Hodgkin-Huxley Neuron Model
The Equations
The model consists of four non-linear ordinary differential equations (ODEs). The total membrane current is given by:
\[C_m \frac{dV}{dt} = I_{ext} - \bar{g}_{Na}m^3h(V - E_{Na}) - \bar{g}_Kn^4(V - E_K) - \bar{g}_L(V - E_L)\]Key Features of my Julia Implementation
- Gating Variables: Visualization of the $m, n,$ and $h$ variables to show how channel opening/closing lags behind voltage changes.
- Refractory Period: Demonstration of the absolute and relative refractory periods through dual-pulse stimulation.
- Interactive Parameters: My Pluto.jl implementation allows for real-time manipulation of maximal conductances ($\bar{g}$) to simulate channel-blocking drugs (like TTX or TEA).
Insights Gained
Implementing this model highlighted the “all-or-nothing” nature of the action potential. By visualising the phase plane of $V$ vs. $n$ (the potassium activation variable), I explored the stability of the resting state and the limit cycle of repetitive firing.
Note
This model was created using Google Gemini 3 to focus on learning and understanding the fundamentals of the Hodgkin-Huxley model, rather than the implementation details.
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🤝 Let’s Connect
Are you working on neural modeling or systems neuroscience? I am always looking for opportunities to collaborate or contribute to computational research. Feel free to reach out via LinkedIn or Email.