Action Potential V: Design and Analysis of Complex Neurons

Introduction

• We started the analysis of a multi-conductance nerve cell in the previous class, and began to learn how the different conductances can affect the behavior of a neuron.

• Using current clamp, as we did in the previous class, we saw how each current could affect the shape of action potentials, their frequency, and the response of the neuron to different inputs.

• In this class, we will use voltage clamp to dissect apart the different currents, as Hodgkin and Huxley did in their classic studies on the squid giant axon.

• We will also see that as more conductances are added, neurons can show more complex "personalities"; for example, they can spontaneously burst.

• Now that you have both current clamp and voltage clamp tools at your disposal, you can begin to apply them as if you were doing neurophysiological experiments on a new neuron.

• Doing so can allow you to understand how mutations in ion channels, or the process of development, or the process of aging, or an environmental toxin can each alter neuronal function, which can often lead to changes in behavior.

• In addition, you now know enough about different ion conductances that you can actually design your own neurons. Since we now know enough of the molecular biology of neurons that we can instruct neurons to insert ion channels into their membranes, the design ideas that you develop in this class could actually serve as a "blueprint" for creating neurons with particular properties.

Lab Notebooks and Analysis and Design Problems

• This will be the first unit where your lab notebook will start to play a role more similar to the role such notebooks play in actual laboratories.

• As we already mentioned on the first day of class, and specified here, when you are doing an analysis or a design problem, you need to articulate a plan first, then describe the sequence of steps you took, document your results, and draw careful conclusions from your observations.

• Thus, plan to present your results to the instructors by showing us the logic you followed and the results you got in your laboratory notebook on the wiki.

• Questions 1-7 below are REQUIRED work. You then have the option of completing EITHER Questions 8-10, which continue your analysis of a rat hypoglossal motor neuron, OR Questions 11-14, which involves designing a spontaneously bursting neuron. After completing one of these sets of questions, you may work on the other set for up to 1 extra credit point.

Analysis

• This unit will provide you with the first opportunity to do a more extended analysis of a neural simulation.

• Although it would be nice if this were ever true, it is never the case that biological neurons come with helpful, labeled parameter boxes that allow you to easily and quickly change their properties.

• Instead, each neuron is a novel and unknown system.

• Thanks to the evolutionary history of neurons, it is usually very likely that a novel neuron will have many of the conductances that are found in other neurons that have been studied previously, even in very different species, though of course there will be variations, and on occasion, you may find an entirely new type of ion channel.

• The major tools at a neurophysiologist's disposal when studying a new neuron will be those you have learned about: current clamp, voltage clamp, and patch clamp.

• In addition, he or she may have access to a range of pharmacological agents. These are generally drugs that have been found (or have been created) to block a specific ion channel.
  • For example, the cone snail injects its prey with a venom consisting of a variety of peptides (short sequences of amino acids), and many of these act to paralyze prey by binding to specific ion channels.
  • In particular, $\omega$-conotoxin is known to bind to N-type calcium ion channels.

• Thus, you will be provided with current clamp and voltage clamp simulations that include options for adding pharmacological agents. Using these simulations, you will be studying the properties of hypoglossal motor neurons in neonates (newly born rats) and in adult rats.
  • Using these tools, you will be asked to define how the neuron changes as an animal matures, and, in particular, to measure changes in the maximum conductance of the specific ion channels that are relevant to this difference.

• It is intrinsically interesting to understand how the nervous system changes with development, since this clarifies the way in which it self-assembles.

• It is also of considerable medical interest, since many diseases are the result of problems with the developmental processes. Understanding how a neonatal neuron differs from an adult neuron can be the basis for a rational therapy that allows a neuron that has not properly developed to be manipulated pharmacologically to act in ways that are more similar to an adult neuron, and also helps to pinpoint the genetic defect that caused the changes, which in turn could lead to a genetic therapy for the disease.

Here is a voltage clamp simulation of the multi-conductance neuron that you studied in the previous class. The simulation is based on studies of neonatal rat hypoglossal motor neurons:

Choose the Voltage clamp simulation with additional conductances. Set the Holding potential to -80 mV, the Step delay to 100 ms, the Step duration to 100 ms, and the Total duration to 300 ms. Looking at the graphs of the currents, conductance, and gates, please answer the following questions:

• Question 1: What is the reason that the fast potassium current shuts off during the depolarizing pulse? What other current that you have learned about does this?

