Simulation of squid axon with Hodgkin-Huxley ion channels
Table of Contents
1 Navigation: navigation toolbar is located at bottom of the plots
This uses the built-in navigation toolbar of matplotlib [click to open in your default web-browser].
You can hover the mouse cursor on any icon on this toolbar to get a brief tool-tip. To summarize:
1.1 Zoom
- Zoom-in:
- Zoom-in both X and Y axes:
- click on the subplot you want to zoom and scroll mouse wheel down, or
- click magnifier icon and press left mouse button on the subplot and drag. This will zoom the subplot to the rectangle you cover by this.
- click compass icon and press right mouse button on the plot and drag towards top-right.
- Zoom-in along X-axis:
- click compass icon and press right mouse button on the plot and drag towards right.
- Zoom-in along Y-axis:
- click compass icon and press right mouse button on the plot and drag upwards.
- Zoom-in both X and Y axes:
- Zoom-out:
- Zoom-out both X and Y axes:
- click on the subplot you want to zoom and scroll mouse wheel up, or
- click magnifier icon and press right mouse button on the plot and drag. The whole visible axis area will fit into the rectangle you cover by this.
- click compass icon and press right mouse button on the plot and drag towards bottom-left.
- Zoom-out whole plot window along X-axis:
- click compass icon and press right mouse button on the plot and drag towards left.
- Zoom-out Y-axis:
- click compass icon and press right mouse button on the plot and drag downwards.
- Zoom-out both X and Y axes:
- Go forward/backward in zoom stack: click right/left arrow icon.
1.2 Pan:
click compass-icon and left click-and-drag
1.3 Reset to initial plot state:
click home icon.
1.4 Change spacing and position of subplots:
click button with four green arrow-heads pointing (this is called the Subplot-Configuration button).
1.5 Configure axes:
click green tick-mark. In the pop-up dialog select the axis you want to modify and click OK. In the next dialog you can set the range of X and Y values for the axes and modify several other properties.
1.6 Save plot:
click floppy-disk icon.
2 Rearranging the frames on small screens
The default layout of the squid demo may exceed available screen size on your system. But you can always undock the control panels and put them one over the other to save screen space. To undock all panels in one go, click the "Undock all" button in the tool bar.
To move or float a single panel, click the left mouse button on its title bar (in the same horizontal line with the expand buttons) of any of the panels and drag. You can choose to leave it floating or drop it somewhere (top, left, bottom or right of the plot window) in the main window to reposition it. You can drop multiple panels in the same location. Then they will be put as multiple tabs over one another.
An undocked panel will be always on top of the main window. If this is a problem, you can close it by clicking the close button. You can make it visible again by clicking "Show all" button on the tool bar.
3 The SQUID tutorial
The following is adapted from the GENESIS squid demo notes with modifications for MOOSE by Subhasis Ray, September 2012.
The original header was:
SQUID
An Introductory Tutorial for GENESIS, XODUS, and the HODGKIN-HUXLEY model
By M. Nelson, Caltech, April 1989 - Modified by D. Beeman, June 1991, Dec 1994 Modified by E. Vigmond, September 1993
In the process of working through this tutorial, you will learn something about the Hodgkin-Huxley model. This program may serve as a good starting point for those of you who plan to work on single-cell models for a course project.
3.1 The Model
For the time being, we are going to simulate a single axon compartment with active Na and K conductances, as described by Hodgkin and Huxley for the squid giant axon. In other tutorials we will link compartments together to form a simple model of an entire neuron with a soma and dendrites (the Neuron tutorial), model a cable with many compartments (the cable tutorial), and build neural circuits with connected neurons (MultiCell and tritonia). For now, we confine ourselves to a single axon compartment.
3.2 Running the Simulation
The model has already been initialized with some reasonable parameter values, so all you have to do to run the simulation is:
click on the ``Run`` button in the toolbar.
The simulation which you just observed was for a constant current pulse, which is shown in the lower left graph panel. The upper left graph shows the membrane potential. You can see that 3 action potentials were generated during this 50 msec simulation. Now let's change the injection current and see what happens.
