lecture 15: membrane potential

7/27/2019 Lecture 15: Membrane Potential

http://slidepdf.com/reader/full/lecture-15-membrane-potential 1/6

Transcribed by David Landsman 1/30/2014

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Neuroscience 15 – Membrane Potentials by Dr. Schiff

No slides

[Dr. Schiff] – What I’m going to be talking about today is membrane potentials. Nowthis was mentioned a number of times already, and specifically as Dr. Kinnally

pointed out (I hope you remember what she taught), whenever you have a cellmembrane, the main purpose is to separate the inside of the cell from the outside.

They have a limited amount of permeability for certain solutes, solutes is the stuff

that is dissolved in the solvents, and specifically what you have to keep in mind is

that if here’s a cell and this is your lipid bilayer with hydrophilic endings on these

fats and the fats are in the middle of the membrane and you got all that stuff from

Dr. Kinnally. There are passageways for solutes to move into and out of the cell,

there are also passageways, channels, carriers, whatever that allow the solvent

which is water to move into and out of the cell, because remember the cell’s

membrane is largely lipid and water and fat don’t mix so there has to be a way of

getting water across the membrane, and there are specific water channels called

porins that go through the membrane. When you have a solute that’s present onboth sides of the membrane at different concentrations, let’s say you just take a

beaker or some sort of vessel with two compartments, you divide it in half with a

membrane and you put some water in. And then you dissolve a lot of some solute,

sucrose/glucose any solute on one side and a little bit on the other. There’s going to

be movement even if that solute is not permeable across the membrane, there’sgoing to be movement of stuff, what stuff? Water, because there is an osmotic effect.

In this side of the membrane, where sucrose is at a high concentration, then water

must be at a low concentration. Think about that. The more solute you have the less

water you have proportionally to the total, so water is going to move from where it

has a higher concentration to where it has a lower concentration and this is the

whole basis of osmosis.

Osmotic effects sort of result from a lot of the other things I’m going to be talkingabout. Suppose you have […] What you have typically in a cell is the outside of thecell is seawater, after all we evolved in sea water or at the shores of the oceans, so

the extracellular fluid, the fluid outside, has a lot of sodium, a lot of chloride and

assorted other solutes, a little potassium, some calcium and stuff (magnesium,

whatever). Inside the cell, you tend to have much higher potassium levels and much

smaller sodium concentrations. So sodium and potassium are not at equilibrium,

they aren’t balanced across the membrane, and whenever you have a membranethat is at least a little bit permeable to some solute, that solute is going to move

across the membrane and it will tend to move in the direction -- well there are twofactors involved here -- from higher concentration to lower concentration, but also if

that solute is charged and all of these are ions the solute will move, will be

influenced by any electrical forces around because remember opposite charges

attract and same charges repel. Let ’s start with a rough approximation here, if this is

a cell membrane here, and inside the cell you have lots of potassium and outside the

cell you have very little potassium. What ’s going to happen? Well the potassium is

going to move across the cell membrane from the high concentration towards the




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low concentration and it takes an electric charge with it. So you end up building up

some sort of a charge differential or electrical differential with more positives going

here and leaving negatives on the other side. But if you are dealing with only one

ion, this will tend to push the potassium ions this way as the concentration

difference, concentration gradient/ratio, is going to be pushing it right to left, out of

the cell, but at the same time you are going to build up an electrical field, anelectrical charge differential, potential or voltage that will tend to pull the potassium

ions into the cell. Eventually you reach some sort of equilibrium, which Dr. Kinnally

also discussed, and it was all worked out in the 1930s by a fellow by the name of

Nernst. And if you have 1 ion able to cross the cell membrane then eventually you

reach an equilibrium where depending on the concentration ratio you have a certain

voltage building up across the membrane, at which movements in opposite

directions, this arrow and this arrow are equal and you’ve reached the steady state.And these conditions, you are setting delta G, your Gibbs free energy equal on both

sides (I’m not going to go into the full chemistry business) but you eventually reach

a membrane potential that depends on the log of the ratio of the concentrations. And

this multiplicative factor here, what is it? Well this is in over out, and you’remeasuring the membrane potential of the inside with respect to the outside of the

cell, this is generally something like minus 61, 62, I’ll just call it 60 millivolts. Allnumbers that you come across in biological things are different for different cells, a

little bit, plus or minus 10% is a good range. And this is referred to as a Nernst

potential or Nernst equilibrium. If you have a membrane that only allows one ion to

cross it, in this case potassium, eventually you will reach an electrical potential

given by this Nernst expression (which Dr. Kinnally discussed). And this equilibrium

is fine, this is an equilibrium, because once it’s set up, nothing’s moving. The left to

right arrows and the right to left arrows, the movements of ions are exactly equal

and opposite and everything stays the same, it ’s in equilibrium in the sense that if

you have a bowl or basin and you put a bowl at the bottom it just stays there,nothing’s happening. And typically, Kin in most cells in your body is something like

