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Current time:0:00Total duration:12:42

Video transcript

so I've got four empty cells here let's imagine these are four cells in someone's body and the inside of the cells are the same and the outside of the cells are the same so they're really completely the same except for one thing and that one thing is that let's say that these cells each of them is only permeable to one ion and I'm going to write the ion that they're permeable to underneath them right so each of them can only let in or let out one ion so in the first cell you know that there's a lot of potassium that wants to get out so it's going to have potassium leaving in the second cell you know that we generally have sodium more sodium on the outside that wants to get in and the same is true for chloride that wants to get in and the same is true for calcium that wants to get in so this is kind of how the the four cells are going to have movement of ions and these are the concentration gradients and so then of course if you want to figure out what the membrane potentials are you have to think okay well if it's a positive ion leaving then it's going to make the membrane potential negative in fact we even calculated it to be negative 92 millivolts and for sodium it turns out to be positive 67 millivolts and these are estimates based on rough concentrations of course concentrations aren't exact everywhere in different cell types have different concentrations but these are kind of rough approximations and chloride would be somewhere around let's say negative 86 millivolts and you know it's negative because a negative ion is entering and finally calcium is going to be positive 123 millivolts and just to remind us the reason that calcium isn't simply sodium times 2 because you might think that you know because calcium has two positive charges the reason it's not just sodium's number times two is that these numbers are actually based on concentration gradients and the concentration gradient for calcium might be very different in fact it is very different than it is for sodium so that's how these numbers are made using that Nernst equation that we went over previously so now we know that these are the resting potentials for each individual ion but what is the potential for a cell a real cell you know we're not actually using a real cell as an example because you know real cells are permeable to multiple ions so let me actually give you an example of what a real cell might look like of course it looks slightly different than that because you actually have potassium leaving and at the same time you might have sodium entering you might have chloride entering and you might have calcium entering so this is what a real cell would look like and let's figure out maybe using an example how to actually work through calculating the membrane potential for a real cell like that so I'm going to write out the four ions and make it really clear so that we don't get confused about the four we're talking about again potassium sodium chloride and calcium and the reason I chose these four I could have chosen others as well but that these four probably contribute the majority to the resting potential in particular I would say potassium but but you'll see that all of them have a tiny little role in contributing to it so let's first get to the idea of permeability so until now we've been assuming that each cell is in the first example only permeable to one ion and now the whole difference is that now we have cells that have permeability to multiple hands so here's how you think about it think about the fact that all ions crossing back and forth along the membrane make up permeability okay so permeability is all ions crossing back and forth permeability is all ions crossing I'll just write crossing but you get the idea across back and forth along the border so what percentage what percentage is going to be from potassium what percent is from sodium chloride and calcium and of course the total the total permeability has to be 100% right we have to add up 200% and let's assume right now that we only have four ions going back and forth so I'm just going to make up some quick numbers so let's say that of the hundred percent potassium is ninety five percent meaning that 95% of all border crossings if we think about our cell border cell membrane ninety-five percent of the crossings are with the ion potassium and that means that only five percent of the crossings are with the other three ions so let's say that it's one percent from sodium and 2% from chloride and two percent from calcium so really in terms of dominating the the permeability in this case I've set it up so that potassium is dominating the permeability right and actually in most cells that's about right potassium is the dominant ion in most cells in fact sometimes even more than ninety five percent so how do you actually calculate the membrane potential based on this so we've started with good information we got the permeability and now I need to multiply it by potassium ideal membrane potential what would potassium like it to be it would like it to be negative 92 millivolts right and sodium would like it to be positive 67 millivolts and chloride would like the membrane potential to be negative 86 millivolts and calcium would like it to be positive 123 I mean that's ideally where those ions would like to be but again 95% of the voting in a sense for what the cell is going to agree upon comes from one ion it comes from potassium and so we just have to add all this up and get a total so this part right here 95% of the ions being permeable multiplied by the membrane potential for potassium 95% times negative 92 I'm just going to quickly do the math on a calculator works out to negative eighty 7.4 millivolts and this bit right 1% of 67 well that's easy that's 0.7 millivolts that's just 1% and then this bit 2% times negative 86 millivolts that works out to about negative 1.7 millivolts and finally this part right here for the calcium ends up being positive 2 point 5 millivolts so if you add up all this stuff what do you get you get um a total of 85 negative eighty five point nine millivolts so this would be the membrane potential for a cell that ended up having 95 percent permeability to potassium and only one percent and 2 percent to the other 3 ions so if it's going to be dominated by potassium you can see that this final number is going to be really close to what potassium would like it to be at negative 92 because 95 percent of it came from there now that would be one way of doing it let me do it one one more time and you'll see how I can actually change so just as before let's say that in the second case so again this is case one this is case one and let's say case two now I make potassium not very permeable at all let's say I drop it all the way down to 16% okay 16 percent and I raise sodium all the way up to 80 percent so now all sudden our same cell as before is very permeable to sodium and you might think well how would that be the case let's imagine that sodium channels get put into the cell membrane so that sodium can just go right through those channels so something like that but let's say that the other two ions stay about the same 2 percent and 2 percent so you've got a similar setup as before and this time you've got let me do the math so we've got negative 92 millivolts and again the permeability this is actually an important point adds up to 100% again right because you've got 16 plus 80 plus 2 plus 2 so overall we're still talking about um percent permeability but in this case most of that permeability is going to sodium so negative 92 millivolts millivolts for the potassium you've got positive 67 for the sodium negative 86 over here and you've got positive 123 over here so I'm going to do the last two first because those are going to be the same as before right and we add them all up together so here of course as before I have negative 1.7 that doesn't change and as before I have positive 2.5 that doesn't change so some of its going to be the same but some of its going to be different so these two numbers let me just check out what my math works out to be this is negative fourteen point seven millivolts so a lot less than the negative 87 and now this is going to be a huge number right compared to that measly 0.7 that we had before now we have 53.6 coming from sodium so now sodium is playing a much bigger role than it was last time and if I was to add up these four numbers my overall permeability it was a hundred percent and my overall membrane potential as a result of that is going to be thirty nine point seven so let me just in this positive thirty-nine point seven so we went from negative eighty five point nine two positive thirty nine point seven and here the dominant thing was this so you can see how it's starting to approach positive 67 simply because we just had so much of the permeability coming from sodium so in a way the permeability becomes almost like a vote like the more permeable one of the ions is relative to the other ones the more votes it gets in terms of what the final membrane potential is going to be and in this case the the more on ion votes the more it's going to be close the final membrane potential will be close to what it wants which is its resting potential so we have these two membrane potentials and finally I'm just going to show you a little graph what this might look like so let's say you've got a little graph here and I'm going to draw a positive and negative so this is positive this is negative and this is millivolts and and what I'm drawing for you is the cell's membrane potential the cell's membrane potential membrane potential in millivolts right so at time point one let's say time point one was right here and time point two is right here at time point one we had a very negative I forget the number I think it was like negative eighty something I'll just say it was negative eighty six or something down here and then at time point two we had a number up here this is our thirty nine point seven and as you let me just double check the number I don't want to get it wrong here yep negative 86 okay this is negative 86 or eighty five point nine so really what you had is in just a matter of switching the perm abilities you can actually change the membrane potential for something very low to something very high so let's stop there and we'll pick up