hello everyone we're back again and we're continuing our discussion of potentials when we left off last I was asking you to remember and kind of get into your head this concept of equilibrium potentials equilibrium potentials to remind you just briefly I have the slide returning so that you can kind of see some of the things we talked about last time we have the concentration of a particular ion in this case ion X positive ion X on either side of the membrane of a cell the membrane semi-permeable meaning it's actually permeable to that solute all right or that ion if the concentration is higher in outside versus inside and the membrane is permeable that ion is going to be able to diffuse across that membrane diffused because it wants to equal out the concentrations on either side of that membrane got that well in moving across that membrane remember inside of the cell is very small in comparison to outside these ions moving in all it takes is a few ions moving in to kind of change I guess you could say the properties inside of the cell one of those properties is the charge since it's a positive ion moving into the cell well because it's a small area just a few positive ions is going to increase the positivity dramatically inside the cell increase the positivity remember like charges repel each other so as the charge on the inside of the cell gets more positive well for more positive ions to try to move in that's going to be difficult they're going to be opposed there's going to be a force pushing back on them Force pushing back on them all right now remember when this voltage this voltage on the inside perfectly opposes the diffusion of the ion here x trying to move in it is called the the equilibrium potential a voltage that is opposing any more movement of that ion a voltage opposing any more movement of that ion and so we call it an equilibrium potential even though potassium or excuse me even though this ion wants to move into the cell because of the concentration difference something's pushing back on it and so there's a force pushing in there's a force pushing out neither side is moving it's come to a stalemate that's equilibrium for that particular ion or solute that's equilibrium well that equilibrium we can measure we can calculate actually and calculate calculate it using an equation called the nernst equation the nernst equation so we're going to jump into that right now in this slide I know you're panicking already you're looking at this equation and it's the worst kind of equation you can think of because it has no numbers it just has letters which means that could be almost anything well let's let's set this up for us all okay over to the left e x refers to the equilibrium potential for X whatever that solute or ion may be here in the Middle where you see RT over ZF these are all giving you measurements of the cell the constraints of the cell and this has been studied millions and millions of times let me tell you and so let me set up what these these letters are actually referring to first of all the r refers to the gas constant so gases across inside outside the cell and the and the force that it has on or the constraints it has on the cell itself the temperature of the cell inside and outside temperature plays a role but for us since we're playing uh with the human body and or just a mammalian body temperature doesn't change a whole lot so that nut that t up there the the actual number that comes along it doesn't change a whole lot so but we still have to include it in this equation Z refers to the valence of the ion that we are referring to okay or that we're trying to determine the equilibrium potential for so the charge on that on that ion and last but not least we have f f refers to What's called the Faraday constant 96 000 coulombs per mole all right now all of these together give us kind of the constraints of the cell you remember me talking about that a couple of lectures ago so that's part of the equation over to the right you see Ln Ln refers to What's called the natural log of this what's sitting in the parentheses over here natural log well we'll we'll tell you how to calculate that here fairly fairly soon hang on for a moment in the parentheses whenever you see these brackets around X or an ion that we'll be talking about that refers to the concentration the concentration of that ion so the concentration here referring to this this uh o over to the right that o refers to outside the cell I refers to inside the cell so the concentration of this Ion on either side of the membrane what I want you to kind of pay attention to with this whole equation it's actually bringing out what we talked about a couple of lectures ago last the in our last module the forces on each of these solutes concentration difference across the membrane charge difference across the membrane and the constraints of the size of the cell remember me talking about that well here concentration difference here the constraints of the cell and Z the valence the charge all right all of these are put into this equation to help us determine okay well what voltage given a particular concentration over here of this of this ion what kind of voltage would perfectly keep this concentration or any of these solutions from moving outside in or inside out let's let's take this a step further I'm going to take this and and and this is what we do in math now I'm going to let you know you're not going to have to do this you're not going to have to do all of this but there are parts of it you're going to have to kind of hang on to so here I'm going to get rid of let's see here's some like uh units here so that we can come out here and that's what we get joules over coulombs is equal to volts well that's what we're hoping to get over here in the equation over here and then we're going to kind of modify the equation now make it a little easier for you after canceling out some things so if you look at this nernst equation this is setting it up well you don't see what we saw before all those other letters well