• Question 2: What is the reason that the sag current does not return to its resting value after the depolarizing pulse?

• Question 3: Please look at the Intracellular calcium concentration, and the Calcium Currents, Conductances and Gates. Note that the calcium concentration continues to increase after the depolarizing pulse. Explain.

• Question 4: What is the reason that the calcium-dependent potassium current goes to zero after the depolarizing pulse ends, even though its conductance has not fallen to zero? Explain.

You are now ready to start analyzing the differences that occur in hypoglossal motor neurons that arise over the course of development. Below, there is a link to a current clamp simulation that allows you to "toggle" between the adult and the neonatal hypoglossal motor neurons. You may want to open the simulation twice, in two different tabs or windows, and click on the button labeled "Adult simulation" in one of these windows (the default simulation is the "Neonatal simulation"). This way you can directly compare data from the two phases of development in two different windows.

In this current clamp simulation, all of the cell parameters are hidden from you; you are measuring only the membrane potential. For the following questions, you will make observations about the behavior of the neonatal and adult neurons, and develop hypotheses explaining your observations. Make sure to take snapshots of the data that you get, and to write down your hypotheses. You will test your hypotheses later, using voltage clamp.

• Question 5: Compare the action potentials in the neonatal hypoglossal motor neuron to the action potentials in the adult hypoglossal motor neuron. How do they differ? Which of the different conductances you have previously studied could be responsible for this difference?

• Question 6: Set the Total duration of the simulation to 150 ms, and set the Pulse duration to 100 ms. How do the responses of the two kinds of neurons differ from one another? Which of the different conductances could be responsible for this difference?

• Question 7: Change the Stimulus current first pulse from 2 nA to -2 nA (i.e., inject hyperpolarizing current into both model neurons). How do the responses of the two kinds of neurons differ from one another? Pay attention to the scales on the plots. Which of the different conductances could be responsible for this difference?

Given your results from Questions 5, 6, and 7, you are now ready to test your hypotheses about which currents may change during development from birth through adulthood. To test these hypotheses, you can use the simulation below, which provides you with voltage clamp tools and pharmacological agents that can specifically block different conductances. Unlike the previous voltage clamp simulations, all you will be shown is the total membrane current, which is equivalent to the sum of all the individual currents; by using the drugs, you can dissect out the sources of this current (which is what you would do in a laboratory). Once again, you are encouraged to create two windows, one containing the "Adult simulation" and one containing the "Neonatal simulation" so that you can directly compare data from the two phases of development in two different windows. Again, make sure to take snapshots of the data that you get, and to write down your hypotheses prior to doing your experiments, and make sure to reflect on whether the data do or do not correspond to your hypotheses. Note that in these simulations, the capacitative current has been subtracted out to make your analysis easier.

The different abbreviations used with each drug are the same that you saw in the multiple conductance simulations and are summarized here:

K	Delayed rectifier potassium conductance (this is the original Hodgkin-Huxley potassium conductance you first learned about)
A	Fast transient potassium conductance
SK	Calcium dependent potassium conductance
Na	Fast transient sodium conductance (this is the original Hodgkin-Huxley sodium conductance you first learned about)
NaP	Persistent sodium conductance
H	Sag conductance
T, N, P	Various calcium conductances

You can assume that the differences you observe between the neonatal and adult neurons are caused by changes during development in the levels of expression of different types of ion channels. That is, the neonatal and adult neurons differ because some of the conductances strengthened or weakened as the animal matured. In Question 8, you will begin to determine how these conductances change by first determining the leak conductance.

