A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

Abstract

Two different bifurcation scenarios of firing patterns with decreasing extracellular calcium concentrations were observed in identical sciatic nerve fibers of a chronic constriction injury (CCI) model when the extracellular 4-aminopyridine concentrations were fixed at two different levels. Both processes proceeded from period-1 bursting to period-1 spiking via complex or simple processes. Multiple typical experimental examples manifested dynamics closely matching those simulated in a recently proposed 4-dimensional model to describe the nonlinear dynamics of the CCI model, which included most cases of the bifurcation scenarios. As the extracellular 4-aminopyridine concentrations is increased, the structure of the bifurcation scenario becomes more complex. The results provide a basic framework for identifying the relationships between different neural firing patterns and different bifurcation scenarios and for revealing the complex nonlinear dynamics of neural firing patterns. The potential roles of the basic bifurcation structures in identifying the information process mechanism are discussed.

Mixed Stimulus-Induced Mode Selection in Neural Activity Driven by High and Low Frequency Current under Electromagnetic Radiation

“…The latest researches described the complex bifurcations related to real experiments and HR neuron model; the experimental results [38,39] demonstrate the dynamics of a neuronal transition from chaotic bursting to chaotic spiking in the nervous system, which agree with published findings in theoretical neuronal models [40,41]. In addition, it is found that the firing, spike frequency, and instantaneous spike frequency observed in the experiment were simulated and explained using HH models.…”

“…As it can be known, the relevant experiments of the neuron electrical activity play a vital role in achieving biological functions of the nervous system [38][39][40][41][42][43]. The latest researches described the complex bifurcations related to real experiments and HR neuron model; the experimental results [38,39] demonstrate the dynamics of a neuronal transition from chaotic bursting to chaotic spiking in the nervous system, which agree with published findings in theoretical neuronal models [40,41].…”

Energy expenditure computation of a single bursting neuron

“…To understand neural processing mechanisms we also need to study the dynamics of neuronal subthreshold electrical activities. Neuronal bursting, a common firing pattern of these electrical activities observed in many electrophysiological experiments, has been studied extensively (Ji et al 2015 ; Izhikevich 2000 ; Kepecs and Wang 2000 ; Wang et al 2011 ; Shi et al 2017 ; Zhang et al 2016 ; Perc and Marhl 2005 ; Gu et al 2015 ; Jia et al 2017 ; Duan et al 2017 ). These studies mainly focus either on mathematical models for numerical analysis or on elucidating the time coding characteristics of bursting activities (Ji et al 2015 ; Izhikevich 2000 ; Kepecs and Wang 2000 ; Wang et al 2011 ; Shi et al 2017 ).…”

“…These studies mainly focus either on mathematical models for numerical analysis or on elucidating the time coding characteristics of bursting activities (Ji et al 2015 ; Izhikevich 2000 ; Kepecs and Wang 2000 ; Wang et al 2011 ; Shi et al 2017 ). The latter approach is more common because it is assumed that the coding information is contained in the precise time structure between spikes or between bursts (Zhang et al 2016 ; Perc and Marhl 2005 ; Gu et al 2015 ; Jia et al 2017 ; Duan et al 2017 ). However, most such studies rely mainly on data calculation and cannot explain the biological significance of the bursting phenomenon.…”

Computational study on neuronal activities arising in the pre-Bötzinger complex

“…The firing patterns of neurons in the respiratory system are very rich and can be divided into two categories: bursting and spiking (Rekling and Feldman 1998;Gray et al 1999;Butera et al 1997Butera et al , 1988bButera et al , 1998a. The experimental results show that the mode of bursting can be presented in single cell or network (Rybak et al 1997;Butera et al 1999b;Jia et al 2017). Based on a large number of experiments and investigation, researchers have proposed different computational models of respiratory rhythm of pre-BötC (Smith 1997;Balis et al 1994;Botros and Brace 1990;Duffin 1991;Gottschalk et al 1994;Ogilvie et al 1992;Rybak et al 1997).…”