part iii- the action potential. הודעות ספרים מומלצים: להולכה פסיבית:...

Part III- the action potential

הודעות

from neuron to ספרים מומלצים: להולכה פסיבית:•brain/Nicholls (4-5)פרקים

)פרק principal of neural science/Kandelלפוטנציאל פעולה: •nicholls ב6( או פרק 9

Rehearsal

As we said• Membrane potential is the adjusted sum of equilibrium potential

of it’s ions )mostly K, also Na and Cl(.

These are all concentration dependent channels.

Which other type of channels are possible?• The flow for each Ion is determined by it’s conductance and

driving force. The flow in each channel can be described by V=IR.

In which cases is the curve non linear?

• The entire flow can be described as parallel RC circuit.

time constant is τRC, )exponential increase(

• The membrane also serve as a cable: Input is transmitted till trigger zone where action potential is created and it is transmitted from there to axon.

Space constant is and resistance can be retrieved.

Axonal size effect R’s )preserves voltage better(-safety factor, myelin…

Conductance velocity is determined by

a

m

r

r

the paradigmatic view

• Input arrive to dendrites in the form on Voltage change.• Voltage flow passively to axon hillock• In axon hillock starts the active process of Action Potential.• Action potential travels )regenerated( along the axon to cause Transmitter release in the synapse )gap( between neurons.

This is the output• Transmitter attaches to receptors in dendrites of following

neuron, causing voltage change…

)starting point sensing receptor-skin, eyes… end- muscle. All that is in the middle between sensation and action, is in the input-output relationship, somehow…(

The action potential- phenomenology

Shortly: It’s an electrical signal –high amplitude )up to 100mV(

lasting ~0.5-1ms non-attenuated

The ending first: positive feedback through depolariztion dependent Na channel, followeed by a negative feedback through depolarization dependent K channel

Action potential phenomenology - different time periods

• A-resting potential• B-threshold

)sufficient depolarization(, followed by rapid depolarization until a certain peak

• C-re-polarization• D-after hyper-

polarization

The action potential phenomenology- what would you check for?

• You have intra- and extra-cellular recordings• You can change the stimulus• You can try dissociating ions )how(• You can influence Vm )how?(

=>What would you do to DECRIBE the phenomena?

The action potential- phenomenology)what Hodgkin did( I

Threshold- “all or none” either full action potential, or nothing

)note- “big enough stimulus” can indicate bigger amplitude of stimulus or longer duration(

)first intuition- what does it tell us about the mechanism? can it be dependent solely on driving forces changes?)

all

None

1. it’s the conductance

• If it was the driving force it would be linear )no threshold(• Also, Curtis found it )Cole and Curtis, 1938( :

How would we call such I-V curve? What it is assumed to be influenced by?

(note: this dependence start at about half of the voltage of the AP threshold- the process starts before)

The action potential

mechanism-

• How can g be calculated? Ii=gi)Vm-Veq( =>gi= Ii/ )Vm-

Veq(. In voltage clamp we manipulated Vm and measure I- we can extract g.

• But not in intra-cellular recordings since g & Vm are now interdependent g(Vm) Vm(g)

Vm is controlled)Vm=Vc) in voltage clamp

Rtotal

C

II

Idt

dV

0

0


mechanism

The action potential- phenomenology)what Hodgkin did( II

Refractory period• Absolute: No amount of current will produce a second action

potential• Relative: Second action potential will be achieved with only with

larger currents )threshold increased(

The action potential- phenomenology)what Hodgkin did( III

Accommodation - extension of the refractory period concept-• If a cell is held )by voltage clamp!( at long sub- threshold

depolarization, threshold increased )analogous to relative refractory period(

Also taken to the extreme-a big/long enough depolarization will

increase threshold to ∞ (analogous to absolute refractory period(- Depolarization block

• Also opposite- if held at hyper- polarization, threshold decreases. With enough hyper-polarization- Vm is above threshold )anodic break response(

The action potential mechanism- what did Hodgkin & Huxley check?

• Is it all ions or part? Separating ion currents• Understanding the mechanism causing ion changes

2. it’s not all ions

• Overshoot- if permeability would have been increase for all ion the maximal peak of the action potential would have been 0mV. It’s bigger )Hodgkin and Huxley, 1939(

What is it closer to?

(1909-K is in repolarization. 1945-K is sufficient)


mechanism

So far we know that there are:

depolarization dependent Na channels->positive feedback

Later depolarization dependent K channels->Negative feedback

What can this alone explain?

How can we prove it is Na and K indeed?

