AXON LABORATORY
April 2005
gK
g
g
 E K + Na  E Na + Cl  E Cl
gt
gt
gt
Em =
60
TEST
40
20
mV
0
-20
-40
CONTROL
-60
-80
0
10
20
30
40
50
msec
35
Na conductance in TEST
30
conductance
25
20
15
10
K conductance in TEST
5
0
0
10
20
30
40
50
msec
GOALS
Your goal for this exercise is to develop an understanding of the threshold,
refractory period, and conduction properties of an action potential and the role of sodium
and potassium conductances in these phenomena. Beyond this, it is possible to gain
some understanding of the quantitative natures of these conductances, their
pharmacology, and the channel gating at the bottom of it all. This hand out will provide
some instructions to get you started and guide you through some important exercises.
There is nothing to write up or turn in. You are expected to develop a lot of
questions for the instructor who will be available.
BACKGROUND
It is worth noting that although the fact of electrical signaling in the nervous system
was known in the 18th century, only the crudest mechanistic explanations of the action
potential were available until the middle of the 20th. Starting in the 1930s, Alan Hodgkin,
Andrew Huxley, and Bernard Katz conducted experiments on the large axons of marine
invertebrates. These preparations and the prepared minds of the investigators enabled
Hodgkin and Huxley to complete a series of experiments that provided a complete
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mechanistic description of electrical excitability in the giant axon of the squid. The
essential experiments were completed by 1952 (following a hiatus between 1939 and
1946) and earned the Nobel prize for Hodgkin and Huxley. Briefly, they used a method
known as the voltage-clamp technique to record the membrane currents evoked by step
depolarizations and interpreted these currents as changes in membrane conductance. By
seeing how the currents changed in response to alterations in bath Na+ and K+
concentrations, Hodgkin and Huxley concluded that squid axons had three significant
conductances: sodium conductance (gNa), potassium conductance (gK), and a much
smaller constant leak conductance. From their voltage-clamp measurements they
determined how gNa and gK changed as functions of time and voltage and developed a
series of differential equations to describe these changes. By solving these equations
using numerical methods (not a trivial exercise in 1952) they demonstrated that the
conductances they observed were sufficient to explain all of the interesting activities of
the squid axon action potential. That is, the equations can be thought of as an axon that
we can do experiments with. In this laboratory we will use a computer program that
performs calculations that took Huxley a day in less than a second. The way to approach
the system is to imagine that there is a real axon hooked up to a recording device and
assorted stimulators and to do experiments.
STARTING AND CONTROLLING THE PROGRAM
The Neurons in Action package (NiA) is tricky to operate until one gets the hang of
it. Attention paid to this introduction will greatly reduce the frustration that the program can
generate.
Start the program by double-clicking on the Neurons in Action icon. This will bring
up the NiA opening page in the Mozilla Firefox browser that accesses the various
modules that will be used. Click on the Start Neurolab button. The NeuroLab Table of
Contents is listed twice: in the bar on the left and in the main page window (see image
below). Exercises in this lab are drawn from Levels I and II can be selected by clicking on
either the blue or green links.
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Peculiarities of NiA include:
1. The Mozilla page will remain behind the control and graphing windows described
below. This page displays text describing exercises that are similar (but not identical)
to those described here as well as interesting background information and Help
information. You can ignore all of this.
2. Each of the windows can be resized by clicking on the margin and pulling. Note that if
you miss the margin and click on the Mozilla background all the windows will be
minimized out of sight. They can be restored by clicking on the Run Control icon at
the bottom of the screen.
3. To close a window that you don’t want, you must click on Close at the upper left.
Clicking on the standard red X at the upper right will not do anything.
4. Parameter values may be changed by clicking in the white field showing the value
and typing in a new value. The cursor MUST be positioned within the white field or
your changes will not register.
5. In some exercises the Stimulus Control window displaying the stimulus parameters
opens automatically whereas in other exercises you must open it. If you open more
than one window they will superimpose perfectly so that you can see only the most
recent window but all will be active. Changing the parameters in the top window will
not change the others and the experiment will not be what you are expecting. If your
experiment does not seem to match the protocol in the visible Stimulus Control
window, try dragging window off to the side to see if you have more than one. Close
all but one.
6. The right mouse button activates a menu of useful tools for managing the graphs.
Put the cursor in a plotting window and click the right mouse button. This will call up
the left-hand portion of the submenu containing useful tools for dealing with plots.
The submenu will persist as long as the right mouse button is held down. Release
the right mouse button over the option to select it. The most useful options are:
 View: If you hold the cursor on View, the right-hand submenu will pop up. Sliding
the cursor to View = Plot automatically adjusts scales on the graph to
accommodate existing plots.
