Ion transport through cell membrane channels

1IonTransportThroughCellMembraneChannelsJanGomułkiewicz1,JacekMiękisz2,andStanisławMiękisz31InstituteofPhysics,WrocławTechnicalUniversity;2InstituteofAppliedMathematicsandMechanics,WarsawUniversity;3DepartmentofBiophysics,MedicalUniversityofWrocławAbstract.Wediscussvariousmodelsofiontransportthroughcellmembranechannels.Recentexperimentaldatashowsthatsizesofionchannelsarecomparedtothoseofionsandthatonlyfewionsmaybesimultaneouslyinanysinglechannel.Theoreticaldescriptionofiontransportinsuchchannelsshouldthereforetakeintoaccountinteractionsbetweenionsandbetweenionsandchannelproteins.ThisisnotsatisfiedbymacroscopiccontinuummodelsbasedonPoisson-Nernst-Planckequations.MorerealisticdescriptionsofiontransportareofferedbymicroscopicBrownianandmoleculardynamics.Oneshouldalsotakeintoaccountadynamicalcharacterofthechannelstructure.Thisisnotyetaddressedintheliterature.Keywords:Ionchannels_IontransportIntroductionEverylivingcellisanopensystem.Continuoustransferofenergyandmassbetweencellsandtheirsurroundingsconstitutesanecessaryconditionforasustainedlife.Cellmembranes,whichensuretheautonomyofseparatedcompartments,shouldbeendowedbymechanismsofaselectivetransportofsubstancesindispensableforthelifeofacell.Inparticular,afundamentalphenomenonisatransportofionsthroughcellmembraneswhichensuresthattheioncontentofacellisdifferentfromtheoneoutsidethecell.Cellmembranes,duetotheirstructureandachemicalcomposition(atwo-lipidlayerwithimmersedmoleculesofintegralproteins)arecharacterizedbyaverylowaveragerelativeelectricalpermittivityεr(alsocalleddielectricconstant)about2,ascomparedtoarelative___________________________Correspondenceto:JacekMiękisz,InstituteofAppliedMathematicsandMechanics,WarsawUniversity,Poland,e-mail:[e-mail]2permittivityofelectrolytewatersolutionsintheirsurrounding–about80.TheBornenergy(theenergyrequiredtomoveaionfromtheoutsidesolutiontothehydrophobicinteriorofamembrane)correspondingtosuchvaluesofpermittivityisabout300kJ/mol.ThisratherhighBornenergyshouldimplyaverylowionpermeabilityofamembrane(inparticularforsuchimportantionsasNa,K,Ca,andCl)–thevaluelowerbyseveralordersofmagnitudethanobservedones.Inevolutionaryprocesses,structuresandmechanismshavebeenformedinmembranes,whichlowerlocallyanenergybarrierforpenetratingions.Suchstructuresconsistofmoleculesofintegralproteinswhosehydrophobicpartsinteractwithtwo-lipidlayersandpolarhydrophilicpartsform:a)relativelywidenon-selectivehydratedporeswhichpenetratemembranes,b)specificionchannels,oftenendowedwithspecialstructuralelementswhichformgatessensitivetoanelectricfield,chemicalligands,orthemechanicalstress,c)ion-bindingcenters(ononeorbothsidesofamembrane)calledcarriersortransporterswhichinteractwithionsandtransportthemtotheothersideofthemembranewhereion-carriercomplexesdissociate.Suchtransportcanusetheenergyobtainedbymetabolicreactions(mainlyATPhydrolysis)–thenitiscalledtheactivetransport,oraninteriorenergy–inthiscaseitiscalledthefacilitateddiffusion.Allabovementionedtransportmechanismsareessentialforcellhomeostasis,thatisforsecuringthecontentoftheinteriorofacell,itsvolumeandanelectricvoltageofthemembrane(inelectrophysiologyandbiophysicsitiscalledthemembranepotential).Theyarealsoessential(toacertaindegree)forthephenomenonofexcitabilityofcells,forwhichanimportantroleisplayedbyionchannels.Investigationsinthisareaarecarriedinmanyscientificcenters.Hugeexperimentaldatahasbeencollectedandvarioustheoriesproposedwhichdescribeiontransportincellmembranes.Despitethis,ourknowledgeisstillnotsufficienttoexplaintransportmechanismsandtoprovideitsfulldescription.IonchannelsInthelatefortiesandearlyfiftiesofthelastcentury,HodgkinandHuxleyinthecollaborationwithKatz(Hodgkin&Katz1949;Hodgkin&Huxley1952;Hodgkinetal.1952;Huxley2002;Moves1984)workedouttheirphenomenologicaltheoryofnerveimpulsesundputupahypothesisthattransportofpotassiumandsodiumionsinexcitablebiologicalmembranestakesplacesinselectiveionicpaths,differentfordifferentions.Thesepaths,besidesahighselectivity,displayedthedependenceoftheconductivityonthemembranevoltage.Although,3suchpathshavenotbeencalledionchannelsinthesepapers,yetawidelyacceptedhypothesiswasformulatedthationspenetratemembranesthroughspecificionchannelsmadeofproteins.Channelpropertiesaswellastransportmechanismsweredeductedfrommacroscopicmeasurements.Particularlyusefulwasthevoltage-clampmethodwhichconsistsofregisteringelectriccurrentsthroughacertainmacroscopicsurfaceofamembraneforfixedvaluesofthemembranepotential.AschematicsetupforsuchmeasurementsispresentedinFig.1.Fig.1.Schematicsetupformeasuringioncurrentsinaxonsbythevoltage-clampmethod.Theregisteredcurrentthroughthemembraneisthesumofioncurrentsandthecapacitycurrent(acurrentofchargingthemembrane’selectricalcapacity).Thesecondcurrentvanisheswithatimeconstantspecifiedbythemembrane’scapacitanceandtheelectricalresistanceofthemeasuringcircuit.ThetotalcurrentImiswrittenas∑+=iicmIII,(1)whereIcisthecapacitycurrentandIiarecurrentscarriedbyrespectivetypesofions(mainlysodiumandpotassiumcurrentsbutalsoachloridecurrentonewhichi