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Minimal Hodgkin-Huxley Model: DC Stimulus

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.


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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
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