0:49

Because you know remember that we already spoke that any ionic current, is actually

according to Ohm's law is the multiplication of the conducatance and

what we call the driving force for this current.

So it's the membrane voltage minus the battery of this particular ion multiplied

by the conductance of this ion that gives rise to this current.

This is true for sodium, potassium. This is true for sodium.

The only difference, of course, is the conductance of the sodium channels.

And this is the battery, or the driving force, for the sodium.

So this is, this holds true for any current.

And remember that in the case of voltage clamp we fix Vm, we don't allow Vm to

change. So if I know Vm, if I fix the voltage,

the, the, the voltage clamp to a given value, and if I know the battery, which,

which depends on the concentration difference between the outside and the

inside of sodium. Or between the outside and the inside of

the potassium. If I know the voltage clamp value.

And if I know the battery of this particular ion.

And I know the current that I measure. They, I can then, then extract the

conductance. So this is exactly what Hodgkin Huxley

did. The voltage clamp, the membrane to

different values. So here is small depolarization, but

still supra-threshold, a stronger depolarization, a stronger

depolarization, voltage clamping the membrane step by step.

3:05

You can see that the conductance of the potassium, becomes stronger and stronger,

as you depolarize more and more, the membrane.

So the larger the voltage clamp the more conductance opening of a conductance,

voltage-dependent conductance. So I can call it voltage-dependent

conductance because when I change the voltage clamp, I get more and more

conductance. You can see, the, the, the potassium

conductance responds slowly to the abrupt change in the, in the voltage.

So, I change the voltage fast. Step, it's a step voltage clamp.

And it takes time, as we saw before, for the opening of the potassium conductants.

It takes time. And by the way this times becomes faster

as your voltage clamp more stronger. So you can see that it grows faster, and

also to a more higher conductance as you depolarize more and more with voltage

clamp. And when you stop the voltage clamp you

can see the continuation of the. Potassium conductance, the continuation

of potassium conductance to it's resting venue.

So I can say again, this is a voltage dependant conductance.

This ion channels that are sensitive to voltage in this case these channels open

slowly, it takes them time to respond. When they respond they are open to a

given value. And this given value the amount of

conductance the degree of conductance change depends on how big the

depolarization you have. You have big depolarization, you have big

conductance change for the potassium. You have small depolarization, you have

smaller conductance. And all this conductance take time to

develop, so this is the later current. This is the later outward current that we

saw which does not inactivate during the voltage clamp.

But if we look now at the sodium conductance, and you see now the

conductance, you are used, you are used to look at the current, which is an

inward current, I showed you before. But now we look at conductance.

So this is the, this is the reverse direction of the current.

So the current is inward, but the conductance of course is not inward,

conductance is always positive. So this is the conductance of the sodium.

5:50

As a function of this voltage clamp, so again, like here, we voltage clamp to

this value, to this value, to this value, to this value And Hodgkin Huxley recorded

that conductance of the sodium for this value, for this value, for this value, of

depolarization. And here again, you see something

interesting. First again, you see that this sodium

conductance responds fast. So as soon as you have voltage clamp,

very early on, you get a conductance change.

Very early on. This is why we call it fast conductance

change. This is a slow conductance change for the

potassium, this is fast conductance change for the sodium, fast conductance

change. And again, like here, when, when you,

when the depolarization is more and more extreme you get more and more

conductance. You get more and more conductance.

So the conductance becomes stronger or larger with depolarization.

From minus 40 millivolts to minus 20 to zero to even plus 20.

You get more and more sodium conductance. This is in the beginning.

But still, you continue to voltage climb, and the conductance fades away.

Somehow it inactivates, and it disappears during the voltage climb.

So this is again this conductance that is early which enables very early on to

carry sodium channels, sodium current inside the cell, early on.

But after some times, this conductance turns off, and there is no sodium current

anymore, although you continue the voltage clamp.

This is not the case for the potassium that continues to be open as long as the

voltage clamp descends to a given depolarization.

So these are the different two conductances that underlying, the voltage

sensitivity of the membrane of the axon. So, I'm, I'm summarizing here.

The slow, the slow potassium current, or potassium conductance, does not

inactivate during voltage clamp. Know that the k conductants rises slower.

Then it attenuates, and this was important for Hodgkin Huxley later on to

write down the appropriate equation to describe these curves.

So it's a slowing growing curve and faster attenuating curve at the end of

the voltage clamp. And you see this sodium current this

early sodium current, or conductance, inactivates during voltage climb.

It's early, so this is the first current that flows when there is voltage change,

it's a sodium current, but this sodium current, early sodium current,

inactivates during voltage climb, unlike the potassium current.

9:08

And here is an example, a direct example of Hodgkin Huxley trying to fit

equations, we should talk soon about equations.

