Action Potential I: Qualitative Introduction and Current Clamp

Passive versus Active Signal Propagation in the Nervous System

• There are two major kinds of electrical signals in the nervous system:
  • Passively propagated signals and
  • Actively propagated signals.

• In the previous two units, we developed an understanding of the underlying electrochemical mechanisms, and the electrical equivalent representation, of passively propagated signals.
  • These signals dissipate over both time and space.
  • In order to propagate from one section of the cell membrane to another, these signals must charge the capacitor of membrane at each point along the way. This process increasingly distorts the shape of the original signal as it travels farther from its source.
  • Despite these drawbacks, passive signals are very important. In dendrites, the highly branching structures of neurons that receive signals from other cells, much of the processing of input signals involves passive propagation, which can serve as a complex spatio-temporal filter of these inputs.
  • Furthermore, many neurons in the nervous system only use graded potentials (i.e., passive signal propogation). These include key cells in the retina, such as the amacrine, horizontal, and bipolar cells, and an important set of neurons in the cortex, known as the granule cells.

• Neurons may need to send signals rapidly over long distances. The anatomical specialization that allows neurons to do this is the axon, and the electrophysiological specialization that allows neurons to do this is the action potential.
  • A metaphor for the action potential is the idea of a burning fuse.
    • As each section of the fuse heats up and bursts into flame, it begins to heat the adjacent part of the fuse, which then itself bursts into flames, and heats the next part.
    • Thus, the process is self-propagating, and can be very rapid.
  • Action potentials play an important role in reflexes. For example, if you put your hand onto a stove burner assuming that it is cool, and suddenly you discover that it is very hot, your hand is saved by a very fast involuntary reflex. The tip of your finger has sensory neurons that can sense heat, and these cells can rapidly transmit this information to your spinal cord using action potentials. This sensory input quickly crosses a single synapse, and the signal rapidly activates motor neurons whose action potentials signal to the appropriate muscles to jerk your hand away from the stove burner. Without action potentials, you would be badly burned.
  • The generation of action potentials determines how weakly and strongly the nervous system can respond to input. Weak inputs generate few and infrequent action potentials; strong inputs generate many action potentials at high frequencies. The dynamic range of the nervous system is, in part, controlled by how action potentials are generated.

• In this unit, we will provide a qualitative overview of how the action potential works. We will then go through the classic studies by Hodgkin and Huxley that allowed them to tease apart the underlying mechanisms of the action potential over 60 years ago. There are several reasons we take the time to do this:
  • First, the studies represent a beautiful experimental analysis of a biological system, and learning how this is done can be very helpful for research that you may do in the future.
  • Second, the studies created a methodology for studying the biophysics of neurons and ion channels that continues to be used to the present day.
  • Third, the studies led to the development of a mechanistic quantitative model of how the action potential works. Not only does this model continue to be used today, but the example of using a quantitative approach to test whether underlying mechanisms could give rise to a macroscopic phenomenon is an important example of how one can very effectively use mathematical and computational modeling to understand a biological system.

A Qualitative Introduction to the Action Potential

Figure 1: A qualitative summary of the action potential cycle

• Here is a very brief, qualitative summary of the action potential:
  • Inputs to the nerve cell that depolarize the membrane begin to increase the likelihood that voltage-gated sodium channels will open.
  • As the voltage-gated sodium channels open, the permeability of the membrane to sodium increases.
  • Because of the concentration gradient across the membrane (sodium ions are in high concentration outside the membrane, and in much lower concentration within the nerve cell), sodium ions begin to flow into the nerve cell as its permeability to them increases.
  • The influx of sodium ions further depolarizes the nerve cell, setting up an explosive positive feedback loop.
  • The system recovers in two ways:
    • Voltage-dependent potassium channels open in response to the depolarization of the nerve cell membrane, allowing potassium ions to rush out, removing positive charges from the inside, and thus repolarizing the nerve cell membrane.
    • After a delay, the voltage-dependent sodium channels shut down due to sodium channel inactivation, so that sodium ions can no longer rush into the nerve cell along their concentration gradient.
• Figure 1 summarizes the qualitative picture briefly, showing both the explosive positive feedback loop and the processes that lead to the termination of the action potential.

