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4.3 The resting potential and the Nernst equation
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Advanced Neurobiology I
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Signaling within neurons & Ion channels and membrane potentials
Let's switch to the electrical properties of the neuron.
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Yan ZhangProfessor
School of Life Sciences, Peking University
Yulong LiResearch Fellow
School of Life Sciences, Peking University
So, why is the resting membrane potential altered when you're changing
potassium but not sodium concentration, okay?
So,
If the cell is permeable to both sodium and
potassium, you will expect either of them,
or both of them, will change the resting potential.
Okay?
Because, what you'll do is, if you're adding a lot of, for example,
sodium here, the concentration is high, and originally there's no change.
Then, if it's permeable to the cell,
then this cell will have more of these positively charged ions.
Then, what will you expect?
The membrane potential goes up.
Right?
Okay.
So, essentially, the experiment here indicates that
the membrane is a little bit permeable to potassium, okay?
Because when you're adding, when you're increasing the potassium concentration,
well, you find the membrane potential increase, okay?
As if this charge gets into the cell, and then the cell will have
a little bit more positive charges, so the membrane potential increases, right?
And, if you are using the sodium which is very similar to potassium, okay?
In the period element table,
they are in the the same column, right?
they both have one positive charge, okay?
Their chemical properties are pretty similar, except their radius are different.
Again, if you still have your college probably highschool chemistry,
you know that they are similar except their radius are a little bit different.
But magically, only potassium is permeable to the cell.
But sodium, when you add it at the similar or
even higher concentration, it does not alter the membrane potential,
so this indicates that somehow sodium does not get into the cell, okay?
All right, that's good,
but how does this membrane potential get generated to start with,
why does it have a fixed number, okay?
Let's start discussing about that,
just using the same diagram, this very pretty cell, okay?
Let's do experiments with that again on the blackboard, okay?
How does the cell generate the resting membrane potential?
Okay.
If you think about it, a cell has different distribution of potassium, okay?
Potassium.
Okay.
And we know, in the resting condition,
potassium can be permeable to the cell from this experiment.
Why would there be a negative membrane potential inside and
How is it generated?
And, how is it maintained?
Okay, let's think about this, okay.
So, for example, we have high potassium at
the beginning for this very pretty cell, okay?
And, we know the cell, in the resting condition,
is permeable to potassium, okay?
Originally, you have a high potassium.
What will happen?
Okay?
What will happen?
Okay, the potassium ion will get into the cell, right?
Okay?
So, potassium ion will get into the cell.
At which condition will the potassium ion no longer keep moving into the cell?
Is the potassium going to keep going, and going, and
going (into the cell)? Because at the end of the day,
it's a tiny cell.
You have a seed of potassium ions.
Let's just put it this way.
For example, you have 100 mmol potassium.
At which condition will the potassium no longer get into the cell?
At which concentration,
will the potassium stop moving inward?
Exactly, so Washi essentially says, keep in mind, potassium,
even though it has a higher concentration, the chemical concentration, but
potassium has one positive charge for each ion, okay?
So initially, you have a charge balance between a membrane,
okay there's no charge separation when there's no net movement of potassium.
But at the moment you start allowing potassium to move,
and there is chemical concentration, or chemical driving force,
or chemical energy, then once potassium moves a little bit,
then it will move a small potassium here but
it will carry a charge across the membrane, okay?
And then, if you move more and move more,
then the positive charge is going to be more and more.
If you can move 100 mmol potassium to be the equal concentration.
Essentially, you will accumulate too
much positive ions charges inside the cell, right?
Essentially, actually even before you reach 100 mmol,
too much positive charge inside already repel
the further net transport of movement of potassium, right?
So, you will never reach 100 mmol, okay?
So, what membrane potential
will this cell have that allows
the balance of potassium movement?
Essentially, this will be the condition where the driving force for
the chemical energy, the concentration.
(This is our chemical energy concentration.)
as I said, be equal to the electrical energy, meaning that,
if there are more positive ions in here, the electrical energy,
the repulsing force will be a different direction okay,
that will be electrical energy.
When these two are the same.
Then, that would be the equilibrium condition, or balance condition,
where the chemical energy maybe drives a little bits in,
but electrical energy will move
additional things out.
So they're cancelling out each other, so the net flux
will be the same, okay?
And that is the condition for the resting membrane condition.
And, how do we quantitatively determine it in the value?
Well,
Nernst derived the equations to describe this process.
And, this is essentially as Wija said.
On the left is the aqueous diffusion,
the equation described the energy generated or the flux generated
by the aqueous diffusion, that is due to the chemical energy.
Okay? The diffusion is because
when the concentration is high, it will diffuse into a low concentration condition.
Okay?
The net diffusion.
On the left, that is the chemical energy, the flux.
So, essentially it describes that this, for
example, is a diffusion constant and then,
this is the gradient of the concentration difference, okay?
That determines the flux, the force for
the molecule to move driven by chemical energy.
And, on the right is the electrical energy.
That is, you divide the electrical field, okay?
The potential divided by the distance, that is the electrical field.
The mobility and
the concentration of ions that they will move under this electrical field, okay?
That determines the electrical driven flux.
When these two are set, that will be the condition of resting potential, okay?
So essentially, the total amount of movement is
determined by the chemical driven movements of
the ions and the electrical driven movements.
These together, are the combined movements.
But when this combined movement is equal to zero, meaning there's no net movement.
Then, you'll get this component equal to
the other component and that's how we get
the equation to describe the process, okay?
And, if you organize this equation, okay,
then you get the Nernst-Planck relationship.
It's just the Nernst equation.
Okay?
And, if you make it even simpler,
this is the very familiar Nernst equation,
where the electrical potential is equal to the log of the chemical
concentration difference times a factor, okay?
And the factor, as you can see, is determined by the temperature,
okay, the temperature will alter the diffusion, for example, and it
also depends on the charge that you carry, okay?
Different charge for different ions.
And, the other two are the constants.
This is the constant.
Therefore, essentially, this equation describes the equilibrium condition
when the ions that are permeable to the membrane
then the ion concentration would determines the,
eletrical potential to balance it, okay?
So, in the resting condition that, when the cells are permeable to potassium,
the potassium inside and outside chemical concentration
will determine the electrical potential across the cell, okay?
So, why does nature choose potassium? I don't think anybody has any idea but
what we do know this seems to be a very conserved mechanism,
so all the cell, it doesn't matter whether it's a bacteria,
yeast, a Hek cell or a neuron.
They all have a negative membrane potential and
they're all permeable to potassium.
So, potassium is thought to be a universal ion that is required for
the cell to survive, and has this negative membrane potential, okay?
So, it's not such a feature just for neurons, okay?
Neuron has this action potential, excitable, that makes it more unique.
But the resting potential is determined by that.
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