140 millimolar and the potassium concentration outside is 4, 5, 6 thereabouts

millimolar. And so when you take the 140 divided by 4, 5 or 6 and take the log of

that, multiply by -60 you end up with something like -80. I’m not going do the

calculation here. You reach this equilibrium which is something like a Nernst

potential for potassium, or an equilibrium for potassium, it ’s something like -80 mV.

But suppose instead of looking at potassium we look at sodium. Potassium in most

cells is the most permeable ion. Sodium is somewhat less permeable, but it’sprobably second or third most permeable. If you do the same calculation for sodium

you have lots of sodium outside the cell, very little sodium inside the cell. Thesodium will tend to move in, bring its positive charges inward and will make the cell

membrane positive inside, eventually the positive inside will push the positive

sodium ions outside and you reach your equilibrium. And -60 times the log of

sodium in, which is about 14 (let’s use 15 for easy arithmetic), and about 150

outside (in the seawater), gives you +60 mV. Well what does this say? Well, if the

membrane has an electrical potential across it that’s -80 mV inside compared to the

outside, then pot assium will be at equilibrium but sodium sure as hell won’t because




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the sodium has a concentration difference bigger outside. Plus it will be building up,

there will be more negative charges inside from the potassium so it will tend to

draw the sodium in again. So sodium will not be at equilibrium, it will be moving

inward, the electrical potential is at -80, potassium is at equilibrium but the sodium

is very far from equilibrium and will tend to move in. On the other hand, at +60,

sodium will be at equilibrium but potassium will be very far from equilibrium. Youhave a concentration difference, more potassium inside than out, which will tend to

move the potassium out, plus you have a positive charge inside the cell which will

move potassium out. So potassium is going to be moving outwards. But neither of

those is the situation that holds in real life, for a real cell. Because for a real cell,

sodium and potassium are both somewhat permeable, potassium more than sodium

and therefore neither one can be at equilibrium, I mean they can’t both be at

equilibrium. And how do you work out the actual electrical potential across the

membrane. Well what you do is this, you apply a modification of the Nernst

equation, remember the Nernst equation only applies to one ion at a time. But if you

have two ions that are permeable, sodium and potassium, you have to tweak the

equation a little bit to allow it to handle two ions at a time, and the way that wasworked out that holds most validly is this: -60 mV times the log of […writing]. It

depends on how permeable these ions are. PK plus PM, plus Sodium […writing onchalk board]. So what’s going on here? You add up all the positive ions inside on top,

outside on bottom, multiplied by their relative permeabilities. So if potassium is

more permeable then generally this will be the dominant term compared to that

because sodium permeability is smaller and so what happens is the membrane

potential, the electrical potential across the membrane will be closer to the

potassium Nernst potential but it won’t be there. On the other hand, if somehow you

increase the sodium permeability then the membrane potential would move closer

to the sodium equilibrium or Nernst potential which is +60 and further away from

the potassium potential. Typically you have potassium permeability is about 20times sodium permeability, for most cells at rest, so this is the predominant term.

And the membrane potential is typically closer to -80 than it is to +60, in fact it is

typically something like -70. This equation by the way is generally named after the

people who came up with it: the Goldman-Hodgkin-Katz equation, or sometimes just

the Goldman equation. And you can add additional terms if it turns out there are

additional ions that might be permeable across the membrane. So let ’s say you work

out this Goldman-Hodgkin-Katz equation after measuring the permeabilities and

you find that for this particular cell the electrical membrane potential is about -70

mV, so potassium is not at equilibrium, sodium is not at equilibrium, so what are

they doing? Well compared to the potassium equilibrium potential, which is about

minus 80, this is positive inside, its -70 that’s more positive than -80, so it’s going totend to push potassium ions out. And you’re going to have an overall leakage of

potassium ions running out of the cell. At the same time, this -70 is very negative

compared to the +60 sodium equilibrium potential, so the sodium will be far from

equilibrium and will move in. Now the key here is that the potassium, the membrane

potential is close to the potassium potential, so the difference between the two,

about 10 mV from -80 to -70 is relatively small but the potassium permeability is

largish. On the other hand, the difference from +60 to -70 is pretty large but the




