mechanism of potassium channel selectivity revealed by na and...

MechanismofpotassiumchannelselectivityrevealedbyNa+andLi+bindingsiteswithintheKcsAporeAmeerN.Thompson,IlsooKim,TimothyD.Panosian,TinaM.Iverson,TobyW.Allen,CrinaM.Nimigean

SupplementaryInformation

Nature Structural & Molecular Biology: doi:10.1038/nsmb.1703

SupplementaryFigure1|LowaffinityblockingsitesforLi+intheKcsAvestibule.a,AviewoftheselectivityfilterandvestibuleofNoK‐Li+showing|Fo|‐Fc|stylesimulatedannealingomitdensity(greenmesh)contouredto4σforthewatermolecules(redspheres)observedinthevestibule.Mapswerecalculatedbyomittingthewatermolecules,anda5Åradiusaroundthewatermoleculesfromthephasecalculation.StickmodelsoftwoopposingKcsAsubunitshighlighttwoputativeLi+blockingsitesintheNoK‐Li+structure:b,betweentheupperringofwatermoleculesandthesidechainhydroxylsofThr‐75,andc,withinthecenteroftheeightwatermoleculesinthevestibule.Li+ionsareshowningreen,watermoleculesofthefirsthydrationshell(notobservedinthedensity)areshowningrey,andwatermoleculesofthesecondhydrationshell(observedinthedensity)areshowninred.


SupplementaryFigure2|ComparisonofNoKLi+toLowKLi+andotherpublishedstructuresofKcsA.TheNoK‐Li+structurewascomparedtoLowK‐Li+and8othermodelsofKcsAdepositedintheProteinDataBank(PDB):Low‐K+(PDBID=1k4d),High‐K+(PDBID=1k4c),NoK‐Na+(PDBID=2itc),High‐Tl+(PDBID=1r3k),Low‐Tl+(PDBID=1r3k),Rb+(PDBID=1r3i),Cs+(PDBID=1r3l)andBa+(PDBID=2itd).a.Rootmeansquared(RMS)deviationsofCα‐atomswerecalculatedusingLSQKAB5andplottedasafunctionofresiduenumber.Theblackbarrepresentstheregionoftheselectivityfilter.b.Atablesummarizingthemodelingofionsintheselectivityfilterofeachstructure.c.QuantificationofelectrondensitywithintheKcsAselectivityfilter.ElectrondensitypeakheightsofcompositeomitmapsweremeasuredusingtheprogramPEAKMAX5andwerenormalizedtothepeakcorrespondingtothebackbonecarbonylofCys88(onchainBoftheFABfragment).Theionlistedaboveeachgraphistheionmodeledatthesite.Forreferencetheoreticalratiosofpeakheights(proportionaltonumberofelectronsineachion)areplottedasdottedlines:K+:O=14:10=1.4,HOH:O=10:10=1.0,Na+:O=10:10=1.0.ThesequantificationssupporttheassignmentofwatermoleculesintheselectivityfilterofboththeNoK+‐Li+andLowK+‐Li+structures.


SupplementaryFigure3|Selectivityfilterbackbonealignment.Stereoviewofcompositeomitelectrondensitycontouredto1.25sigma(bluemesh)foronemonomeroftheselectivityfiltermodeledasyellowsticksfromeithera,NoK‐Li+orb,LowK‐Li+.TheselectivityfilterLow‐K+wasalignedtoeitherstructureusingthealigncommandinPyMolandisshownasgreysticksforreference.


SupplementaryFigure4|Convergenceanderrorplotsforfreeenergycalculations.Panelsa,canderevealtimeconvergenceofumbrellasamplingfor3samplefreeenergyprofilescorrespondingtothoseofpathsI,IIandII’fortheLi+ioninFig.6ofthemaintext.Panelsb,dandfshowthesamefreeenergyprofiles,butwheretimeissplitintotwosamplesof0.5ns,withthedifferencerepresentingameasureoferror.Therootmeansquare(RMS)differenceisreportedineachgraph.PathIIIisalsoshownindwithanarbitraryoffsetforclarity(matchingS1/S3minima).


Positions and Solvation Coordination number K+ Na+ Li+ Bulk Water

H2O Rmax

7.1±0.2 3.62 Å

5.9±0.5 3.22 Å

4.2±0.3 2.82 Å

H2O

5.4±1.2

4.8±1.2

3.8±0.6

C=O - - - Thr OH 1.6±0.9 1.1±0.3 0.4±0.6

Cavity (S1/S3/Cavity)

Total 7.0±1.4 5.9±1.2 4.2±0.8 Mean and range of z See Fig.4b.

