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.