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- Permeability and membrane potentials
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.
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.