Action Potentials and Overall Membrane Excitability

I covered a number of excitable membrane topics in the last post, but this post clears up a few more.  Again, please allow the conversation to continue as needed as sometimes others questions inspire questions of your own.  If you are embarrassed regarding asking a question, please don't be, but feel free to post anonymously and so we can all work together to determine the answers!  Any question that pops into your head is one that someone else undoubtedly has as well, if not, then I am SURE it will challenge me and that is one of the most exciting parts of my day :)!

1.  In the CTL innervation meeting yesterday, there was a physio question similar to the one we did in class yesterday regarding the -60 mV. I was confused as to why K+ & Cl- (ans choice D) was incorrect and ans choice B (only Cl-) was correct. Could you please explain this?

For those of you not familiar with the question this is it:

The figure below represents a solution system at 37^oC with a membrane separating the two compartments.  What ion or ions was the membrane permeable to in order to create a membrane potential of approximately -60mV on the right with respect to the left?

A) Na⁺

B) K⁺

C) Cl^-

D) Ca²⁺

E)  Equally permeable to K⁺ and Cl^-

F)  Equally permeable to K⁺ and Ca²⁺

As I had mentioned in class when we did the turningpoint question #3, I could give you a question that gave you the actual membrane potential on one side of the membrane with respect to the other (exactly the question above).  Therefore, if in this system you record that it is -60 mV on the right with respect to the left, you are asked to determine the permeability of which ion would cause that.  Now, you need to use the Nernst Equation.  You can either calculate the equilibrium potential for all of them or simplify it to be only those ions that would cause the right to be negative with respect to the left (K+ or Cl-).  If you calculate them out given the concentrations given (please do this...it is good practice) you determine that EK = -120 mV on the right with respect to the left and ECl = -60 mV on the right with respect to the left.  Therefore, if you were only permeable to Cl- you would record the system to be -60 mV on the right with respect to the left.  

If you were equally permeable to these two ions, as stated in answer E), the membrane potential would be a combination of their equilibrium potentials of equal value from both, so half-way between their two equilibrium potentials (halfway between -120 mV and -60 mV) or -90 mV, there fore E) is not a correct answer.

There is, however, a second correct answer for this question besides B).  Can you determine which one it is? (Caution, that the most updated version of this question has been changed to have only one correct answer, but the version above has 2 correct answer choices).

Speaking of CTL questions, I had a question regarding their location on the G-drive.  CTL questions that are distributed during the cognitive skills sessions for the week are posted on the G-drive on Friday afternoons.  Now, I know that prior to this many of you have access to these questions from students in past semesters.  These are the same questions, however, they will contain any editing that needs to be done to the questions and possibly a few additional questions for that semester (when we recognize incorrect answer choices or other editing needs these are changed as best as possible).  They are available in the CTL folder under Student Resources and within the Sem 1 folder: G:\CTL, Centre for Teaching and Learning\student resources\sem 1.

2.  Also in today's lecture you mentioned something about the funny bone and the ulnar nerve and the action potential. I didn't get the connection between these things. Please clarify.

The second turningpoint question asks about the propagation of action potentials (AP).  The AP typically is initiated at the axon hillock and initial segment of the axon (I checked with Dr. Yin and we both agreed that voltage-gated Na+ and K+ channels are located in both places and they both contribute to the initiation of the action potential) which is where the summation of the charges coming into the cell body occurs and the membrane itself is brought to threshold and an AP is fired.  The initial depolarization of this AP spreads away from that space back into the cell body and to the next segment of the axon.  The depolarization in the cell body simply dissipates away while the depolarization spreading down the axon initiates the opening of the next voltage-gated Na+ channel causing the AP to propagate down the axon.  Therefore, typically under normal circumstances where the AP is initiated at the axon hillock, it will only propagate down the axon.  

