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Membrane potentials - part 1

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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  • leaf green style avatar for user kareem
    You say that () that the resting potential is at -92. mV
    in my book and my teacher both said it is at -70 mV, who is right?
    (12 votes)
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    • leaf blue style avatar for user dysmnemonic
      In the video, he says that the equilibrium potential for K+ is -92mV, which means that there's an outward gradient for potassium ions. The membrane potential is a little bit different: it accounts for the permeability of the membrane to the relevant ions, and includes the equilibrium potentials for sodium and chloride ions. It varies depending on cell type, but the resting membrane potential is usually around -70mV.
      (33 votes)
  • leaf green style avatar for user Kunal Khatke
    @ when you draw those channels for the K+ ions.
    When they are in the cell you, say they are attracted to the anions and that's the way they are hold up in a cell.
    How then they break the force of attraction between them (K+ and anions) when they move out through the channels?
    I mean they do need some energy to break the force, where do they get the energy? Can you explain in some other video or give me reference to this doubt?
    (6 votes)
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    • leaf green style avatar for user andyman310123
      The K+ are moving along the concentration gradient from inside the cell (cytosol) to the space surrounding the cell (extracellular space), because (as he correctly mentioned in the video) the ratio of K+ in- and outside the cell is 150:5! Since the K+ Channels are specific to K+ Ions the Anions are held up within the cell.

      The energy for the K+ to "break" their bond with the Anions is provided by the concentration gradient provided by the Na+/ K+ ATpase which is the pump he drew in the beginning of the video. This pump uses a LOT of energy in most cells in our body (usually about 1/3 of all the energy that is used in our cells!)

      I hope this answered your question!
      (6 votes)
  • blobby green style avatar for user HylkeWaalewijn
    at : how does the k+ channels of the cell determine if it is a potassium ion knocking on its door and not some other ion?
    I love your videos btw!
    (3 votes)
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    • leaf green style avatar for user andyman310123
      The Ion channels of our cells are made up of proteins. In the case of the K+ channels the proteins within the channel twist and form in a way that only allows K+ ions to pass!

      To further explain: The channels vary both in size and their electrical charge, depending on what ion they need to let through the membrane.

      In the case of the K+ channels the channel must be just broad enough to let K+ (and no other ions!) through and it's electrical charge must be just right for the K+ not to be either repelled or "stuck" in the channel because the attraction is too big for it to pass through.

      I hope this answered your question!
      (4 votes)
  • piceratops tree style avatar for user Ziyin Chen
    At , Rishi points out that anions exist within the cells for the potassium cations, etc. to sit with, what are these anions and why do they pre-exist in the cell? Also why do they stay within the cell when the potassium cations cross the channels due to the concentration gradient? Is it because no protein transports are available for this to happen or something else that I missed? Thanks
    (3 votes)
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  • leaf orange style avatar for user Adrien PYB
    at , Rishi is basically saying that - regarding the actual number of ions we are considering - few movements of ions in and out don't really change the concentrations.

    However, in the "correction to Sodium-potassium pump" video (health and medicine > Advanced nervous system physiology > Nervous system introduction), Sal mentions the importance of the Sodium-potassium pump in maintaining the concentration gradient. Why is it so, if - as it said in this video - the change in concentration is neglectable? Does it have something to do with the number of cells we are talking about?
    (2 votes)
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  • mr pink red style avatar for user Jamie Claren Gacias Canon
    Are the concentrations of K+ inside (150mMol/L) and outside (5mMol/L) the cell as shown in this video constant?
    (2 votes)
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  • leafers ultimate style avatar for user felix.alexandre.lavoie
    At , while you are right that this is an enormous number of ions, the electric charge of an electron, 1.6×10^(−19) ref wikipedia, is similarly an extremely small number. While I take your word for the negligible concentration difference required, i've been trying to play around in excel with the nernst equation to figure out what the impact of a few (say 1 mmol) potassium ion moving across the membrane actually has on the membrane potential... I'm getting a .18 mV reduction in potential. However, without knowing the actual volume within the cell, I don't know how to relate the concentration to an actual number of ions.
    (2 votes)
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  • spunky sam blue style avatar for user Emil
    Correct me if im wrong: -92 mV is not the charge of the inside of the cell, but the difference in charges between the inside&outside across the membrane? The charges themselves are not important as much as the difference between them - volts?
    (1 vote)
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    • leaf blue style avatar for user dysmnemonic
      That's exactly right - the potential comes entirely from the ratios of charges on either side of the membrane, and the membrane conductance. Playing with numbers in the Nernst and GHK equations can help you to get a feel for this. The cell will probably have other problems if the ion concentrations are very high or low, though.
      (3 votes)
  • blobby green style avatar for user Vanessa Palmer
    How does the sodium get in and the K get out? I don't understand the equilibrium potential. When would there be an EP? Could you help me understand this concept?
    (2 votes)
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  • male robot hal style avatar for user Parth Agrawal
    Why don't the anions move out of the cell? Isn't there a high concentration inside and a low concentration outside?
    (1 vote)
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Video transcript