Video of the Qualitative Introduction to the Action Potential

A Qualitative Introduction to the Action Potential

A Schematic Introduction to the Membrane Potential and Voltage Gated Channels During the Action Potential

Figure 2: A schematic view of the charges across the membrane during the action potential

Figure 3: The change in potential during an action potential, with its components labeled. The x-axis here is time.

• What happens to the charge separation across the membrane during the action potential? We can see a schematic portrayal of the changes in charge separation in Figure 2.
  • At rest, there is an excess of negative charges inside the nerve membrane near the inner leaflet of the membrane, and an excess of positive charges on the outer leaflet of the membrane.
  • The charge separation gives rise to a potential across the membrane, the resting potential, due to the steady state influx of sodium ions and efflux of potassium ions though the ungated sodium and potassium ion channels (not shown in this figure), which we worked out in detail in units 1 and 2.
  • In addition, we have shown three schematic "gates" in the membrane, which are labeled m, n and h.
    • The m and h gates are associated with the voltage dependent sodium ion channels. At the resting potential, the m gates are closed, and the h gates are open. Both gates must be open for ions to pass through the channel.
    • The n gates are associated with the voltage dependent potassium ion channels. At the resting potential, the n gates are closed.
  • The schematic labeled Depolarizing shows what happens to the gates and the membrane as it begins to depolarize.
    • First, note that the charge separation across the membrane has been reduced.
    • Second, note that m gates have rapidly begun to open, allowing an influx of sodium ions. The other gates, which respond more slowly, have not yet changed their states. The more sodium ions that rush in, the less charge separation there is across the membrane, and the more likely that additional m gates will open, creating a positive feedback loop.
  • The schematic labeled Peak Action Potential shows what happens as the positive feedback loop proceeds up until the processes that stop it begin to operate.
    • Note that the charge separation across the membrane has reversed — there are now an excess of positive charges near the inner leaflet of the membrane, and an excess of negative charges near the outer leaflet. The increased permeability to sodium ions has pulled the membrane towards the Nernst or equilibrium potential for sodium ions (in the squid giant axon, this is about +55 mV).
    • Note also that although the m gate remains open, the slower h gate has shut, and the slower n gate for the potassium channels has opened.
    • As a consequence, influx of sodium ions has stopped, and potassium ions begin to flow out along their concentration gradient.
  • The schematic labeled After Hyperpolarization shows what happens as the potassium ions continue to flow out, pulling the membrane close to the Nernst or equilibrium potential for potassium.
    • Note that the charge separation across the membrane is now greater than it was at rest.
    • In response to the hyperpolarization of the membrane, the m gate shuts; more slowly, the voltage-dependent n gate for the potassium ion channels also closes, stopping the efflux of potassium ions.
  • Finally, the schematic labeled Rest at the far right of the figure shows that the ungated sodium and potassium ion channels return the membrane to the resting potential.
• Given the schematic changes shown in Figure 2 during the action potential cycle, it is now possible to understand the voltage changes that are recorded in a nerve cell during an action potential. These changes are shown in Figure 3.
  • Initially, the neuron is at the resting potential. For the squid giant axon, this is about -60 mV.
  • In response to an external depolarizing input, the neuron undergoes a rapid, self-generated depolarization due to the increased sodium permeability and increased influx of sodium ions.
  • At the peak of the action potential, the potential of the membrane goes more positive than 0 mV. For the squid giant axon, the peak of the action potential is about +30 mV. Note that this is much closer to the sodium ion Nernst or equilibrium potential (+55 mV in the squid giant axon), but the membrane potential does not reach this value because of the processes that shut off the depolarizing phase of the action potential.
  • After the peak, the neuron membrane potential falls rapidly. The potential actually goes to more negative values than the resting potential because of its increased permeability to potassium ions (the Nernst or equilibrium potential for potassium ions is about -75 mV in the squid giant axon, and the membrane approaches this value during the "afterhyperpolarization").
  • The membrane slowly returns to the resting potential.
• Many neurons show a clear threshold: below a certain level of input (initial depolarization), no action potential is generated; above this level, the positive feedback loop is induced, and the nerve cell explosively depolarizes.
• Many neurons also show a clear refractory period: because of the inactivation of the sodium channels and the activation of the potassium channels, inducing the regenerative positive feedback loop can be either not possible (right after the peak of the action potential; the absolute refractory period) or more difficult than when the neuron was at rest (the relative refractory period).