• Question 8: To begin to assess the source of the differences between the neurons at the different developmental stages, it is useful to see if they can be made more similar to one another if the voltage-dependent conductances are removed. Change the First step potential to -90 mV, and apply all the drugs to the Neonatal simulation (by checking all the boxes) and to the Adult simulation (by checking all the boxes).
  • What is the response of the total membrane current to the hyperpolarizing voltage step?
  • Calculate the conductance of the membrane for both the neonatal and adult from these data. To do this, use the change in total membrane current and the change in membrane potential with Ohm's law to find the total membrane conductance, $$g_\text{total} = \frac{ \Delta I } { \Delta V }.$$ Since all other conductances are blocked, the total membrane conductance must be equal to the leak conductance, i.e., $g_\text{total} = g_\text{leak}$.
  • What can you say about the conductance of the leak current in the neonatal and in the adult based on this calculation? Is it the same or different?

• Question 9: You will now begin to analyze the voltage-dependent conductances one at a time. You will design voltage clamp protocols that allow you to estimate the maximum conductance for each voltage-gated current in both the neonatal neurons and the adult neurons.
  • Create a table in your lab notebook for organizing your data. Click this link, and copy the table template into your notebook. For all your measurements and calculations, always include appropriate units!
  • For each of the nine voltage-gated conductances, do the following:
    • Using the pharmacological agents provided, block all conductances except the one you are currently studying.
    • Find a voltage clamp protocol that strongly activates the conductance. That is, find a holding potential, a step potential, and a step duration that results in a total membrane current that is significantly different from the leak current alone. Once you have done so, record the holding and step potentials in your table, and compute and record the step size ($\Delta V$). Remember to include the right units! Here are some things to keep in mind:
      • Both the current you are interested in and the leak current are summed together in the plotted membrane current, so you need to elicit a large current in addition to the leak current.
      • Since some conductances are activated by depolarizations and others by hyperpolarizations, you should try both to see which works best. Your previous experiences studying these conductances should help you get started.
      • Extreme steps in voltage can damage cells, so you should avoid clamping the membrane potential far outside its normal range.
      • Since some conductances take a long time to activate, you may need to significantly extend the duration of the step (and the simulation) to see the maximum current. In some cases, this may take hundreds of milliseconds.
      • If you note that a current takes a long time to activate, you may want to measure the conductance using a tail current protocol:
        • When a conductance takes a long time to activate, this means that several gates must open. Thus, at the end of a long hyperpolarizing or depolarizing pulse, the conductance reaches its maximum value.
        • However, it only takes one gate closing to stop the current, and this usually happens with very little delay.
        • Thus, if you measure the maximum current through a specific channel near the end of a long hyperpolarizing or depolarizing pulse, and then find the minimum value of the current after the pulse ends, the difference in these two current values can be used as a fairly accurate measure of the peak channel conductance.
      • If a current inactivates after a short time, you may need to record the change in current right after the step begins.
      • Take a picture of the simulation once you have selected a voltage clamp protocol.
      • The calcium-dependent potassium (SK) conductance poses an added complication: in the absence of calcium, this conductance is inactive. You will first need to identify one of the calcium conductances which does not differ between the neonatal and adult neurons, and then unblock it in addition to unblocking the SK conductance when you are measuring the SK current.
    • Measure the maximum change in membrane current ($\Delta I$) seen when you step from one potential to another. Record the value in your table. Remember to include the right units! Do this for both the neonatal neuron and the adult neuron. For both types of neurons, you should use the same voltage clamp protocol and record the maximum current change in the same way.
    • Compute the total membrane conductance for neonatal and adult neurons each using the data you have collected, just as you did in the previous question, $$g_\text{total} = \frac{ \Delta I } { \Delta V }.$$ Unlike in Question 8, you have unblocked one of the conductances, so $g_\text{total} \ne g_\text{leak}$. Instead, the total membrane conductance is the sum of the leak conductance and the conductance(s) you have unblocked, i.e., $g_\text{total} = g_\text{leak} + g_x$, where $g_x$ is the conductance you are studying. For each kind of current, find the value of the conductance by subtracting the leak conductance (found in Question 8) from the total membrane conductance, $$g_x = g_\text{total} - g_\text{leak} = \frac{ \Delta I } { \Delta V } - g_\text{leak},$$ and record each value in your table (under the column heading $g_x$ for neonatal and adult neurons). Remember to include the right units!
      • For the calcium-dependent potassium (SK) conductance, you will additionally need to subtract out the conductance of the calcium current you have enabled (which you will need to find independently using the same voltage clamp protocol and measurement timing that you are using for the SK conductance).
    • Finally, compute the ratio of the adult conductance to the neonatal conductance.