3.Separating ions- several methods

• Changing concentration of extra-cellular ions. Or better-exchange )putting choline extra-cellularly instead of Na )why is it better to put something instead?) .problem-changes more then we wished.

• Changing Vm )by voltage clamp()note- NO AP!(

• Specific toxins, if you have ones, of course.

TTX is one


mechanism

Separating ions-results from concentration change

• The amplitude of the action potential increase as

extra-cellular concentration of Na are increased.

=>:the amplitude of the action potential is due to Na current!

If Na was replaced by choline

What would have happened?


mechanism

Separating ions-results from Voltage clamp

• A fuller explanation: When voltage is held constant above threshold there is inward current )which ion would move inward passively?), followed by outward current )which ion would move outward passively?)

• The inward current is Na, K is probably outward )no proof yet(

• Notice I-K is slower. Why?• Notice II- Na stops while stimulus

continue- why?


mechanism

Separating ions-results from toxins

• TTX - High affinity voltage dependent Na+ channel blocker )also Saxitoxin and cocaine to a lesser extend( (, proves that early current is Na- a specific voltage dependent channel!

• TEA - Low affinity voltage dependent K+ channel blocker )also apamin(, proves that later current is K- a specific voltage dependent channel!


mechanism

How did they find the right ions?

Changing concentrations, voltage clamp, specific toxins

)with voltage clamp(

Rehearsal

• Each ion current’s direction is determine by Nernst, Vm by all ions that have channels )dependent on their Z(

• Ion pass passively according to V=IR, with an exponential charge )rate dependent on RC), and decay )rate dependent on (

• In parallel, depolarization dependent Na and K channels exist in the cell )highest distribution- on the axon hillock, the paradigmatic “spike initiation zone”(. H & H found that action potential is due to conductance change )“depolarization dependent”(, leading to first a flow of Na, then K.

a

m

r

r

Re-constructing the currents: • Na faster and Stubbed, • K slower and longer

Open questions- • Why is Na faster then K?• Why is NA current terminated while

K continues?

How did they find the right ions?

Changing concentrations, voltage clamp, specific toxins

)with voltage clamp(

The basic mechanism

• Conductance increase and is voltage dependent• The ions flowing are first Na )inward( until peak, followed by

K )outward(

Conclusion about mechanism- positive feedback for Na causes rapid depolarization.

Negative feedback for K causes later

re-polarization )maybe also after-hyper

polarization?(


mechanism

Re-constructing the currents: • Na faster and Stubbed, • K slower and longer

Open questions- • Why is Na faster then K?• Why is NA current terminated

while K continues?

Explaining phenomenology- threshold

Two possibilities-

1. Enough voltage is needed to open the voltage dependent channels?

2. Enough Na current )in voltage dependent channel( is need to overcome K hyper polarization to create positive feedback

-what do you think?

-How would you test it?

Explaining phenomenology

Explaining phenomenology-the action potential

• Resting potential Σcurrent=0 -> K=Na+Cl -> K>Na

With depolarization Na voltage dependent channels open )K not yet(, increasing Na threshold: Na=K.

Then Na increase to create depolarization to increase… this is the rapid depolarization. Maximal peak= ENa )55mV(

Maximal peak isn’t always reached:

K voltage dependent current opens,

Causing hyper-polarization and the

re-polarization and

after-hyperpolarization phases.


Evidences from single channel recording

• From a much later times, when there were single channels recording and Na voltage dependent channel was known )and traceable(


mechanism

more issues : 1. what do we see in voltage clamp

Voltage dependency:

what do we see?

Reversal potential


mechanism

2. The currents

• currents dependency on voltage- as extracted from voltage clamp:

K current is outward above -60mV

inward below

Na current is inward, decreasing

when bigger then 0mV and outward

above 55mV. Why the decrease?

G and driving force interplay


I-V curve

K

Naoutward

intward

3. conductance

• Conductance time dependency as extracted from voltage clamp

=>Well someone will have to

explain this Na inactivation

Someday…

gion=Iion

Vm-Eion

Explaining phenomenology- what is missing here?

• We are yet unable to explain refractory period and accommodation, so lets do discuss this inactivation..

Activation: Increased probability of channel opening with depolarization )in case on voltage sensitivity(.

Deactivation: the natural closing of the channel.

Inactivation- active blocking of a channel )a type of control mechanism over opening type(

De-inactivation- the natural ceasing of the inactivation process…

=>The Na Channel goes through inactivation

The PEAK conductance

• Conductance )peak conductance!( voltage dependency as extracted from voltage clamp:

1. Conductance is

monotonically increasing

2. It isn’t an exponent, it’s a

Sigmoid )several exponents,

Indicating reaction of higher

degree(


gion=Iion

Vm-Eion

A second look at conductance

We have two channel )for K and for Na( that are:• Voltage dependent• Sigmoid )few exponents(

Shaped• Similar, but not identical

)K is more sigmoid then Na(• Na have inactivation

(why not visible in the

voltage dependency graph?)