H2O 1.6±0.4 2 2 C=O 4 4 3.9±0.1 Thr OH 2.8±0.7 0 0

S4 region (S0/S2/S4)

Total 8.4±0.9 6 5.9±0.1 Mean and range of z -5.5 [-6.6,-4.3] -4.5 [-5.3,-3.7] -4.2 [-4.7,-3.6]

H2O 1.9±0.2 1.2±0.4 2.5±1.0 C=O 4.0±0.1 3.5±0.5 1.8±0.3 Thr OH 2.7±0.4 1.9±0.2 0.7±0.7

S4 Cage (S0/S2/S4)

Total 8.5±0.4 6.6±0.6 5.0±1.2 Mean and range of z -5.5[-6.0,-4.8] -5.4[-6.0,-4.8] -5.5[-6.1,-4.7]

H2O 2.2±0.2 2 2 C=O 4 4 4 Thr OH 0.1±0.1 0 0

S4 Plane (S0/S2/S4)

Total 6.3±0.2 6 6 Mean and range of z -4.2[-4.9,-3.4] -4.2[-4.7,-3.6] -4.1[-4.5,-3.5]

Supplementary Table 1 | Ion solvation number and position analysis. Thenumber of oxygen atoms within distance Rmax of the ion are given for differentcoordinatingspecies.Bulk,CavityandS4regioncalculationsarebasedonunbiasedsimulationswheretheionwasfreetomove.TheS4cageandinplanecalculationswerebiasedwithplanarharmonicpotentials corresponding toRMS fluctuationof0.1Å.Uncertaintieslessthan0.01arenotshownaserrorbars.


SupplementaryTable2|FreeEnergyPerturbationCalculations.Freeenergies(ΔG) for KNa and NaLi were calculated from dedicated FEP simulations andWHAManalysiswhileKLiwasderivedbyadditionofthesetwonumbers.ValuesofΔΔGforNaandLi,relativetoKandexpressedrelativetobulkareprovidedintheright hand columns. Cage and plane calculations were biased with harmonicpotentialsandthenunbiasedasdescribedinthesupplementarymethods.Valuesinbracketscome fromsimulationswith the1K4Cstructurewhereasallotherscomefromsimulationswith the1BL8 structure. Errorbars areone standarddeviationbased on 25‐50 blocks of 20ps. Values for free energy decomposition viathermodynamic integration(TI)dueto interactionswithwater,carbonylsandThrOH groups are also provided for each S4 calculation (contributions from otherinteractions, including with neighboring residues and other ions, were found tocontributelittletotheperturbationfreeenergiesandarenotreported).

FreeEnergies

ΔG(K+Na+) ΔG(Na+ Li+) ΔG(K+ Li+) ΔΔG(K+Na+) ΔΔG(K+ Li+)

Bulk

17.7±0.1(17.8±0.1)

22.4±0.3(22.6±0.3)

40.1±0.3(40.4±0.4)

Cavity(S1/S3/Cavity)

17.9±0.2(18.2±0.2)

21.7±0.6(22.1±0.5)

39.6±0.3(40.3±0.6)

0.2±0.2(0.4±0.3)

0.5±0.6(0.1±0.7)

S4RegionUnbiased(S0/S2/S4)

19.2±0.5(19.0±0.4)

25.6±0.2(25.4±0.3)

44.8±0.5(44.5±0.5)

1.5±0.5(1.2±0.4)

4.7±0.6(4.1±0.5)

TIH2OTIC=O(53)TIThrOHTITotal

‐9.22±0.37‐10.93±0.44‐0.51±0.2120.55±0.49

14.10±0.20‐12.96±0.330.22±0.00526.71±0.39

‐23.32±0.64‐23.89±0.55‐0.29±0.2147.27±0.62

S4Cage(S0/S2/S4)

13.7±0.3 21.9±0.5 35.6±0.6 4.1±0.4(3.2±0.6)

4.6±0.6(4.0±0.8)


‐5.32±0.64‐6.63±0.33‐2.85±0.24‐14.74±0.38

‐14.20±1.43‐6.68±0.89‐2.51±0.8623.34±0.52

‐19.52±1.57‐13.31±1.57‐5.36±0.8938.08±0.64

S4Plane(S0/S2/S4)

23.9±0.2 26.5±0.2 50.4±0.3 6.1±0.3(4.4±0.4)

10.2±0.4(7.9±0.6)


‐11.46±0.13‐14.14±0.250.23±0.0125.19±0.28

‐14.50±0.24‐13.69±0.210.21±0.00227.85±0.28

‐25.96±0.28‐27.83±0.330.44±0.0153.04±0.40


1

SUPPLEMENTARYDISCUSSIONInteractionbetweenLi+andK+duringblockintheKcsAcavityLi+andNa+fastblock1aredependentonpermeantionconcentration.Theequilibriumblockingparameterswereextractedusingamodelthatassumestheblockerdissociatesfromthesitefasterthanthetimeresolutionavailable.Theresultisanapparentreductioninsinglechannelamplitudeproportionaltothefractionoftimetheblockeroccupiesitssite:

€

I(V ) =I0(V )

1+BKB

ap

, (Eq.S1)

whereBistheblockerconcentrationandKB

ap isitsapparentequilibriumdissociationconstant.KB

ap varieswiththemembranepotential,evidenceofvoltage‐dependentLi+block,expressedas:

KBap (V ) = KB

ap (0)exp −zFVRT

, (Eq.S2)

whereKBap(0)isthezero‐voltageblockingaffinityandzisthevoltage‐dependenceparameter,alsoknownastheeffectivechargemovementassociatedwiththeblock.ThedatainFig.2aarefittedusingeqs.S1andS2(redandbluelines).

