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# Membrane potentials - part 1

Find out how a cell that is permeable to one ion can become charged (either positive or negative) if there is permeability and a concentration gradient. Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.

Video transcript

I'm going to draw a
little cell here for us. This cell is going
to be a typical cell, and it's going to be
full of potassium. We know that cells love
to hold onto potassium. So let's draw lots
of potassium in here. And the concentration
of potassium, let's say, is something like 150
millimoles per liter. That's a lot of potassium. And I'm going to put
brackets because brackets indicate concentration. And of course, there's some
potassium on the outside, too. Let's say the
concentration here is something like 5
millimoles per liter. And I have to also show you
how this concentration gradient gets set up, right? It's not like it just
happens to be set up. It's something that we put a
lot of energy into creating. So you get two
potassiums pumped in, and you actually kick
out three sodiums. So that's how you get all
those potassiums in there in the first place. So now that they're
in there, are they hanging out by themselves? The answer is definitely no. They are finding anions, little
negatively charged molecules, or atoms, to sit next to. And so the net charge is
going to be neutral, right, because every
cation has an anion. And usually these anions are
things like proteins, something that has maybe like a negative
side chain like a protein. It could be a chloride. It could be phosphate. It could be a number of things. So any one of these
anions would be fine. And actually let me draw a
couple of anions here as well. So these two potassiums
that just got welcomed into our cell, and
so this is how things look. If things are nice and
static, this is how they look. And actually, to
be quite honest, there's also a little
anion hanging out here as well for this potassium. So now the truth is
that we have little gaps in our cell, little holes,
where we allow potassium to actually leak out. So let's actually show
how that would look and how that would
affect what's going on. So we have these
little channels. And they only allow
potassium through. So these channels are actually
very specific for potassium. They're not going to
allow any anion through or any other thing out. The protein certainly
can't get out. And so these potassiums
are kind of looking at these channels that are
there, and they're thinking, huh, this is interesting. There's a lot of
potassium in here. We're going to want
to just slip out. And so these potassium just
kind of bail on the cell. They just get right outside. Now, when they do that, an
interesting thing happens. Most of them move outside. But there are some
potassiums outside as well. I said that there was this
one little fellow over here, and he could theoretically kind
of make his way in over here. He could come into this
cell if he wanted to. But the truth is, overall
on the whole, on net, you have more movement
outside than you do inside. And so I'll just,
for the time being, erase that path
just because I want you to remember that overall
we have more potassium that's going to move outside because
of the concentration gradient. In fact, that's
point number one. So actually let me
write that down here. Concentration gradient is
going to make the potassium move outside, and that's on net. So the potassium starts
moving out, right? So K out. And what happens next? Well, when it
moves outside-- let me actually draw
it moving outside. So this K is now over here,
and this K is over here. And what it's left
behind is an anion. In fact, this guy's left
behind an anion as well. And those anions, all
by their lonesome, they start generating
a negative charge, a big, big negative charge. Actually, just a few anions
moving back and forth will create a negative charge. And these potassiums
on the outside, they're thinking to themselves,
huh, that's interesting. There's a negative
charge in there. And if there's a
negative charge in there, they're attracted to it
because they're thinking, well, I'm positive. This is a negative charge. I want to go back inside. And so on the one
hand-- think about it. You have a concentration
gradient driving potassium out. But on the other
hand you have this, what we call, membrane
potential-- in this case a negative one-- a membrane
potential that gets set up because the potassium
has left behind an anion that's actually going to
drive the potassium to want to be back inside. So you have one force, the
concentration, driving K out, and another force, the
membrane potential that gets created by
its absence, that's going to drive it back in. So I'm going to actually
make a little space here. I'm going to show you something
that's kind of interesting. So let's create two curves. Let's say we have--
actually, I don't want to lose everything
on this slide. Let me actually just
set this up here so you can see the
last little bit of it. So let's set up two curves. One will be for the
concentration gradient and one will be for
the membrane potential. So this is, let's say, K out. And actually if you
followed it over time-- this is time-- you'd actually
see that you actually have something like that. K is actually going
to move out over time, and it's going to, at some
point, get to an equilibrium. And if we did the exact same
thing with time on this axis right here, and let's say
this is membrane potential. And we start at time zero and
this is also negative access. So this is going more and
more negative this way. And we start at zero for
the membrane potential, and this is at the
point where you start letting the K
kind of wander out, you get something like this. Basically looks the
same, but is kind of a parallel of what's going
on with the concentration gradient. And when the two
equal each other, when the amount of K moving out
equals the amount of K moving in, we get to this
kind of plateau. And it turns out, it's about
negative 92 millivolts. So that's the point
where you really have almost no difference in
terms of the net movement of K. It's equal. And in fact, we even
call that term-- we call that the equilibrium
potential for potassium. So when you get to
that negative 92-- and it differs
depending on the ion-- but when you get to the
negative 92 for potassium, you've hit its
equilibrium potential. So let me just write that
out for K is negative 92. And again, this is
assuming that the cell is only permeable to one
thing, which is potassium. Now this actually
might still bring up a certain question in your head. You might be
thinking-- and I want to make sure I address
this-- well, wait a second. If potassium ions
are moving out-- and that's what I said
is happening-- then at some point don't we have
a lower concentration in here because the potassium has
actually left and a higher concentration out here because
potassium is moving outside? And technically that is correct. I mean, of course you have more
potassium ions on the outside. And I haven't said the
volume has changed. So, yes, you would have
a higher concentration. And the same is
true for the cell. You'd have a lower
concentration technically. But realistically, I
haven't changed the numbers. And the reason I haven't
changed the numbers is because if you look at
the numbers, these are moles. And this is a huge
number, right? 6.02 times 10 to the 23rd,
that's not a small number. And if you multiply
it by 5 then you get something--
this kind of works out to about-- I'm going
to quickly do the math. 6 times 5 is about 30. And then you've got
millimoles here to consider. So about 10 to the
20 moles, right? I mean that's an enormous
number of potassium ions. And really you just
need a handful of ions to create this negative charge. So if only a handful of ions
are moving back and forth, you're not going to
really make a difference to that enormous
number, 10 to the 20th. So that's why we don't really
think of the concentrations as changing very much at all.