BURSTING INDUCED BY EXCITATORY SYNAPTIC COUPLING IN THE PRE-BÖTZINGER COMPLEX

2012 ◽  
Vol 22 (05) ◽  
pp. 1250114 ◽  
Author(s):  
LIXIA DUAN ◽  
DEHONG ZHAI ◽  
XUHUI TANG
Keyword(s):  
Brain Stem ◽  
Bifurcation Analysis ◽  
Cell Model ◽  
Mammalian Brain ◽  
Synaptic Coupling ◽  
Model Network ◽  
Cell Network ◽  
Bötzinger Complex ◽  
Coupled Cells ◽  
Slow Decomposition

In this paper, we study and classify the bursting in a two-cell network of excitatory neuron within the pre-Bötzinger complex of the mammalian brain stem. We investigate the effects of parameters g Na and g K on the bursting generation and pattern transitions in the two-cell model network with synaptic coupling by the fast–slow decomposition and bifurcation analysis approach. Comparing the firing patterns of the uncoupled and coupled cells, we found that the bursting patterns are the same both for a single and two-cell model network with the parameter g Na changed, while they are different with the parameter g K changed. Our results are instructive for further understanding the dependence of the complex firing activities of the network on the firing activities of the single cell in the network.

Transition Mechanisms of Bursting in a Two-Cell Network Model of the Pre-Bötzinger Complex

2015 ◽  
Vol 25 (05) ◽  
pp. 1550069 ◽  
Author(s):  
Lixia Duan ◽  
Dandan Yuan ◽  
Xi Chen ◽  
Xiangying Meng
Keyword(s):  
Network Model ◽  
Parameter Space ◽  
Respiratory Rhythm ◽  
Rhythm Generation ◽  
Synaptic Coupling ◽  
Cell Network ◽  
Bötzinger Complex ◽  
Respiratory Rhythm Generation ◽  
Two Parameter ◽  
Slow Decomposition

Persistent sodium and calcium activated nonspecific cationic currents play important roles in the respiratory rhythm generation of the pre-Bötzinger complex. In this paper, we study the bursting patterns and their transition mechanisms in the two-parameter space of a two-cell network model of the pre-Bötzinger complex with synaptic coupling. Using the methods of fast/slow decomposition and two-parameter bifurcation analysis, we divide the two-parameter space into four different regions according to the multiphase oscillations, and reveal the possible transition mechanisms of bursting between these different regions. We also study the dynamics of the system with varying synaptic coupling strength. This work provides insights of how currents and synaptic coupling work on the respiratory rhythm generation.

scholarly journals Dynamics Analysis of Firing Patterns in Pre-Bötzinger Complex Neurons Model

2021 ◽  
Vol 15 ◽  
Author(s):  
Quan Yuan ◽  
Jieqiong Xu ◽  
Huiying Chen
Keyword(s):  
Respiratory Rhythm ◽  
Compartment Model ◽  
Mammalian Brain ◽  
Firing Patterns ◽  
Cation Current ◽  
Stimulus Current ◽  
Bötzinger Complex ◽  
Single Compartment Model ◽  
Respiratory Rhythms ◽  
Slow Decomposition

Pre-Bötzinger complex (PBC) neurons located in mammalian brain are the necessary conditions to produce respiratory rhythm, which has been widely verified experimentally and numerically. At present, one of the two different types of bursting mechanisms found in PBC mainly depends on the calcium-activated of non-specific cation current (ICaN). In order to study the influence of ICaN and stimulus current Iexc in PBC inspiratory neurons, a single compartment model was simplified, and firing patterns of the model was discussed by using stability theory, bifurcation analysis, fast, and slow decomposition technology combined with numerical simulation. Under the stimulation of different somatic applied currents, the firing behavior of neurons are studied and exhibit multiple mix bursting patterns, which is helpful to further understand the mechanism of respiratory rhythms of PBC neurons.

scholarly journals Population dynamics of the modified theta model: macroscopic phase reduction and bifurcation analysis link microscopic neuronal interactions to macroscopic gamma oscillation

