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Membrane potentials - part 2

Find out how a cell that is permeable to one ion can become charged (either positive or negative) if there is permeability and a concentration gradient. Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.

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  • blobby green style avatar for user stef
    At you said you don't know what 'V' stands for. Isn't it referring to Voltage?
    (27 votes)
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  • blobby green style avatar for user Morgan
    I am curious about one thing. If the resting concentration of K+ inside the cell is 150mMol/L and is 5 mMols/L outside the cell, then why is the membrane potential negative? Shouldn't it be positive since there are more K+ inside than outside at any given time? Thanks!
    (4 votes)
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    • leaf green style avatar for user Anurag Singh
      The K+ on the inside and outside are coupled with negatively charged proteins and therefore the cell and the outside are neutral. Now when the concentration gradient drives K+ outside, the cell only allows K+ to get outside as (certain) cell gates are only permeable to potassium (specifically) but their partners which are the larger (negative) protein molecules, can't get through the gates.
      So , as the positively charged K+ cations move outside , the negatively charged protein molecules remain on the inside of the cell.
      Therefore the cell ends up being more negatively charged than its surroundings and thus gets a NEGATIVE POTENTIAL!
      (23 votes)
  • blobby green style avatar for user jboulahoud
    In the equation, you said the constant is 61.5. My teacher has been using 58. Which is correct?
    (3 votes)
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    • leafers ultimate style avatar for user felix.alexandre.lavoie
      The constant Rishi is using is based on the Nernst Equation (google/wikipedia it), which can be calculated by ''(R*T)/(F)'' (assuming you are using the natural log, otherwise you add log10(2.72) in the denominator, which you have to in Rishi's case) While R & F are constants, the temperature, T in kelvin, will actually change your constant. By plugging in different values for temperature, you can find out that in fact, both Rishi and your teacher are correct, although at different temperatures. Rishi used 37 Celcius (310.15 Kelvin) for his calculations, your teacher used 20 Celcius (293.15 Kelvin) for his. At thus, Constant(310.15)=61.537mV, while Constant(293.15)=58,164mV.

      TL;DR Rishi is right because he did the calculations at body temperature, which would be the most likely temperature conditions at a cell membrane of a live human being. Therefore 61.5mV is correct. This is why everyone should state their assumptions/conditions under which they answer their problem, to allow reproducibility of their data by other researchers.
      (13 votes)
  • piceratops ultimate style avatar for user AleksandrHovhannisyan
    Literally nobody has been able to answer me this one question: if Potassium is always driven out by leak channels, why is the interior concentration of Potassium said to be higher than the exterior?
    (2 votes)
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    • piceratops ultimate style avatar for user ILoveToLearn
      Higher K+ charges are on the interior of the cell than the outside in the "starting" scenario, so the K+ flows out through leakage channels. The concentration gradient drives K+ out, because in the same starting scenario the interior of the cell is more positive than the outside.
      This outflow leaves anions in the cell, which re-attracts the K cations. This all stabilizes net-net at about -92mV, the equilibrium potential for K+ when the cell is only permeable to K+.
      Hopefully that all made sense to you, and even more hopefully, you got your question answered.
      (8 votes)
  • leaf green style avatar for user Courtney Smith
    At you say that if there's a concentration gradient but no permeability, then there will be no membrane potential because there's no way for the ions to leave. Why would that mean there's no membrane potential if there'd still be a voltage difference (as indicated by the concentration gradient)?
    (6 votes)
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  • blobby green style avatar for user Adrian mendez
    At , Rishi mentions the the voltage created through membrane potential of ions. If the equation for it is a constant x LN ([out]/[in]) , then CL-, which has a negative potential, should have a higher concentration inside the cell than its surroundings. Wouldn't this want CL- to flow out of the cell then due to concentration gradient?? (Rishi states it flows inwards)
    (5 votes)
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    • blobby green style avatar for user Ryan Tuley
      There is actually a higher concentration of CL outside the cell than inside the cell in the body, thus creating a "desire" for the ion to move from the higher concentration, outside, to a lower concentration, inside. Hope this helps!
      (1 vote)
  • blobby green style avatar for user Sadullah Samadi
    It is a great video and just to let you know that the speakers says where the Vm come from as there is no letter V in the Membrane Potential....I would say that V is for Voltage which is potential and M is for membrane.
    (3 votes)
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  • blobby green style avatar for user rithikas8005
    at 8.20, when Dr. Rishi tells us the concentration gradients of each of the ions, he tells us about the direction of flow of ions. Does the sign of the membrane potential (positive or negative) give us the direction of flow of ions?
    (3 votes)
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  • marcimus pink style avatar for user Sammy Rea (>")> <("<) <3
    Is the goal of the cell to get back to 0mV ? or does it want to say at -92mV?
    (1 vote)
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    • leaf green style avatar for user andyman310123
      The goal of the cell is to maintain a membrane potential that is between -70mV and -90mV, this potential is used for a variety of things, for example the depolarisation of nerve cells or muscle cells!

