hello everybody we're back again we're continuing our our lecture lectures on potentials we spent a good deal of time in our last two little mini lectures trying to bring you up to speed we we've talked about uh recording uh the signal from the inside of the cell finding out that the inside is negative compared to outside the cell uh we determined that that negativity on the inside is something that the cell wants to maintain that's its resting membrane potential and the actual voltage told you I know the actual number itself I'm not so concerned with you remembering because it's going to change depending on the the concentrations of solutes that we include in whatever equation that we're going to be kind of playing with we got started at looking so at at equations to try to help us determine what is called the equilibrium potential and remember these equilibrium the equilibrium potential equation is used to help us determine what would be the voltage necessary to maintain a particular concentration of a single solute single ion and for us to use that equation we have to assume that that ion is the only one that can move across the membrane everybody else has to state where they're at they can't move so we that time already dealing with the equilibrium potentials for sodium and potassium and utilizing the special equation the nernst equation for us to determine that those equilibrium potentials now equilibrium potentials and doing that calculation is great experimentally it helps us to determine the forces on any one of these solutes I have sodium and potassium listed here but we could use it for any of the solutes that is trying to get across the membrane but remember that's an experimental equation or an experimental situation I said for us to use that equation we have to assume that that whatever solute we're looking at whatever ion we're looking at that it is the only one that can get across the membrane well that's not real life again the nernst equation helps us to understand okay for a single ion these are the forces on that one well in real life we have multiple ions trying to get across membranes and that means multiple forces uh on all those solutes so for us in the end we're going to use the information we have from the nernest equations and help us to try to determine okay so what's the real resting membrane potential and the forces associated with it and for us to do that we have a second equation that we need to include and you see it listed here it's called the Goldman Hodgkin's cats equation or ghk equation let's get started on this this image here here for your slide we're going to take the numbers that we calculated with our nursed equation for sodium and for potassium so on this image you can see up at the top there e with the n a for sodium that's the equilibrium potential for sodium and if you remember we calculated using a particular set of concentrations high sodium concentration outside versus inside we found that if we use that first equation for for sodium to be held or keep that high concentration outside versus Insight even though it may be able to get across the membrane we'd have to have it the positive inside of the cell positive inside of the cell for potassium its equilibrium potential when we did that calculation High concentration inside the cell versus outside the cell well when we use that nerst equation to calculate the equilibrium potential we find that for potassium it wants the cell to be minus 94 millivolts on the inside that's what would hold High concentration of potassium inside versus outside versus outside if potassium had free rain across the membrane well again we know that these two ions don't have necessarily free reign across the membrane so we need to be able to figure out um well what what is the real voltage across the membrane so to do that we're going to use the ghk or Goldman Hodgkin's caps equation now remember in our first set of lectures on potentials I told you on a membrane sitting at about minus 70. well it ranges and again it ranges depending on the concentrations that are actually used uh from different research experiments and so forth and so I'm giving you a ranger minus 70 minus 86 for the resting membrane potential that's where our resting membrane potential usually sits well if we just take what we have here is voltages and what we just know I'm hoping you can see that the actual resting membrane potential sits very close to the equilibrium potential for potassium scientists saw this and said here's our clue this is how the nernst equation helps us remember to calculate the nernst equation for or use the Ernst equation for potassium we had to assume that the membrane was completely permeable to potassium and no others no other ion to calculate it for for sodium we had to assume sodium was the only one that can get across well if that's the case and the actual resting membrane potential sits closer to potassium that tells us that potassium probably has a much easier time getting across the membrane than sodium does this gave scientists all kinds of of of of excitement and kind of of impetus to start moving and trying to see if this is really the case and what they found was yeah potassium literally can get across the membrane 100 times greater than sodium can 100 times greater well they still needed to be able to figure out okay well we we need to verify this what's the calculation that will allow us to do that that's where the Goldman Hodgkin's cats equation comes into play so let's use it let's use it so first I guess I should show you it here's the ghk equation now again before you panic I want you to pay attention to some things look over to the left here over here we have the voltage the resting membrane potential across the membrane the voltage across the membrane 61 millivolts that should be familiar to you again that's all of those constants that tell us about the constraints on the cell now you'll notice here we don't have valence here and the reason we don't have valence is because you're going to see we're not looking at one ion so there's not one valence so we're going to have to include it someplace else we'll show you that in a few moments we have long to the base 10 you've seen that before and here's our parentheses now parentheses looking at the concentrations and if you look inside well I have two solutes here sodium and potassium sodium and potassium and they have their bracket so that we are still looking at concentration concentration outside versus inside outside always on top inside on the bottom so sodiums here potassium here what we've added is p and you can see that P for sodium P for sodium P for potassium P for potassium over here p is the permeability so we're going to include permeability into our equation as we add solutes now again I only I'm only including sodium and potassium here so they're I'm limiting the equation right at the moment again sodium and potassium tend to be the biggest players uh in this voltage across the membrane so we're going to utilize them here and I'll tell you about adding the rest of the rest of the solutes a little bit later so for us here folks literally the Goldman equation is about kind of taking all of the concentration differences across the membrane and kind of getting an average getting an average and this will tell us about who's the major players here remember P is for permeability how easily how easy is that solute able to get across the membrane for cons the brackets refer to the concentration of the particular solutes outside versus inside of the cell and in this case we're playing with just sodium and potassium all right let's put this to the test folks let's put this to the test here's our equation we're going to use the same concentrations we used for our initial nernst equation uh calculations so in our equation here sodium 142 millimolar outside 114 inside potassium four millimolars outside 140 