2014 ◽  
Vol 11 (95) ◽  
pp. 20140058 ◽  
Author(s):  
Kiyoshi Kotani ◽  
Ikuhiro Yamaguchi ◽  
Lui Yoshida ◽  
Yasuhiko Jimbo ◽  
G. Bard Ermentrout
Keyword(s):  
Bifurcation Analysis ◽  
Field Potential ◽  
Reversal Potential ◽  
Planck Equation ◽  
Gamma Oscillations ◽  
Gamma Oscillation ◽  
Synaptic Coupling ◽  
Time Constants ◽  
Shunting Inhibition ◽  
Synaptic Interactions

Gamma oscillations of the local field potential are organized by collective dynamics of numerous neurons and have many functional roles in cognition and/or attention. To mathematically and physiologically analyse relationships between individual inhibitory neurons and macroscopic oscillations, we derive a modification of the theta model, which possesses voltage-dependent dynamics with appropriate synaptic interactions. Bifurcation analysis of the corresponding Fokker–Planck equation (FPE) enables us to consider how synaptic interactions organize collective oscillations. We also develop the adjoint method (infinitesimal phase resetting curve) for simultaneous equations consisting of ordinary differential equations representing synaptic dynamics and a partial differential equation for determining the probability distribution of the membrane potential. This method provides a macroscopic phase response function (PRF), which gives insights into how it is modulated by external perturbation or internal changes of parameters. We investigate the effects of synaptic time constants and shunting inhibition on these gamma oscillations. The sensitivity of rising and decaying time constants is analysed in the oscillatory parameter regions; we find that these sensitivities are not largely dependent on rate of synaptic coupling but, rather, on current and noise intensity. Analyses of shunting inhibition reveal that it can affect both promotion and elimination of gamma oscillations. When the macroscopic oscillation is far from the bifurcation, shunting promotes the gamma oscillations and the PRF becomes flatter as the reversal potential of the synapse increases, indicating the insensitivity of gamma oscillations to perturbations. By contrast, when the macroscopic oscillation is near the bifurcation, shunting eliminates gamma oscillations and a stable firing state appears. More interestingly, under appropriate balance of parameters, two branches of bifurcation are found in our analysis of the FPE. In this case, shunting inhibition can effect both promotion and elimination of the gamma oscillation depending only on the reversal potential.

Bifurcation Analysis of a Modified Cardiac Cell Model

2022 ◽  
Vol 21 (1) ◽  
pp. 231-247
Author(s):  
André H. Erhardt ◽  
Susanne Solem
Keyword(s):  
Bifurcation Analysis ◽  
Cell Model ◽  
Cardiac Cell

scholarly journals Influence of Electric Current and Magnetic Flow on Firing Patterns of Pre-Bötzinger Complex Model

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Wenchao Ji ◽  
Moutian Liu ◽  
Lixia Duan
Keyword(s):  
Electric Current ◽  
Respiratory Rhythm ◽  
Complex Model ◽  
Neuronal Firing ◽  
Essential Factor ◽  
Firing Activity ◽  
Magnetic Flow ◽  
Bötzinger Complex ◽  
Bistable Structure ◽  
Slow Decomposition

The dynamics of neuronal firing activity is vital for understanding the pathological respiratory rhythm. Studies on electrophysiology show that the magnetic flow is an essential factor that modulates the firing activities of neurons. By adding the magnetic flow to Butera’s neuron model, we investigate how the electric current and magnetic flow influence neuronal activities under certain parametric restrictions. Using fast-slow decomposition and bifurcation analysis, we show that the variation of external electric current and magnetic flow leads to the change of the bistable structure of the system and hence results in the switch of neuronal firing pattern from one type to another.

scholarly journals Strain differences in pH-sensitive K+ channel-expressing cells in chemosensory and nonchemosensory brain stem nuclei

2014 ◽  
Vol 117 (8) ◽  
pp. 848-856 ◽  
Author(s):  
Paul F. Martino ◽  
S. Olesiak ◽  
D. Batuuka ◽  
D. Riley ◽  
S. Neumueller ◽  
...  
Keyword(s):  
Brain Stem ◽  
Nucleus Tractus Solitarius ◽  
Ph Sensitive ◽  
Nucleus Ambiguus ◽  
Female Rats ◽  
Brown Norway ◽  
Motor Nucleus ◽  
Male And Female ◽  
Male And Female Rats ◽  
Bötzinger Complex