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sodium permeability is relatively small. So even with this big force, relatively little

sodium moves in, comparable amounts of potassium are leaking out. Ok, you have a

cell, you have potassium inside the cell but it’s leaking out, you have sodium outside

the cell it’s leaking in, eventually you are not going to have a cell anymore because

there won’t be any difference between the inside and the outside. So what evolved

to take care of all of this? The sodium-potassium ATPase, which is an ion pump. Itmoves 3 sodium ions outward, it moves 2 potassium ions inward and it hydrolyzes 1

ATP (inorganic phosphate). So the energy of hydrolyzing 1 ATP into ADP plus

phosphate is enough to move 3 sodium ions out of the cell and in exchange bring 2

potassium ions int o the cell. That doesn’t sound quite kosher does it? Because you

are moving more electrical charge outwards than you are moving inward. So what

actually is going on here? First let me say a word about this. This molecule, this

sodium-potassium ATPase, with very little variation is probably the same sodium-

potassium ATPase that was present in the earliest cells that evolved in the foam at

the shores of the early oceans and the first creatures and one of the keys of

evolution is that once you’ve done something right it tends not to change. So this is

probably one of the oldest enzymes around, it’s essentially unchanged becausewhen you do it right, don’t mess with it. It’s the cockroach of enzymes, it hasachieved perfection -- it doesn’t change. It’s the crocodile of enzymes. And it really is

more or less the same in every cell in your body as it was in the first amoebas or

whatever. Of course the point is, once you’ve got that you’re no longer in any sort of

equilibrium, an equilibrium is where you are sitting there and things don’t change.Your cell has to run a metabolism, generate an ATP, hydrolyze an ATP, pump the

ions out that were leaking in, pump the potassium ions in that were leaking out to

maintain what we call a steady state. A steady state is when all of the overall

parameters don’t change but you are doing work to keep it that way, it’s running upand down an escalator. Doing work to stay in the same place. And there are a lot of

situations in physiology that require you to do this, all of this is to maintainhomeostasis. And the key to homeostasis is doing work to stay in the same place, we

spend our entire lives running up and down an escalator. But that’s a good thing,

because remember you live through yesterday if you were in the same shape you

were yesterday morning, then you should live through today and so on. So

homeostasis is the way we stay alive, and we are running up and down an escalator.

Now, so here we have a situation where this pump is going according to the

Goldman-Hodgkin-Katz equation. We have this situation where a combination of the

ion concentrations, and for the most part, membrane potentials/electrical potentials

across the membrane is determined by sodium and potassium ions. If you look at

the Goldman-Hodgkin-Katz equation you find that the membrane potential isdetermined by two things: the concentrations of the ions inside and outside and the

permeabilities of these ions, their ability to cross the cell membrane, because an ion

with a high permeability will be able to get across fairly easily. With low

permeability the ion has great difficulty in getting across the membrane so you need

a large force to drive it, that’s why the membrane potential is far from theequilibrium for sodium, because sodium has low permeability for potassium. You

have a membrane potential that is close to its equilibrium but it has a high




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permeability. So you get comparable amounts of sodium moving in and potassium

moving out, and that way the pump can handle it. Now as I mentioned before, you

notice that this is 3 and this is 2. The pump is generally referred to as electrogenic,

that is, it is generating a certain amount of electrical potential. It’s moving more ionsout than it is moving in. So what does all this mean? First of all, one thing you have

to keep in mind is that generally any bulk solution, any solution with a finite volumeis electrically neutral, there are always as many negative ions as positive ions in a

given volume of fluid. So what are you doing here? You are moving 3 sodiums out, 2

potassiums in, there’s a net movement of one extra positive charge outwards --

which would tend to make the cell more negative. If you do very careful

measurements you can actually see that. But nature doesn’t like charges to be

separated so what typically happens is 1 chloride moves out along with the sodium.

It takes 3 sodiums out but one chloride gets dragged along just to maintain electrical

balance. OK. So now what is the movement across the cell membrane look like?

You’ve got 3 sodiums and 1 chloride going out and 2 potassiums going in. You are

moving more particles of solute outwards than inwards, this is going to have

osmotic effects. Because if you start moving amounts of solute across a membranethen water is going to want to follow osmotically because you are raising the

concentration of solutes on one side of the membrane. So the water will move to

where effectively you’ve lowered the concentration of water. Is this good or bad?