inside now remember we need to add something to this equation and that's permeability so I told you previously scientifically we know permeability for potassium at rest in the cell is a hundred times better for potassium than it is for sodium so we just made this kind of simple for ourselves here one for potassium and a hundred times less point zero one for sodium we could have made this one and this a hundred it would not change this equation in fact you can play with it yourself and check that out alrighty well let's finish the calculation here so as you do a calculation like this this is the Goldman Hodgkin's caps equation and this is for trying to include as many solutes as possible to give us the true resting membrane potential so to do this equation you take .01 and multiply it times the concentration here you take one multi multiply it by four over here once you've done either side of the addition then you add then you do down here you do .01 times 14 1 times 140 add once you've done that you take that divide it log it and then multiply the product that you get here times 61. times 61. what you should get minus 86.2 millivolts negative inside of the cell and this is just including potassium and sodium potassium and sodium this is pretty close to what we see in real life now I want I need to preface this that's close it's not perfect I guess you could say for it to be perfect we would have to include in this equation all the other solutes that we find on either side of the membrane of a cell and there are a ton of them so what you'll see is that at the more solute you add the closer this number comes to whatever you physically are actually measuring inside of the cell inside of the cell now for you to do this calculation as well we played with just sodium and potassium both of these are positive ions well as Goldman Hodgkin's and cats were were creating or trying to figure out what to put into this equation one of the biggest problems they had was the the issue of negative ions it's intended to kind of throw everything off if you added in a chloride concentration for outside and inside um and kept it in the same format that you had here it just doesn't work out it seems to throw the whole thing off well The Story Goes that that as these three very famous biologists uh were trying to figure all this out it actually took a graduate student who came in one day and saw them toiling over trying to figure out what to put into this and and said well why don't you know I see you're having problems well why don't why don't you just modify me they said what do you mean modify it well what he did is he came and said okay let's do the equation and let's do it with chloride and you say it keeps getting messed up when you put it in in the same fashion outside over in so what did he do he reversed it this graduate student and it happened to be a male he said make it inside over out for negative ions and when they did this it worked miraculously the numbers came out exactly the way that that they had all proposed or hypothesized pretty pretty fascinating so remember this Goldman Hodgkin's cat's equation now let's review we use the nursed equation to try to determine the equilibrium potential for a single solute a specific solute and in doing so we have to assume that that's the only solute that can move across the membrane so this is an experimental an ideal to give us an idea of where that's all you would like to be voltage wise inside of the cell given a certain concentration outside and inside of the cell if we want to look at real life and not necessarily an experimental situation we utilize the Goldman Hodgkin's cats equation this will help us to determine the resting membrane potential the resting membrane potential for a cell or a group of cells whatever you'd like to to kind of call it and in doing so in doing so is for a specific area of the membrane or a part of the membranes based on the solute concentrations of all of the ions we want to include do we want to include just sodium and potassium for uh example purposes here yes that's what we do okay you'll see I'll probably be giving you equations where I'm going to ask you to utilize all the solutes so keep that in mind as you're playing with this now overall this I know this image is probably a mess to many of you take your time look at this it's putting together both sodium and potassium ions and the forces across the membrane all of the forces across the membrane that we have talked about trying to determine the resting membrane potential and at the bottom two you can see sitting somewhere around minus 70 millivolts for the way that this set of concentrations have been set up what's important to remember about all this is Wells because I don't want you to forget about this is that the membrane while we'd like to believe it's perfect it is not it leaks it has cracks in it and so all solutes may leak across and so the membrane even though or the cell even though we want it to be negative inside it's going to have to be maintained that way well what maintains it that's the sodium potassium pump the sodium potassium pump an exchanger where we're throwing sodium out against uh its will and throwing potassium into the cell against its will remember concentration gradients potassium doesn't want to be inside there's too much of it already sodium doesn't want to be outside too much of it too much of it but let me give you another another bit of information here if we didn't have the sodium potassium pump in the membrane trying to manage all of this and the walls are are leaky which way do you think sodium would want to move think about that for a moment sodium positive ion High concentration outside versus inside and when we calculated the nurtzed equation for the equilibrium potential for it given that that concentration of high outside versus inside it wants the inside to be positive to kind of maintain that well it's negative it's a negative insight so think about that again sodium outside a positive ion and the concentration for it is really high outside so just the concentration alone wants it to go inside of the cell now the inside of the cell is negative as well so negative and positive they attract each other so that means sodium has two forces on it trying to push it into the cell concentration difference and charge difference that means sodium has a whole bunch of pressure on it trying to get into the cell I'm bringing this up because this is how the cell gets work done because sodium has so much pressure it really wants to be inside the cell the cell util uses sodium to bring other molecules in or to get rid of particular molecules there are co-transporters out there and this is just one example this is a sodium glucose co-transporter glucose doesn't necessarily want to come in the cell sodium wants in bad well we have these proteins on the membrane that kind of have put out the news that well if sodium if you go and grab a glucose and Link it onto yourself we'll consider letting you into the cell as soon as that happens sodium goes over links up to a glucose they get close to the to this protein this channel carrier in the membrane it grabs them brings them in they separate sodium is excited because now it's inside of the cell it loves it that it's negative inside and there isn't so many sodiums on the inside well as soon as it gets in it gets kicked out the sodium potassium pump throws it out throws it out and the cell it wins because it gets glucose to produce ATP and gets glucose to produce ATP kind of strange huh but this is how the cell gets work done for itself so we've spent time trying to understand this voltage difference in Char concentration difference across the membrane and how the cell utilizes that to get work done go over this little lecture again folks and ask questions in the discussion session and in lab I'm happy to talk about this stuff we'll talk to you later bye-bye