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Bioelectricity: action potential Principle As a type of a propagating disturbance of the nerve (or muscle) membrane potential the electrotonic propagation has been described in Bioelectricity: electrotonic propagation . It happens in dendrites, axons and muscle fibers. These structures can be some mm long, but axons and muscle fibers are mostly some cm and axons may reach many meters (as in whales). However, mostly an electrotonic potential is strongly reduced along distances of centimeters, is propagating slow and, due to temporal filtering, the peak time at the nerve terminal will not be very well defined. Therefore it is not very appropriate to transmit information over long distances in living organisms. There exist a better way of propagating nerve information. This is via action potentials (spikes), an active way of propagation. With spikes information transport is faster, with higher temporal resolution and more information can be transmitted. Spikes arise from the somatic potential, the sum of the dendritic potentials, at the axon hillock and then propagate along axons (sometimes certain types of dendrites), muscle fibers and also heart muscle fibers. Fig. 1 visualizes this propagation. Fig. 1 Principle of propagation. Fig. 2 depicts the 3 main types. Spies are found in vertebrates and invertebrates, but also some plants (relying on K + and Ca ++ , with the phloem as channels). Fig. 2 From left to right action potential of axon, muscle fiber and heart muscle cell. Depolarization and repolarization Below the axonal spike, the ‘common’ one is described, first for an unmyelinated axon. Fig. 3 gives the various phases which can be distinguished during its time coarse. Often one dendritic potential can give rise to a couple of spikes, depending on its amplitude. A propagating spike generally maintains its waveform and amplitude. This is caused by the fact that the membrane conductance g m (= 1/r m ) of the axon is not constant. An excellent way to investigate the changes of the conductances is the voltage clamp technique (holding the membrane potential at a constant value whatever injected current is needed, see Electrophysiology: clamping techniques ). Essential for this technique is that there flows no axial current through the axon. In a thick axon (squid), this is achieved by inserting a fine silver wire longitudinally in an axon. By an intracellular electrode and an extracellular electrode current is injected into the axon to compensate for changes in current through the membrane. The current needed in the clamp technique compensates the ionic currents (and the initial capacitive current) and is measured as a function of time. According to Ohm's law the total ionic current at any time is proportional with the total membrane conductance since the membrane potential is kept constant. The Na + and K + conductances can be measured separately by applying certain drugs which make either the Na + or the K + conductance zero. The Na + and K + have different types of pores, i.e. selective channels. The permeability for Na + and K + appears to be a function of the membrane potential. In rest, most Na + channels are closed, but the K + channels open, causing a constant leaking out of K + . This is way the rest potential is mainly determined by K + with its 75 times higher conductivity. The outflow of K + is constantly compensated by Na + inflow. If now the membrane is stimulated and either depolarized or hyperpolarized the membrane potential will change with time, resulting in timeandvoltage dependent ionic resistances. Now r m is composed of a resistance r Na formed by the Na + channels, a resistance r K formed by the K + channels and r L formed by other passive ionic channels, mainly for Cl ─ , each of them connected with the Nernst equilibrium potential (see Bioelectricity ). The channel mechanisms involved in the generation of a spike are the rapid increase in the permeability for Na + and the delayed and slower increase in the permeability for K + if the cell is depolarized (socalled cathodal stimulation). Na + moves in under the influence of the driving force, the difference between the membrane potential and the equilibrium potential of Na + . In the squid axon this occurs in a few ms. As soon as the Na + permeability (or conductance) increases, more Na + streams into the axon or soma, diminishing the membrane potential still further. This causes a further increase of the Na + permeability and at a certain critical value, the firing threshold (about 15 mV more positive than E rest ) this becomes so strong a positive feedback that the cell even reverses its potential to positive values in the direction of the Na + equilibrium potential. Actually, the threshold is reached when the inward Na + current exceeds the outward K + current. Very shortly afterwards

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  • 5/22/2015 Generalliterature

