Hodgkin-Huxley Cells

### Questions regarding Spike Generation

Conduct a current clamp experiment by inserting a short current pulse of 1 ms duration and variable amplitude as follows:
Begin stimulation: 5 ms.
Duration: 1 ms
Amplitude: start first with a value of 0.2.

Repeat the experiment several times, lowering the amplitude stepwise down to 0.02.

Set the end of the simulation to 30 ms.

1. What is the minimal amplitude necessary to excite a spike?
2. Does the form of the spike vary between different runs/different stimulation amplitudes?
3. Does the delay of spike initiation vary between different runs/different stimulation amplitudes?
4. Why is the sodium channel faster than the potassium channel? What is the time difference between the maxima of sodium and potassium current, respectively?

### Questions regarding channel time constants

Conduct a voltage clamp experiment by applying a voltage step as follows:
Begin stimulation: 5 ms.
Duration 25 ms.

Set the end of the simulation to 30 ms.

Repeat the exeriment several times with a target voltage after the step between -50 mV and +10 mV.

This is pretty much the type of experiment that Hodgkin and Huxley conducted to measure the (voltage-dependent) time constant and equilibrium state of the K-channel. For an overview, read the chapter in the book `Genesis', edited by Jim Bower.

1. Study the K-current (suppress all the other currents in the second graph). Convince yourself that the `time constant' of the K-current depends on the voltage.
2. Is the channel faster for high or for low voltage?

3. Now look at the lower graph and study the dynamics of n,m, and h.
1. Convince yourself from the graph that m faster than n and h.
2. Convince yourself that h and n have roughly the same dynamics except that (a) h is inverted with respect to n and (b) h starts at a resting value of 0.6 whereas n has a resting value close to zero.
3. The above two points are the basis of a reduction of the Hodgkin-Huxley model to 2 dimensions (Rinzel, Morris-LeCar, FitzHugh, Nagumo, Abbott and Kepler).