TheaffinityforLi+decreaseswithanincreaseinK+concentrationasshowninFig.2b,consistentwithaprocesswhereK+competeswithLi+fortheblockingsite1.IfblockerandK+occupythecavityinamutuallyexclusivemanner,theapparentblockerdissociationconstant(KBap(0))willfollowacompetitionrelation:

KBap (0) = KB (0)+

KB (0)KK (0)

K , (Eq.S3)

whereK+isthepotassiumconcentration,andKB(0)andKK(0)aretheintrinsicaffinitiesat0mVforblockerandK+,respectively.Weusedeq.S3tofittheKBap(0)vsK+relationshipinFig.2b(redline).Theslopeofthelinearfit(theratioofKB(0)/KK(0))is2indicatingthattheblockingsiteprefersK+toLi+byafactoroftwo.AnidenticalanalysisdoneforNa+blockyieldedaratioof5,indicatingasitethatpreferredK+overNa+byafactorof5(dashedlineinFig.2b,from1).K+isstillpreferredoverbothLi+andNa+,butLi+appearstobepreferredtoNa+inthecavity.

Furthermore,Fig.2cshowsthatthevoltagedependenceofLi+blockremainsunchangedovera10‐foldchangeinK+concentration,incontrasttothesignificantincreaseinthevoltagedependenceofNa+blockoverthesameK+range(dashedline,from1).OuroriginalmodeltoexplaintheincreaseforNa+invokedinteractionbetweenNa+andthepermeantionsintheporethatappearstobelessstrongforLi+.Interestingly,thiscouldresultfromamoreshallowbindingofLi+inthecavity,asseenintheMDsimulations(Fig.4).Thesedatapointtoapermeationandblock


2

modelwhereLi+andNa+bindatsomewhatdifferentlocationswithintheporeandinteractdifferentlywiththepermeantions.KineticmodelsfortheeffectofLi+andNa+ondecreasingburstdurationsKcsAburstdurationsaredramaticallyshortenedinaconcentrationandvoltage‐dependentmannerbyapplicationofintracellularNa+andLi+.Aswestateinthemaintext,anobviousmechanismforthisisthatbindingofNa+/Li+inthechannelpore,atthesitethatleadstotheobservedfastblock,inducesinactivation.ThisisshowninSchemeI.SchemeIIpresentsanalternativemechanism,moreconsistentwithourmoleculardynamicsandX‐raycrystallographydata,thatpositsthattheburstdurationsareshortenedbecauseNa+orLi+bindtoanadditionalbindingsiteintheporewithhigheraffinity,blockingtheflowofK+ionsonalongtimescale,similartotheinactivationtimescale.Inbothschemes,theclosed(C)toopen(O)transitiondescribesthegatingwithintheburst,whereIistheinactivatedstateresponsibleforthelongclosedinactivatedintervals,Bfisthefastblockedstatethatcontributestothedecreaseincurrentamplitudeduetothefaston‐andoff‐rates(kBf,kuf)oftheblocker,andBistheslow‐blockedstate,responsibleforthedecreaseinburstdurations.

SchemeI

SchemeII

ThemodelinSchemeIpredictsthattheobservedeffectofdecreasingtheburstdurationswilloccuroverasimilarrangeofconcentrationsasthefastblockeffect.Thehalf‐maximalconcentrationthatinducesthedecreaseinburstdurationsis~1mMat100mV(forbothNa+andLi+)whileaminimumof10mMLi+/Na+isrequiredtoseeanyeffectat100mVondecreasingthesingle‐channelcurrentamplitude.ThissuggeststhatSchemeImaynotbethecorrectmodeltoexplainthedata.

