Characterizing ISI and sub-threshold membrane potential distributions: Ensemble of IF neurons with random squared-noise intensity | Shiv Nadar University
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Characterizing ISI and sub-threshold membrane potential distributions: Ensemble of IF neurons with random squared-noise intensity

Research
10 Oct 2018

Sanjeev Kumar and Karmeshu, "Characterizing ISI and sub-threshold membrane potential distributions: Ensemble of IF neurons with random squared-noise intensity", Biosystems, 2018

A theoretical investigation is presented that characterizes the emerging sub-threshold membrane poten-tial and inter-spike interval (ISI) distributions of an ensemble of IF neurons that group together and firetogether. The squared-noise intensity 2of the ensemble of neurons is treated as a random variable toaccount for the electrophysiological variations across population of nearly identical neurons. Employingsuperstatistical framework, both ISI distribution and sub-threshold membrane potential distribution ofneuronal ensemble are obtained in terms of generalized K-distribution. The resulting distributions exhibitasymptotic behavior akin to stretched exponential family. Extensive simulations of the underlying SDEwith random 2are carried out. The results are found to be in excellent agreement with the analyticalresults. The analysis has been extended to cover the case corresponding to independent random fluc-tuations in drift in addition to random squared-noise intensity. The novelty of the proposed analyticalinvestigation for the ensemble of IF neurons is that it yields closed form expressions of probability dis-tributions in terms of generalized K-distribution. Based on a record of spiking activity of thousands ofneurons, the findings of the proposed model are validated. The squared-noise intensity 2of identifiedneurons from the data is found to follow gamma distribution. The proposed generalized K-distribution isfound to be in excellent agreement with that of empirically obtained ISI distribution of neuronal ensemble.

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