The Cell as a RC Circuit

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Do curso por Hebrew University of Jerusalem

Sinapses, Neurônios e Cérebros

723 classificações

Hebrew University of Jerusalem

Sinapses, Neurônios e Cérebros

723 classificações

These are very unique times for brain research. The aperitif for the course will thus highlight the present “brain-excitements” worldwide. You will then become intimately acquainted with the operational principles of neuronal “life-ware” (synapses, neurons and the networks that they form) and consequently, on how neurons behave as computational microchips and how they plastically and constantly change - a process that underlies learning and memory. Recent heroic attempts to realistically simulate large cortical networks in the computer will be highlighted (e.g., “the Blue Brain Project”) and processes related to perception, cognition and emotions in the brain will be discussed. For dessert we will deliberate on the future of brain research, including the questions of “brain and art”, consciousness and free will. For more information see the course promo below and read “About the course.”

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Electrifying Brains –Passive Electrical Signals

In this module we will discuss the "Electrifying brain – passive electrical signals". We will show that neurons are electrical device and learn what enables neurons to become “electrifying”. Here we will describe only the passive (vs. active) electrical properties of neurons. We will show that, at the quiescent state, the difference in electric potential across the cell’s membrane is always negative inside the cell (“the “resting potential”); we next show that the membrane behaves like an electrical (resistance-capacitance) RC circuit and highlight the notion of “membrane time constant” and, consequently, the ability of neurons to summate (in time) successive (synaptic) inputs (“electrical memory”) – a fundamental mechanism utilized by the brain. We will also show that when the synapse is activated, it generates an analog electrical signal (“the post-synaptic potential”, PSP) in the receiving (“post-synaptic”) cell. Most interestingly, there are two types of synapses in the brain – “excitatory” and “inhibitory” – we will discuss how these two opposing signals interact in the receiving ``neuron. This module is more technical than the more descriptive first two lessons; we encourage those of you who are not familiar with basic electricity (resistance, capacitance, Ohms law and Kirchoff’s law) to read about these in the sources links for this week’s lecture.

The Cell as a RC Circuit11:01

The Voltage Equation for the Passive Cell9:20

The Membrane Time Constant14:03

Temporal Summation9:31

The Resting Potential8:54

The Synaptic Potential Part 19:38

The Synaptic Conductance6:19

The Synaptic Battery10:34

The Synaptic Potential Part 28:02

The Voltage Equation for the Synapse and EPSP and IPSP13:33

Conheça os instrutores

Idan Segev
Professor
Computational Neuroscience

Okay, so welcome to the third lesson of our course,

synapse, neurons, and the brains.

Today, we shall focus on the passive properties of neurons,

the passive properties.

And actually, we'll start with passive properties and we'll continue to the very

interesting signal, the synaptic potential that we already mentioned before.

So just to remind you,

we are talking about the synapse, this is the presynaptic element, the axon.

This is the postsynaptic element, the dendritic spine.

And, this is the connection, the communication through a synapse gap.

So, this is a synaptic gap.

And we already mentioned that in the axon, in the presynaptic part of the synapse,

we have the spike, we have the axon potential.

This is a signal we shall talk about on the fourth lesson.

It's an all or none, excitable, active signal.

We are not going to talk about this, this lesson.

In this lesson,

we shall focus on the synaptic potential which appears in the dendrites.

So in the presynaptic path, there is this very special phenomena,

the axon potential, the spike.

In the postsynaptic element, in the dendrite, there is the synaptic potential,

which will be the focus of the present study or lesson.

So I want to start this lesson by showing you neuron,

discussion neurons as passive R-C circuits.

So we should make the transformation between some anatomical structure

into its electrical representation.

We will continue to discuss the membrane of neurons and

especially the time constant.

The very important parameter, the membrane time constant which we call tau, tau m.

We'll talk about the very special phenomena in neurons,

the temporal summation whereby repeated inputs coming one after another in time,

can summate, and this formed a sort of electrical memory for neurons.

So the temporal summation would be an important focus of this course,

of this lesson.

We'll talk about the generation of potential here.

In the postsynaptic membrane, the generation of

the postsynaptic potential we'll continue and

discuss two types of synapses that we already mentioned.

The excitatory synapse and the inhibitory synapse, so

two types of postsynaptic potentials.