InSchemeII,themeanburstdurationisinverselyproportionaltotheon‐rateoftheblockerontheslow‐blocksite(kB)(Eq.1),askBfistoofasttoinduce


3

interruptionsinthecurrentonthegatingtimescale.AlthoughinthisschemekBisnotdirectlydependentontheconcentrationoftheblockerbutontheoccupancyofstateBf,wewillapproximatekBwithasecondorderrateconstant(becausetheconcentration‐dependentprocessisveryfastanddoesnotaffectslowprocesses),bothconcentrationandvoltage‐dependent(Eq.1),astheblockingsiteisinthetransmembraneelectricfield.ByfittingtheburstdurationdatainFig.3a,bwithEq.1,weobtainedanintrinsicblockeron‐rateof0.11M‐1sec‐1forNa+and0.07M‐1sec‐1forLi+,andavoltagedependenceofthisrateof0.5forNa+and0.5forLi+(constrained,seeFig.3legend).ThesenumbersillustratethatalthoughtheNa+/Li+induceddecreaseinburstdurationsatthesingle‐channellevelappearsquiterobustatlargevoltages,theintrinsicrateofthismodeledslow‐blockprocess(kB)isstillveryslowcomparedtotherateofK+permeation.Unfortunately,wecannotquantitativelyanalyzetheoff‐rateconstantsanddetermineaKdasitisimpossibletodistinguishinactivationeventsfromslowblockedeventsundertheseconditionsinthischannel.Theeffectivegatingchargeofthisslow‐blockprocess(z=0.5)issimilartothatofthefastblock(z=0.4),suggestingthattheyoccuratlocationsclosetoeachotherinthepore.CrystallographicallymodeledLi+bindingsitesintheKcsAcavityWhiletheassignmentofwatermoleculesat2.8Åresolutioncanbechallenging,electrondensityforeightputativeorderedwatermoleculesisobservedinthevestibuleoftheNoK‐Li+structure(Fig.5a,SupplementaryFig.1).ThesewatermoleculesareinpositionssimilartothoseofthehighresolutionKcsAstructures2,3wheretheycoordinateK+orNa+(Fig.5b).ThenearesthydrogenbonddonororacceptortothewatermoleculesintheupperringoftheshellisthesidechainhydroxylofThr75,whichis4.5Åaway.Thisistoofartoformahydrogenbondinginteraction.DuetotheresolutionofourNoK‐Li+structure,thelackofhydrogenbondingbetweenthesewatersandtheprotein,andtheproximityofthewaterstothefourfoldcrystallographicaxis,whereartifactscanbemagnified,extracarewastakentoensurethatthesedensitiestrulyrepresentwatermoleculesandnotnoise.Weusedbothcompositeomitmaps(Fig.5a,b)andsimulatedannealingomitmaps(SupplementaryFig.1a)toprovidetwocomplementarymethodsofreducingmodelbiasatthislocation.Inbothcases,theelectrondensitiesappearwell‐defined.Inaddition,thetemperaturefactorsofthesewatermolecules(52Å2forthewatermoleculesnearertheselectivityfilterand51Å2forthelowerringofwatermolecules)matchcloselythoseoftheneighboringaminoacids(57Å2),consistentwiththedensitiesbeingwatermolecules.Finally,watermoleculeshavebeenpreviouslymodeledatthesepositionsinhigherresolutionstructuresofKcsA,andhavebeenproposedtobefunctionallyrelevant.Thus,thesespecificlocationshavebeenpreviouslyshowntobeimportantwaterfocusingsitesdespitethelackofhydrogenbondstotheprotein.Alltheabovelinesofevidence,togetherwiththeelectrophysiologicaldata(Fig.1‐3)andmoleculardynamicscalculations(Fig.4and6)thataccompanythisstructure,allowustoassignthesedensitiesaswatermoleculesratherthannoiseresultingfromthecrystallographic4‐foldandwehavemodeledtheminthismanner.


4

Sincenoneofthe8modeledorderedwatermoleculesinthecavityoftheNoK‐Li+structureishydrogenbondedtotheprotein,wesuggestthattheirpositionsarestabilizedbythepresenceofanionthatisnotobservableinanx‐rayexperiment,i.e.Li+.ThesewatermoleculescanformanidealizedsecondaryhydrationshelltoatetrahedrallycoordinatedLi+.Theprimaryhydrationshelllacksfourfoldsymmetrybutispositionedalongthefour‐foldcrystallographicaxis.Inaddition,theorientationofthistetrahedronmaybeconformationallydegeneratesuchthatitisnotobservedintheelectrondensity.FortheLowK‐Li+structure,theelectrondensityofthewatermoleculeswithinthecavityisnotstatisticallysignificant.CrystallographicallymodeledwatersintheselectivityfilteroftheNoKLi+structureThreespheresofelectrondensityareobservedwithintheselectivityfilteroftheNoK‐Li+structureonthecrystallographicfourfoldaxis(Fig.5a).ThesedensitiesarelocatednearS1,S3,andS4,theS‐sitesinK+‐containingKcsAstructures2,3wheredensitieswereobservedinother,higher‐resolutionKcsAstructures(Fig.5).Wehypothesizethatthesedensitiesresultfromwatermoleculesfortworeasons.First,thecrystallizationwasperformedinLi+astheonlymonovalentcationsandLi+isinvisibleatthisresolution.Second,wequantifiedthesedensitiesinordertocomparethemwithsimilarlylocateddensitiesinotherKcsAstructures,bynormalizingthemtotheoxygenatomofCysB88(SupplementaryFig.2).CysB88providesanidealreferencemeasurementbecauseitisnotinvolvedinbinding,iswellordered,andisconsistentbetweenallfourstructures.Whiletherearecaveatstointerpretationsresultingfromthisanalysis(theatomisfarfromthefilter,itiscovalentlybound,thereisvariabilityintheresolutionofthedatasets,andtheionsorwatermoleculesintheselectivityfiltermayhavepartialoccupancy),bynormalizingthedensitypeakstoareferencepointwithsimilarproperties,weovercomethechallengeofcomparingstructuresofdifferentresolutionswhileaccountingforthevariationinsignaltonoise.