I'm just showing you now a result of an experiment, so this is an experiment of

Hodgkin Huxley, recording the potassium current you see this continuous curve.

This is a recoding from Hodgkin actually, and the dots here are numerical, or

mathematical fitting, that we shall talk soon about, that, about the mathematics,

the fitting of the mathematics to this current.

You see, again, that this potassium current grows slowly, and attenuates

faster at the end of the voltage clamp. So there is a voltage clamp here

somewhere, and this is the response. So you can see, already, now, without

talking abut the equation, that they somehow realized how to write an equation

that will. The equation, the dots.

Will fit very well the actual recorded current.

Actually Hodgkin Huxley realized that the fact that it grows slower, the sodium,

the potassium current grows slower and attenuates faster, they realized that

they can fit. The up stroke of the potassium current or

conductance and the down stroke the decay of the potassium current.

They can mathematically write the up stroke as a function that looks like one

minus exponent to the power of four and this means.

10:52

Minus t here, this means that the growth as you increase the exponent, the growth

here would be slower. So if it would be to the power of one it

would be faster, and if it would be to the power of six it will be even slower.

Yes, because this is the minus t here. So they realized that they can fit very

well this rising phase. By this kind of one minus exponent to the

power of four, and it could fit very well the decay with, with the single exponent,

not to the power of four. So, the decay and the rise time have a

different speed. Of rising and decaying, slow speed and

fast decay speed, and this, on its own, Hodgkin Huxley realized that this must

mean something about the mechanism of this specific potassium pore, or membrane

channel. Something about this channel behaves like

it opens like something to the power of four and attenuates like something

basically to the power of one. And then they wrote this equation.

12:10

This was a big conceptual jump. They said that the potassium conductance

in the membrane, behaves like a maximal conductance, so you may think about this

like the total, absolute total number of channels, potassium channels available in

this patch of membrane. This is what they call the maximal

conductance, this is gK bar. So this is all their valuable conductance

but not always all these conductance is open, because it is multiplied the actual

conductance, is multiplied by a factor that they called n.

It's an activating parameter, it is a voltage-dependent parameter, this n.

This n goes between zero and one. So when n is zero, there is no potassium

conductance. When n is equal to one, the conductance

of the potassium is maximum. Because n to the power of, one to the

power of four is one, so if n is one, you get all the conductance available of this

potassium channels. And if n is between zero to one, you get

less. The claim was, that for a particular

voltage clamp, n gets the value somewhere between zero to one.

13:38

At zero, at zero voltage without any voltage clamp, n is very close to zero.

At the very, very big, at the very, very big voltage clamp, n is becoming close to

one. And this to the power of four is exactly

what makes things fit this growth, as I said.

It looks like, like this, to the power of four.

So this is the basic equation for the potassium conductance, but of course we

have to discuss what is this parameter, which is really the parameter that makes

makes their current both voltage dependent but also time dependent.

So n is between zero and one, but n depends on both voltage and time.

So n represents the proportion of K-ion channels In the open state.

14:42

You can say that if n is equal 0.5, 0.5 multiplied to the power of four is the

propulsion. It's actually not n, but n to the power

of four that represents how much of the conductance is available.

If n equal one, all the conductance, all the conductance is available.

So n is this special parameter, the activating n parameter for the voltage,

for the Hodgkin Huxley equation. So Hodgkin Huxley wrote these equations

may be given a physical basis, if we assume that the potassium ions can only

cross the membrane when four similar particles, particles occupy a certain

region of the membrane. So this is another jump.

They are now trying to interpret bio physically, almost anatomically, what is

this form means. They want to say that this power form

means that this channel, this potassium channel, that this potassium channel is

open. Only if four particles, if four gates in

the channels are open so that the channel enables the flow of the current through

the channel. So they are trying to give now an

interpretation to the number four to the, to the exponent four here, to the to this

four using a biophysical intuition which we are going to talk about in a second.

Okay, may be before we go to talk in a second I just want to complete just

showing you another graph on Hodgkin Huxley.

About the potassium. This is not really another success of the

Hodgkin Huxley. Just to show you this is the potassium

conductance for various voltage clamp. You can see what we discussed before,

that as you increase the voltage clamp, you get more and more and more potassium

current or potassium conductants. And the disconductants does not activate

inactivate, it continues it's maximal, it takes time to reach the maximal but when

it gets to the maximal it stays there so it does not inactivate.

And you can see by the way again that this activation is not only voltage

dependent. Because, with voltage, you get more and

more activation. So n becomes more and more close to one.

It's not only activated more and more. But also, it becomes faster and faster

and faster activated. So the activation end, activation viable

end, is both increase, increases with voltage towards one, and also, this

activation viable end becomes faster. With depolarization faster and faster, or

slower and slower for lower voltages.