      Another example is the filtration of ions in the kidneys: Here the negative membrane potential is used to attract Na+ ions and pull them into the cells, along with other ions and water!
      And just so you know, our cells work hard on maintaining this membrane potential, in most cells the Na+/K+ ATpase (the 2K+ in / 3 Na+ out pump he drew) uses as much as 1/3 of the entire energy that is used by our cells!
      (4 votes)
  • duskpin ultimate style avatar for user MS17155 - Shivanshu Siyanwal
    Why can't anions go through those channel proteins? Does K+ ions return to the cell via those same channel proteins or the Na+/K+ pumps?
    (1 vote)
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    • leaf yellow style avatar for user Jake Masterson
      Potassium can get into the cell in a couple ways, those channels allow a passive entrance/exit of Potassium, but they only allow Potassium through. Their chemical makeup doesn't allow the anions to use them.

      The Sodium-Potassium pump also moves the Potassium in via active transport.
      (4 votes)

Video transcript

So in the last video we talked about how you have a higher concentration of potassium on the inside-- around 150 millimoles per liter --than you do on the outside-- let's say around five millimoles per liter. Just to recap some important points we brought up, we said that essentially what happens is that you have these potassiums that are bound to little anions that are the green dots there. And because the concentration gradient is going to want to make the potassium leave the cell, it will, and so it'll leave the cell. Let's say this little fellow will leave the cell here, and he'll end up on the outside. So by doing that he leaves that anion all by itself. And if this continues to happen, then these anions create this negative charge. And we can actually figure out exactly what that negative charge is. It turns out that that negative charge is going to attract back the potassium. We said that this potassium, then, is going to want to swim back inside to be closer to that negative charge. And this is that interesting idea, the idea that K leaves behind a negative charge. And then it comes right back and wants to be by that negative charge. And the amount of negative charge that's going to offset the concentration gradient is around negative 92, so let me write that in now. So negative 92 is the amount we know that we need to offset the concentration gradient. That's where we left off. And now I want to do a little thought experiment. Let's say that we come at this cell with a little injection full of, let's say, some positive charge. And try to ignore the ridiculousness of what I'm saying, just for the moment. Let's just focus on the positive charge, the fact that I'm going to pour a bunch of positive charge into this cell. And let's assume that we don't know exactly where this is coming from, but that this positive charge is-- essentially, what it's going to do is it's going to make my cell not negative 92 anymore. It's going to make it more positive than it is. Let's say I make it, let's say, halfway back to zero. So instead of negative 92, it's negative 46 millivolts. So this is the new membrane potential, and our cell is still just permeable to potassium. And that's really important. It's only permeable to one ion. That's potassium. So what's going to happen? Well, these potassiums-- these little guys right here --they're going to notice that the charge is actually not drawing them back as strong as it was before. So this potassium might see that, and it might leave. So more potassium basically starts leaving the cell. And if more potassium is leaving and going on the outside, then you have more of these little anions that are left behind. And the process continues. So these anions say, well, if we're off by ourselves, we're going to contribute to this negative charge. We're going to add to it, just as it did before. And that negative 46 is quickly going to go down again. It's going to slide back down. And the question is, how far does it slide down? Well, it goes back to the equilibrium point. And so if we said negative 92 is what you need to make this yellow squiggly attraction-- the membrane potential-- equal the concentration gradient, if that's what's needed, then it will slide back down to negative 92. So think about that for a second. It's pretty powerful stuff. You can