Video of the Changes to the Gates and the Membrane Potential During an Action Potential

Schematic Changes to Gates, Charge Separation and the Membrane Potential During an Action Potential

Analyzing the Action Potential using Current Injection

This provides you with a qualitative overview of how the action potential works, and provides you sufficient information to begin to work with a simulation of the action potential, and analyze some of its properties. Here is a simulation of the action potential and a current clamp that allows you to inject fixed currents into the model neuron.

It may be useful to open the simulation in a separate window as you work on the questions. Please answer the following:

• Question 1:
  • A. Set the Total Duration of the simulation to 100 ms, set Number of Pulses to 1, set the Pulse Duration to 50 ms, set the Fast transient sodium conductance to 0, and the Delayed rectifier potassium conductance to 0 (the simulation will complain, but this is the easiest way to set the values, and it will still work). Inject hyperpolarizing current using the Stimulation Current First Pulse. Try currents of different magnitudes: -1 nA, -2 nA, -4 nA, -8 nA and -16 nA. What is the effect of the hyperpolarizing current on the membrane potential? Please explain these results in terms of the passive properties of the nerve cell, i.e., the membrane capacitance and the membrane resistance (or conductance) that has not been set to zero. You may find it helpful to refer to the previous unit in the course to answer this question.
  • B. Now restore the Fast transient sodium conductance to 120 $\mu$S, and the Delayed rectifier potassium conductance to 36 $\mu$S. Repeat the experiments in part A with the same current values. What do you observe? How do the active conductances that you have just restored to the membrane affect the responses you saw in part A of the question? As you apply the different currents, carefully note the scale of the y axis. An action potential is defined as a change in voltage that goes from negative (resting) values to positive values (usually around +30 mV). Make sure to use this criterion in this and subsequent questions to determine whether or not what you are seeing is an action potential.
• Question 2: Using the same parameters as in Question 1B, inject depolarizing currents of different magnitudes (values to try: +1 nA, +2 nA, +4 nA, +8 nA, + 16 nA). How do the responses to depolarizing currents differ from those to hyperpolarizing currents that you used in the previous question? Explain.
• Question 3: Again using the same parameters as in Question 1B, find the minimum positive current that induces the cell to fire an action potential. Note that you are using a 50 ms pulse in this problem, and the result will differ if the pulse length is different (for example, 4 ms, which is the default pulse length). How sharp is this threshold value? To address this question, obtain an estimate to 4 significant figures (you should not do this for the rest of the problem set; two or three significant figures will generally be enough).
  • Use binary search to narrow down the values.
    • Let us say that 4 nA is too little to fire an action potential, and 8 nA is more than enough.
    • Try the value midway between the two, i.e., 6 nA.
    • Assume that 6 nA is not enough to fire an action potential. This narrows the interval of interest to the range from 6 nA to 8 nA. Once again, choose the middle of the range, i.e., 7 nA.
    • Assume that 7 nA is enough to fire an action potential. So now the range has been narrowed from 6 nA to 7 nA. Once again, choose the middle of the range, i.e., 6.5 nA.
  • Binary search is very fast, because with each repetition, you halve the range, and this can allow you to narrow down to the correct answer within a relatively small number of steps. In general, this is a useful approach whenever you need to estimate parameters, which is likely to happen many times during the this course.
• Question 4:
  • A. To do this question properly, it is helpful to have a much shorter pulse duration. If you press the Reset button, the pulse width will return to 4 ms, which is better for doing this problem. Make sure to set the number of pulses to 1, and set the simulation duration to 100 ms. The drawback is that you will now need to find a new (higher) value for the threshold current, since the pulse is shorter. Please do so using binary search; do not worry about 4 digits of accuracy.
  • B. Now, set the number of pulses to 2, and set the Inter-stimulus interval to 40 ms. Set the Stimulus current subsequent pulses to 70 nA, which is about the maximum amount of current one could inject into a real neuron without causing damage. Run the simulation. What do you observe? Now, systematically decrease the Inter-stimulus interval by decrements of 5 ms, and re-run the simulation. What is the shortest interval at which you can still evoke a second action potential? Once you have found the correct general area, you may vary around it in 1 ms increments or decrements to get a somewhat more precise answer. This defines the absolute refractory period, i.e., the time before which a neuron cannot generate a new action potential in response to extremely strong (but not damaging) inputs.
