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

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. 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 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 how
the four cells are going to have a
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, OK, 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. 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 two-- because you might think
that 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? And you know we're not
actually using a real cell as an example,
because real cells are permeable to multiple ions. And 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 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 ions. 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. So permeability is all ions
crossing back and forth. Permeability is
all ions crossing-- and I'll just write
crossing, and you get the idea-- crossing back
and forth along the border. So what percentage is
going to be from potassium? What percentage from sodium,
chloride, and calcium? And of course, the
total permeability has to be 100% right? We have to add up to 100%. 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
100%, potassium is 95%, meaning that 95% of
all border crossings-- if we think about our cell
border or cell membrane, 95% of the crossings are
with the ion potassium. And that means that
only 5% of the crossings are with the other three ions. So let's say that it's 1% from
sodium, and 2% from chloride, and 2% from calcium. So really, in terms of
dominating 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 95%. So how do you actually
calculate the membrane potential based on this? So we've started with
good information. We've got the permeability. And now we need to multiply it
by potassium's 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
of 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 87.4 millivolts. And this bit right here, 1%
of the 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
2.5 millivolts. So if you add up all the
stuff, what do you get? You get a total of
negative 85.9 millivolts. So this would be the
membrane potential for a cell that ended up having
95% permeability to potassium, and only 1% and 2% to
the other three 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, that negative
92, because 95% of it came from there. Now that would be
one way of doing it. Let me do it one
more time, and you'll see how it can actually change. So just as before, let's say
that in the second case-- so again, 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%. And I raise sodium
all the way up to 80%. So now, all of a
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% and 2%. 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 100% permeability, but in
this case, most of that permeability is going to sodium. So negative 92 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 then we add
them all 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 it's
going to be the same. But some of it's
going to be different. So these two
numbers-- let me just check out what my math works
out to be-- this is negative 14.7 millivolts, so a lot
less than the negative 87. And now this is going to
be a huge number 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
these four numbers, my overall
permeability was 100%, and my overall membrane
potential as a result of that is going to be 39.7. So let me just-- and
that's positive 39.7. So we went from negative
85.9 to positive 39.7. 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
more an 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 on 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 what I'm drawing for you is
the cell's membrane potential in millivolts. So at time point 1-- let's say
time point one was right here, and time point 2 is right here. At time point 1, we had a very
negative-- I forget the number. I think it was like
negative 80 something. I'll just say it was negative
86 or something down here. And then at time point 2,
we had a number up here. This is our 39.7. And actually let me just
double check the number, I don't want to
get it wrong here. Yup, negative 86. This is negative 86, or 85.9. So really, what you had
is, in just a matter of switching the
permeabilities, you can actually change the membrane
potential from something very low to something very high. So let's stop there
and we'll pick up.