However, if you somehow (which happens when you hit your 'funny bone' or unlar nerve at your elbow) provide a stimulus to the axon in the middle of the axon that brings that momentary point to threshold (or above), it will trigger an action potential.  This AP then causes depolarizing charges to come into the cell and diffuse away from that space.  Now that diffusion will spread away from that point and activate voltage-gated Na+ channels all around the area.  As voltage-gated Na+ channels exist all around the area, if there was not an AP coming down the axon, it would activate Na+ channels both anteriorly and posteriorly from the point of stimulation and the AP would continue to propagate away from that point of stimulation being followed by the regular refractory periods.  The AP would, in other words, propagate towards your fingers and back toward the cell body in the CNS.  This is a pathological condition, but has happened to each of us so we can understand it as a common potential brief pathology.  It is not 'normally' what happens because 'normally' APs are initiated at the AP, but if they were initiated somewhere else and there was not a cell body or another large diffusion space lacking voltage-gated Na+ channels to allow for the charges to dissipate away into, that AP would absolutely be initiated and propagate given the channels needed for its propagation and the ions involved.

Now, another challenge to really test if you understand action potential physiology:  If somehow two action potentials were traveling down an axon towards each other, what would happen when they meet?

3.  For the voltage gated Na+ channels, is it only time that inactivates the channels once they have been activated by depolarizing charge? Could it also be a change in the membrane potential caused by the influx of Na+ ions that could attribute to the inactivation of the channels?

That's a great question.  As with most things we know about physiology, much of it comes from previous research.  Where the research stands now is that if voltage-gated Na+ channels are open long enough they will become inactivated, regardless of a change in membrane potential.  Studies were done where there was not a gradient for Na+ movement, and the channels still became inactivated, so they concluded that it was due to the time that they were open, not the change in membrane potential.  The change in membrane potential DOES, however, cause the initial opening of the Na+ channel (depolarization) and the re-setting of the inactivation gate to cause the channels to go from inactivated to closed (repolarization) (and remember that step is critical in order for the channels to open again).

4. In regards to action potential, is it true that sodium uses only voltage gated ion channels to get into the cell, and potassium uses both a voltage gated ion channel and potassium leak channels?  And if for some reason the potassium voltage gated channels were defective, potassium could still leak into the cell via pores, just at a much slower rate?

In regards to the action potential of a neuron we are discussing voltage-gated Na+ channels and voltage-gated K+ channels that allow for the movement of Na+ into and K+ OUT OF the cell down their electrochemical gradients to allow for the depolarization and repolarization of the membrane during the action potential.  The resting membrane potential, however, is maintained by the potassium leak channels and some permeability to Na+ and a tiny bit of permeability to Cl- and Ca2+ through pathways not yet fully defined.  Therefore, at rest you have K+ leaking through the leak channels keeping the membrane potential close to the equilibrium potential for K+ and the permeability of the other ions keeping the membrane potential somewhat depolarized from that equilibrium potential.  However, if you had an action potential that allowed for the movement of Na+ into the cell depolarizing the membrane and then the voltage-gated K+ channels were defective, your membrane would not repolarize as typical.  Over time, you would get a slow depolarization as the membrane re-established its resting membrane potential with the help of K+ moving through the potassium leak channels, but it would take a much longer period of time.  Remember, during this repolarization period the voltage-gated Na+ channels are re-set from inactivated to closed to be ready to open again (and the absolute refractory period lasts until enough of those channels are re-set), so it would cause a very prolonged absolute refractory period and would be a pathological condition.

5.  On the third slide in today's lecture (and a few other ones) the shorter arrow for Cl seems to indicate that the concentration gradient is pulling the Cl out since it is higher intracellularly. The longer arrow should therefore mean that the electrical gradient is pulling the Cl back in. I though that the electrical gradient will be weaker than concentration. If that's the case, the lengths should be reversed. I don't know if I'm totally misunderstanding this. I'm comparing it to K and I guess that's why I am getting confused. Can you please explain? Thank you

