Equilibrium Point Bifurcation and Singularity Analysis of HH Model with Constraint

Zhu, Xinhe; Wu, Zhiqiang

doi:10.1155/2014/545236

Cited by 1 publication

(1 citation statement)

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“…However, by studying Na V activation and inactivation separately, our study indicated that acceleration of activation was the main factor leading to oscillation, while enhancement of inactivation inhibited cells oscillation after a certain extent (Figures 5, 10). There has been considerable research into bifurcation theory in H-H dynamic systems (Doi et al, 2001;Zhang et al, 2014) to indicate that I app leads to a bursting oscillations (Zhu and Wu, 2014). In the brain network, cells receive stimulus from other cells, whose effects on cellular dynamics are non-negligible.…”

Section: Bifurcation Analysis Of H-h Modelmentioning

confidence: 99%

A Potential Mechanism of Sodium Channel Mediating the General Anesthesia Induced by Propofol

Xiao

Chen

2020

Front. Cell. Neurosci.

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General anesthesia has revolutionized healthcare over the past 200 years and continues to show advancements. However, many phenomena induced by general anesthetics including paradoxical excitation are still poorly understood. Voltage-gated sodium channels (NaV) were believed to be one of the proteins targeted during general anesthesia. Based on electrophysiological measurements before and after propofol treatments of different concentrations, we mathematically modified the Hodgkin–Huxley sodium channel formulations and constructed a thalamocortical model to investigate the potential roles of NaV. The ion channels of individual neurons were modeled using the Hodgkin–Huxley type equations. The enhancement of propofol-induced GABAa current was simulated by increasing the maximal conductance and the time-constant of decay. Electroencephalogram (EEG) was evaluated as the post-synaptic potential from pyramidal (PY) cells. We found that a left shift in activation of NaV was induced primarily by a low concentration of propofol (0.3–10 μM), while a left shift in inactivation of NaV was induced by an increasing concentration (0.3–30 μM). Mathematical simulation indicated that a left shift of NaV activation produced a Hopf bifurcation, leading to cell oscillations. Left shift of NaV activation around a value of 5.5 mV in the thalamocortical models suppressed normal bursting of thalamocortical (TC) cells by triggering its chaotic oscillations. This led to irregular spiking of PY cells and an increased frequency in EEG readings. This observation suggests a mechanism leading to paradoxical excitation during general anesthesia. While a left shift in inactivation led to light hyperpolarization in individual cells, it inhibited the activity of the thalamocortical model after a certain depth of anesthesia. This finding implies that high doses of propofol inhibit the network partly by accelerating NaV toward inactivation. Additionally, this result explains why the application of sodium channel blockers decreases the requirement for general anesthetics. Our study provides an insight into the roles that NaV plays in the mechanism of general anesthesia. Since the activation and inactivation of NaV are structurally independent, it should be possible to avoid side effects by state-dependent binding to the NaV to achieve precision medicine in the future.

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Section: Bifurcation Analysis Of H-h Modelmentioning

confidence: 99%