This marks my point. So that's when the voltage is being built

and you can see that if I would inject another time constant.

And another time constant, and another time constant, the voltage would grow and

grow and grow as described here. It will grow and grow and grow

exponentially, like 1 minus exponent. And eventually it will get, if I wait

enough time, I will get close asymptotically, I will asymptotically

close to the maximal value, which is IR. Okay, you can see, you can use the same

equation exactly the same equation, you can use.

And ask yourself, how does the voltage decays?

Decays when I complete the current. So, I stop the current here, and I ask

myself how will the voltage look. How will the attenuation look at the end

of the voltage. I have already told you that it decays

and goes back to its zero value. And one can show from the same equation

that the attenuation of voltage. By the end of the injection, is also

exponential, but in this case not 1 minus exponent, but just pure exponent.

So let's say that we started with some value here, let's call it V zero here.

Oh, sorry, V A, let's call it V star. Which will be the voltage when I stop the

current and I look at the voltage simulation here.

I can tell you that this curve, this attenuation is equal, so, so, sorry.

That voltage. That the voltage after I stop the current

will look like the initial voltage here. Attenuated like the same exponent, into

the power of tau m. That means that if I wait one tau here, I

would get attenuation to 63% from the start.

I start at let's say with 10 I will attenuate it to, by 63%, I attenuate it

by 63%, and I would be left with 37%. So I will get here after one time

constant, or get 0.37 of V star. So, both the growth of voltage during

current is 1 minus exponent. But governed by the same exponent here,

which we call tau m, both the growth of the voltage and the attenuation of the

voltage. After I stop the injection are governed

by the same exponent, by the same tau, but the growth is 1 minus exponent.

And the attenuation is just the initial, initial value multiplied by exponent.

And so both the growth and the decay are mirror-image of one each other.

So if I take this point and put it here and flip it, the tenuation is exactly

like the build-up. It governed, it is governed by

single-exponent, by tau m. And this is called.

[SOUND] The membrane time constant. The membrane time constant.

It's a very important parameter which we should discuss in a second.

The membrane time constant. You really should remember this.

It's a very, very important parameter for understanding nerve cells.

Tau m, the membrane time constant. So, just to complete this part, okay, we

started with an RC circuit that describes.

The RC circuit that describes for a first approximation a spherical, isopotential,

passive structure. And I'm using the word passive now for

the first time. Saying that every parameter that I'm

using, both R, C current, everything is linear and fixed.

It doesn't change during the injection. It's fixed values.

This is in ohms, this is in ferrets. This is in ampere, and this is fixed.

So it's a passive system. And this RC circuit is a good

representation. As an initial representation of a cell.

And this, this would of been the case. Then you can see that when you inject

current I you have during the injection. The voltage develops like 1 minus

exponent. And after you, you finish injecting, you

stop injecting the current, the voltage decays like exponent.

And the, the controlling parameter, the important parameter that controls the

timescale. How fast, how fast the voltage develops

and how fast the voltage attenuates. After the injection is governed by this

time constant, that's why it's so important, remembering time constant.

For example, if the membrane time constant is long.

This means it will take long time for the voltage to attenunate, long time.

If the time constant is short, it will be much shorter to attenuate, or to build

up. So the time constant controls how fast

the membrane voltage responds to current. I inject a very fast current step.

And it takes time for the voltage to respond.

And after I stop the current, it takes time for the voltage to go back to its

initiation value, which is 0. It takes it time, it has a memory.

There is a memory for the membrane, if you want to call it this way, a memory

for the previous current. It takes time to get rid for the, for the

capacitor to discharge, to get rid of the current that I injected.

It takes time, and this time is governed by tau membrane.

It's a very important parameter, because it tells you something about the memory,

the electrical memory of the cell. Show time constant means that the cell

gets rid, develops fast voltage and gets rid of the voltage.

and slow time constant means that it takes very long to get rid of this

voltage. Another important parameter is R.

So you can see that this, this, this equation is governed both by R.

Which appears both here and here, and also by C, which when multiplied by R is

tau. This R, this R, which is sometimes called

R input also. The input resistance of the cell Input

resistance, input resistance is another important parameter.

So this R, or R input, is an important parameter.

Because as you saw before it determines the maximum value of the voltage you can

reach. So i multiplied by R is the maximum

voltage that your voltage can reach. And so if R is very big, if the

resistance of the membrane is very big you get very high, very large voltage.

If R is very small, you will get IR, which is small, you will get less

voltage. So this R is important parameter to tell

you. How much voltage will I get?

How much depolarization will I get when I have a given I?

And RC tells you how fast the voltage develops.

And how much, how fast the voltage attenuates following the current

injection. So both our input and the time constant

are the two critical parameters. Both the R input and the time constant

are the critical parameters for understanding passive, RC circuit.

Which is at first passive, linear approximation, for biological membranes.

And in particular, neuronal membrane.