Simulation of the Hodgkin-Huxley model

Bioelectricity: Electric excitability and action potential

Simulation of the Hodgkin-Huxley model

The following simulation allows you to investigate action potentials using the model of Hodgkin and Huxley. We have slightly modified this model by including a blocking percentage of potassium and sodium channels. The differential equation which is associated with this model is \[C_m\frac{\dd V_m}{\dd t} = -x_\mathrm{K}\overline{g_\mathrm{K}}n^4(V_m-E_\mathrm{K})-x_\mathrm{Na}\overline{g_\mathrm{Na}}m^3h(V_m-E_\mathrm{Na})-\overline{g_\mathrm{L}}(V_m-E_\mathrm{L})+I\] where \(x_\mathrm{K}\) and \(x_\mathrm{Na}\) are the fractions of non-blocked ion channels. In the simulation you can specify the percentage of blocked ion channels and thus \[x_\mathrm{K}=1-\frac{b_\mathrm{K}}{100}\qquad\text{and}\qquad x_\mathrm{Na}=1-\frac{b_\mathrm{Na}}{100}\] Such blocking can be caused by administration of a drug. For example, tetrodotoxin (TTX) from the Japanese pufferfish, will block sodium channels and the cation tetraethylammonium (TEA) will block potassium channels.

Explanation of the user interface

The checkboxes at the channel functions are checked because you then see the time graphs of all of these functions in the upper right diagram.

The checkboxes at the Nernst potentials and leakage potential can be checked when you want to change their value.

You can give two stimuli of injected current: you can specify for each stimulus the starting time, duration and magnitude of the stimulus.
The default values result in only the first stimulus of 1 ms and current 10 µA/cm². This short stimulus is enough to generate an action potential.

With the save checkboxes next to the stimuli you can fix a setting so that the set values do not return to their default values when using the reset button.

In the following tasks it may be handy to use the following simulation of the Hodgkin-Huxley model in widescreen format. This user interface has been simplified in the sense that Nernst potentials cannot be changed.

Tasks

Click on the play button and see what happens. Can you well interpret the graphs?
Also consider what happens at a single stimulus of 1 ms, but with a current magnitude of 20 µA/cm² and also with a current magnitude of 5 uA/cm².
What happens at a single prolonged stimulus of say 200 ms and a current magnitude of 10 µA/cm².
What happens when you apply no current stimulus but block 60% of the potassium channels by TEA?

Answers

At the given stimulus one action potential is generated, because the membrane potential goes up due to the stimulus and passes through a threshold value, after which the excitable cell fires. You can see in the diagram of the conductivities that first only the sodium channel opens and sodium ions flow from the outside into the inside of the cell. As a result, the potential rapidly increases. Due to the high membrane potential (it may even become positive) the sodium channels are quite fast inactivated, which results in a low conductivity, and also the potassium channels open due to the high potential, so that potassium ions flow from the inside into the outside of the cell and the potential decreases again. The latter process takes longer. By inactivation of sodium channels, there is a period after the stimulus in which you can hardly generate a new action potential, however large the stimulus is.
A larger stimulus leads to the same action potential. The magnitude of the stimulus determines only whether the cell is firing, but the shape of the action potential does not depend on it. The second stimulus shows that there is indeed a firing threshold.
With a long-term stimulus of sufficient size the cell will fire periodically.
Even without an electric current stimulus, a cell can fire periodically as a result of blocking sufficiently potassium channels by administering a drug like TEA. In other words, administration of a drug may have a great impact on the functioning of a cell.