 Crosshair: Selecting this option will change the cursor into a set of crosshairs
when you click on a trace. YOU MUST POSITION THE CURSOR ON THE
TRACE. You can determine the numerical values of all points on your plots by
moving the crosshairs to the chosen point; the x and y values will be displayed in
the blue bar at the top of the graph.
 Keep Lines: This option will save existing traces for comparison with new traces
to be drawn. You must have your cursor positioned within the graph when you
choose it.
 Erase: This option erases ALL traces within a particular graph. If "Keep Lines"
remains checked, the next runs of the simulation will be preserved until "Erase"
is again selected.
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What is a “patch”?
In the context of the following exercises a
patch of membrane is a preparation in which the
membrane potential is uniform. This can be a literal
patch of membrane attached to the end of a recording
pipette or the cell body of a neuron (see figure). In the
real world, a typical patch has too few ion channels to
produce a normal action potential but the experiments
described here can be done in a cell body.
Accordingly, where the program refers to “patch” you
can think “cell body”.
What is the alternative to a patch? In general, the potential across the membrane
of a large cell is not the same everywhere. This is important when considering the
conduction of the action potential along the axon of a nerve, along the length of a skeletal
muscle fiber, through the heart or smooth muscle (Exercises 7 and 8).
EXERCISE 1 Electrical properties of “inexcitable” membranes
To appreciate the contributions of voltage-gated ion channels, we will first examine
the electrical properties of a membrane that lacks them and then add them to the
membrane. In addition, this exercise will introduce the NiA system.
Click on The Membrane in Level I. This will open an introductory page that
includes a description of the goals and exercises developed by the authors of the
program. Skip all of this, scroll down a bit, and Click on Start the Simulation. This will
open three windows that you can stretch out a bit but should leave on the left side of the
screen. Essentially identical windows will control each of the exercises.
The Panel & Graph Manager lists the available graphs and protocols that can be
run. We will skip the first two protocols (Plain Bilayer Membrane and Add the Na/K pump)
and start with a cell that has a sodium pump (and the Na+ and K+ gradients it creates)
and leak (or “background”) conductance to give a resting potential of -70 mV. Click on
Add Leak Channels to activate this protocol and the voltage vs. time plot that will
display membrane potential during the experiment. Resize the plot for optimal viewing.
The Stimulus Control lists the available stimulation modes. Click on the diamond
next to IClamp. This will activate the current-clamp mode for injection of current to shift
the membrane potential. Three buttons for the stimulation delay, duration, and amplitude
will appear when the IClamp mode is activated.
The Run Control window has the buttons that execute the experiment. The Reset
& Run button executes the experiment. (The function of the Reset button is unclear and
you should not need it. Stop will presumably stop a long experiment but is not useful in
the short protocols we will run.) Time shows the elapsed time. Total # (ms) allows you to
set the duration of the experiment.
Click Reset & Run to execute the default experiment. The green trace indicates
the injection of positive charge into our cell in the form of a 2 nA current (2 nA = 2x10-9
coul/sec). Note that the amplitude of this trace indicates the timing of the current injection
but not its amplitude. The brown trace shows the time course of the membrane potential.
In response to a step injection of positive charge, the membrane potential depolarizes
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relatively slowly nearly reaching a new steady state at 10 ms. The membrane potential
returns to its resting value when the current injection stops. The exponential time course
of the voltage reflects the charging of the membrane capacitance. This property is
important to a complete understanding of the electrical activity of nerve and muscle, but
for now we will simply note that longer current injections will be more effective in shifting
membrane potential than short injections.
Examine the relationship between the amplitude of the injected current and
membrane potential. Activate the Keep Lines feature. Leave the delay and duration at
their default values and vary the amplitude from -1 to 2 nA in steps of 0.5 nA. This is done by
moving the cursor just to the left of the number to be changed, left clicking, and typing the
new number. The cursor must remain over the window while the new value is entered.
Measure and plot the potential at the end of the pulse as a function of current amplitude
using Cursor tool as described above.
o What is the relationship between membrane potential and current over this range of
currents? Check out Appendix A at the end.
o Is the Na/K pump involved in the return of membrane potential to its resting value?
EXERCISE 2 Electrical properties of excitable membranes
In the Panel & Graph Manager, click on Add HH channels. This will add to the
membrane the voltage-gated Na+ and K+ conductances (channels) first characterized in the
squid giant axon by Hodgkin and Huxley. Close the old graph. Reset the stimulus
parameters in the Stimulus Control Window to their default values. (A red check mark to
the left of a parameter indicates that the value has been changed from the default. Click on
the check mark to reset the default value.) Click on Reset & Run. Compare the time
course and amplitude of the membrane potential with that recorded earlier. The difference
is the action potential.
o Draw a sketch of the graph of the action potential.