At the bottom of the left panel is a widget labeled "Electronics" and inside it there are two tabs labeled ``Current clamp`` and ``Voltage clamp``. Select the ``Current clamp`` tab and you will see a series of labeled text boxes with default values. In order to change the injection current:
position the cursor to the right of the last digit in the "First Pulse Current" field and click in the text box with the left mouse button.
Let's change the peak injection current from 0.1 to 1.0.
type <BACKSPACE> to delete the 0.1 and then type 1.0
The value in the dialog field should now be 1.0.
Now we'll run the simulation again.
click the "Run" button on the toolbar again.
There should be a dramatic change in the time-course of the membrane potential at this higher current injection level. Experiment with the injection level to see what happens to the axon at higher injection currents. Also try decreasing the injection level until an action potential is no longer elicited by the stimulus. What is the threshold for producing an action potential in this compartment?
You may also experiment with trains of short pulses. Set the "First Pulse Width" dialog field to 1 msec and click on the "Single Pulse" drop down box and select "Pulse Train". Now vary "First Onset Delay". What is the minimum interval between action potentials that you can achieve?
3.3 Voltage Clamping
You can also perform voltage clamp experiments in this simulation.
click on the "Voltage clamp" tab header at the bottom of the control form under "Electronics".
Again, reasonable default values have been selected , so all you have to do to run the voltage clamp simulation is:
click the "Run" button on the control form
3.4 Changing Extracellular Concentrations
You can alter the extracellular concentrations of the ions through the "Channels" panel. Any changes in concentration will cause the reversal potentials to be recalculated. To reset the values back to the initial ones, just click on the "Restore defaults" button in the top tool bar.
3.5 Controlling Graphs
The graph of the clamp current (lower left panel) has gone off scale. In order to rescale the graph:
click on the button with green tick mark in the navigation toolbar at the bottom of the plots.
A dialog containing drop-down to select the subplot should appear. Select the "Injection current" and click OK. Another dialog box will appear with text boxes for `Min` and `Max` values for X-Axis and Y-Axis. Adjust for Y axis to bring the graph into range and press "Apply".
The top toolbar has an "Overlay plots" button. When it is checked, any existing plots in the graph will be held and new simulation results will be overlayed. Try this now.
Click "Overlay plots" and run the simulation at several values of the clamp voltage. Do the first run with "Overlay plots" button unchecked so that all previous graphs are cleared at this run. Then click this button to checked state and do the subsequent runs.
3.6 State Plots
One can learn a great deal by studying plots in which one of the Hodgkin-Huxley channel activation parameters (the K activation "n", the Na activation "m", or the Na inactivation "h") is plotted as a function of the membrane potential, V. (See, for example, Chapter 5 of "Methods in Neuronal Modeling", by Koch and Segev.)
In order to view such a plot, click the left mouse button on the button labeled "State plot" in the top toolbar. The label will change to "State Plot Visible", and a state plot graph will appear. Clicking the button again will hide the graph. The default plot is to show the K channel "n" parameter on the y-axis and the membrane potential on the x-axis. The drop-down menus at the top of the window allow you to change these defaults.
3.7 Channel Blocking
In order to explore the effects of blocking one of the channels, you may click on one of the check boxes in the "Channels" panel for blocking and unblocking a channel. When a channel is blocked, its conductance is set to zero. Activation parameters for a blocked channel are still calculated and may be plotted, but are relatively meaningless because they will have no effect on the membrane potential.
3.8 Saving Graphs
You can save a graph to file by clicking the save button in the navigation toolbar. In the file dialog you can select from several formats including PDF, JPEG, PNG and SVG.
3.9 Units used in the simulation
Units:
quantity | unit |
---|---|
time | msec |
length | um (microns) |
potential | mV |
conductance | mS (mmho) |
resistance | kohm |
capacitance | uF |
specific axial resistance | kohm-cm |
specific membrane conductance | mS/cm2 |
specific membrane capacitance | uF/cm2 |