because we put them all together because the cell doesn't change a whole lot in mammalian tissues we can we only have a very set group of numbers we put those together and that gives us 61 millivolts 61 millivolts and then we divide that by the valence of the ion so if we're talking about sodium that would be a plus one we're talking about chloride that's a negative one sitting down here because of what we did with the calculations here it actually affects what's happening over to the right as well instead of seeing that Ln that you saw before the natural log well now we can do something that's probably a little simpler for many of you we're going to be doing what's called log to the base 10. this is you simply logging the concentration you've played with this on your calculators before in other classes all right so again Z is for valence the brackets sitting around the ion or X over here that refers to the concentration of that ion and whether it's outside or inside of the cell whether it's outside or inside of the cell now we can do use this calculation for any solute any solute or ion we want to but to use it we have to remember this ion that we're looking at it must be permeable across the membrane or we have to at least make the assumption that it's permeable across the membrane permeable across the membrane and we have particular concentrations outside versus inside we want to know the voltage that will keep this concentration constant concentration that we had outside stays the same concentration on inside the same show you how we do this let's take let's take an ion that we've already been talking a little bit about let's talk about potassium potassium here so we're going to calculate the equilibrium potential for potassium in cells in our body e x is the equilibrium potential voltage now do you remember the concentration of potassium outside versus inside where is potassium higher outside or inside giving you a sec a couple of seconds there concentration of potassium is higher inside the cell versus outside well by how much we can measure that and we have numbers and tables that show this for almost every cell group in our body here it's trying to show you remember this what was sitting in the parentheses was the concentration outside versus inside concentration outside four millimolar for potassium concentration inside the cell 140 millimolar on the inside of the cell okay well let's go through this calculation all right oh I forgot something over here we have our our constraints of the cell 61 millivolts divided by the valence from well we're talking about potassium positive one is the is the valence so here it is positive one so let's solve for everything in parentheses okay 61 divided by 1 is 61. 4 divided by 140 is .0286 everybody good so far point zero two eight six we need to log that so we're going to log that press the calculator you put in that number and hit log it's going to give you this number negative 1.54 negative 1.54 that number times 61 gives us minus 94 millivolts this is the voltage that would need to be inside the cell inside the cell to keep the concentration across the membrane of the cell at this level four outside 140 inside hmm so here we're looking and trying to determine the different forces and putting them against each other and trying to figure out what the charge would actually be what the charge would actually be now the signature it's actually looking at sodium but I I don't want you to kind of worry about the sodium in a Cell I want you to just think about chemical forces so that's concentration difference electrical forces that's charge differences and we have to figure out what is going to how do they play against each other when do they come to a stalemate pushing against each other for potassium it would have to be that the inside of the cell is negative negative 94. to keep this kind of a concentration difference from what we see in real life let's let's do another calculation let's do it for sodium let's do it for sodium for sodium where was it higher outside or inside the cell higher outside higher outside 142 outside 14 millimolar on the inside so let's remember how we did this before let's solve for the uh for the parts of the equation that are inside the parentheses the valence of sodium is plus one 61 divided by one 61. 142 divided by 14 10.14 now we're going to long 10.14 and it gives us 1.06 multiply that times 61 and that gives us 61.4 millivolts for a cell to be able to keep sodium high outside versus inside even though that that ion can move across the membrane we'd have to have the inside of the cell be positive keep all those positive ions outside that makes sense folks I'm going to bring back that picture that I used prior here I'm showing you again chemical forces sodium outside higher than inside so it's going to want to move inside the cell as soon as it moves inside the cell just a few ions it's going to cause the inside of the cell become more and more positive well as it becomes more positive those positive ions are going to repel any more sodium from trying to get in when the electrical force is on the inside of the cell push equally push out and match the forces that are trying to move in that's what this is trying to show over here that's what we call equilibrium and so the voltage because that's the only thing we don't have quite yet the voltage that equally opposes any of that concentration driving force that's called the equilibrium potential here they have it as 60 millivolts we calculated using concentrations that I took from a group of cells that I was looking at many years ago gives you 61.4 millivolts so what you can see here is that sodium to keep it at this concentration difference outside versus inside needs to be positive on the inside of the cell for a potassium we saw it needed to be negative to maintain its concentration difference how are we doing folks go back and listen to this and go through the equation and let's talk about some of this in the discussion group and in the lab talk to you later