Download Lecture 10 : Neuronal Dynamics

Lecture10:NeuronalDynamics
DrEileenNugent
OriginoftheCellsRestingMembranePotential:
NernstEquation,DonnanEquilbrium
ActionPotentialsintheNervousSystem
EquivalentElectricalCircuitsandtheDerivationoftheCableEquation
Voltage-GatingHypothesis,Hodgkin-HuxleyMeasurements
OsmoticPressure
Osmosis–flowofwateracrosssemi-permeable
membraneduetoconcentrationdifferenceof
non–permeablesolutes
OsmoticPressure–Pressuredifferenceneeded
acrossmembranetostoposmoticflow
Equilibrium(c)–Fluidpressureconstantinthepore
Osmosis(d-solidline)–Pressureequalonboth
sidespressuredropinchannelcancelsosmotic
pressurejump
Reverseosmosis(d-dashedline)–Pressure
generated>c0kBTonrighthandside.Reverseosmosis
OsmoticPressureandtheCell
GlobularProteinConcentration
CorrespondingSurfacetension
Rp/2=1.5x10-3N/m
⇒ Enoughtorupturecell
SaltConcentration
⇒ BilayerMembranesalmost
Impermeable
⇒ Concentration1027ionsperm-3
⇒ Redbloodcellscan’tmanagethisin
purewater
⇒ Howcanthecellmaintainthisinthe
body?
Whydocellsnotburst?
⇒ Thecytoplasmhasaverydifferent
compositionfromtheextra-cellular
environment
⇒ Whydoesn’tosmoticflow
throughthemembraneburstor
shrinkthecell
⇒ Predictionsforequilibriumstate
don’tquitefitwithrealcellbehaviour
MembranesandIons
⇒ MembranepermeabletoK+
butnotCl-
⇒ HigherconcentrationofK+
insidethanoutside.Samefor
negativecharges(neutrality)
⇒ K+ionscouldincreaseentropy
ofsystembycrossingmembrane
butelectrostaticattractionpulls
themback
Measuringmembranepotential
NernstPotentials
⇒ K+ionscrossthemembranetotry
toerasethedifferencein
concentrationuptoapoint.They
arestillattractedtoCl-ions
⇒ Theyformadiffuserlayeratthe
outermembraneboundary
⇒ Similarlythereisadiffusenegative
layerattheinnerboundary
⇒ Thisgivesrisetoapotential
differencecalledtheNernst
Potential
⇒ InequilibriumtheNernstrelation
givestheNernstpotentialofthe
permanentspecies(K+ions)
NernstRelationandIonFlow
DonnanPotential
(1)
(2)
(3)
IonPumps
OriginoftheCellsRestingMembranePotential:
NernstEquation,DonnanEquilbrium
ActionPotentialsintheNervousSystem
EquivalentElectricalCircuitsandtheDerivationoftheCableEquation
Voltage-GatingHypothesis,Hodgkin-HuxleyMeasurements
Neurons
Synapse
⇒ Input=dendrites(oneofmany)
⇒ Output=axons(onecansplitintotwo)
⇒ Computation:performedinsomasometimescalledcellbody
⇒ Connections:synapse
⇒ Signalinsulation=myelin
Image:Axon
cross-section
NervousSystem:Howareelectricalsignals
transmitted?
⇒ Axonlengthscales:mmtom
⇒ Sciaticnervelongestinhumanbody
withaxons~1mlong
⇒ Howareelectricalsignalstransported
overlongdistancesdespite:
*lossofionsthroughcellmembrane
*ionicfluidresistance
⇒ REGENERATIONmechanismneeded
ImpulseResponse:GradedPotentials
⇒ Membranepotentialactivelymaintainedat-60mV
⇒ Applyadepolarizingimpulse(e.g.injectsomepositivecharges)
⇒ Smalldepolarizingimpulse(membranepotentialvariesbycouplemV)
Gradedpotential
-Thestrengthofthedepolarizationdiminishesovertimeanddistance
(asittravelsdownaxon)andspreads.
-Strengthofsignaldependsonstimulusstrength
-Passivepropagation:signaltravelsonlyashortdistancedownaxon.
