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LastClass:Passiveproper/esofthecellularmembrane

Membranepoten/alEquivalentcircuitmodelforthecellmembraneAenua/oninleakycables

ThisClass:Ac/veproper/esofthecellularAc/onpoten/alsElectrophysiologicaltechniques(VoltageClamp)Equivalentcircuitmodel:Hodgkin&Huxley

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Recapques/ons

Definethefollowing:Membranepoten/al Res/ngmembranepoten/al

Reversalpoten/alDepolariza/onHyperpolariza/on

Whatarethemajorionsthatdeterminethemembranepoten/al?

Howisposi/vecurrentdefined?

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Recap:IonicImbalances

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Posi/veionsflowingintheagivendirec/onareequivalenttonega/veionsflowingintheotherdirec/on.

Membranecurrentsareconsideredposi/vewhenthereisposi/veionflowOUTOFthecell.Inwardcurrentis

nega/ve,outwardcurrentisposi/ve.Na+cominginisnega/ve,Cl-cominginisposi/ve.

MoreRecap

IfcurrentIisdefinedinthisdirec/on

I>0 I

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Fromlastclass:Aenua/oninneuralcables

a

m

a

m

R

aR

r

r

2==

Where a is the radius of theprocess, or d/2

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TheAc/onPoten/al

Inthislecture,wewilllookat:

Theac/onpoten/al

Howitarises

Whationsareinvolved

NaandKcurrentsandtheir/medependence

TheHodgkinHuxleymodel

Alilemoreonmyelina/on

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NobelPrize,1963

AlanHodgkin AndrewHuxley

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TheSquidGiantAxon

FirstdiscoveredbyJ.Z.Youngin1936 Controlswaterjetpropulsionduringthe

escaperesponse

1mmindiameter Unmyelinated Thecytoplasmcanbesqueezedoutand

canbereplacedwithar/ficialmedium

Solargethataglasscapillarycanbeinserteddownthelengthofthecellfor

recordingmembranepoten/als

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TheAc/onPoten/alHodgkinandHuxley,1939

Aglassmicropipee,about100min

diameter,wasfilledwithseawaterand

loweredintothegiantaxonofthesquid

aerithadbeendissectedfree.Theaxon

isabout1mmindiameterandis

transilluminatedfrombehind.

Oneac/onpoten/alrecordedbetweentheinside

andtheoutsideoftheaxon.Peaksofasinewave

attheboomprovidedascalefor/ming,with

2msbetweenpeaks

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Percent seawater

Percent seawater

ImportanceoftheNa+ConductanceEffectofreducedNa+onamplitudeandwaveformofac/onpoten/alofsquid

giantaxon

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Increasein

Naconductance

Influxof

+charge

Depolariza/on

Moreincreasein

Naconductance

Moreinfluxof

+charge

Moredepolariza/on

Localdepolariza/on

Regenera/veResponse

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VoltageClamp

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Current-VoltageRela/onsforearlyandlate

Conductances

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Whatischangingwithvoltage?

Couldbe:

1.Ensembleofionchannelsthatareeitheropenorclosed

withaprobabilitythatdependsonvoltage

2.Conductanceofeachionchannelisacon/nuousfunc/on

ofvoltage

Spoileralert!Thecorrectansweris#1

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InstantaneousI-VCurves

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1.Establishthereversalpoten/al(Ex)

fortheinwardandtheoutwardcurrent

2.Ionsubs/tu/onexperiments.

3.Pharmacologicalexperiments

WhatIonsContributetotheCurrents?

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1. Establishingthereversalpoten/al(Ex)fortheinwardandtheoutwardcurrent

WhatIonsContributetotheCurrents?

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2.Ionsubs/tu/onexperiments.

WhatIonsContributetotheCurrents?

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3.Pharmacologicalexperiments.

WhatIonsContributetotheCurrents?

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ConductanceofNa+andK+Channels

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TheHHGateModel

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TheAc/onPoten/al:AQualita/veOverview

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Computerexperiment

hp:www.afodor.netHHModel.htm

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Ac/va/on(noinac/va/on)

MeasuringParametersofK+Currents

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TheNa+Current

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KNalCmiiiii +++=

)(KmKK

EVgi =

)(NamNaNa EVgi =

)()()( KmKNamNalmlm

mm EVgEVgEVgdt

dVCi +++=

4ngg KK =

hmgg NaNa3

=

where,

Therefore,

)( lmll EVgi =

Hodgkin-HuxleyEqua/ons

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Manygatesareinvolved

4ngg KK =

N.B.y=n

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closed open

(1-n) n

ForKcurrents:

n =n (1n)nn

n

t

e

nnnn

=

)( 0

n=

n

n+

n

nn

n

+

=

1

Hodgkin-HuxleyEqua/ons

n

n

n = n(V) n( ) / n (V)

Changingvariables:

Note:alpha,andbetaarefunc=onsofV

Thereforen_infinityandtauarealsofunc=onsofV

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VoltageDependenceofGates

Kcurrent

Nacurrent

nn

n

n

+

=

nn

n

+

=

1

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(V) =Cbase +Camp exp Vmax V( )

2

2

"

#

$$

%

&

''

m(V)=1

1+ expV1/2 V

k

#

$%

&

'(

Generalformofthegatevoltagedependence

Channel V(1/2) K Vmax sigma Camp Cbase

Naac/va/on -40 15 -38 30 0.46 0.04

Nainac/va/on -62 -7 -67 20 7.4 1.2

Kac/va/on -53 15 -79 50 4.7 1.1

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RevisitModel

hp:www.afodor.netHHModel.htm

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TheAc/on

Poten/al:more

quan/ta/vely

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TheoryVs.Experiment

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Myelina/onHelpsSpeedConduc/on

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Recap:

Fundamentalsofac/onpoten/als Wheredoesthethresholdcomefrom? Whatabouttherefractoryperiod?NextClass:

Ionchanneldiversity Howthisleadstodiverseneuronalbehavior Simplifiedneuronalmodels

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Techniques Part 2: Single Channel Recordings

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Techniques Part 2 (contd): Single Channel and Macroscopic Currents

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1. Latency to first opening

2. Duration of channel opening

3. Multiple openings..

Kinetic models

Techniques Part 2 (contd): Single Channel Currents: Parameters

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An Action Potential Arises from the Activity of Single Channels