QuantificationofthedensityattheS3andS4sitesintheNoK‐Li+andLowK‐Li+structuresshowsthatthesearenearlyequalinmagnitudeandofsimilarintensitytoacarbonyloxygen(SupplementaryFig.2).Incontrast,intheS4siteoftheLow‐K+andatallS‐sitesintheHigh‐K+structureKcsAstructures2,3(Fig.5a,b,c,SupplementaryFig.2),thedensitiesarestrongeraswouldbeanticipatedforK+ions.OurcrystallographicdataarethusbestexplainedbytheassignmentofwatermoleculesintheselectivityfilteroftheNoK‐Li+structure.WehypothesizethatthewatermoleculesatS3andS4arerequiredtocompletetheshellofahexa‐coordinatedLi+boundattheB‐site,withtheotherfourligandscontributedbyfourThr75carbonyloxygenatoms(Fig.5).

WhiletheselectivityfilteroftheLowK‐Li+structureappearstoadopttheconductiveconformation,otherfeaturesoftheelectrondensitysuggestthatamixedstateispresentinthiscrystal,withsomeKcsAmoleculeshavingLi+andothershavingK+inthepore.Reflectingthislikelyaveragingovertwostates,theelectrondensitywithintheselectivityfilter(Fig.5b)islessclearlyresolvedthanitisfortheNoK‐Li+structure(Fig.5).Thepatternoftheintensitiesofelectrondensitywithin


5

theporeofLowK‐Li+issimilartoNoK‐Li+anddistinctlydifferentfromLow‐K+(Fig.5b,SupplementaryFig.2).Whenallofthesedensitiesaremodeledaswatermolecules,thetemperaturefactorsrefinetoapproximatelythatofthesurroundingpeptidechain.Bycomparison,modelinginthemannerofLow‐K+,withaK+atS1andS4andawatermoleculeatS3,resultsinsignificantlyelevatedtemperaturefactorsascomparedthesurroundingatoms.Takentogether,thissuggeststhatevenin3mMK+,KcsApreferentiallybindsLi+ionsattheBsiteratherthanadoptingacollapsedporeconformation.Paradoxically,thedecreaseinelectrondensityqualityaccompaniesaslightimprovementinresolutionfortheLowK‐Li+structure(seeTable1).FreeEnergyPerturbationCalculationsResultsforaverageandrangeofpositionsfordifferentionsineachlocationoftheporeareincludedinSupplementaryTable1.PositionsarenotlistedinthecavitybecauseofthevastrangeoflocationsthatarebetterdescribedbythedistributionsinFig.4bofthemaintextobtainedusingumbrellasampling.Errorbarsarestandarddeviationsbasedon25‐50blocksof20ps,andmayoverestimatetheuncertaintycomparedtoastandarderrorofmeans.SupplementaryTable1alsoincludesaveragecoordinationanalysisfromthesesimulationsinbulk,cavityandS4,includingbiasedS4simulationswheretheionwasheldeitherintheplaneorinthecageofS4(seesupplementarymethods).Interestingly,thesmallerLi+iondoesnotsiton‐axiswhenheldintheenergeticallyunfavorablecagesite,butinsteadmoveslaterallyforoptimumcoordinationbyfewerproteinligandsandwater.