    http://onderwijs1.amc.nl/medfysica/doc/Biolectriciy%20actionpotential.htm 1/5

    Bioelectricity:actionpotentialPrincipleAsatypeofapropagatingdisturbanceofthenerve(ormuscle)membranepotentialtheelectrotonicpropagationhasbeendescribedinBioelectricity:electrotonicpropagation.Ithappensindendrites,axonsandmusclefibers.Thesestructurescanbesomemmlong,butaxonsandmusclefibersaremostlysomecmandaxonsmayreachmanymeters(asinwhales).However,mostlyanelectrotonicpotentialisstronglyreducedalongdistancesofcentimeters,ispropagatingslowand,duetotemporalfiltering,thepeaktimeatthenerveterminalwillnotbeverywelldefined.Thereforeitisnotveryappropriatetotransmitinformationoverlongdistancesinlivingorganisms.Thereexistabetterwayofpropagatingnerveinformation.Thisisviaactionpotentials(spikes),anactivewayofpropagation.Withspikesinformationtransportisfaster,withhighertemporalresolutionandmoreinformationcanbetransmitted.Spikesarisefromthesomaticpotential,thesumofthedendriticpotentials,attheaxonhillockandthenpropagatealongaxons(sometimescertaintypesofdendrites),musclefibersandalsoheartmusclefibers.Fig.1visualizesthispropagation.

    Fig.1Principleofpropagation.Fig.2depictsthe3maintypes.Spiesarefoundinvertebratesandinvertebrates,butalsosomeplants(relyingonK+andCa++,withthephloemaschannels).

    Fig.2Fromlefttorightactionpotentialofaxon,musclefiberandheartmusclecell.DepolarizationandrepolarizationBelowtheaxonalspike,thecommononeisdescribed,firstforanunmyelinatedaxon.Fig.3givesthevariousphaseswhichcanbedistinguishedduringitstimecoarse.Oftenonedendriticpotentialcangiverisetoacoupleofspikes,dependingonitsamplitude.Apropagatingspikegenerallymaintainsitswaveformandamplitude.Thisiscausedbythefactthatthemembraneconductancegm(=1/rm)oftheaxonisnotconstant.Anexcellentwaytoinvestigatethechangesoftheconductancesisthevoltageclamptechnique(holdingthemembranepotentialataconstantvaluewhateverinjectedcurrentisneeded,seeElectrophysiology:clampingtechniques).Essentialforthistechniqueisthatthereflowsnoaxialcurrentthroughtheaxon.Inathickaxon(squid),thisisachievedbyinsertingafinesilverwirelongitudinallyinanaxon.Byanintracellularelectrodeandanextracellularelectrodecurrentisinjectedintotheaxontocompensateforchangesincurrentthroughthemembrane.Thecurrentneededintheclamptechniquecompensatestheioniccurrents(andtheinitialcapacitivecurrent)andismeasuredasafunctionoftime.AccordingtoOhm'slawthetotalioniccurrentatanytimeisproportionalwiththetotalmembraneconductancesincethemembranepotentialiskeptconstant.TheNa+

    andK+conductancescanbemeasuredseparatelybyapplyingcertaindrugswhichmakeeithertheNa+ortheK+

    conductancezero.TheNa+andK+havedifferenttypesofpores,i.e.selectivechannels.ThepermeabilityforNa+andK+

    appearstobeafunctionofthemembranepotential.Inrest,mostNa+channelsareclosed,buttheK+channelsopen,causingaconstantleakingoutofK+.ThisiswaytherestpotentialismainlydeterminedbyK+withits75timeshigherconductivity.TheoutflowofK+isconstantlycompensatedbyNa+inflow.Ifnowthemembraneisstimulatedandeitherdepolarizedorhyperpolarizedthemembranepotentialwillchangewithtime,resultingintimeandvoltagedependentionicresistances.NowrmiscomposedofaresistancerNaformedbytheNa+channels,aresistancerKformedbytheK+channelsandrLformedbyotherpassiveionicchannels,mainlyforCl,eachofthemconnectedwiththeNernstequilibriumpotential(seeBioelectricity).ThechannelmechanismsinvolvedinthegenerationofaspikearetherapidincreaseinthepermeabilityforNa+andthedelayedandslowerincreaseinthepermeabilityforK+ifthecellisdepolarized(socalledcathodalstimulation).Na+movesinundertheinfluenceofthedrivingforce,thedifferencebetweenthemembranepotentialandtheequilibriumpotentialofNa+.Inthesquidaxonthisoccursinafewms.AssoonastheNa+permeability(orconductance)increases,moreNa+streamsintotheaxonorsoma,diminishingthemembranepotentialstillfurther.ThiscausesafurtherincreaseoftheNa+permeabilityandatacertaincriticalvalue,thefiringthreshold(about15mVmorepositivethanErest)thisbecomessostrongapositivefeedbackthatthecellevenreversesitspotentialtopositivevaluesinthedirectionoftheNa+equilibriumpotential.Actually,thethresholdisreachedwhentheinwardNa+currentexceedstheoutwardK+current.Veryshortlyafterwards

