Minimal Hodgkin-Huxley Model: DC Stimulus

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applied current
6.3
sodium equilibrium potential
115
potassium equilibrium potential
-12
membrane capacitance
leakage channel conductance
Electrical properties of neurons are described by the Hodgkin–Huxley (HH) model with multiple phenomenological parameters. They include the axon-membrane capacitance and the equilibrium potentials and conductances for sodium, potassium, and leakage channels. A signature of an HH neuron is the spiking membrane-voltage response to a stimulus current above a threshold. This Demonstration plots the "action potential" response, and shows that it is robust even in the absence of membrane capacitance or leakage channels, or a significant variation in the equilibrium potentials for the sodium (potassium) channel, shown by the top (bottom) dashed red line.

Details

The memristive nature of sodium and potassium channels in the HH model, along with increasing interest in memristors, raises the following question: What is the minimal HH model that shows the salient properties of a neuron? This Demonstration selectively eliminates parts of the HH model and plots the resultant voltage response for a DC stimulus current.
Snapshot 1: for an HH model, sub-threshold stimulus current gives graded membrane voltage response that decays with time
Snapshot 2: the action-potential behavior persists after removing the capacitor and increasing the sodium equilibrium voltage
Snapshot 3: the action-potential behavior persists with only sodium and potassium channels, and vanishing potassium equilibrium voltage

External Links

Hodgkin-Huxley Action Potential Model
The Alpha and Beta Components of the Hodgkin-Huxley Model
The Hodgkin-Huxley Equations for Transmission of Electrical Impulses along an Axon

Permanent Citation

Qurat-ul-Ann (Anna) Mirza, Yogesh Joglekar
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​"Minimal Hodgkin-Huxley Model: DC Stimulus"​
​http://demonstrations.wolfram.com/MinimalHodgkinHuxleyModelDCStimulus/​
​Wolfram Demonstrations Project​
​Published: February 13, 2013