SupplementaryTable2reportsallfreeenergycalculationsfortheperturbationsfromK+toNa+,Na+toLi+andthecumulativeperturbationfromK+toLi+.Thesenumbersarealsogivenrelativetobulkwaterasameasureofselectivityofeachsite.TheS4regionoverallisslightlyselectiveforNa+overK+andstronglyselectiveforLi+ions.Separatesimulationswheretheionisconstrainedtobeincageorinplane(B‐site)revealastarkdifferenceintheselectivityofthesetwodifferentcoordinationgeometries.AnalysisofthesesimulationswasalsousedtogeneratethefreeenergyprofilesofFig.4cinthemaintext.DecompositionsintocontributionsformparticularinteractionsviathermodynamicintegrationarealsoprovidedinSupplementaryTable2. Thereareseveraldeterminantsofthein‐planeB‐sitelocationforNa+andLi+intheS4regionofthefilter.Simplistically,anionsmallerthanK+residinginS4musteithermoveupwardtofillfreevolume(duetoitssignificantlysmallerionicradius)orelsesufferthecostsofadownwardmovementofboundwaterandionsinS0‐S3abovetheion.Secondly,thein‐plane6‐ligandsiteprovidesatleastthebulkcoordinationneedsofthesesmallerions(basedonbulkwaterandignoringdifferencesinligandchemistry),withnoobviousobstructionsforclosecoordination,yetdoesnotmatchtherawcoordinationneedsofthelargerK+ion.Decompositionofthecalculatedfreeenergyvaluesshowsthation‐waterandion‐carbonylinteractionscontributemoretothestabilizationofNa+andLi+whenintheplanecomparedtothecagesite,i.e.thein‐planesitecanmoreeffectivelystabilizeasmallerionduetostrongerinteractionswiththosecoordinatinggroups.Weproposethat,inadditiontotheseenergeticcontributions,thestronglycoordinating


6

watermoleculestothesmallionsactasobstaclestotheinwardmotionofligandstotheionwheninthecage4.


7

SUPPLEMENTARYMETHODS

DetailedMolecularDynamicsmethodsThesimulationsystem,showninFig.4a,consistsoftheKcsAproteinimmersedinadipalmitoylphosphatidylcholine(DPPC)membranewithexplicitwatermoleculesandwasconstructedusingextensionstothemembranebuilderprotocoldescribedelsewhere6.TheKcsAproteinstructurewastakenfromPDBfiles1bl8or1k4c(fortwoindependentsetsofcalculations),threeboundK+ionsandrequiredwatermoleculeswereplacedintheselectivityfilterandenoughwatermoleculestofilltheentirechannellumenwereaddedbyoverlayingpre‐equilibratedwaterandkeepingonlythoseinsidethepore.115hydratedDPPClipidswererandomlychosenfromapre‐equilibratedmembraneandoptimizedaroundtheproteinwithanasymmetrytoaccountforthenon‐cylindricalshapeoftheprotein(65lipidsinthebottomleafletand50inthetopleaflet).Themembrane‐proteinsystemwasthenplacedbetweenbulkelectrolytesolutionsof∼150mlKCl,correspondingtoanadditional13K+and23Cl‐ions(tobalancenetcharge)andatotalof7630watermoleculesand∼43,770atomsoverall.TheprogramCHARMM7version32b2,withthePARAM27forcefield8,9(DPPClipids10andTIP3Pwater11)wasusedforallMDsimulations.ElectrostaticswerecomputedusingtheParticleMeshEwaldalgorithm12withoutcutoff,a12ÅLennard‐Jonestruncation,andbondstoHatomsweremaintainedwiththeSHAKEalgorithm13.Simulationswereperformedunderconstantnormalpressure(1atm)withanextendedLagrangianalgorithm1415andtemperature(330K,abovethegelphasetransitiontemperatureforDPPC)wascontrolledbyaNose‐Hooverthermostat16,17.Hexagonalperiodicboundaryconditionswithxy‐translationlengthof77.0Åandaverageheightof~90Åwaspreservedwithpistonmass(750.0amu)andcollisionfrequency5ps‐1,normaltothemembrane(z‐direction).Topreventtheproteinfromdriftinginthexyplane,acylindricalconstraintof5kcal/mol/Å2wasappliedtothecenterofmass(COM)ofKcsAandaplanarconstraintinz‐directionwasalsoappliedtoCOMoflipidmembranewithforceconstant5kcal/mol/Å2(neitheroftheseconstraintshavinganyeffectonresults). Withregardstothechoiceofionparametersandtheiraccuracy,wehavepaidcarefulattentiontotheagreementwithrelevantexperimentalbenchmarks,whereavailable.ItisknownthatCHARMMdescribeshydrationfreeenergieswellwithoutanyforcefieldmodification18,19.ModificationshavebeenmadeintheLennard‐Jonesparameterfortheioninteractionwithfiltercarbonylstoensurethatnotonlyisthecorrecthydrationfreeenergyofeachionachieved,butthatsolvationinN‐methylacetamide(NMA)isclosetoexperimentalbenchmarkstoensurecorrectenergeticsforsolvationbyproteinbackbone19,20.ThechosenparametersarethoseusedpreviouslyforK+andNa+thatapproximatelymatchwaterandNMAsolvationfreeenergies,withasmallpreferencefortheioninNMA21.TheabsolutefreeenergiesofK+solvationinwaterandNMAare‐79.6kcal/mol18and‐83.2kcal/mol,respectively2223:valueswhichprovidereasonableK+ioniccurrentcharacteristicsforthechannel24.BasedonFEPcalculations(K+Na+andNa+Li+)usingboxesof


