The Voltage Equation for the Synapse and EPSP and IPSP

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En provenance du cours de Hebrew University of Jerusalem

Synapses, Neurons and Brains

642 notes

Hebrew University of Jerusalem

Synapses, Neurons and Brains

642 notes

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.”

À partir de la leçon

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

Rencontrer les enseignants

Idan Segev
Professor
Computational Neuroscience

Okay, so now, we are looking at the end result.

We are looking at the current equation, for the circuit containing of the

capacities, of capacitative currents. passive conductance, the passive current,

through passive ion channels and also the synaptic current.

The red current which is the synaptic current.

The sum of all these three in a close circuit without external current should

be 0. If I inject current I, then I should

write I. But since I don't inject to cells usually

unless I'm an experimentalist and I want to inject current, but usually I don't,

then this is the current equation for the synaptic current total.

And if you solve this equation for V, this V will be the voltage change due to

the activity of the synapse. Then you get this equation where you

have, you see, in this part, which is the steady state part.

Let's not look at this part yet, only this part is the steady state part.

You see that the contributors for the voltage, is the conductance related to

the passive battery. So g rest multiplied by E rest plus the

synaptic conductance multiplied by the synaptic battery, and the summation of

the two. And this relationship tells you what will

be in the steady ca, the steady case, steady state case in case the gs and the

gr are steady open and you wait enough time.

This is the voltage that will be developed in the system.

Let's take the case where the synaptic conductance is 0.

No synaptic conductance. In this case, this is 0, this is 0, and

your voltage will be your resting potential.

This is your minus 70. Suppose your synaptic potential is very,

very, very, very strong. Suppose the G synapse, the conductance,

the red conductance, due to the synapse. The Gs is very, very, very strong.

This mean that this is very big, compared to that.

This is very big, compared to that and you will stay with gs divided by gs,

which is 1. You will stay with this, with es.

Okay? So this means, really, that, in this

system you can, the 2 extreme will be either when the synaptic conductance is

zero. Then you get the resting potential or

when the synaptic conductance is very strong, then you will get the full

synaptic battery. And this is where the synapse can move,

this is where the voltage of the synapse, we can call it Vs, the voltage due to the

synapse, the voltage due to the synapse here will move, will be shifted between

the resting potential and the synaptic battery somewhere between.

So this is something important to remember that in the nervous system,

because you don't have an external current and everything is coming from

within the system. And the system is being built, or ch-,

changing voltage view to changing conductances.

You will always be limited by the related batteries.

It's because with an external current you can get any voltage that you want, in

principle if you have R and multiply big I, you will get big IR.

But here you don't inject current from the outside, you, you, you change

conductance, you change conductance for a particular ion, this means that you may

express more and, or less a given battery, depending on how strong your

conductance for this battery in the circuit.

So this is very important. This means the following.

Let's look for a second at the voltage scale, let's say that this is your E

rest. This is your resting voltage, let's say

minus 70 millivolts. That's where you start from.

The cell always sits here. Now suppose you have a positive battery

here. This positive battery may be the battery

due to the opening of sodium channels. It would be a positive battery inside

because as we said before, Sodium tends to go from the outside to the inside

because of this drop, or this change in concentration, very big outside small

inside. So in this case if I open a conductance G

for the sodium, my voltage will start to grow this direction, because the battery

of the sodium will be more and more if g of the conductance for the battery, for

the sodium will be strong, the voltage will go there.

So, your synaptic potential will be depolarizing.

Suppose you have another conductance, synaptic conductance.

This will be your battery, let's say for the case of potassium.

In this case whenever you open new conducts for the potassium your membrane

voltage will go below, the resting potential.

More negative, or more positive depending on the battery, this is exactly what is

written there. So this is what we will call depolarising

Synoptic potential. This is what we will call hyperpolarizing

Synoptic potential. This will be, again,

depolarization[SOUND] less, depolarized in the resting potential and this will be

hyperpolarization more polarized. Hyperpolarization.

