Can someone explain the basis of the membrane potential? (conc gradient + electric + ion interaction

[manohman]

Im having a hard time understanding how the interaction of the concentration gradient, the elctrical gradient, and the existence of the other ions play into and interact with eachother to result in the membrane potential we know and love.

So as i understand it,

-More potassium inside than outside.
-More sodium outside than inside.
-This concentration difference is maintained by the ATP sodium potassium pump (3 Na+ out, 2 K+ in)
-BUT the negative membrane potential difference comes not from the greater number of sodium pumped out compared to potassium but rather due to the fact that the membrane is much more permeable to Potassium than to Sodium (more potassium channels)

-Chloride ions also exist but are small enough to pass through the membrane on their own and follow the electrical gradient so Chloride doesnt really affect the membrane potential on its own? ( confused about this)


So what has me confused is, how these factors interact. The concentration gradient pushes potassium out and sodium in, more potassium out due to greater permeability leads to a negative membrane potential.

BUT there is also the electrical gradient at play, as potassium leaves, it creates a negative potential difference on its own which pulls positive charges back in, but the force of the concentration gradient is stronger than that caused by the voltage difference?

so 1) how do the electrical and chemical forces/gradients interact here
2) How do the electrochemical gradients of different ions interact (like the elctrochemical gradient of sodium interact with that of potassium with that of chloride to give us our ~78 mv).
3) How or why does chloride's ability to flow through the membrane freely not change the membrane potential?


Thanks for any info on this trying to piece it together!

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[Neuroplasticity]

You may want to look up Goldman and his model/equation. He mathematically describes how ions have two types of forces impacting their movement, an electric field and the entropic force of diffusion, based on concentrations. The entropic force acts independently for each type of ion, so the concentrations of one ion don't affect another, but the electric field is determined by the combination of all ions. Chloride is not freely permeable and does change the membrane potential, this simulator on the Goldman setting may also be helpful: The Nernst/Goldman Equation Simulator

 

[desperadoflakes]

The gradient is setup due to the pumping certain cations out of the cell and certain cations into the cell, and then works because of the membrane being selectively permeable only to one of those cations.

Let's pretend we have a cell with equal amounts of both Na+ and K+ on both sides of its membrane, and lets pretend that it has no permeability to either ion. Now, let's start ATPase pumping. Every time you pump, 3Na+ leave the cell and 2K+ come in. After a while, most of your sodium is going to be on the outside, and most of your potassium is going to be on the inside, and the amount of positive charge on the outside will be somewhat greater than the inside BUT this isn't really the major contributor to the negative resting membrane potential. Let's get to that.

Now, in this state, let's add some channels into our cell for the passive diffusion of only K+. Now K+ is free to flow wherever it wants, and we know that stuff flows down its concentration gradient, so K+ will want to leave the cell. This is the 'chemical' part of the electrochemical gradient. So as K+ starts leaving the cell, even more positive charge is going to accumulate on the outside. Eventually, when enough K+ leaves the cell, the build up of positive charge is going to be so great that it will actually begin to repel K+. This means, at some point, even when K+ still wants to move down its concentration gradient, the force of the repellant positive charge on the outside will prevent it from being able to.

So the electrochemical gradient is really two opposing forces. K+ wants to flow down its concentration gradient (inside --> outside), but as it does that the buildup of positive charge on the outside creates an electrical gradient in the opposite direction (outside --> inside). Now, there will be a point where these two forces equilibriate, and there will be no net flow of K+. We can measure the concentration of K+ inside and outside of the cell when that happens, and we can also measure the difference in charge across the membranes, or voltage. It turns out that this is around -70mV.

So the Na/K+ ATPase sets up a concentration gradient for K+ to want to flow from inside to outside. However, it is the action of the plasma membrane (when at rest) to be ONLY permeable to K+ that allows for the balanced electrochemical gradient that at some point allows for the build up of charge that we see. This is what the Nernst potential measures.

Let's play with this. What if we were to suddenly make the membrane much more permeable to Na+ than it is to K+? Well, this is actually exactly what happens during an action potential, when a ton of Na+ voltage-gated channels open. This allows Na+ to now create ITS own electrochemical gradient. But intead of flowing in to out, it goes out to in (again, because the ATPase pump set this gradient up). This will now cause the inside of the cell to be POSITIVE with respect to the outside. If the cell were ONLY permeable to Na+ then we could measure this new voltage difference using the Nernst equation. However, because the cell still retains some K+ permeability from its K+ 'leak' channels, the voltage difference will actually be a weighted average created by both (Ion electrochemical gradient) * (ion permeability/total cell permeability).

The Nernst equation would tell us that if the cell were only permeable to Na+, the membrane potential would be around +60mV. If it were only permeable to K+, the potential would be around -95mV. But the cell is never really only permeable to one ion. So when it's mostly permeable to K+, the potential is -70mV, because a slight amount of Na+ is leaking in (or maybe anions are leaving?). When it's mostly permeable to Na+, like at the top of the action potential, the voltage is around +35mV.

