So in the last video we talked about how
you have a higher concentration of potassium
on the inside-- around 150 millimoles per liter
--than you do on the outside-- let's say
around five millimoles per liter.
Just to recap some important points we brought up,
we said that essentially what happens
is that you have these potassiums that
are bound to little anions that are the green dots there.
And because the concentration gradient
is going to want to make the potassium leave the cell,
it will, and so it'll leave the cell.
Let's say this little fellow will leave the cell here,
and he'll end up on the outside.
So by doing that he leaves that anion all by itself.
And if this continues to happen, then these anions
create this negative charge.
And we can actually figure out exactly what
that negative charge is.
It turns out that that negative charge
is going to attract back the potassium.
We said that this potassium, then,
is going to want to swim back inside to be
closer to that negative charge.
And this is that interesting idea,
the idea that K leaves behind a negative charge.
And then it comes right back and wants
to be by that negative charge.
And the amount of negative charge
that's going to offset the concentration gradient
is around negative 92, so let me write that in now.
So negative 92 is the amount we know
that we need to offset the concentration gradient.
That's where we left off.
And now I want to do a little thought experiment.
Let's say that we come at this cell with a little injection
full of, let's say, some positive charge.
And try to ignore the ridiculousness of what
I'm saying, just for the moment.
Let's just focus on the positive charge, the fact
that I'm going to pour a bunch of positive charge
into this cell.
And let's assume that we don't know exactly where this
is coming from, but that this positive charge is--
essentially, what it's going to do
is it's going to make my cell not negative 92 anymore.
It's going to make it more positive than it is.
Let's say I make it, let's say, halfway back to zero.
So instead of negative 92, it's negative 46 millivolts.
So this is the new membrane potential,
and our cell is still just permeable to potassium.
And that's really important.
It's only permeable to one ion.
That's potassium.
So what's going to happen?
Well, these potassiums-- these little guys right here
--they're going to notice that the charge is actually not
drawing them back as strong as it was before.
So this potassium might see that, and it might leave.
So more potassium basically starts leaving the cell.
And if more potassium is leaving and going on the outside,
then you have more of these little anions
that are left behind.
And the process continues.
So these anions say, well, if we're off by ourselves,
we're going to contribute to this negative charge.
We're going to add to it, just as it did before.
And that negative 46 is quickly going to go down again.
It's going to slide back down.
And the question is, how far does it slide down?
Well, it goes back to the equilibrium point.
And so if we said negative 92 is what
you need to make this yellow squiggly attraction--
the membrane potential-- equal the concentration gradient,
if that's what's needed, then it will slide back down
to negative 92.
So think about that for a second.
It's pretty powerful stuff.
You can do all sorts of funky things to this cell.
You can add positive charge or negative charge.
And as long as you maintain two things,
two important things, one of them being the concentration
gradient-- so one is this concentration gradient of 150
versus just five.
That's one thing.
And the other is the permeability to only potassium.
As long as you maintain the permeability,
you'll get back to negative 92.
Let me even hammer this point harder
by showing you a little diagram.
So let's say we have a concentration
gradient over here, and I also have permeability over here.
And this is permeability to potassium.
OK?
And assuming that we only have permeability-- so assume-- I'll
write that very clearly --the cell
is only permeable to one ion.
So assume only one ion for this permeability.
So if you have, let's say, permeability
yes and permeability no, and you have concentration gradient yes
and concentration gradient no, then what do you get exactly?
So let's say you have four possibilities here.
And let's say we have no concentration
gradient and no permeability.
Would we get a membrane potential?
Well, no, because the potassium would never
have a way of leaving in the first place.
And it would have no desire to leave.
Now what if you have concentration gradient--
so you have the desire to leave-- but you don't have
a way for that potassium to actually leave the cell.
Well, again, you don't actually have any membrane potential.
And the same is true if you have a permeability,
but you have no concentration gradient.
Then the potassium, again, has no desire to actually leave.
And then finally, if you have permeability
and a concentration gradient, then you actually
get down to negative 92 millivolts.
So the concentration gradient is when I use the word desire.
Does the potassium have a desire to leave?
And permeability is does it have a means?
Does it have a way to leave?
So these are the two things to think about when you're
thinking about whether you would create a membrane potential
or not.
So if we have that setup-- let's actually move down a little bit
and make some space and actually talk
about how you actually get your negative 92.
Where in the world does that number exactly come from?
So there is a formula, and that formula
is-- I'm going to write it out over here.
It's Vm, and all that means is membrane potential.
Now, if you're like me, the first thing you notice
is that there's no V. There's no letter V in the word membrane
or potential.
So how do they come up with that?
And I don't know the answer to that.
I don't know where the V comes from exactly.
But Vm stands for membrane potential,
and the formula is actually surprisingly simple.
It's 61.5.
And this is a simplified version,
because there are a lot of constants in here
that get thrown together in that 61.5.
And you just take the log of the concentration of potassium
on the outside-- I'll say K out-- potassium
on the outside --over the concentration of potassium
on the inside of the cell.
So you take these two concentrations,
and you get this fantastic little formula.
And you can actually-- now I can write for you
potassium-- over here we said it was
equal to negative 92 millivolts.
So that would be the membrane potential.
And I can even walk through a few other ones,
some other key ones.
There's sodium.
Let's do chloride and calcium.
So a few of them-- and all of them have the same formula.
You just take their concentrations
on the inside and outside and plug it into the formula,
and you get positive 67 for sodium.
You get negative 86 for chloride,
and you get positive 123 for calcium.
And now keep in mind, calcium has a two plus charge.
So for calcium this 61.5 actually gets changed to 30.75,
and that's rounded off.
But that's because of that two positive charge.
And all you do is, as I said, throw
in the concentrations on the inside and outside.
So, actually, let's even write that down, so concentration
gradient.
And keep in mind exactly which way things are moving.
So concentration gradient for potassium,
I mean, really, you're looking at a positive ion that's
moving out of the cell.
And for sodium you have a positive ion,
but it's moving into the cell.
For chloride you have a negative ion moving into the cell.
And for calcium you have a positive ion
moving into the cell, really just like sodium.
So this is how you can think about the four major ions that
contribute to our cell's membrane potentials.