ImpulseResponse:ActionPotentials
⇒ Largedepolarizingimpulse(membranepotentialcrossesathresholdvalue)
Actionpotential
-Largesignalwhichdoesnotdiminishpropagatesdownaxonatconstant
speed(0.1–120m/s)
-Propagatingimpulsehasconstantform(‘actionpotential’)
-Peakvalueofresponsetoimpulseindependentofstimulusstrength
-Allornothingpulsegeneration
ActionPotentialMeasurements
~500um
2ms
HodgkinHuxley1939
⇒ Giantaxonofsquid
⇒ Featuresofactionpotential:Changesign,
overshoot
OriginoftheCellsRestingMembranePotential:
NernstEquation,DonnanEquilbrium
ActionPotentialsintheNervousSystem
EquivalentElectricalCircuitsandtheDerivationoftheCableEquation
Voltage-GatingHypothesis,Hodgkin-HuxleyMeasurements
CellMembraneModeling:ElectricalNetworks
fluidinside
Membrane
Fluidoutside
DISCRETE-ELEMENTMODELS
⇒ Modelforsmallpatchofmembrane
ofareaA
⇒ Battery:Nernstpotential
⇒ Resistance:Ionchannels
⇒ Capacitance:Membrane
IonicConductioninaNerveFibre
DISTRIBUTED-ELEMENT
MODELOFAXON
⇒ Eachcylindricalsegment
isdiscretecircuitelement
⇒ ResistanceRRforions
movingacrossmembrane
(passivediffusion)
⇒ dRx,dRx’resistancesto
currentflowingfromone
axialelementtothenextin
cellinterior/exterior
⇒ AssumedRx’negligible
CableEquation
dx
ionicconductivityinsideaxon
ionicfluxacrossmembrane
CABLEEQN
LinearCableEquation
AssumingOhmicconductancethroughmembranegives:
LINEARCABLEEQN
Withresponse
tolocalized
impulse:
Axonspace
Constant
Axontime
Constant
MembraneRestingpotential
⇒ Restingpotentialelectricalpotentialacrossplasmamembraneof
acellthatisnotconductinganimpulse
⇒ Restingpotentialisdynamicallymaintainedbyactivetransport
⇒ Na+concentrationmaintainedfarfromequilibrium
⇒ Rapidincreaseinsodiumconductancewouldrapidlydepolarize
themembrane
SodiumConcentrationandVoltageGating
⇒ Shapeofactionpotentialdepends
onexternalsodiumconcentration
⇒ Peakofactionpotentialtracks
sodiumNernstpotential
OriginoftheCellsRestingMembranePotential:
NernstEquation,DonnanEquilbrium
ActionPotentialsintheNervousSystem
EquivalentElectricalCircuitsandtheDerivationoftheCableEquation
Voltage-GatingHypothesis,Hodgkin-HuxleyMeasurements
VoltageGatingHypothesis
Assumeconductanceis
voltagedependent
NonlinearTravellingWave
Na+channels
closed
Na+channels
open
⇒ Non-lineartermgivestravellingwaveoffixedamplitude✓
⇒ Shape✗
⇒ Onlypossibletosendoneactionpotential
Hodgkin-Huxley
ELECTROPHYSIOLOGYEXPT:EVIDENCEFOR
VOLTAGE–GATEDION-SELECTIVECONDUCTANCES
⇒ Spaceclamping
⇒ Voltageclamping
⇒ Separationofioncurrents
ActionPotentialFeatures
Na+channels Delayedopening K+channels
K+diffusion
Na+channels starttoclose ofK+channels close
open
⇒ Timedependentconductances
letmembranereturntobase
level
⇒ Newpulsecanthenbe
generated
⇒ Cellplayspartofactively
maintainingnon-equilibrium
restingconcentrationofions
⇒ Hodgkin&Huxleyhypothesized
voltagegatedion-specific
channelswhichwerelater
discovered!
ActionPotentialGeneration
• Cellmembranesabilitytoconduct
sodiumisvoltagedependent
• Membranepatch:bistableswitch
betweenVKnernstandVNanernst
dependingonwhethersodium
channelsareopenornot
• Depolarisationofonepatchraises
theneighbouringpatchabove
thresholdgivingaspikeof
membranedepolarisationdownthe
axonatfinitespeed