This leads to all sorts of MCAT-style questions about what may happen to the voltage if you change the number of K+ leak channels, or if you change the number of Na+ v-gated channels, etc. etc.

Hope that makes sense!

 

[manohman]

The gradient is setup due to the pumping certain cations out of the cell and certain cations into the cell, and then works because of the membrane being selectively permeable only to one of those cations.

Let's pretend we have a cell with equal amounts of both Na+ and K+ on both sides of its membrane, and lets pretend that it has no permeability to either ion. Now, let's start ATPase pumping. Every time you pump, 3Na+ leave the cell and 2K+ come in. After a while, most of your sodium is going to be on the outside, and most of your potassium is going to be on the inside, and the amount of positive charge on the outside will be somewhat greater than the inside BUT this isn't really the major contributor to the negative resting membrane potential. Let's get to that.

Now, in this state, let's add some channels into our cell for the passive diffusion of only K+. Now K+ is free to flow wherever it wants, and we know that stuff flows down its concentration gradient, so K+ will want to leave the cell. This is the 'chemical' part of the electrochemical gradient. So as K+ starts leaving the cell, even more positive charge is going to accumulate on the outside. Eventually, when enough K+ leaves the cell, the build up of positive charge is going to be so great that it will actually begin to repel K+. This means, at some point, even when K+ still wants to move down its concentration gradient, the force of the repellant positive charge on the outside will prevent it from being able to.

So the electrochemical gradient is really two opposing forces. K+ wants to flow down its concentration gradient (inside --> outside), but as it does that the buildup of positive charge on the outside creates an electrical gradient in the opposite direction (outside --> inside). Now, there will be a point where these two forces equilibriate, and there will be no net flow of K+. We can measure the concentration of K+ inside and outside of the cell when that happens, and we can also measure the difference in charge across the membranes, or voltage. It turns out that this is around -70mV.

So the Na/K+ ATPase sets up a concentration gradient for K+ to want to flow from inside to outside. However, it is the action of the plasma membrane (when at rest) to be ONLY permeable to K+ that allows for the balanced electrochemical gradient that at some point allows for the build up of charge that we see. This is what the Nernst potential measures.

Let's play with this. What if we were to suddenly make the membrane much more permeable to Na+ than it is to K+? Well, this is actually exactly what happens during an action potential, when a ton of Na+ voltage-gated channels open. This allows Na+ to now create ITS own electrochemical gradient. But intead of flowing in to out, it goes out to in (again, because the ATPase pump set this gradient up). This will now cause the inside of the cell to be POSITIVE with respect to the outside. If the cell were ONLY permeable to Na+ then we could measure this new voltage difference using the Nernst equation. However, because the cell still retains some K+ permeability from its K+ 'leak' channels, the voltage difference will actually be a weighted average created by both (Ion electrochemical gradient) * (ion permeability/total cell permeability).

The Nernst equation would tell us that if the cell were only permeable to Na+, the membrane potential would be around +60mV. If it were only permeable to K+, the potential would be around -95mV. But the cell is never really only permeable to one ion. So when it's mostly permeable to K+, the potential is -70mV, because a slight amount of Na+ is leaking in (or maybe anions are leaving?). When it's mostly permeable to Na+, like at the top of the action potential, the voltage is around +35mV.

This leads to all sorts of MCAT-style questions about what may happen to the voltage if you change the number of K+ leak channels, or if you change the number of Na+ v-gated channels, etc. etc.

Hope that makes sense!

Im gettng back to this so late but i have to say this was an amazing explanation.

one question you said when its only K its nornally -70 at first. But im guessing you meant when its mostly K+ (like you say later on).

Why would sudden Chloride permeability not affect the resting membrane potential? doing a berkley problem where they say it wouldnt affect

 

[desperadoflakes]

Im gettng back to this so late but i have to say this was an amazing explanation.

one question you said when its only K its nornally -70 at first. But im guessing you meant when its mostly K+ (like you say later on).

Why would sudden Chloride permeability not affect the resting membrane potential? doing a berkley problem where they say it wouldnt affect

It’s been a while since I took the MCAT so take it with a grain of salt, but if you go ahead and calculate the Nernst for potassium with an intracellular [K] of 400mM and extracellular of 20mM, the Nernst potential comes out to about -76. The resting membrane potential is -70 because almost all of the cells permeability is in the K leak channels. Of course, there are some other leak channels that are making the actual potential a little more positive.

I would say just don’t worry about resting chloride lol

 

[manohman]

It’s been a while since I took the MCAT so take it with a grain of salt, but if you go ahead and calculate the Nernst for potassium with an intracellular [K] of 400mM and extracellular of 20mM, the Nernst potential comes out to about -76. The resting membrane potential is -70 because almost all of the cells permeability is in the K leak channels. Of course, there are some other leak channels that are making the actual potential a little more positive.

I would say just don’t worry about resting chloride lol

I see. Thanks man. Hope the MCAT went well! IM sure it did!