This question brings up a great point.  ALL IONS move down their ELECTROCHEMICAL gradients.  Remember, that is a gradient that is the combination of the electrical gradient (difference in charges) and the chemical gradient (difference in molecule concentrations).  As the electrochemical gradient is the sum of those two gradients, it will be in the same direction as one of those two gradients and sometimes in the same direction as both of those gradients.  Now, in the slides depicting the resting membrane potential, the lines for Cl- are indeed depicting the chemical gradient going into the cell (remember the concentration for Cl- is high OUTSIDE the cell and low INSIDE the cell) and the electrical gradient going out of the cell (since the inside of the cell is negatively charged and so is the Cl- ion) and that the chemical gradient is greater than the electrical gradient in that case.  Now, remember from the end of the Membrane Potential lecture I stated that this is not always the case and sometimes the concentrations of Cl- are such that the chemical gradient is less than the electrical gradient and so the size of those arrows would be reversed.  

Now, the sum of those two gradients makes up the electrochemical gradient, so if the inside of the cell was -70 mV and the equilibrium potential for Cl- was -75 mV, then the electrochemical gradient for Cl- would be into the cell (to bring the membrane from -70 mV to -75 mV, its equilibrium potential) and in that case the chemical gradient would be greater than the electrical gradient.  If, however, the membrane potential inside of the cell was -70 mV and the equilibrium potential for Cl- was -65 mV, then the electrochemical gradient for Cl- would be out of the cell and the electrical gradient would actually be greater than the chemical gradient.

6.  I have a question regarding slide number 15 of Action Potentials. At the repolarization stage, the K channels are closed; But what happens with the Na channels?--do they close or are they just inactivated? First you said that they are inactivated, but still open. But then in your explanation of step 6-hyperpolarization, it says that the "open" gate closes and the "inactivation" gate also closes. But weren't they closed at the end of repolarization?

Please refer to slides 15 and 16 for this question.  If you follow along the figure of the action potential changes in membrane potential, under that picture there is a picture that shows you what is happening to the voltage-gated Na+ and voltage-gated K+ channels during the AP.  At the beginning of the repolarization phase (the peak of the AP), the Na+ channels become inactivated while simultaneously the K+ channels become open.  This allows for the movement of Na+ into the cell to stop and the movement of K+ out of the cell to start and the membrane repolarizes.  Na+ channels that are inactivated do not allow for the movement of Na+ across the membrane, but are different from being closed (see slide 16).  Voltage-gated Na+ channels can go from closed to open (by a depolarization of the membrane) and back again if that happens quickly, but once they are open long enough they will become inactivated.  Now, once they become inactivated they must go to a closed state before they can open again.  That inactivation to closed happens with a repolarization of the membrane that happens by the opening of the voltage-gated K+ channels and the movement of K+ across the membrane.

 

7.  Could you also please explain to me the reasoning behind the answer choice for practice problem number 10 from the Action Potential lecture? I understand why current would flow from outside to inside, but why would they move away from that region?  

The practice question is: 

10.  If a ligand-gated channel permeable to both sodium and potassium was briefly opened at a specific location on the membrane of a typical resting neuron, what would result?

  A.  Local currents will flow from the outside to the inside of the membrane and away from that region

  B.  Local currents will flow from the inside to the outside of the membrane and away from that region

  C.  Local currents will travel without decrement all along the cell’s length

  D.  A brief local hyperpolarization of the membrane would result

  E.  Fluxes of sodium and potassium would be equal, so no local currents would flow

If a channel were equally permeable to both Na+ and K+, then when it opened the potential that that channel would want to bring the membrane to would be a membrane potential halfway between the equilibrium potentials for both ions (ex. if ENa = +60 mV and EK = -90 mV, then the potential for that channel, its 'equilibrium potential' would be -15 mV).  Therefore, the electrochemical driving force for that channel would be from the resting membrane potential (~-70mV) to that channels potential or -15 mV and would cause the movement of + charges to move into the cell. Now, remember that the movement of ANY ion (or molecule) for that matter passively is down its electrochemical gradient (or concentration) and with the movement of ions into the cell, they would want to get as far away from their 'like' molecules as possible and would therefore move into the cell through the channel, but would then move away from the region that they entered continuing to increase the entropy of the system.

