Hodgkin-Huxley Cells

Introduction

This applet gives an introduction to the Hodgkin-Huxley model. It outlines the dynamics of the membrane voltage and membrane currents.

For further information

A good overview of detailed modeling of biological neurons is in "The Book of Genesis" by Jim Bower.

Credits

This applet was written by Thomas Pollinger.

Notes

Notice that these applets may only be viewed with a browser that has a Java virtual machine for Java 1.1 built-in.

Hodgkin-Huxley model

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

• Compartment Charateristics: This section defines the compartment physics like its diameter, the membrane capacitance C_m, the axial resistance R_a, the sodium conductance G_Na, the potassium conductance G_K and the leakage conductance G_l. It is also possible to alter the concentration of potassium and sodium inside and outside the compartment with the four variables K_i, K_o, Na_i and Na_o.
• Applying External Current/Voltage: The external excitation of the compartment is normally a steplike function of current or voltage. You can taggle between voltage and current excitation by choosing the corresponding switch. In the field next to the switches you may enter the target value for either voltage or current stimulation.

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'.

• Simulation Parameters: The begin and end values control the total interval of a simulation. This allows you to continue the integration of the Hodgkin-Huxley model even after the stimulation has stopped. The time step is important for the numerical implementation of the ordinary differential equations. Finally, the time scale resolution indicates at which resolution the graph will be displayed. Normally, this value is automaticallychoosen so as to fit the resolution of one pixel of the grahical output.
• Output Control: To view the graphs, you can click on "show" to open a window that displays the different variables of interest. "hide" closes this window but stores the graphs beeing displayed.

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

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.

Experiment instructions

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 I_c is set to zero.

1. Click on "show" to open the graphic output window
2. Press on "Voltage clamp" in the field "Applying External Current/Voltage" to set the voltage clamp simulation mode. The voltage actually is 10mV. You may increase or lower this target voltage to see different effects.
3. Press "run" to start the simulation.

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 i_C = dV_m/dt

Current Clamp Experiments

(A note on the name: Current clamp is also called space clamp since it shunts the inner axial resistance R_a. 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.)

1. Click on "Current Clamp" to switch to the space/current clamp mode.
2. Press "clear" to empty the previously drawn graph.
3. Press "run" to begin the new simulation.

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.

Spike Variations

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).

1. Change the value in the field current clamp from 0.5 to 0.05.
   Click on "run" to start a new simulation.
   What can you observe?
2. Click on "clear" to clear the graphical output.
   Restore the old value to 0.5.
   Restart the simulation.
3. Replace 0.5 by 1.5.
   Start a new simulation.
   Observations?

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.