Hodgkin Huxley model

The Hodgkin Huxley Links to an external site. model (J. Physiol. 117, 500-544 (1952)) describes how action potentials in neurons get generated an propagate. They received a Nobel prize for their work.

Why did Hodgkin and Huxley do their experiments on this particular squid axon?

The equations describing their model are summarized on P. 518, namely Eqs 26, 7, 15, 16, 12, 13, 20, 21, 23, and 24. These equations are implemented in the attach SciPy scripts.

Derive Eq 26 from Eqs 1-6 and 14. What are the approximate values of $V_{Na}$ $V_{Na}$ and $V_K$ ? What is the meaning of the "gating" variables n, m, and h? Can you think of any biologically sensible explanation for their behavior? Why do they obey Eqs 7, 15, and 16? How do $\alpha_n$ $\alpha_n$ , $\beta_n$ $\beta_n$ , $\alpha_m$ $\alpha_m$ , and $\beta_m$ $\beta_m$ , influence the variables n and m?

Run hodgkin_huxley_i.py Download hodgkin_huxley_i.py
. Relate figures 0, 1, and 2, to the equations above from Hodgkin and Huxley. Look at Figures 3 and 4. Which gating variable rises fastest? Which channel is opening first, $Na$ or $K$ ? (Note that this can be modified to clamp the voltage Download clamp the voltage
instead.)

When the sodium channel conductivity increases, what effect does this have on the voltage? See Fig 1 of Hodgkin and Huxley's paper. Compare this with Figure 5 of the simulation.

Why causes the voltage to start increasing after reaching a minimum? Refer to Figures 3 and 4 of the simulation to understand this.

In this simulation a short initial current pulse was injected to create this large voltage spike. The magnitude of the initial spike was I0 = -70. Now change the value to below threshold by uncommenting the appropriate line of code. What fo you see now?

The above analysis of Hodgkin and Huxley is for a local area of the axon. They extend this to the full axon in Eq 30, by coupling separate areas together. The equations shows waves that travel along the axon. hodgkin_huxley_wave.py Download hodgkin_huxley_wave.py
simulates their model. An initial voltage pulse is applied as a spike of height Vmax to trigger a propagating voltage wave. Try running it with the program. Now uncomment the line for Vmax so that the initial pulse is below threshold. What happens?