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    theNa+permeabilityreturnstoitsoriginalvalueandtheK+permeabilityincreasestemporarily.AswiththeNa+influx,itisnotthemovementofK+thatchangesE.ItisthevalueforgKrisingabovethatforgNa,draggingEbacktowardstheequilibriumconstantforK+.SincethevoltagegatedK+channelshaveadelayedresponse,suchthatK+continuestoflowoutofthecellevenafterthemembranehasfullyrepolarized.Thiscausestheundershoot(shorthyperpolarization).ThereisacommonmisconceptionthattheNa+/K+pumprestorestherestingpotentialduringthespikefallingphasebyactivelypumpingNa+outandK+intotheneuron.This(alongwiththemisconceptionthatsodium'floods'thecelltocausethespike),isnotcorrect.TheNa+/K+ATPase(thepump)doesultimatelymaintaintherestingpotentialbymaintainingtheconcentrationgradientsforNa+andK+,butdoessoonamuchslowertimescale.

    Fig.3Basictimecoarseofactionpotential.RefractoryperiodDuringashortperiodaftertheoccurrenceofaspikethecellcannotbestimulated.Thisistherefractory(15ms)periodconsistingofanabsoluteandrelativephase.Intheformer,theNa+channelscannotbeopenedbyastimulusirrespectiveofappliedvoltage.Inthesubsequentrelativephase,spikescanbeinitiated,sinceNa+channelsarereactivated(inastochasticmanner)butthethresholdisgreater.ThisiscausedbytheslightlyhyperpolarizedstateduetostillhigherthanrestingvalueforgK,somorevoltageisrequiredtoreachthreshold,andalsothethresholditselfishigherthanusualbecausesomeoftheNa+channelswillstillbeinactivated.(NotethatNa+channelhasatleastthreestates:closed,openandinactivatedclosedandnotabletoopen).Therefractoryperiodisimportantbecauseitensuresunidirectional(oneway)propagationofthespike.Thebasictheoryofspikepropagation,theHodgkinHuxley(HH)theory,isdescribedinMoreInfo.ApplicationSpikes,mostlyintheformofspiketrains,areusedmostextensivelybythenervoussystemforcommunicationbetweenneuronsandfortransmittinginformationfromneuronstootherbodytissuessuchasmusclesandglands(neurohypophysis).SpikesaremeasuredwiththerecordingtechniquesofelectrophysiologyandmorerecentlywithneurochipscontainingEOSFETs(electrolyteoxidesemiconductorfieldeffecttransistor).Suchchipsareappliedinretinalandcorticalimplantstorecordandstimulateneuronalactivity.(Acochlearimplantisformallynotaneurochipsinceitisonlyusedforstimulationitisaneuroprosthesis).Anoscilloscopeshowingthemembranepotentialrecordingfromasinglepointonanaxonshowseachstageofthespikeasthewavepasses.Aspeakerisveryusefultolistentotheelicitedspike(trains).Spikesingeneralcannotbemeasuredatdistance,since,dueoitsdipolenature,itdiminisheswiththethirdpowerofdistance.Theelectrotonicpotentialchangescausedbysynaptictransmissionwhich,ifstrongenough,giverisetothespike,havealessstrongdecaywithdistance.Theyalsolastlonger.Ifthereisenoughgeometricalcoordinationbetweenagroupofexcitedneurons,socalledsloworgradedpotentialscanberecordedforinstanceontheskullofman.Theyarealwayssignofmassaction.IftheyarespontaneouswespeakoftheEEG,iftheyareexcitedbylight,soundorperipheralnervestimulationwespeakofvisual,auditoryorsomatosensoryevokedpotentials(EPs)respectively.Alsotheelectroretinography(ERG)reflectsgradedpotentialsandnotthespikesoftheopticnerve.Somediseasesreducethespeedofspikeconductance.Themostwellknownofthesediseasesismultiplesclerosis,inwhichthebreakdownofmyelinimpairscoordinatedmovement.MoreInfoTheconductancesforNa+andK+changeaccordingto:gNa+=Na+m3h,gK+=K+n4,(1)whereNa+andK+arethemaximalconductances.Thevariablesn,m,andhhaveavaluebetween0and1.IntheequationfortheK+conductancen4denotesthefractionoftheK+channelswhichareopen.Ifallchannelsareopenthenn4n1.Ifallareclosedn=0.ApparentlyfoureventsofequalnaturehavetocoincidetoopenthefourfoldedlockedK+

    channel.FortheNa+channeltwokindsofkeys(events)areused.Threeidenticalkeysareneededtoopenthethreefoldedmlock.Anotherlock(h)isopeninrest,butcloseswhenthemembraneisdepolarized.Thesefractionsm,handn