We will see that this question comes into an important role in the next lecture as this ligand-gated channel is exactly what is continuing the communication at a chemical synapse on the postsynaptic side and allows for the initiation of graded potentials.

Membrane Potential Student Questions

I realize that this subject is difficult.  I also realize how tempting it is to simply decide that there won't be very many exam questions on them and so you do not need to learn them.  I must caution you, however, in that this is a fundamental concept and will come back up in skeletal muscles, cardiac muscles, and in the neuro unit next semester.  Here are a number of confusions of your classmates, but please feel free to continue the discussion below so as to ensure that we all understand these concepts as best as possible!

1.  I know that you had said that during these calculations we should make a estimate, although in class it was very low compared to its actual value, -log30 = -1.47 and you used -1.2, when i approximated 1.2 x 61, I got about -70. I also know you said that on the test you will use good numbers to work with, but I wanted to clarify this with you and see what my best approach will be for these kinds of problems.

This is a perfect example of how we need to use accurate approximations.  I exemplified to you a not quite correct approximation.  Indeed -log (30) is about -1.47 (not the 1.2 that I wanted it to be).  Therefore, the -90 mV approximation for K+ is more accurate if you use these numbers.  Approaching these types of problems how we did in class will allow for close enough approximation to allow for accurate results of a question of this sort.  I could not give you numbers to calculate that were not approximate-able and answer choices that required a calculator on the exam, however, and your answer choices would be something like -30 mV, -90 mV, and -120 mV or something so that even a close approximation would get you the correct answer.  I think that would be dishonest and wrong, and therefore approximating is your only true way of being able to do math problems on an exam.

2.Would it be right to think about Equilibrium Potential in this way:

If you had a high number of K+ inside the cell and a low number outside the cell, the K+ ions would want to move from higher concentration to lower concentration.  But when the K+ moves out of the cell, it makes the inside of the cell more negative, and this electrical drive starts pulling back some of the K+ ions to reestablish the electrical difference caused by the movement of K+ out of the cell.

Indeed, that would be an accurate way to think about the equilibrium potential.  You could also say that the moment that K+ moves across the membrane it turns around and causes a force on the rest of the K+ positive charges not to cross the membrane establishing an electrical difference.  The only missing piece, however, is that if we are discussing equilibrium potential, it is important to mention that it is the potential difference (difference in charges across the membrane) where that chemical gradient is equal and opposite to the electrical gradient.  

Now, from no permeability (or 0 mV), the chemical gradient always starts the movement, but if we start from a given membrane potential (ex. -50 mV), the movement of the ion would be down its electrochemical gradient which is the gradient created by the net of the chemical and electrical drives from the given membrane potential (ex. if EK = -90 mV then the chemical gradient is still from inside to outside, while the electrical gradient is for the + charges to move from outside to inside, but the electrochemical gradient (the net) would be to move from -50 mV to -90 mV, and therefore be from inside to outside of the cell).

3. I was just wondering what you wanted us to know about circuitry, and how it relates to the cell. Specifically, would you expect us to calculate current/resistance/voltage using Ohm's law, or do we just need to be able to use the chord conductance equation? 

I typically do not answer 'what do we need to know' questions, because truthfully I am not an MD, so there may be some of this that, although I have not been told by anyone, you may still utilize in practice.  However, I will not be testing you on Ohm's law.  I do expect you know the Nernst Equation by heart, and can use the Goldman-Hodgkin-Katz and Chord Conductance Equations.  The electrical circuitry was simply allowing the set-up of membrane potentials and how your biological system of electricalness (your neurons) are just like the electrical systems that you have learned about in physics and have seen throughout your daily lives when using electricity. 

4.  Just a question about one of the captions from the slides:

"It is important to note, though, that the pumping activity of the Na-K ATPase is essential in maintaining the ion concentration gradients across the membrane.  Without this pump, the gradual leak of K⁺ out of the cell and Na⁺ into the cell would slowly dissipate the ionic gradients, resulting in a membrane potential of zero."

