Download PDF Steady State of Living Cells and Donnan Equilibrium

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.
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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).
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