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    arevoltageandconsequentlytimedependent.Theycanbefoundbysolvingthreeexperimentallyfounddifferentialequations.Fornthisequationis:dn/dt=n(1n)nn(2a)wherendenotestheopenconditionandntheclosedcondition.ThisisvisualizedinFig.4a.Aftersolving,nappearstobeapositiveexponentialfunctionofthemembranepotentialEandnisanegativeone(Fig.4b1).SinceduringexcitationEchangeswithtimethetwovariablesalsochangewithtimewhatfinallyresultsintheinitiallyprogressiveincreaseofn4,forastepwisechangeofE(Fig.4c1).Fig.4c2givesthefinalvalueofnandn4measuredduringvoltageclamp.ForNa+wehavetodowithachangeofmandh.Bothcanbecalculated.Thedifferentialequationsare:dm/dt=m(1m)mmand(2b)dh/dt=h(1h)hh.(2c)

    Fig.4Thegatingmodelforpotassiumandsodium.b2)ande2)depictthedependencyofnandn4,andm,handhm3,whenavoltagestepisappliedverylong(infinite).Thetimecourseofmlookslikethatofnbutisfaster.However,hbehavesdifferently.Itdecreasesinsteadofincreasesduetothedecreaseofhandincreaseofhwhenthemembraneisdepolarized(Fig.4e2).Therefore,alsoforlonglastingdepolarization(voltageclamp)theNa+conductancerestorestoitsoriginallylowrestvaluewithinabout5ms(Fig.4e2).Theoppositebehaviorofhandmduringlonglastingdepolarizationisclearlyshown.ThecurrentswhichflowthroughthemembranearecomposedofthecapacitivecurrenticandthreeioniccurrentsofNa+

    (throughthevariablegNa)ofK+(throughthevariablegK)andtheanioncurrent(mainlyCl,throughthefixedgI),togetherii.Fig.5givesthetimecoarseofaspike,togetherwithic,ii,theresumim,andalsotheunderlyinggKandgNa.Forthe4composingcurrentstogethertherelationis(seeequation(2)and(3)ofBioelectricity:electrotonicpropagation):im=(1/ra)2E/x2=cmE/t+n4K(EEK)+m3hNa(EENa)+L(EEL).(3)

    Fig.5Timecoarseofconductancesandcurrentsduringanactionpotential.AttimeAandBtheslopesoftheactionpotentialaremaximalandimzero.AtBbothreachtheirextrema.Supposethatbysummationofdendriticandsomaticpotentialsattheaxonhillockaspikearises.Atthatsitethelocalcurrentsbecomesostrongthatalsothenextpartofthe(axonal)membranebecomesenoughdepolarizedtobeexcited

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    andapropagatedspikewithoutdecrementrunsalongtheaxon.Therefractoryperiodmakesthatthespikewillnotreverseandoccuronlyonceforashortlastingstimulus.Ifanerveisstimulatedinthemiddleofanaxontheimpulsewillpropagatetobothsides.Longerlastingstimulimaycausetrainsofspikes.Justlikeforthepropagationofadendriticpotentialitcanbeshownthattheconductionvelocityisaparameteroftheequation:2d2E/dt2=cmdE/dt+n4K(EEK)+m3hNa(EENa)+L(EEL).(4)Thenumericalsolutionofthisnonlineardifferentialequationgivesaquitecomplicatedexpressionof.Spikesrecordedclosetothesoma(oraxonhillock)arebiphasic,astheoneofFig.3,butwhenrecordedinthevicinityofanaxontheyaretriphasic.OnecouldthinkthatanerveimpulsewhichreversesthenervepotentialwouldbringaboutanimportantdepletionofK+