• Question 10: Your table should now summarize the differences between the adult and the neonatal neurons.
  • Which conductances are unchanged during development?
  • Which conductances differ between adult and neonatal neurons?
  • Do these data support the hypotheses you formulated in Questions 5, 6, and 7?
  • As a final test, open the Current clamp simulation with additional conductances used in the previous class. This model is identical to the current clamp model of the neonatal neuron you were working with earlier. For each conductance that varies between neonatal and adult neurons, change the maximum conductances using the ratios you computed in Question 9 as scaling factors. Do this for all the differing conductances simultaneously so that you can reconstruct the adult neuron. (You may notice that some of the maximum conductances shown in this simulation are larger than the maximum conductances you measured for the neonatal neurons. This may be because your voltage clamp protocol did not fully activate the conductance. This is why you should use the ratio to scale the conductances in this simulation, rather than use the maximum conductances you found for the adult simulation.)
    • Repeat the measurements done in Questions 5, 6 and 7 above using your reconstructed adult neuron. (You will need to increase the Stimulus current first pulse to 2 nA so that this simulation matches the simulation you used in those questions.) Do you obtain the same results? Include pictures in your notebook.
  • Provide a summary of your experimental analysis of the adult versus the neonatal neurons in your wiki-based lab notebook.

Design

• Design questions are another way of mastering complex material.

• The physicist Richard P. Feynman said "What I cannot create, I do not understand", and he was right.

• As our knowledge of the molecular biology of neurons and their ion channels has advanced, it has begun to relate details of the structures of ion channels to their permeability and gating properties.

• At the same time, as our knowledge of the molecular biology of cells has advanced, it has also become possible to induce neurons (and other cells) to insert artificial ion channels into their membranes.

• In parallel, another technique, dynamic clamp, makes it possible to compute the currents due to any ionic conductance, and to either inject this current (effectively adding a novel conductance) or to remove this current (effectively blocking the conductance) in intact nerve cells. A recent review of this technique is here.

• Finally, it is important to realize that many engineers are continuing to develop neuromorphic devices, i.e., devices that have many properties similar to those of biological neurons, including multiple conductances. A recent review of some of the attempts to create artificial neurons and neural-like devices is here.

• These new advances mean that if you come up with a novel design of a neuron, you might either be able to make an existing neuron work this way using dynamic clamp, or may be able to implement your neuron in a biological system, or even in silico, i.e., in a silicon-based artificial device.

• Here is a current clamp simulation of the hypoglossal motor neurons that you studied in the previous class and earlier in this class:

• Press the button labeled "Spontaneous burster simulation".

• By combining the different conductances we have explored in this problem set, and the many other conductances that have been found so far, nerve cells are capable of vastly expanding their repertoire of behaviors. Nerve cells can be active in the absence of input, and their conductances can allow them to filter and transform inputs in very complex ways. Note that the neuron now bursts repeatedly, even though no current is injected into it. We have changed several conductances in order to do this: the Fast transient potassium conductance, the Calcium dependent potassium conductance, the calcium conductances, and the sag conductance.

• Before you attempt to design your own model neuron, you will need to understand more about how this model neuron works. Please answer the following questions:

• Question 11: How does the value of the Fast transient potassium conductance compare to the original value in the Full simulation? If you re-run the oscillator simulation, but increase (or decrease) towards the original value in steps of 0.1, how does this affect the oscillation?

• Question 12: Press the Spontaneous burster simulation button again. How does the value of the Calcium dependent potassium conductance compare to the original value in the Full simulation? If you re-run the oscillator simulation, but increase (or decrease) towards the original value in steps of 0.1, how does this affect the oscillation?

• Question 13: How do these two conductance contribute to creating oscillatory bursting? You should also refer to some of the other currents in your explanation, and you should test your hypotheses about their role by slightly changing their conductances (one at a time).