Leave the delay and duration at their default values and vary the amplitude from -1 to 2 nA in
steps of 0.5 nA as you did previously.
o What is the relationship between membrane potential and current over this range of
currents?
o Is there a range of current injections that elicit responses similar to those observed in
the “inexcitable” membrane examined above? Compare your observations with
Appendix B at the end of this handout.
Physiologists refer to this behavior as “all or none” in the sense that if the
membrane potential is shifted positive to about -57 or -56 mV it pops up to positive values
with nothing in between. The nature of this threshold will be examined in more detail
below. “All or none” does not imply that all action potentials are identical. How do the
action potentials observed here differ one from the other?
Close exercises 1 and 2 by clicking on Quit in the Panel & Graph Manager.
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EXERCISE 3 The ionic conductances that underlie the action potential
Open the next exercise by clicking on Action Potential in Neurolab contents (to
the left of the Mozilla page) and then scrolling down to click on Start the Stimulation.
Click on Stimulus Control and then on IClamp in the Stimulus Control window. Click
on Voltage vs. Time Plot and Membrane Conductance Plots in the Panel & Graph
Manager window. Stretch the windows to improve visibility. Click on Reset & Run to
execute the default protocol. Note that in this protocol the duration of the current injection
is much shorter than in the previous exercise. The current injection ends before the action
potential begins. How can the action potential begin after a delay?
The lines marked ENa and EK indicate the Na+ and K+ Nernst equilibrium
potentials.
o What does ENa and EK mean?
In the Membrane Conductance Plots, you can observe the time courses of the
Na+ and K+ conductances with the rising and declining phases of the action potential.
o Which conductance dominates during depolarization?
o Which conductance dominates during repolarization? Sketch a graph.
o What opens the Na channels? What opens the K channels?
o How does reducing or increasing the amplitude of the current injection (0.1 and
0.3 nA) effect the membrane potential and the conductances? (The Keep Lines
feature is useful here.)
In the Panel & Graph Manager, click on Patch
Parameters. This opens a window that enables you to
modify the properties of the voltage-gated Na+ and K+
conductances and the ionic gradients.
Na Channels. There are compounds that that
specifically block the Na+ or K+ channels. Tetrodotoxin,
produced by a several species (including an octopus
and a salamander native to California but most notably
Tetrodotoxin
the puffer fish) blocks neuronal Na+ channels thereby
causing paralysis. Puffers in the genus Fugu are a delicacy and from 1974 through
1983 there were 646 reported cases of puffer fish poisoning in Japan, with 179
fatalities. (See http://vm.cfsan.fda.gov/~mow/chap39.html for more information.)
Cardiac Na+ channels are insensitive leading to the suggestion that paralysis by TTX
intoxication and later recovery may underlie the legends of zombies. Emergency
therapy consists of artificial respiration (See Dr. No by Ian Fleming).
The effects of TTX on the resting and action potential can be modeled by
reducing Na chan density, gnabar (The gnabar notation comes from the original
publication of the equations where gNa with a bar over it was used to denote the
maximum sodium conductance).
o Increasing the concentration of TTX also reduces the activation of gK. Why
does this happen?
Tetraethylammonium (TEA) ions inhibit a wide variety of K+ channels including
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many neuronal channels. The effects of TEA on the resting and action potential can be
modeled by reducing K chan density, gbark. First, return the Patch Parameters to
their default values.
o Does reducing gK alter gNa? How?
In the Run Control window set the Total # parameter to 60 ms (i.e. a longer time
base) and return the Patch Parameters to their default values. In the Stimulus Control
window set the amplitude to 0 nA (i.e. turn off the current injection). Click on Reset &
Run. This should record 60 ms of resting potential. Reduce gK by half and run.
o Explain what you see.
Close this exercise by clicking on Quit in the Panel & Graph Manager.
EXERCISE 4 Threshold and the "all or none" action potential
Open the next exercise by clicking on the II under Level in Neurolab contents (to the
left of the Mozilla page) followed by Threshold and Start the Simulation. Then click on and
Voltage vs. Time plots in the Panel & Graph Manager to open two windows that will plot
membrane potential as a function of time at low and high gains. In addition, click on
Conductance Plots to display gNa (red line) and gK (blue line). Resize the windows for best
viewing. If there is not enough room for all three plots close
or hide the low gain voltage plot and focus on the high gain
voltage and the conductance vs. time plots.
Click on IClamp to open the stimulus parameter
buttons.