    whichleavesthecellbecausethereisnopotentialgradientanymorekeepingitintheinterior,andthattheinflowofNa+wouldcauseapermanentdisturbanceofthemembranepotential.However,theamountsofionsdisplacedaresmallcomparedtotheactualnumberpresent.EveninverysmallnervesseveralthousandsofspikescanbegeneratedwithoutasignificantlyincreasedmetabolismtoexpelNa+.Thebehaviorofthechannelshasextensivelybeenstudiedbyclampingtechniques(seeElectrophysiology:clampingtechniques),inwhichthei/E(soconductance)isinfluencedbyadministratingallkindofdrugs.Adiscussionofthesephenomenaisbeyondthescopeofthischapter.MyelinatedaxonsPropagationspeedcanbeincreasedbyincreasingtheaxondiameter.Takingforsimplicityequation(8)ofBioelectricity:electrotonicpropagation(=2/=0.5Cm1(d/(RmRi))0.5)thisspeedisproportionalwiththesquarerootofdiameter(d).However,formetabolicreasons,thediameterislimited(onlythecoldbloodedsquidreachesavalueof1mm).Unmyelinatedfibers(about2m)aregenerallyfoundintheautonomicnervoussystemofvertebrateswherespeedsofabout1m/saresufficient.Invertebrates,sensoryandmotoronesaregenerallymyelinated.Thisismoreeffectivetoincrease.Theeffectofmyelincanalsobeevaluatedsinceallaboveconsiderationscanbeappliedinprincipletothemyelinatednerve.Myelincanbeconsideredasthedielectricumbetweentwocondenserplates.Itdecreasesmembranecapacitance,sincemyelinhasalowerrelativedielectricconstantm(about718)thaninterstitialfluid(mclosetomofwater,beingabout80Cm~m/d).Now,Cmisonlyabout4nF/cm2.andRmisabout105cm2.Increasingtheeffectivemembranethicknessbyusingmyelin(leavingtheinnerfiberdiameterconstant)alsodecreasesCm,so.Whenmyelinthicknessandinnerdiameterincreasewiththesamefactor,thenincreaseslinearwiththisfactorasfollowsfrom(5).Thisshowstheefficiencyofdiameterincrease.Experimentallythishasbeenfoundindeedforvertebrateperipheralfibers.However,amyelinatedfiberlongerthansome100mdoesnotworkproperly.Myelinallowstherapid(essentiallyinstantaneous)conductionofions,butpreventstheregenerationofspikes.Therefore,thecylindricalshapeofthemyelinsheathisinterruptedevery0.010.1mmbyanodeofRanvier,anakedpieceofca.0.5mofaxon.TheirCmisabout4F/cm2andRmisonlyabout15cm2.AnabundanceofvoltagegatedNa+channelsonthesebaresegments(upto104morethantheirdensityinunmyelinatedaxons)allowsspikestobeefficientlyregeneratedatthenodesofRanvier.Theexcitationjumpsfromonenodetotheother,whichisapassive,soelectrotonictransmission(seeBioelectricity:electrotonicpropagation)implyingsomedecrement.Basically,thiscangoineitherdirections,butthespiketravelsunidirectionalbecausethenodebehindthepropagatingspikeisrefractory.Thiswayofpropagationofthespikeiscalledsaltatoryconduction:atthemyelinatedsegmentsthepropagationisveryfast(duetotheinsulation),whereasatthenodesthereisasmalldelayof0.01to0.1ms.Thelengthoftheinternodalsegmentsaresuchthatone,orsometimeseventwonodescanbepassedandthattheamplitudeisstillsufficienttoreachthethresholdforrestoringtheamplitudeofthespike.Thus,thesafetyfactorofsaltatoryconductionishigh,allowingtransmissiontobypassnodesincaseofinjury.Mammalianmyelinatedmotorneuronscanreach100m/s.Saltatoryconductionincreasesnerveconductionvelocitywithouthavingtodramaticallyincreaseaxondiameter.Withoutsaltatoryconduction,conductionvelocitywouldneedlargeincreasesinaxondiameter,resultinginorganismswithnervoussystemstoolargefortheirbodies.AlternativemodelsAfewobservationsarenoteasilyreconciledwiththemodel.Asignaltravelingalonganeuronisaccompaniedbyaslightlocalthickeningofthemembraneandaforceactingoutwards.Also,aspiketravelingalonganeuronresultsinaslightincreaseintemperaturefollowedbyadecreaseintemperature,whereaselectricalchargestravelingthrougharesistoralwaysproduceheat.TherecentsolitonmodelexplainstheaboveobservationsandpossiblyallpropertiesoftheHHmodel.Asolitonisaselfreinforcingsolitarywave(awavepacketorpulse)thatmaintainsitsshapewhileittravelsatconstantspeedsolitonsarecausedbyacancelationofnonlinearanddispersiveeffectsinthemedium.Thistheoryattemptstoexplainsignalsinneuronsaspressure(orsound)solitonstravelingalongthemembrane,accompaniedbyelectricalfieldchangesresultingfromPiezoelectricity.LiteratureHHmodel:Noble,Physiol.Review,46,150,1966.Solitonmodel:HeimburgT,JacksonAD.Onsolitonpropagationinbiomembranesandnerves.PNAS,102,122005.HeimburgT,JacksonAD.Thethermodynamicsofgeneralanesthesia.BiophysicalJournal,9,February2007.

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