• Question 14: Now you are ready to tackle a design problem. Start with the spontaneous burster. Change some of its conductances so that (a) in the absence of input, the model neuron is silent, and (b) while a small amount of depolarizing current (e.g., 0.2 nA) is injected into the neuron for an extended period of time (e.g., hundreds of milliseconds), the neuron switches into a regular oscillatory mode, similar to what you observe in the spontaneous burster.
  • Think through your approach carefully (and write your thoughts in your wiki notebook). What conductances could affect the excitability of the neuron? Test your ideas using the simulation.
  • If your first idea does not work out, make sure to document this, and then reflect on what it means you should do next. Experiments that don't work are as valuable (sometimes more valuable) than experiments that do work.
  • Once you succeed in creating the conditional burster, characterize it. Over what ranges of currents does it work? What happens if you put in large currents? If it stops bursting in response to large currents, what conductances are responsible for this?
  • Make sure you document the process, as well as providing clear "snapshots" of your data, and then carefully describe the final neuron that you have designed.

Recent Developments

• A review by Bruce P. Bean, "The action potential in mammalian central neurons", was published in Nature Reviews in 2007 (Volume 8, pages 451 - 465) which you are encouraged to read here. The following comments are brief summary statements of results reported in that review, which has 206 references to the technical literature up to the time of the review, along with helpful comments about some of the references that the author considers especially important.

• Subsequent studies of the sodium channels that were initially described by Hodgkin and Huxley have suggested that the model that they developed for this conductance is too simplistic.

• Instead, experimental work suggests that activated sodium channels have a higher probability of inactivating, and that the inactivation process is neither independent of activation, nor is it voltage-dependent.

• Investigators have begun to develop more detailed models of actual sodium channel kinetics which take these new findings into account.

• Because of the relative computational simplicity of the Hodgkin and Huxley model of the squid giant axon, the equations that we have presented continue to be used both by modelers and even by current investigators who are not focused primarily on the detailed biophysics of sodium channel function.

• Two new tools have been added to the repertoire of biophysicists studying the role of different ionic conductances in the function of nerve cells: dynamic clamp (see the previous section) and action potential clamp.
  • Given a model of a particular conductance, and how it changes with voltage, investigators can "subtract it out" using dynamic clamp by predicting the current that should be generated through a particular class of ionic channels, and then injecting equal and opposite currents into the nerve cell. Alternatively, a conductance can be added to the neuron using the same technique. Thus, without using drugs (which often have unpredictable or unknown side effects), an entire conductance can be removed or added, and the function of the nerve cell in its absence can be studied.
  • The technique of action potential clamp is equally ingenious: pre-recorded voltage patterns that occur during an action potential are used as the command voltage to a voltage clamp, so that the membrane is "played through" the same set of voltage changes that ordinarily occur, even if specific ionic conductances have been blocked. This ensures that the time course of voltage changes remains unchanged for all the other conductances. Given the time and voltage dependence of the conductances, this makes it possible to understand much more clearly how each functions during a "normal" action potential, even if other conductances are absent.

• In mammalian central neurons, individual neurons show a large repertoire of expression of conductances beyond those identified by Hodgkin and Huxley, so that there may be multiple components (due to multiple distinct ionic channels) responsible for the total sodium, calcium, and potassium ion fluxes across a nerve cell's membrane.

• These different channels, due to their differences in activation and inactivation, and their susceptibility to modulation by chemical released by other neurons, give rise to a very wide range of action potentials and responses to input, which greatly enhance the range of responses of different neurons.

• A few examples will suffice to suggest the complexity and richness of the different responses.

• Specific types of voltage-gated potassium channels (designated Kv3) are extremely effective in generating sharp spikes and short refractory periods, and thus allow neurons endowed with this complement of channels the ability to fire at extremely high rates.

• Calcium influx during an action potential can have a profound effect on the neuron due to the ability of calcium ions to activate calcium-dependent potassium channels, thus leading to more rapid repolarization of the action potential.

• In presynaptic terminals, the width of an action potential can significantly affect the amount of calcium that enters the terminal, and this in turn (as we will learn in a future unit) can have a profound impact on the amount of transmitter released from the presynaptic terminal. Thus, the "weight" or strength of a synapse can be controlled, in part, by action potential width, which in turn may be due to control of specific voltage or calcium dependent potassium channels.