The ventilatory CO2 chemoreflex is inherently low in inbred Brown Norway (BN) rats compared with other strains, including inbred Dahl salt-sensitive (SS) rats. Since the brain stem expression of various pH-sensitive ion channels may be determinants of the CO2 chemoreflex, we tested the hypothesis that there would be fewer pH-sensitive K+ channel-expressing cells in BN relative to SS rats within brain stem sites associated with respiratory chemoreception, such as the nucleus tractus solitarius (NTS), but not within the pre-Bötzinger complex region, nucleus ambiguus or the hypoglossal motor nucleus. Medullary sections (25 μm) from adult male and female BN and SS rats were stained with primary antibodies targeting TASK-1, Kv1.4, or Kir2.3 K+ channels, and the total (Nissl-stained) and K+ channel immunoreactive (-ir) cells counted. For both male and female rats, the numbers of K+ channel-ir cells within the NTS were reduced in the BN compared with SS rats ( P < 0.05), despite equal numbers of total NTS cells. In contrast, we found few differences in the numbers of K+ channel-ir cells among the strains within the nucleus ambiguus, hypoglossal motor nucleus, or pre-Bötzinger complex regions in both male and female rats. However, there were no predicted functional mutations in each of the K+ channels studied comparing genomic sequences among these strains. Thus we conclude that the relatively selective reductions in pH-sensitive K+ channel-expressing cells in the NTS of male and female BN rats may contribute to their severely blunted ventilatory CO2 chemoreflex.

Multitime Scale Study of Bursting Activities in the Pre-Bötzinger Complex

2017 ◽  
Vol 27 (11) ◽  
pp. 1750172 ◽  
Author(s):  
Zhuosheng Lü ◽  
Cui Zhao ◽  
Bizhao Zhang ◽  
Lixia Duan
Keyword(s):  
Cell Model ◽  
Excitatory Input ◽  
Maximal Conductance ◽  
Single Cell Model ◽  
Bötzinger Complex ◽  
Geometric Decomposition ◽  
The Mean ◽  
Slow Variables ◽  
Slow Timescale ◽  
Input Formula

In this paper, we consider a single cell model of pre-Bötzinger complex, which is derived by adding an external tonic drive ([Formula: see text]) to the model developed by Park and Rubin. Using fast–slow geometric decomposition and bifurcation analysis, we study firing activities of the system and try to reveal the mechanisms underlying the bursts related to the mean level of excitatory input ([Formula: see text]) and the maximal conductance associated with the sodium ([Formula: see text]). Since a regular bursting requires at least two timescales, we consider the effects of timescale, especially of the slow timescale, on the bursting oscillations. Unlike the previous works, in this paper, we conduct our investigation by choosing different slow variables. We show how [Formula: see text] and [Formula: see text] affect bifurcations of the fast subsystem and how the bifurcations further determine firing activities of the full system with different slow variables.

Synchrony and Clustering in Two and Three Synaptically Coupled Hodgkin–Huxley Neurons with a Time Delay

1997 ◽  
Vol 07 (04) ◽  
pp. 889-895 ◽  
Author(s):  
S. G. Lee ◽  
S. Kim ◽  
H. Kook
Keyword(s):  
Time Delay ◽  
Phase Diagrams ◽  
Bifurcation Analysis ◽  
Critical Time ◽  
Phase Model ◽  
Excitatory Synapses ◽  
Synaptic Coupling ◽  
Cluster States ◽  
Cortical Dynamics ◽  
Phase Dynamics

Synchrony and clustering in phase dynamics of two and three Hodgkin–Huxley neurons coupled globally by excitatory synapses with a time delay have been studied by numerical simulations and bifurcation analysis. In particular, we have obtained phase diagrams for the synchronous state and various cluster states in the parameter space of the synaptic coupling strength, G syn , and the synaptic time delay, τd, by computing the phase shifts of action potential spikes. In the weak coupling limit the computed phase diagrams are found to be consistent with the results of phase model analysis. The bifurcation analysis shows the phase model predictions break down at G syn ~ 0.3 and new complex phase dynamics appear. For all numbers of neurons explored, the critical time delay at which the nature of synaptic coupling changes completely is found to be typically about 2–4 msec, which may have some implications in modeling cortical dynamics.

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