Well, what else is the cell doing? Remember I haven’t really mentioned what kind of

cell this is. Everything I’ve said up to now refers to every cell in your body. What elseis the cell doing, well among other things it is doing what its job is (if it’s a gland cell

it is secreting something, if it’s a muscle cell it’s making movement) but what is it

doing? It has to generate ATP, which means it has to metabolize something. You’ve

gone through all your building blocks class to learn how you get ATP. Hydrolysis of

glucose, glycolysis, breakdown of glucose, and eventually you end up with pyruvate

and then it goes into the TCA cycle and you metabolize that and you generate lots ofATP, and the mitochondria (which I’m sure Dr. Kinnally discussed building up the

hydrogen ion gradient across the mitochondrial membrane, all that stuff to generate

ATP.)

But what are you starting out with, you are starting out with a molecule of let ’s say

glucose, which is a six carbon sugar. What ’s the first step after you phosphorylate it?

You break it into two 3-carbon sugars. So now you have twice as many particles as

you started out with. You didn’t lose the phosphates that attached on because they

were transferred from something else. So when it was phosphorylated those

phosphates would just transfer, but then you split the 6-carbon sugar into two 3-

carbon sugars and then eventually it goes down even smaller. What you’re endingup with is your metabolism is producing more particles of solute so if you just let

the metabolism run while its generating more ATP, it ’s generating additional

particles of solute which has an osmotic effect. It’s going to draw water into the cell

and if that ’s the only thing going on the cell will swell bigger, bigger, bigger and pop!

Lysis. Breakdown. How do you avoid that? That ATPase is pumping 2 ions in but 4

ions out, effectively if you count the chloride going along with the extra sodium. So

what the ATPase is also doing is having an osmotic effect keeping the solute




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concentration inside the cell form getting too high so that you don’t lyse the cell. All

these things work together and so far I’ve cited two of your old courses. I keep goingback to them so don’t throw away your folder and notes.

One of the things that you have as a result of this Goldman-Hodgkin-Katz equation is

this, if you change the concentration of the ions inside or outside the cell and youcan do this sort of thing in the laboratory, you take the seawater that is around the

outside of the cell and you replace it with something that has higher potassium or

lower sodium or something like that -- you can do that artificially but that’s notreally related to life – and it will change the membrane potential if you change these

concentrations. But in real life, these ion concentrations don’t change very much at

all, not significantly. What can happen is this. If you do something to change the

permeability, those Ps, PK, Psodium, if you change those Ps that will change the

membrane potential. Because remember this is -70 in a normal cell at rest because

PK is much larger, it is about 20x Psodium, but suppose you had some way of

increasing the sodium permeability. If you increase the sodium permeability, then

the membrane potential you’d have t o recalculate the Goldman equation, if youincrease the sodium permeability the membrane potential will end up closer to +60,

that sodium equilibrium, it will move up and become less negative, more positive.

Let me just clarify a couple of vocabulary words here. Here’s membrane potential,

it’s always the script ‘E’ which is short for electromotive force which is what they

called electrical potential or voltage back in the 1920s or 30s or even further back. It

was referred to as EMF, electromotive force, because it would move things that had

a charge and that ‘E’ stuck around for a century or so. So membrane potential,

measured in volts or in this case, millivolts, is always an ‘E’. Membrane potential, if

this is zero, most membrane potentials are negative, close to the EK this is the

potassium Nernst potential, at +60 is the sodium Nernst potential or equilibrium

potential. If a membrane potential shifts from the -70 upward in most cases whenthey first started studying this sort of thing, the electrical voltage became smaller in

magnitude, it went from -70 to -60, which is smaller than 70 if you forget about the

signs. So this was referred to as a depolarization. We generalize, a depolarization is

any movement upward on an algebraic scale. So if it moves from +10 to +40, that’s a

depolarization. A depolarization is any movement upward. And the opposite of a

depolarization, any movement more negative is referred to as a hyperpolarization.

And that’s a downward movement, where the cell becomes more negative inside.

There’s one other word that you’re going to come across and that is that if a

membrane potential leaves its resting potential and is depolarized, that is it goes up,

as it comes back to the resting potential that’s called a repolarization. That’s

towards normal. Hyperpolarization, repolarization all tend to be sort of jumbledtogether. Now what we are going to be getting into tomorrow is exactly how

neurons take advantage of this fact, that changing permeabilities can alter the

membrane potential and that’s what makes what we call excitable cells exciting, orat least interesting. So I’ll think we’ll pick this up again tomorrow.

lecture 15: membrane potential

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