HH model

Introduction to action potential- first order reactions

Probability to open a channel is Probability to close a channel is (P(close) ≠1-P(open) (

Voltage dependent=> changes with voltage

closeopen

1-n α(V) n

closed β(V) open

An exponential process with )(

1

)()(

0

tN

dt

dN

nndt

dn 1

)(1)( V

t

neVnn

At a given V, n will approach n∞ in an exponential rate with time constant biggerfaster reaching n ∞(

)()( Vnndt

dnVn

ndt

dn

nndt

dn

1

1At equilibrium

For specific V

The Hodgkin Huxley model for channel conductance )“gating model”(

Assumptions:• membrane can be describe by RC circuit analogy• Membrane channels are separated and independent of each

other• Membrane channel are ion selective• Membrane channel transit between two states- “open” and

“close”

First order reaction is the probability to open. to close.

are independent of each other )as if there are infinite ions(. How many gates will be open at equilibrium?

HH model

nopen nclose

1-n α(V) n

closed β(V) open

For a first order reaction )Hodgkin Huxley(:

nndt

dn 1

nndt

dnVn )(

)(1)( V

t

neVnn

HH model

If is P)open(, =P)close(n opened, 1-n closed

Then a change is

exponential increase and decrease

ndt

dn

nndt

dn

1

1

n ∞ =a/a+b=1/a+b

K+ conduction is sigmoid= 4 first order reactions=4 n gates

10

),( 4

n

ngtVg KK

HH model

With a pencil, H& H found that 4 mounted exponents fit the K sigmoid=>The K channel have 4 gates, opens only when all have opened

nn4

n∞

Na+ conduction is sigmoid= 3 first order reactions=3 m gates

HH model

With a pencil, H& H found that 3 mounted exponents fit the K sigmoid=>The Na channel have 3 gates )m( and an inactivation gate )h( opens only when all have opened

10

),( 3

n

mgtVg NaNa

Implications I- the voltage dependent element is

• For gates N and M-increase with depolarization, decrease

• For gate h- M-decrease with depolarization and increase

HH model

αβ

α β

V

Gates time constants

m

h

n

Dependence of time constants on voltage: m only in depolarization, n& h are slower at it )but available also in hyper -polarization

Time constants at threshold depolarization:M>n~>h

Gates voltage sensitivity

• Dependence of channels on depolarization>m>h

The final Hodgkin Huxley equations

)()(

)()(

)()(

34

Vhhdt

dhV

Vmmdt

dnV

Vnndt

dnV

VVhmgVVngVVgIdt

dVC

h

m

n

NamNaKmKlmlext

HH model

M=α (u) (1 - m) - β (u) mN=α (u) (1 - n) - β (u) nH=α (u) (1 - h) - β (u) h

The Hodkgin-Huxley model of action potentials - currents

extRC III

extNamNaKmKlml IEVgEVgEVgdt

dVC )()()(

extKNaNaKmKlml IEVhmgEVngEVgdt

dVC )()()( 34

extNaKl IIIIdt

dVC

L-leak )passive channels(

Real numbers

3.036120 LKNa ggg

h v 0.07exp v /20

h v 1

exp 30 v /10 1

m v 0.125 v

exp 25 v /10 1

m v 4exp v /18

n v 0.0110 v

exp 10 v /10 1

n v 0.125exp v /80

Evidences- a biochemical model for the gates and inactivation

HH model

And the K channel as 4 voltage sensitive domains

The ball and chain model for inactivation

Armstrong and Benzilla, 1977

Basic structure

3-D Na+ )and Ca+( channel specificity

• )Na is smaller then K( outer mouth:2 p loops with glutamic acid )-(, select cations

• inner mouth: 0.3x0.5nm pore )enough for Na+•H20 or smaller-not K(

More elaborated structure )Na and K(

Shaker A type K+ channel

Voltage activated Na+ channel

pore

voltage sensor

Inactivation segment

HH model

Selectivity filter )both Na and K(

For K:

Ion flow

Voltage sensor -S4 helix • Present in all voltage

sensing channels• Every 3rd residue is a charged lysine or arginine • Depolarization causes movement of their C termini from

cytosolic to exoplasmic surface → gate opening• Activation involves movement of 12-14 charges

Inactivation segment-• Na+ channel: Cytoplasmatic plug connecting S3 and

S4)Evidence:Pronase is a proteolytic enzyme specific for blocking inactivation

For K calculation show the ion transfer

Energy states for more/less ions

Selectivity to K by size

Berneche S & Roux B 2001

Explaining phenomenology- the action potential

• Resting potential Σcurrent=0 -> K=Na+Cl -> K>NaWith depolarization Na voltage dependent channels open

)K not yet(, increasing Na threshold: Na=K.Then Na increase to create depolarization to increase…

this is the rapid depolarization. Maximal peak= ENa )55mV(

Maximal peak isn’t always reached:K voltage dependent current opens,Causing hyper-polarization and the re-polarization and after-hyperpolarization phases.

