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Download PDF Steady State of Living Cells and Donnan Equilibrium
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Charge out of equilibrium: ion pumps SteadyStateandMembraneRestingPotential ThepreviousPDFhandoutpointsoutthatsincetheNernstpotential, Vi Nernst ≠ ΔV is notequaltothemembranepotentialtherearecurrentflowofionsoftheamount, Ii = Vi Nernst − ΔV / Ri ,whereions,Na+,K+,Cl−,intooroutofthecells.Theflowofions The massive Na+ difference between in & out balances the osmotic willchangetheconcentrationofionsinsidethecell, C Na+ ,in , C K + ,in , CCl − ,in .Thisshould pressure (along with other ionic species too – like calcium ions) leadtoachangeinthemembranepotentialofΔV .Butitiswellknownthataliving cellmaintainsaconstantmembranepotentialofΔV ∼ −60mV . USEFULQUESTIONSyoushouldknowhowtoanswer:1)Whydotheflowofions So the cell is not in equilibrium donotsignificantlychangetheionconcentrationsoutsidethecell?;2)Howdoes thecellmaintainaconstantmembranepotentialΔV ∼ −60mV . It burns energy to pump Na+ out of the cell Na+/K+-ATPaseionpumppumpsNa+outofthecellandK+intothecell. ( ) Asillustratedinthediagramabove,Na+/K+-ATPaseisaproteinthatpumpstwoK+ potassiumionsintothecell,andthreeNa+sodiumionsoutofthecell,percycle. ThiscompensatefortheleakcurrentandofK+potassiumionsoutofthecell, ohmic I ohmic < 0 ,andofNa+sodiumionsintothecell, I Na > 0 ,asshowninquestion2of K+ + assignment8.Thismaintainsconstantionconcentrationsinsidethecell, C Na+ ,in , C + , C − ,whichinturnsmeansthatthemembranerestingpotentialremains K ,in Cl ,in constantatΔV ∼ −60mV .Inphysicswesaythatthemembraneisinasteadystate. Theimageonthenextpageillustratewhathappensinalivingcell: Figureshowshowalivingcell maintainsasteadystate membranepotentialof IMPORTANTPOINT:membrane isnotatequilibrium. DonnanEquilibrium:WhenacelldiestheNa+/K+-ATPasestopspumpingions,but < 0 ,andof thecellwillcontinuetoleakofK+potassiumionsoutofthecell, I Kohmic + ohmic > 0 .Thiswillchangetheionconcentrationinside Na+sodiumionsintothecell, I Na + thecellandwillchangethemembranepotentialΔV .Thiswillcontinueuntiltheall Nernst = VKNernst = VClNernst Nernstpotentialsequalthemembranepotential: ΔV = VNa .When + + + thishappensthecellwillbeatequilibrium,knownasDonnanequilibrium.A typicalDonnanequilibriumpotentialisΔV = −10mV . QUESTIONYOUSHOULDKNOWHOWTOANSWER: 1)Examinethecurrentleakequation, Ii = Vi Nernst − ΔV / Ri ,toexplainwhythe currentofionsiszeroatDonnanequilibrium. 2)Giventhatchargesusuallyflowuntiltheelectricpotentialdifferenceiszero,why doyouthinktheDonnanpotentialisnotzero,ΔV ≠ 0 ? HINTforoneofthequestion:Lipidmoleculesthatmakeupmembranesare usuallycharged,andnegativelychargedproteinsinside(intracellular)cellscannot permeatetotheextracellularfluidoutsidethecell(seefigurebelow). ( )