8

400wateror200NMAwith22windowsof4ns(SergeiNoskov,personalcommunication;allvalueswithstandarddeviationsof∼0.3kcal/mol)weestimateabsolutesolvationfreeenergiesof‐98.1and‐99.9kcal/molforNa+inwaterandNMA,respectively.Despitenothavingthisexperimentalbenchmark,weusethesameapproachforLi+withparametersthatgivehydrationandNMAsolvationfreeenergiesof‐121.9and‐123.3kcal/mol,respectively(previouslyparameterizedbyS.Noskov21).Whilesomeerrormayexistinthesefreeenergies,weremarkthatthelargebindingandrelativefreeenergies(K+‐Li+)intheB‐site,of5‐10kcal/mol,suggestrobustresults.

Priortoanyfreeenergycalculationsthemembrane‐proteinsystemwassimulatedfor30nswithoutanyconstraints.AS1/S3/cavityconfigurationofK+ionsinaconductingstate(withallVal76carbonylspointingintothepore)waschosenforfurtherstudies.PreviouslyithasbeenreportedthatthecarbonylgroupsatVal76flipawayfromtheselectivityfilterduringMDsimulations19,25‐27,possiblyassociatedwithC‐typeinactivation27‐29.InordertosampleappropriateconductingconformationsofKcsAduringallofthefollowingsimulations,aharmonicdihedralconstraintwithforceconstantof0.0030kcal/mol/deg2,centeredon‐90°,wasappliedtoψdihedralanglesofeachVAL76ofthefoursubunitsofKcsA.Usingthisconstraint,afurther700psofdynamicswasusedtoequilibratethesystembeforefreeenergycalculations.TogenerateastartingS0/S2/S4configurationweexchangedionsandneighboringwatermolecules,carriedoutconstrainedminimizationandthenafurther700psofequilibrationwasperformedbeforeanyfreeenergysimulation.

Freeenergyperturbation(FEP)andpotentialofmeanforce(PMF)umbrellasamplingcalculationsWehavecarriedouttwotypesoffreeenergysimulationinthisstudy:FEP30,31,wherewealchemicallymutateionstofindtherelativefreeenergiesofK+,Na+andLi+,asdonepreviouslybyseveralgroups19,21,22,25,32‐36,aswellasPMF‐umbrellasampling37calculationswhereweextractfreeenergyprofilesalongdifferentpositionalcoordinateswithbiasedsampling.Allcalculationswerecarriedoutwithamultipleionconfigurationinthechannel(3K+ions,or2K+ionswith1Na+orLi+ion),asexplainedinthetext,withexcessKClsolutioninthebaths.FEP:WefirstcarriedoutunconstrainedFEPsimulationsoneitherthecavityioninaS1/S3/cavityconfiguration,orontheS4ioninanS0/S2/S4configurationtodeterminetherelativefreeenergies,ΔG,ofK+,Na+andLi+ineachofthosesitesandcomparedtoasimilarcalculationinbulkwater(neartheedgeofthesimulationbox).Wefoundoptimumconvergenceiftheperturbationswerecarriedoutintwosteps,fromK+toNa+andthenfromNa+toLi+ineachsite.Alinearcouplingschemewasusedwith11simulationwindowsfromλ=0to1.Toavoidhysteresis,perturbationswerenotcarriedoutsequentially.Instead,all11windowsweresimulatedconcurrentlyondifferentcomputersuntilfreeenergieswerewellconverged,excludinginitialdataof20‐40psforequilibrationwitheachperturbedHamiltonian.Simulationsforeachwindowwerecarriedoutfor500ps‐1nseach,representing5‐10nsofsimulationforeachΔGcalculation.Therelativefree


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energieswerecalculatedusingtheweightedhistogramanalysismethod(WHAM38,39).

Inadditiontounbiasedsimulationswithineachsite,wecarriedoutconstrainedFEPsimulationsof500ps/windowusingtheS0/S2/S4configurationwiththeS4ionheldineitherthecageof8carbonylsorintheplaneofthefourThr75carbonylsoftheS4site.Planarharmonicpotentialswiththreedifferentforceconstantsof60kcal/mol/Å2,10kcal/mol/Å2,and2.5kcal/mol/Å2,allowingRMSDfluctuationsof∼0.1,0.25,and0.5Å,respectively,wereappliedtoensuretheionstayedclosetotheCOMofthecageformedby8carbonyloxygenofTHR75(Cage)orneartheplanedefinedbytheCOMofthe4carbonyloxygenatomsofTHR75.Theconstraintwasthenrigorouslyunbiasedbyaddingthefreeenergy,−ΔGcons ,forturningofftheconstraint,−ΔUcons ,inpost‐trajectoryanalysis:

consln exp( / )kT U kTΔ ,wherethebracketssignifyensembleaveragecalculationwithaHamiltonianthatincludestheconstraint,kisBoltzmann’sconstantandTisthetemperature.Thiswascomputedforλ=0and1endpointsonlyandwaswellconverged.

