Effects of Maximal Sodium and Potassium Conductance on the Stability of Hodgkin-Huxley Model

Zhang, Yue; Wang, Kuanquan; Yuan, Ye; Sui, Dong; Zhang, Henggui

doi:10.1155/2014/761907

Cited by 11 publications

(5 citation statements)

References 32 publications

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“…Reduction of V K and the subsequent increase in g K and decrease in g Na help us to match the experimental facts in the squid neurons. The variability in maximum conductance of different channels has been reported in many experiments [38][39][40][41][42].…”

Section: Discussionmentioning

confidence: 83%

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Modeling activity-dependent reduction in after hyper-polarization with Hodgkin-Huxley equation of action potential

Talukdar¹,

Shrivastava²,

Ghosh³

2019

Biomed. Phys. Eng. Express

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From the perspective of learning and memory, intrinsic plasticity of neurons is an immensely important phenomenon. The hallmark of intrinsic plasticity is detectable in the form of activity dependent reduction in the After Hyper-polarization. But, as of now, it is not very clearly understood how neurons manage to do this. Keeping this in view, the dynamics of After Hyper-polarization reduction in a single neuron has been investigated in this work. The approach that has been adopted is that of biophysical modeling based on the Hodgkin-Huxley equation of Action Potential. The parameters in the Hodgkin-Huxley equations, which contribute to the threshold and the reduction of After Hyper-polarization, have been investigated in different neuron types, namely, the classical Hodgkin Huxley squid giant neuron, rodent cortical pyramidal neuron and rodent hippocampal interneuron. The potassium reversal potential (V K ) has been found to be the Hodgkin Huxley parameter that modulates the After Hyper-polarization in all kinds of neurons. The potassium reversal potential (V K ) has been modeled as sigmoid and modified exponential function of the number of input stimulus. Computational results show that increase in the number of input stimulus results in decrease in After Hyper-polarization.

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Section: Discussionmentioning

confidence: 83%

“…Zhang et al has also shown mathematically that g K and g Na can vary within a certain range of values where the AP curve is stable [38].…”

Section: Discussionmentioning

confidence: 98%

Modeling activity-dependent reduction in after hyper-polarization with Hodgkin-Huxley equation of action potential

Talukdar¹,

Shrivastava²,

Ghosh³

2019

Biomed. Phys. Eng. Express

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“…To study this more comprehensively, we extended the numerical investigations by performing a parameter study on the maximum conductance G s , which is commonly known as the maximum stretch-activated ion channel conductance or the sensitivity of the electrical current to deformation. Note that diseased hearts can cause abnormal changes in the maximum conductance (Zhang et al, 2014). Thus, this value can be considered as a key variable to study the MEF effects.…”

Section: Resultsmentioning

confidence: 99%

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study

et al. 2019

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In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

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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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Effects of Maximal Sodium and Potassium Conductance on the Stability of Hodgkin-Huxley Model

Cited by 11 publications

References 32 publications

Modeling activity-dependent reduction in after hyper-polarization with Hodgkin-Huxley equation of action potential

Modeling activity-dependent reduction in after hyper-polarization with Hodgkin-Huxley equation of action potential

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study

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

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