Explaining phenomenology- the action potential-conductance

• Resting potential G)Na(>G)k( )but I)k( is bigger(.• With depolarization g)na( increases )m gates(, if enough for

I)Na(>I)K( the depolarization will increase G)Na( )m gates( - rapid depolarization.

• Then G)k( increase )n gates( and G)Na( decrease)h gate(- re-polarization and

after-hyperpolarization )because G)k( decreases with delay(-refractory period• Returning to Vm G)Na( react faster then G)K(-Supra normal period)

Explaining phenomenology- refractory potential again

• Refractory period depend upon the time constant of gate h-

at the re polarization period of the action potential gate h is closed. Re-polarization and after hyper-polarization will open it, but with delay.

All closed- absolute refractory

some opened- relative refractory.

Accommodation, Depolarization block and anodic break

• True on longer time scale- long depolarization will close h gates, elevating threshold.

If elevated so that no threshold is feasible- Depolarization block

• also the opposite-long hyper-polarization will open h gates, lowering threshold.

If lowered so the Vm is above threshold- anodic break response.

What does it means that hyper-polarization can open more h gates?

Not all h gate are opened at Vm- Inactivation function

• Accomodutions

Effects = fraction of

h gates opened.

What else is this line

Similar to?

In Vm-60% .Why?

pronase

• Blocks Na channel inactivation

how will it effect- the Action Potential?

refractory period?

accommodation?

general information

transmit?

Method to see only Na activation: pronase conditioning hyper-polarization very brief stimulus

Side note pronase allows viewing Na+ deactivation

1. Pronase

Vm

INa

Oddities

• A second look at the Na current

Now do you understand better the time constant for h and m?

voltage

current

Oddities II-current window

Behavior of H and M gates is opposing. The depolarization required for the transition in interleaved. Result- depolarization window where there’s constant current

Improvement) few examples(

• Azouz 2000- since the h gate in depolarization dependent, a slow increase in depolarization will close more h gate then a fast increase-> Action potential threshold will be smaller for lager depolarization pulse then a slow one. When do we see large depolarization pulse- when the input is synchronized. Meaning- threshold prefer coincidences

• Naundorf 2006- the m gates are not independent )at least in the

cortex where they measured, but cooperative- opening one increase the likelihood of the other gates to open, making the rapid depolarization steeper )as indeed they find( and making synchronous input more preferable.

Action potential conductance

• Saltatory conductance- only in nodes of renviar.

• Formally- depolarization should be carried from dendrite to axon hillock, and then action potential should be carried across )myelin coated( axon. Actually- from all places to all place.

Speed is depend upon myelin and size and )locally( upon

Action potential conductance is unidirectional

Depolarization spread passively to both sizes, but depolarization is unidirectional- in the place last AP occur there is still refractory.

Notice- depolarization will spread passively back to dendrites-Back propagation

Hyper-polarization will spread passively-how will it effect future activation?

Variations in excitability along the neuronAxon hillock: lowest threshold:High density of Na+

channels,Voltage gated channels sensitive to near Vr

Nodes of ranvier: many Na+ and leak channels )1000-2000 chnls/μm2(

And also:Presynaptic terminals: Voltage sensitive Ca2+ channelsDendrites: voltage gated Ca2+, K+ and Na+ channels capable of

producing APs

The H&H variations-in space

Action potential propagation

Depolarizatin fades in time and space, action potential regenerates.

In the Axon-Salutatory conductance jumping between nodes of renviar.

Formally- depolarization should be carried dendrite-> axon hillock)action potential(

->axon)ranier(->pre synaptic terminal Actually- from all places to all place.