do all sorts of funky things to this cell. You can add positive charge or negative charge. And as long as you maintain two things, two important things, one of them being the concentration gradient-- so one is this concentration gradient of 150 versus just five. That's one thing. And the other is the permeability to only potassium. As long as you maintain the permeability, you'll get back to negative 92. Let me even hammer this point harder by showing you a little diagram. So let's say we have a concentration gradient over here, and I also have permeability over here. And this is permeability to potassium. OK? And assuming that we only have permeability-- so assume-- I'll write that very clearly --the cell is only permeable to one ion. So assume only one ion for this permeability. So if you have, let's say, permeability yes and permeability no, and you have concentration gradient yes and concentration gradient no, then what do you get exactly? So let's say you have four possibilities here. And let's say we have no concentration gradient and no permeability. Would we get a membrane potential? Well, no, because the potassium would never have a way of leaving in the first place. And it would have no desire to leave. Now what if you have concentration gradient-- so you have the desire to leave-- but you don't have a way for that potassium to actually leave the cell. Well, again, you don't actually have any membrane potential. And the same is true if you have a permeability, but you have no concentration gradient. Then the potassium, again, has no desire to actually leave. And then finally, if you have permeability and a concentration gradient, then you actually get down to negative 92 millivolts. So the concentration gradient is when I use the word desire. Does the potassium have a desire to leave? And permeability is does it have a means? Does it have a way to leave? So these are the two things to think about when you're thinking about whether you would create a membrane potential or not. So if we have that setup-- let's actually move down a little bit and make some space and actually talk about how you actually get your negative 92. Where in the world does that number exactly come from? So there is a formula, and that formula is-- I'm going to write it out over here. It's Vm, and all that means is membrane potential. Now, if you're like me, the first thing you notice is that there's no V. There's no letter V in the word membrane or potential. So how do they come up with that? And I don't know the answer to that. I don't know where the V comes from exactly. But Vm stands for membrane potential, and the formula is actually surprisingly simple. It's 61.5. And this is a simplified version, because there are a lot of constants in here that get thrown together in that 61.5. And you just take the log of the concentration of potassium on the outside-- I'll say K out-- potassium on the outside --over the concentration of potassium on the inside of the cell. So you take these two concentrations, and you get this fantastic little formula. And you can actually-- now I can write for you potassium-- over here we said it was equal to negative 92 millivolts. So that would be the membrane potential. And I can even walk through a few other ones, some other key ones. There's sodium. Let's do chloride and calcium. So a few of them-- and all of them have the same formula. You just take their concentrations on the inside and outside and plug it into the formula, and you get positive 67 for sodium. You get negative 86 for chloride, and you get positive 123 for calcium. And now keep in mind, calcium has a two plus charge. So for calcium this 61.5 actually gets changed to 30.75, and that's rounded off. But that's because of that two positive charge. And all you do is, as I said, throw in the concentrations on the inside and outside. So, actually, let's even write that down, so concentration gradient. And keep in mind exactly which way things are moving. So concentration gradient for potassium, I mean, really, you're looking at a positive ion that's moving out of the cell. And for sodium you have a positive ion, but it's moving into the cell. For chloride you have a negative ion moving into the cell. And for calcium you have a positive ion moving into the cell, really just like sodium. So this is how you can think about the four major ions that contribute to our cell's membrane potentials.