If there is no ATPase and the membrane is permeable to both K+ and Na+ then the higher [Na+] outside would go down its electrochemical gradient trying to push the Vm to +60mV whereas the K+ would leak out trying to push Vm towards -90mV. They would average out to -15mV not in my opinion to a potential of 0.

Can you please explain?

That would be true if you were EQUALLY permeable to both Na+ and K+.  However, that is not the case.  At rest you are actually more permeable to K+ than to Na+ (due to K+ leak channels), therefore, you would have more movement of K+ out of the cell trying to bring the membrane potential to its equilibrium potential.  The movement of Na+, however, prevents this from happening and therefore the [K+] would initially build up outside of the membrane.  If this continued, however, the equilibrium potential for K+ would depolarize (become less negative) due to the decrease in concentration gradient.  This would similarly happen for Na+ with its equilibrium potential becoming less negative.  Eventually (over a LONG period of time), the concentration of K+ and Na+ ions would continue to move trying to get the membrane to their equilibrium potentials until finally there would be no difference in concentration across the membrane and the concentrations of Na+ and K+ on both sides of the membrane would be equal.  This would cause a membrane potential of 0 mV in that case.

5.  I was working on my study product for today's lecture and I had a question regarding the Goldman-Hodgkin-Katz Voltage equation. On the side notes of the powerpoint slides, you mentioned

Notice that in Goldman equation, the [Cl^-]_i is put on top the equation because Cl^- has negative charge and movement of an anion across the membrane causes the opposite changes on membrane potential compared with a cation.

But on the equation that you provided in the slide, [Cl-]i is still at the bottom, like all the other ions. 

Should this be flipped? If so, does it also have to be flipped when we calculate for the equilibrium potential of Cl- with the Nernst Equation.

I have received A LOT of questions about the GHK Equation.  Now, I could write this many ways, and remember that logs have the arithmetic properties of manipulation where log (A/B) = -log (B/A).  So, because Cl- is a negatively charged ion, I could put it into the equation as [Cl]o/[Cl]i as we have seen the concentration for the other ions in which case I need to put a negative sign out front (as seen in the slides), or I could switch the denominator and write it as [Cl]i/[Cl]o and remove the negative sign.  They are actually the exact same thing.  

I have also gotten questions regarding the Chord Conductance equation.  It is indeed just another way of calculating the resting membrane potential.   It utilizes the conductance of each ion instead of the permeability of each ion relating the membrane potential to the ability of a charge to move across the membrane rather than the molecule.

6.  Nernst Equation Calculation.

I received a request to calculate out the Nernst Equation from its original values:

Using , , (assuming body temperature) and the fact that one volt is equal to one joule of energy per coulomb of charge, the equation

can be reduced to

 

(sometimes Wikipedia can be very helpful if you know what you are looking for :))

 7.   The chemical gradients I am fine with but this electrical gradient is confusing me. 

This is an important concept of this lecture.  Now, chemical gradients seem basic to us because we've been learning about them for so long.  It is the driving force for a molecule moving down its concentration gradient.  However, electrical gradients confuse us for some reason.  Just like a molecule moves down its chemical concentration gradient, SO TOO does an ion want to move away from areas of like-charge (lots of + or -).  Therefore, you can have an electrical gradient as well.   The important point is to understand how these two gradients can work together and/or apart.

8. One of the thought questions asks: 1.Contrast the abilities of intracellular and extracellular fluids and membrane lipids to conduct electrical current. 

I am not sure how to answer this. Just the fact that the membrane lipids don't contribute to the conduction of signals, and the other two kind of work together in order to create a potential difference?

 

Indeed membrane lipids DO contribute to the conduction of signals.  Remember that the membrane acts as a capacitor (A device used to store an electric charge, consisting of one or more pairs of conductors separated by an insulator), therefore the membrane allows for the electrical charges TO be separated across the membrane.  Therefore the membrane plays an INTRICATE role in separating charges in the ICF and the ECF and allowing for the difference in charges (the membrane potential) to exist.  The charges in the ICF and ECF are, therefore, separated across a membrane and are what make up the charges that actually create the membrane potential and the initiation of an electrical current.