And this is what a synapse can do. Some of the synapse will be depolarizing

synapses, depending on the battery. Some synapses will be hyperpolarizing

synapses depending on their battery. But that's what they can do, and they are

limited by the battery. You cannot get more voltage than the

battery. You are limited by this ceiling.

There is a ceiling to the synaptic voltage.

The ceiling is the battery. Maximum you will get the most positive

battery, or maximum you will get the most negative battery, depending on what

conductance is being opened. And that's what the synapse can do.

And just to summarize, what we just said is, we said that in your brain, there are

these batteries, which depends on the ion concentration of sodium, potassium,

chloride, calcium, not many ions. But the concentration difference of these

ions from inside to the outside determine the batteries.

And these are the ceiling or the floor, where the voltage of the Synapse can go.

It can go either so much positive and it can go so much negative, no more negative

and no more positive. That's your brain limitation, that's the

signal that the brain can generate and just to tell you that the maximum one.

Could be something let's say, like 200 micrometer 200 millivolts, or something

like that, more positive than the resting potential, something like that.

Most negative could go maybe to minus 90 or minus 100 millivolts.

More negative than the resting potential, so minus 24 mil-, millivolt more

negative, so you really cannot go much, you can either go this direction by minus

20 millivolts. You can maybe go this direction by plus

200 or 250 millivolts. And that's the limitation of your signal

in the brain. The brain cannot generate 110 volts.

Or in Israel 220 volts. It can only generate few 100 or so

milli-volts. Maybe 200th positive, maybe minus 90

negative. That's all.

That's all. So that's the regime of signals in the

brain, and these are the signals you have to deal with, in order to represent the

whole world. The whole world, is represented by

signals, that are moving between these two extremes, because, just because.

You are dependent on opening of r channels the signal's in the brain

mostly. This is true also for the action

potential, the spike, which we discuss next lesson.

It all depends on opening of ion channels or closing of ion channels.

And these iron channels are for particular, channel for particular ion.

For example, sodium or potassium or chloride or calcium, and this is

signified by a battery. And this battery is not too big.

That means you can not get more than this battery.

Maybe plus 200 for calcium. Maybe minus 90 for potassium.

But that's your limitiation. So these are the signlas in the brain.

This is the steady state case. The transient case depends also on this

part which you can see that develops the synaptic potential, takes time to

develop. So there is a time constant for the

synaptic potential. We don't need it to discuss it now,

exactly the equation, but in principle you understand whenever you open,

whenever you open a conductance like this for the synapse[SOUND] .

This is your synoptic conductance and you measure the voltage in the circuit, you

will get the synoptic voltage. It could be when you open this

conductance, you will get a synoptic voltage that looks like this because you

open the conductance for a given period of time and then it is closed.

The transmitter interacts with the receptor for a short period of time.

[SOUND] Then you'll get the synaptic voltage here, V of the synapse.

It will look like this if it's a positive, if it's a depolarizing signal.

It will go more positive than the resting potential, and it will attenuate/g.

I will correlate excitatory post synaptic potential, typically.

This is one case. In the other case, when the battery is

reversed, if the battery is reversed. And it's more negative inside, then when

I open these channels, when I change the synoptic conductant g, I will get, a

negative voltage I will call it inhibitory post synoptic potential.

It will go from the resting potential more negatively and then will attenuate

back to the resting potential. This will be my post synoptic potential

which is hyperpolarizing/g. I will collate inhibitory post synaptic

potential and then this one will be a positive post synaptic potential

excitatory. And these are the two synaptic potentials

in the brain. You have two types of synapsis, we've

already discussed it last lesson. Some of the synapsis tend to do negative

voltage, some synapses tend to do positive voltage relative to the resting

potential typically, we will call those that are doing positive voltage,

inhibitory. They tend to inhibit the activity of the

cell, we'll discuss what does it mean. And then, you have some of them, many of

them that are excitatory that tend to excite the cell to make it more

excitable, more firing, the cell, the cell will be more active when you have a

lot of them, and less active when you have a lot of them.

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