ThemultiplebiasedFEPtrajectoriesaboveforthein‐planeandin‐cageconfigurationswithinS4constituteaseriesofbiasedsimulationsforK+,Na+andLi+,aswellasallhybridionsbetween.Byusingendpoints,λ=0and1,fromtheK+Na+andNa+Li+perturbationswehaveenoughdatatoproduceaPMFacrosstheS4site,fromcagetoplane(6umbrellasamplingwindows,withdifferentconstraints,periontype).EmployingWHAManalysisonthebiasedtrajectories,wehavecomputedthefreeenergyprofileacrossS4foreachiontype.Becausethecoordinatesoftheconstraintswererelativetothecenterofmassofeither4or8ligandcarbonyloxygenatoms,profilesweretransformedintoacommoncoordinateframeforthisstudy,whichisthezcomponentofthepositionoftheionrelativetotheCOMoftheselectivityfilterwithresultsshowninFig.4bofthemaintext.UmbrellaSampling:Wehavecarriedoutseveralumbrella‐samplingcalculationstoexplorekeypathsinthemultipleionpermeationmechanisminthepresenceofNa+andLi+ions(showninFig.6).InthepresenceofK+ionsinS0andS2,orinS1andS3,wehavemovedanion(K+,Na+orLi+),atequilibrium,fromdeepinthecavityatz=‐15Å(definedrelativetotheCOMoftheselectivityfilter)upabovetheS4sitewithz=‐3Åinaseriesof25umbrellasamplingwindows,spaced0.5Åapart,withforceconstants10kcal/mol/Å2.Eachwindowwassimulatedfor1ns,yielding10‐30ns/calculation.Because,forsomeextremepositionsofthislowerion,theuppertwoions(ions1and2),maybeunstable,thosetwoionswerekeptintheirplacewithasteepflat‐bottomharmonicpotentialthatisnotfeltunlesstheionsattempttoleavetheirsites.Theallowedrangeofthecenterofmassofthosetwoions,z12,was0‐2ÅforS0/S2(arangethateasilyencompassestheS1/S3freeenergyminimumseenpreviously19and3‐6ÅforS0/S2,alsoeasilyencompassingthatstate’sminimuminthefreeenergysurface.UmbrellasamplingwasalsousedtoobtainfreeenergyprofilesformovingapairofK+ionsinS1/S3toS0/S2whilethethirdion(K+,Na+orLi+)wasresidingeitherinthecavityortheS4site.Ifthelowerionwaskeptinthecavity,thiswasachievedwithasteepflat‐bottompotentialactingatz=‐7Åsuchthattheioncouldobtainanequilibriumdistributionof


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positionsthroughoutthecavity,butnotentertheS4site.AsimilarconstraintwasusedifwewishedtokeeptheionintheS4siteandnotletitfalloutintothecavity.ThesecalculationswererepeatedwherethelowerioncouldventureanywhereinthecavityorS4site(unconstrained)astheuppertwoionsweremovedatequilibrium(toexploreaconcertedmovementoflowerandupperions).Thechosenreactioncoordinateforthese2‐ionPMFcalculationswastheCOMoftheupperionpair(twoKionsresidingatS1/S3orS0/S2orinbetween)withcoordinatez12relativetotheCOMoftheselectivityfilter.Atotalof15windowsimulationswereneededtospan‐1to6Åin0.5Åintervalswiththesameforceconstantasgivenabove. ConvergenceandErrorEstimatesforFreeEnergyProfilesWehavecalculatedthetimeconvergenceforthefreeenergyprofilespresentedinFig.6ofthemaintext,from0‐1ns,todemonstratethatallprofileshaveconvergedtowithinasmallfractionofakcal/mol(seeleftpanelsofSupplementaryFig.4).Wehavealsodoneablockanalysisbydividingthe1nsinto2partsandusingthedifferenceinthetwoprofilesasameasureoferror.InSupplementaryFig.4rightpanels,weshowtheLi+iononly.Wechosetoshowtheseasanexamplebecausetheyrepresenttheworstconvergenceofallcalculations.Inthiscase,pathsI,II,II’andIIIrevealedRMSDerrorsof0.7,1.4,1.6and1.0kcal/mol,respectively.FortheK+ion(notshown)theseerrorswere0.6,0.5,0.6and0.6kcal/mol,respectively,andfortheNa+ion(alsonotshown)theywere0.4,1.0,0.7and0.6kcal/mol,respectively.RMSDerrorsforFig.4cofthemaintextwerecalculatedinasimilarway.


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mechanism of potassium channel selectivity revealed by na and...

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