Speed is depend upon myelin and size and )locally( upon



Notice- depolarization will spread passively back to dendrites-Back propagation

Part IV- Single neuron computation

Models of action potential

H&H is a good “conductance model”, but most models are simpler: They use “integrate and fire neurons”-

• point neurons )no spatial considerations(• every input give small depolarization / hyper-polarization -

excitatory or inhibitory but of costant size)+1 or -1(.• The inputs are summed. The only determining factor is

above/below threshold)and the threshold is constant(

1.linearly summing all inputs )conductance is passive(2.threshold impose non linearity is a low pass filter(= AND &

OR functions

=>McCullough and Pitts)1943(- This is sufficient to allow any computation

Integrate and fire models

Simple common model- leak integrate and fire:Summing input across time: V)t(=Vm+Rm*Ie)1-exp)-t/Time difference )isi( between spike is linear to input amplitude

1

ln1

thLem

resetLemm

isiisi VEIR

VEIR

tr

I&F : What will input integration be dependent upon? integration in time

Two stimuli arrive with a time difference. Will they be united to a bigger stimulation or be separated? Dependent on As increase, stimuli are less separable

Very brief: low firing rate, coincident detectionProlonged: higher rate, lower sensitivity

Problems with I&F

I & F models are DETERMINISTIC- Same input will necessarily lead to same firing rate, and all the cell can do is add up inputs )not only the AP is “all or none”, the neuron is “all or none”(.

Theoretically, this played a big part in the bottom up approach to visual processes- basic features are added up to more complex features…

In reality input and threshold ARE NEVER CONSTANT

Inadequacy of I&F models• Problems:

1. No inactivation )or other conductance references(-can be imposed on the models

2. Regular firing- if input is same on average , I&F model will produce very regular periodic firing rate with constant Inter Spike Interval )ISI(

Tal & Schwartz 1999

1

ln1

thLem

resetLemm

isiisi VEIR

VEIR

tr

3.Nonlinear I-V curve

In reality, neurons have near Gaussian firing rate.

Rate/Noise: for Gaussian =1, for integrate and fire ∞, for neuron ~1.2).

Tal & Schwartz 1999

Realistic ISI distribution

I&F inadequacy solutions

TYPE I-assume that the neurons ARE DETERMINISTIC therefore their only source of variance is the input. Therefore claiming that input is naturally Poisson-like )true(. Especially true for high threshold and small

Cannot explain why experiment

controlling input give variable results

Increasing input variance will broder ISI distribution,

Stevens & zador 1997

Variable input make variable

firing rate

TYPE II- assuming non deterministic response and implementing it by any of the various non linear component of the neuron-voltage gated ion channels, channel is difference kinetics, differential distribution of channels, morphological changes…

Strong VS weaker negative feedback, softky & koch 1993

Sometimes give good predictions

Conductance models

Adding to H&H specific channels known to be found in various cells, or known geometry…

Multitude of voltage activated channels:• 4 subtypes of voltage activated Ca2+ channels• Voltage activated Cl- channels• Voltage activated non-selective cation channels• Activation in hyperpolarization )h type(• Ca2+ activated voltage dependent K+ channel• Rapid, inactivating K+ channel )A type(

“Allows complex information processing”

Example: Epilepsy in mutant mice lacking Ka channels

Example of other channels’ importance- Action potential is not the only spiking mechanism

Burst firing due to Ca firing:• Exist cells with 2 additional type of channels:

1. T type voltage activated Ca channels )T for transient(- open at very low threshold, inactivate fast.

2. L type voltage activated Ca channels )L for long(- open only at higher threshold, very very slow de-activation )not inactivation-what is the difference?(

=>T open at low threshold )Vm(->inward current->depolarization-> action potential )T close(->higher depolarization->L open for long period- chain of action potential

)what stops it?(

Burst firing due to Ca firing:

=>T open at low threshold )Vm(->inward current->depolarization-> action potential )T close(->higher depolarization->L open for long period- chain of action potential

what stops it?

When will it start again?

How are the action potential effected?

• Burst firing due to Ca firing: what will happen at these cells if held depolarized?

Conclusion- Action potential isn’t everything!

Action potential conductance

• Saltatory conductance- only in nodes of renviar.

• Formally- depolarization should be carried from dendrite to axon hillock, and then action potential should be carried across )myelin coated( axon. Actually- from all places to all place.



Hyper-polarization will spread passively-how will it effect future activation?

Variations in excitability along the neuronAxon hillock: lowest threshold:High density of Na+

channels,Voltage gated channels sensitive to near Vr

Nodes of ranvier: many Na+ and leak channels )1000-2000 chnls/μm2(

And also:Presynaptic terminals: Voltage sensitive Ca2+ channelsDendrites: voltage gated Ca2+, K+ and Na+ channels capable of

producing APs

The H&H variations-in space

part iii- the action potential. הודעות ספרים מומלצים: להולכה פסיבית:...

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