences at the junctions: aqueous solution (I)/membrane, respective membrane/aqueous solution (II), have been obtained. To get the diffusion potential across the membrane, the Planck's theory has been used. The sum of these three contributions gives the expression of the rest potential (and a comparison with the Goldman-Hodkin-Katz formula is made, showing in what conditions they become identical formulae).
Oscillations in networks of inhibitory interneurons have been reported at various sites of the brain and are thought to play a fundamental role in neuronal processing. This Letter provides a self-contained analytical framework that allows numerically efficient calculations of the population activity of a network of conductance-based integrate-and-fire neurons that are coupled through inhibitory synapses. Based on a normalization equation this Letter introduces a novel stability criterion for a network state of asynchronous activity and discusses its perturbations. The analysis shows that, although often neglected, the reversal potential of synaptic inhibition has a strong influence on the stability as well as the frequency of network oscillations.