 

9. In the notes section of the lecture for today in slide #23, you wrote about Calcium having to move to produce a +127mV membrane potential, and chloride having to move to produce a -88 mV potential. Where are these potentials coming from? And later you ask: Thought Problem 1:  The instant membrane potential is +10 mV when a potassium channel opens.  Will potassium influx or efflux?  What would be the driving force?

 This is in relation to what? The -90 mV potential that K likes, in which case K would move outside the cell to answer the above question? Or the -70 mV that the cell likes, in which case again the K would move outside yet again, to get the potential to -70?

 

Another way to ask that same question:  If the membrane potential was at +10 mV, and you made the membrane permeable to potassium, which direction would it go and what would be the driving force?

Now, remember from that slide, the driving forces are either electrical or chemical.  Ions move ALWAYS down their electrochemical gradient, but as this gradient is the sum of an electrical and a chemical component, the movement of the ion will then be in the same direction of at least one of these driving forces and will have a mV size.  So, for the question above, if the equilibrium potential for K+ was -90 mV (and given the context we can assume that), and the membrane was at +10 mV, which direction would K+ have to move to bring the membrane from +10 mV to  -90 mV? (out)  Is that movement in the same direction as the chemical driving force?  (yes) Is that movement in the same direction as the electrical driving force? (yes) What is the size of this movement? (+10 mV - -90 mV = 100 mV driving force).

10. 6.  In a normal cell membrane, if membrane permeability to K⁺ was reduced to zero, V_m would:

            A.  The membrane potential will become more positive (depolarize) until it reaches zero.

            B.  Become equal to the Na⁺ equilibrium potential, E_Na.

            C.  Become more positive but would be less than E_Na.

            D.  The membrane potential will become more negative (hyperpolarize).

I picked B, but the answer was C. Why would it not reach the equilibrium potential for Na?

Is the cell ONLY permeable to K+ and Na+?  If so, then if you eliminated the permeability for K+, the membrane potential would go to the equilibrium potential for Na+, but if the cell is actually permeable to other ions as well (ex. Cl- and Ca2+), then the membrane potential will not go to the equilibrium potential of another ion, but to a new balanced membrane potential that is due to the concentrations of those ions across the membrane with respect to their relative permeabilities.  If this troubles you, try putting in some relative permeabilities into the Goldman-Hodgkin-Katz equation (ex. 0.7 for K+, 0.2 for Na+, and 0.05 for Cl- and Ca2+, then remove the permeability for K+ and make it 0...)what happens to the membrane potential?

11. 15.  BONUS:  A woman with sever muscle weakness is hospitalized.  The only abnormality in her laboratory values is an elevated serum K+ concentration.  Why does the elevated serum K+ causes muscle weakness?

             A.  The resting membrane potential is more negative than normal

            B.  The K+ equilibrium potential is more negative than normal

            C.  The Na+ equilibrium potential is more negative than normal

            D.  Na+ channels are inactivated by a movement in the membrane towards less negative values

            E.  K+ channels are inactivated by a movement in the membrane towards less negative values

I picked E over D. No idea why one would be more correct over the other.

First note that BONUS questions are questions with material not yet fully covered.  If you ever have trouble with a BONUS question, sit on it for a bit because you WILL get the material to answer it, we just have not covered it yet.

 

However, as you will see in today's lecture, K+ channels actually do not become inactivated, however a K+ equilibrium potential that is depolarized (which happens with increased extracellular [K+]) will cause the resting membrane potential to become depolarized and limit the ability for the membrane to repolarize after an action potential.  This repolarization phase is required for proper function of the Na+ channels to recover from inactivation.  Therefore, this depolarization of the membrane causes the Na+ channels to get stuck in an inactivated phase no longer allowing action potential propagation.  The action potential's role in skeletal muscle contraction, however, will be covered next week.