One that tries to excite the neuron, the excitatory synapse E, and

the one that tries to dampen, to quieten the neuron, the inhibitor synapse.

And then, we shall end this lesson by showing what kind of interaction exists

between excitation and inhibition.

Between E and I, so let's move to the classical

technique which will be board, a green board, with white chalk.

So, let's start with the most simple thing.

We start with a patch of membrane, a very small patch of membrane.

So this will be a patch of a membrane,

very small patch and we can wrap this patch and make it a sphere.

So this little sphere will represent a small nerve cell, a small neuron.

Spherical, no structure.

Unlike what we know, the dendrites and the axons, and

the who structure of neurons but in this case it will be a very simple neuron.

A representative of a simple neuron and this very simple neuron which is built

from a membrane wrapped around, we shall place an electron.

So this will be our symbol for an electrode, a recording electrode.

We shall penetrate into the cell, and we shall record the voltage,

the difference between the inside and the outside of the cell.

So this will be the inside of the cell, and this will be the outside of the cell.

And we should record the voltage between the inside and the outside.

And now what happened actually at the middle of the 20th Century,

people started to record from themselves and they did a very simple thing.

They injected current through this electrode.

So I will now show you a current that is being injected into the cell,

inside the cell, the current looks like this.

So this would be my current I, I will symbolize the current.

In this direction of the drawing.

So if I do this direction, I will call it the positive current.

Meaning that I inject into the cell body, inside the cell body a positive current.

A positive ion inside the cell body.

So when you do this to a cell body, when you do it to real neurons,

what you see is that there is a voltage change because you inject a current.

There is a voltage change here, but the voltage change doesn't look square.

Like the current that are injected but it looks like this.

It grows with time.

The voltage.

So this is my voltage V.

So it grows with time while I'm injecting a constant current.

So I jump from zero to something, to current I.

I get voltage change, and when I stop the current injection,

when I seize the current injection, the voltage

slowly drops back into zero.

So, this is the current injection I, This is the voltage response inside the cell.

So this is very basic and you can see something important.

You can see that you cannot represent the cell as a mere resistance.

Because if the cell behavior would of been like a resistor, then if I were to inject

I, I would get voltage that is I multiplied by R.

Which means the voltage should have been looking like

this I, R, but it is not.

The voltage doesn't look like this in the cell,

it takes time to grow, so this is time here.

It takes time to develop when after injecting

what we call the step current pulse, the step current.

There is a voltage growth, and when I stop the current,

the voltage decays back into its original voltage, before I injected the current.

But that's a very typical response of any cell if you inject small enough current.

So let's make some nomenclature.

Again, this will be a positive current.

This will be a positive voltage response, which we shall call depolarization.

This will be a depolarizing current.

Okay, so when people looked at this, as I said in the beginning or

in the middle of the 20th century, they said this reminds us an electrical signal,

an electrical circuit that behaves like this.

So what could I now say about a cell that behaves like this electrically?

I told you already, that it cannot be a resistance only

because otherwise it would not have such a shape.

What is the simplest circuit that represents such a behavior?

So, people realize very fast, very early on that I can represent a cell like

this electrically as a first approximation with an RC circuit.

So if you have an R, resistance, and a C,

capacitance circuit describing the behavior of this membrane

electrically, this will be the outside of the cell,

this will be the inside of the cell like we did here.

So this is representing the patch of a membrane from the outside to the inside.

From the outside to the inside,

I'm now representing the properties of the patch of membrane here.

This patch of membrane according to its electrical behavior seems to behave

like an RC circuit.

I'll show you in a second why.

So we remember from now on R will be resistance, R, C be capacitance,

C, and when you inject to a circuit like this.

When I take a circuit like this, and I inject current I

between the inside and the outside like I did before.

So when I inject I between the two sides of such a circuit, I get such a response.

It takes time to grow while I inject the current and

after injecting the current, when I stop injecting the current, no current anymore.

The voltage between the two sides of these circuits is attenuating with time to zero.

So I developed the equation very soon that represents such a circuit.

Showing you that such an RC circuit is a good first approximation

to the actual behavior of cells, when they received kind of a step current.

So this is my next mission.

So let me show you that this is a good representation of such a behavior.

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