Activate the Keep Lines function and then
record the response to the default pulse of 2.4 nA and
to 2.2, 2.3, (well below threshold) 2.486 nA (just below
threshold), 2.500 nA (just above threshold), and 2.600
nA (well above threshold). The voltage traces here are the result of increasing gNa and
gK in response to the depolarization caused by the current injection. For subthreshold
stimuli gK dominates and the membrane potential falls back. For suprathreshold stimuli
gNa dominates and the membrane potential depolarizes causing further increase in
gNa and depolarization (see Figure). The battle between gNa and gK can be seen if
you expand the Y-axis on the Conductance plot by moving the cursor over the graph,
holding down the right mouse button, moving the cursor over View and then View=plot
and then releasing the button. This will set the scale to match the data.
Is there a “voltage threshold”, i.e. a voltage above which there will be an action
potential and below which there will not be an action potential? This is not a simple
question. In the exercises above, you may have observed that if a stimulus depolarizes
the membrane positive to -57 mV there will be an action potential and it is reasonable to
identify this as a voltage threshold. Another approach to the question is to observe that
an action potential elicited by a 2.5 nA stimulus “takes off” at -59 mV (see Figure)
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suggesting that this is the threshold voltage.
However, -59 mV cannot be the threshold voltage
because the subthreshold 2.48 nA stimulus
depolarizes the membrane potential to -58 mV. So,
if one is willing to accept “around -57 mV” as a
threshold then there is a voltage threshold. If one
wants a more specific value there is not a simple
answer to this question.
Close this exercise by clicking on Quit in the Panel & Graph Manager.
EXERCISE 5 The refractory period
During an action potential gNa gets big and then small. The decline in gNa is largely
due to the "inactivation" of the sodium channels. That is, the sodium channels lose the
ability to open during an action potential and must recover before they can respond
normally to another stimulus. In this exercise you will use a second stimulus to examine
how soon after an action potential another one can be elicited.
If necessary, click on Level II in Neurolab contents (to the left of the Mozilla page).
Click on Refractoriness and Start the Simulation. In the Panel Manager, click on Insert
Stimulus Electrodes (to open the control panels for the first and second stimulations)
and Voltage vs. Time Plot and Membrane Conductances. Click on IClamp in both
Stimulus Electrode windows. Resize the windows for optimal viewing.
Click on Reset & Run to execute the default protocol in which the first pulse is
delivered at t = 0 ms and the second at t = 9 ms. The amplitudes of the pulses are set
to a large value, 125 nA, approximately 1.5 times the threshold value (84.5-84.6 nA) for
brief pulses. The first stimulation will elicit an action potential whereas the second will
not. Increase the delay of the second stimulation in the Stimulus Electrode (1) window
until the second stimulation also elicits an action potential. The time after the first action
potential when the second stimulation fails to elicit an action potential is the Refractory
Period.
Increase the amplitude of the second stimulation to 1000 nA and reduce the
delay to 5 ms. At this delay the cell is refractory and the depolarization that you see in
response to the second stimulation is due to the current injected by the stimulator
without significant contribution from gNa and gK. Increase the delay until you see a
clear action potential (the Keep Lines feature may help). The time after the first action
potential when a stronger stimulation can elicit an action potential is the Relative
Refractory Period.
o How can a cell be “relatively” refractory?
o Is the second action potential all-or-none? Can you explain what you see?
Close this exercise by clicking on Quit in the Panel & Graph Manager.
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EXERCISE 6 - Ion substitution
Return to Level I of Neurons in Action, click on Action Potential and Start the
Simulation. In the Panel and Graph Manage click on Stimulus Control, Voltage vs.
Time Plot, Membrane Conductance Plots and Patch Parameters. In the Stimulus
Control window Click on IClamp. Stretch the windows to improve visibility. Click on Reset
& Run to execute the default protocol and activate the Keep Lines function.
Return all the parameters to their default values if they are not already there.
Examine the effect of increasing extracellular K+ on the resting potential. First close the
Stimulus window (click on Close, not the red X) to inactivate the current injection
stimulus and then increase the Total # (ms) in the Run Control Window to 25 ms.
Return the value of extracellular Na+ to the default (click the red check); also, right click
in both graphs to Erase the existing lines.Then click on Reset & Run. The Voltage vs.
Time plot will show the normal resting potential. Activate the Keep Lines function.
Increase the Extracellular K (mM) in the Patch Parameters window to 20 mM and
monitor the relationship between the resting potential and EK.
o What causes the action potential in these experiments where there is no current
injection? (Hint: In this simulation the membrane potential before time 0 on the
graph is the normal resting potential. At time 0 the new parameters are
instantaneously applied.)
Close this exercise by clicking on Quit in the Panel & Graph Manager.
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APPENDIX A
Relationship between membrane potential and injected current in Exercise 1.
Voltage vs. Current
nA
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0
-20
mV
-40
-60
-80
-100
-120
Appendix B
Relationship between membrane potential and injected current in Exercise 2.
Voltage vs. Current
60
40
mV
20
-2
-1
0
-20 0
1
-40
-60
-80
-100
nA
10
2
3
Series1