• Question 5: What underlying mechanisms of the action potential could account for the absolute refractory period?
  • Understanding the behavior of the ion channel gates before, during, and after the action potential is important for answering this question properly. Individual ion channels and their gates can only ever be in an open state or a closed state; the opening and closing of gates is a random process, and the probability of a voltage-dependent gate being in the open state is determined by the membrane potential. Neurons have many copies of each ion channel, so we can speak of populations of channels and gates. Since individual gates can only be open or closed and the process of switching states is random, in a large population of channels some gates of one type will be open and others will be closed. Notice the plot of the m, h, and n gates. It shows you the proportions of each type of gate in the population that are open as a function of time. The m gates are represented by a blue line, the h gates are represented by a purple line, and the n gates are represented by a red line.
  • Note also the conductances and currents (sodium conductance and current are represented by solid blue lines, potassium conductance and current are represented by solid red lines).
  • Once you have found the absolute refractory period in the previous question, first set the Inter-stimulus interval so that the simulation can just generate a second action potential, and observe what happens to the m, h and n gates and the conductances and currents. Run it again with the Inter-stimulus interval shortened by 1 ms so that an action potential is not generated, again observing the m, h and n gates and the conductance and currents. Explain how the gates change on either side of the absolute refractory period, and their effect on conductance and current.
• Question 6:
  • A. Find a duration after the first action potential for which a pulse of the same exact amplitude and duration as the initial pulse can again evoke an action potential. Change the Stimulus current subsequent pulses to the threshold current you found in question 4A (this should be the same value that the Stimulus current first pulse is currently set to). Start the Inter-stimulus interval at 40 ms for the second pulse, and shorten it by decrements of 1 ms. When does the second action potential fail? This time represents the end of the relative refractory period, i.e., after this time the neuron acts as if it has no memory of firing a previous action potential. What underlying mechanisms of the action potential could account for the relative refractory period? Once again, looking at the gates carefully will help you answer this question. Explain in terms of the gates.
  • B. Look closely at the n and h gates shortly after the neuron has finished its after-hyperpolarization. Are they in steady state? What would you predict will happen if you inject a second pulse equal or even slightly less than the threshold pulse during this time? Run the simulation, observe what happens, and explain in terms of the gates.
• Question 7: Press the Reset button. Set the Total Duration of the simulation to 400 ms, set the Pulse Duration to 390 ms, and set the Number of Pulses to 1. We can use this simulation to explore repetitive firing. Set the stimulus current for the first pulse so that you induce a single action potential. Once again, you may need to use binary search to find this value. Find the minimum amplitude of the pulse that induces two action potentials. Now, find the minimum amplitude of the pulse that induces three action potentials. Repeat this to find the current that induces four and five action potentials. Plot the number of action potentials (on the y-axis) against the current needed to induce that number of action potentials (on the x-axis). How does the amount of current increase? Can this neuron easily use the number of pulses it generates to represent a linearly increasing input (e.g., a linear increase in mechanical deformation of the skin)?
• Question 8: Find the minimum current value that induces firing of action potentials throughout the pulse. Measure the time between the pulses (use action potentials after the 5th to do this, to ensure that the value has stabilized; zooming in on the plot will make it easier to take these measurements). Call this period $t$. Convert the period into a frequency (in Hertz, Hz) by calculating $1000/t$, since $t$ is measured in milliseconds. Inject double, triple and quadruple the original current into the neuron, and redo the frequency measurement for each of these current levels. Plot the amount of current injected (x-axis) against the firing frequency (y-axis). Based on your results, what kind of messages can a neuron like this send from one point to another? Can it faithfully represent a signal that changes linearly in intensity using its rate of firing? Explain.
• Question 9: Increase the current until the neuron no longer fires action potentials beyond the first. Explain what might cause the failure of action potentials in terms of the gates.
• Now that we have a deeper understanding of the qualitative properties of the action potential, we need understand its underlying biophysical mechanisms more quantitatively.