I'm going to draw a little cell here for us. This cell is going to be a typical cell, and it's going to be full of potassium. We know that cells love to hold onto potassium. So let's draw lots of potassium in here. And the concentration of potassium, let's say, is something like 150 millimoles per liter. That's a lot of potassium. And I'm going to put brackets because brackets indicate concentration. And of course, there's some potassium on the outside, too. Let's say the concentration here is something like 5 millimoles per liter. And I have to also show you how this concentration gradient gets set up, right? It's not like it just happens to be set up. It's something that we put a lot of energy into creating. So you get two potassiums pumped in, and you actually kick out three sodiums. So that's how you get all those potassiums in there in the first place. So now that they're in there, are they hanging out by themselves? The answer is definitely no. They are finding anions, little negatively charged molecules, or atoms, to sit next to. And so the net charge is going to be neutral, right, because every cation has an anion. And usually these anions are things like proteins, something that has maybe like a negative side chain like a protein. It could be a chloride. It could be phosphate. It could be a number of things. So any one of these anions would be fine. And actually let me draw a couple of anions here as well. So these two potassiums that just got welcomed into our cell, and so this is how things look. If things are nice and static, this is how they look. And actually, to be quite honest, there's also a little anion hanging out here as well for this potassium. So now the truth is that we have little gaps in our cell, little holes, where we allow potassium to actually leak out. So let's actually show how that would look and how that would affect what's going on. So we have these little channels. And they only allow potassium through. So these channels are actually very specific for potassium. They're not going to allow any anion through or any other thing out. The protein certainly can't get out. And so these potassiums are kind of looking at these channels that are there, and they're thinking, huh, this is interesting. There's a lot of potassium in here. We're going to want to just slip out. And so these potassium just kind of bail on the cell. They just get right outside. Now, when they do that, an interesting thing happens. Most of them move outside. But there are some potassiums outside as well. I said that there was this one little fellow over here, and he could theoretically kind of make his way in over here. He could come into this cell if he wanted to. But the truth is, overall on the whole, on net, you have more movement outside than you do inside. And so I'll just, for the time being, erase that path just because I want you to remember that overall we have more potassium that's going to move outside because of the concentration gradient. In fact, that's point number one. So actually let me write that down here. Concentration gradient is going to make the potassium move outside, and that's on net. So the potassium starts moving out, right? So K out. And what happens next? Well, when it moves outside-- let me actually draw it moving outside. So this K is now over here, and this K is over here. And what it's left behind is an anion. In fact, this guy's left behind an anion as well. And those anions, all by their lonesome, they start generating a negative charge, a big, big negative charge. Actually, just a few anions moving back and forth will create a negative charge. And these potassiums on the outside, they're thinking to themselves, huh, that's interesting. There's a negative charge in there. And if there's a negative charge in there, they're attracted to it because they're thinking, well, I'm positive. This is a negative charge. I want to go back inside. And so on the one hand-- think about it. You have a concentration gradient driving potassium out. But on the other hand you have this, what we call, membrane potential-- in this case a negative one-- a membrane potential that gets set up because the potassium has left behind an anion that's actually going to drive the potassium to want to be back inside. So you have one force, the concentration, driving K out, and another force, the membrane potential that gets created by its absence, that's going to drive it back in. So I'm going to actually make a little space here. I'm going to show you something that's kind of interesting. So let's create two curves. Let's say we have-- actually, I don't want to lose everything on this slide. Let me actually just set this up here so you can see the last little bit of it. So let's set up two curves. One will be for the concentration gradient and one will be for the membrane potential. So this is, let's say, K out. And actually if you followed it over time-- this is time-- you'd actually see that you actually have something like that. K is actually going to move out over time, and it's going to, at some point, get to an equilibrium. And if we did the exact same thing with time on this axis right here, and let's say this is membrane potential. And we start at time zero and this is also negative access. So this is going more and more negative this way. And we start at zero for the membrane potential, and this is at the point where you start letting the K kind of wander out, you get something like this. Basically looks the same, but is kind of a parallel of what's going on with the concentration gradient. And when the two equal each other, when the amount of K moving out equals the amount of K moving in, we get to this kind of plateau. And it turns out, it's about negative 92 millivolts. So that's the point where you really have almost no difference in terms of the net movement of K. It's equal. And in fact, we even call that term-- we call that the equilibrium potential for potassium. So when you get to that negative 92-- and it differs depending on the ion-- but when you get to the negative 92 for potassium, you've hit its equilibrium potential. So let me just write that out for K is negative 92. And again, this is assuming that the cell is only permeable to one thing, which is potassium. Now this actually might still bring up a certain question in your head. You might be thinking-- and I want to make sure I address this-- well, wait a second. If potassium ions are moving out-- and that's what I said is happening-- then at some point don't we have a lower concentration in here because the potassium has actually left and a higher concentration out here because potassium is moving outside? And technically that is correct. I mean, of course you have more potassium ions on the outside. And I haven't said the volume has changed. So, yes, you would have a higher concentration. And the same is true for the cell. You'd have a lower concentration technically. But realistically, I haven't changed the numbers. And the reason I haven't changed the numbers is because if you look at the numbers, these are moles. And this is a huge number, right? 6.02 times 10 to the 23rd, that's not a small number. And if you multiply it by 5 then you get something-- this kind of works out to about-- I'm going to quickly do the math. 6 times 5 is about 30. And then you've got millimoles here to consider. So about 10 to the 20 moles, right? I mean that's an enormous number of potassium ions. And really you just need a handful of ions to create this negative charge. So if only a handful of ions are moving back and forth, you're not going to really make a difference to that enormous number, 10 to the 20th. So that's why we don't really think of the concentrations as changing very much at all.