Elimination of One More Gating Variable

FitzHugh made the observation that when the Hodgkin/Huxley equations exhibit periodically firing action potentials, the following approximately holds:

$$n(t) + h(t) \approx 0.8.$$ (1)

This is verified in Figure 3 for input currents of $I=6.5 \mu A/cm^2$ and $I=20 \mu A/cm^2$ after the transient behavior has decayed away.

Figure 3: Timeseries for $n(t) + h(t)$.

Again, the code used to generate this figure can't be given here because of its similarity to the code you're writing for Homework #1. But, again, you are encouraged to modify your own code to generate similar plots.

Equation (1) should be viewed as an observation only - it has no rigorous mathematical or biological basis. However, it does allow us to further simplify the Hodgkin/Huxley model. We choose to eliminate the gating variable $h$ by taking $h(t) = 0.8 - n(t)$.