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# Membrane potentials - part 2

Video transcript

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.