Dynamical Analysis of a Stochastic Neuron Spiking Activity in the Biological Experiment and Its Simulation by INa, P + I K Model

An irregular on-off like spiking activity is observed in the rat neural pacemaker experiment with the changes of extracellular calcium concentration. The spiking activity is simulated using a minimal model, the stochastic INa,P + I K model. The nonlinear time series analysis on ISI series shows the similar stochastic dynamical features of both experimental and simulated results. The power spectrum and SNR analysis suggests that this spiking activity is the autonomous stochastic resonance induced by noise near a subcritical Hopf bifurcation. Thus, it becomes easy for us to compare different stochastic firing patterns observed in the same experiment and stimulated under one same model. Besides, some deterministic-like characteristics by the analysis results on ISI series were also explained in this paper.

[1]  Huaguang Gu,et al.  Understanding of physiological neural firing patterns through dynamical bifurcation machineries , 2006, Neuroreport.

[2]  Huaguang Gu,et al.  Identifying type I excitability using dynamics of stochastic neural firing patterns , 2012, Cognitive Neurodynamics.

[3]  San-Jue Hu,et al.  PERIOD-ADDING BIFURCATION WITH CHAOS IN THE INTERSPIKE INTERVALS GENERATED BY AN EXPERIMENTAL NEURAL PACEMAKER , 1997 .

[4]  Teresa Ree Chay,et al.  Chaos in a three-variable model of an excitable cell , 1985 .

[5]  K. Schäfer,et al.  Oscillation and noise determine signal transduction in shark multimodal sensory cells , 1994, Nature.

[6]  De-Shuang Huang,et al.  Pupylation sites prediction with ensemble classification model , 2017, Int. J. Data Min. Bioinform..

[7]  Huaguang Gu,et al.  COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION , 2011 .

[8]  Mannella,et al.  Fast and precise algorithm for computer simulation of stochastic differential equations. , 1989, Physical review. A, General physics.

[9]  Zhao Zhiguo,et al.  Dynamics of On-Off Neural Firing Patterns and Stochastic Effects near a Sub-Critical Hopf Bifurcation , 2015, PloS one.

[10]  Sergey Petrov.  Dynamics properties of knowledge acquisition , 2018, Cognitive Systems Research.

[11]  Zhiguo Zhao,et al.  Bifurcations and enhancement of neuronal firing induced by negative feedback , 2016 .

[12]  Christoph Börgers,et al.  An Introduction to Modeling Neuronal Dynamics , 2017 .

[13]  Daniel S. Levine,et al.  Modeling the instinctive-emotional-thoughtful mind , 2017, Cognitive Systems Research.

[14]  Lei Xue,et al.  A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space , 2017, Cognitive Neurodynamics.

[15]  Y. Wan,et al.  Subthreshold membrane oscillations underlying integer multiples firing from injured sensory neurons , 2001, Neuroreport.

[16]  Partha Pratim Roy,et al.  EEG based word familiarity using features and frequency bands combination , 2018, Cognitive Systems Research.

[17]  Huaguang Gu,et al.  The distinct stochastic and deterministic dynamics between period-adding and period-doubling bifurcations of neural bursting patterns , 2017 .

[18]  Wiesenfeld,et al.  Stochastic resonance on a circle. , 1994, Physical review letters.