This applet gives an introduction to the Hodgkin-Huxley model. It outlines the dynamics of the membrane voltage and membrane currents.
A good overview of detailed modeling of biological neurons is in "The Book of Genesis" by Jim Bower.
This applet was written by Thomas Pollinger.
Notice that these applets may only be viewed with a browser that has a Java virtual machine for Java 1.1 built-in.
The applet simulates the dynamics of the membrane voltage, the membrane current and the Hodgkin-Huxley variables h,m,n of the ordinary differential equations. The neuron model has no spatial structure, i.e., only a single compartment is simulated.
The four sections of the applet are
The beginning of the simulation indicates the time at which the current or voltage step is applied. The duration of the stimulus should be entered in the field marked `duration'.
The "run" button begins the simulation whereas the "stop" button ends an ongoing simulation. Click on "clear" to empty the graphs. Click on the "refresh" button if the graphs won't display continuously. The refresh button forces the graphs to be repainted.
Questions for this exercise are here. You will need to understand how to carry out voltage clamp experiments and current clamp experiments, described in the next section.
Voltage Clamp Experiments
The characteristics of Hodgkin-Huxley cells may best be studied by considering some voltage clamp experiments. In voltage clamp experiments, the voltage is fixed. Hence the capacitive current Ic is set to zero.
The graphs on the output window reveal important characteristics of the dynamics of the underlying variables.
Hide the blue and cyan graphs by clicking on the corresponding checkboxes below the middle graph (current display).
The red and the green graph together is the yellow graph, the sum of the ionic currents sodium i_na and potassium i_k.
Hide the yellow and bring the red and green graphs to the front. The red current belongs to the sodium current that is inward (positive) at the beginning and ceases soon. The green current represents the potassium current which is negative (outward current).
Study how the various currents react to a voltage step. Which of the currents is the fastest?
Leave only the cyan graph that shows the capacitive current.
As expected, this current is 0 except at the moments, where the
imposed target voltage changes.
A voltage change leads to a delta-peak of capacitive current since
iC = dVm/dt
Current Clamp Experiments
(A note on the name: Current clamp is also called space clamp since it shunts the inner axial resistance Ra. Injected current is therefore uniformly distributed over the part of axon which is investigated. The effect is that an axon which normally has some spatial characteristics will be transformed to an axon that behaves like one single big compartment.)
Hide all graphs but the yellow one on the middle display. You can identify the membrane current as beeing the sum of the ionic currents, the capacitance current and the leakage current i_l. Try to apply a membrane current which is switched on at time 10 ms and lasts for 40ms.
Now, hide all currents except the green (potassium current) and the red (sodium) one. As in the voltage clamp experiments, the potassium current is outward and the sodium current inward. In particular, the sodium current reactes rapidly to an increase in the potential whereas the potassium current reacts more slowly.
Study the dynamics before, during, and after an action potential. At the beginnning, the membrane voltage is negative. If voltage rises above a certain level, the sodium channels open. The membrane becomes permeable to an inward current which raises the potential even further. A short time after the sodium current, the potassium current starts. At the same time the sodium current ceases. Once the potassium current is stronger than the sodium current, it pulls the membrane back -- and even below the baseline.
Now try to explain how this typical shape of the membrane voltage is created. Keep in mind that the membrane voltage influences the membrane currents, and vice-versa (since inward or outward flows of positive ions alter the membrane voltage). Moreover, the concentration of sodium is higher outside the cell. The concentration of potassium is higher inside the axon than outside.
The third display shows the kinetics of the three variables n, m, h of the ordinary differential equations.
The spike shapes can mainly be controlled by the intensity of the current that flows into the cell (simulated here by the externally applied current).
The amount of time needed to produce a new spike after a first one is called the "refractory period". The shorter this time, the less time the spike has to attain its peak value. In the extreme case, it oscillates around some value between the resting state and the peak value.
Here is another link to the Questions page.