ElectrophoreticMobilityofDNAinSolutionsofHighIonicStrengthEarleStellwa - PDF document

ElectrophoreticMobilityofDNAinSolutionsofHighIonicStrengthEarleStellwagenandNancyC.StellwagenDepartmentofBiochemistry,UniversityofIowa,IowaCity,IowaABSTRACTThefree-solutionmobilitiesofsmallsingle-strandedDNA(ssDNA)anddouble-strandedDNA(dsDNA)havebeenmeasuredbycapillaryelectrophoresisinsolutionscontaining0.01–1.0Msodiumacetate.ThemobilityofdsDNAisgreaterthanthatofssDNAatallionicstrengthsbecauseofthegreaterchargedensityofdsDNA.ThemobilitiesofbothssDNAanddsDNAdecreasewithincreasingionicstrengthuntilapproachingplateauvaluesationicstrengthsgreaterthan0.6M.Hence,ssDNAanddsDNAappeartointeractinasimilarmannerwiththeionsinthebackgroundelectrolyte.FordsDNA,themobilitiespredictedbytheManningelectrophoresisequationarereasonablyclosetotheobservedmobilities,usingnoadjustableparameters,iftheaveragedistancebetweenphosphateresidues(theparameter)istakentobe1.7A.ForssDNA,thepredictedmobilitiesareclosetotheobservedmobilitiesationicstrengths0.01Mifthe-valueistakentobe4.1A.Thepredictedandobservedmo-bilitiesdivergestronglyathigherionicstrengthsunlessthe-valueisreducedsignicantly.TheresultssuggestthatssDNAstrandsexistasanensembleofrelativelycompactconformationsathighionicstrengths,with-valuescorrespondingtotherelativelyshortphosphate-phosphatedistancesthroughspace.INTRODUCTIONTheconformationandstructureofdouble-strandedDNA SubmittedNovember18,2019,andacceptedforpublicationFebruary27,*Correspondence:nancy-stellwagen@uiowa.eduEditor:WilmaOlson. SIGNIFICANCECapillaryelectrophoresishasbeenusedtostudytheelectrophoreticmobilitiesofsmallsingle-strandedDNA(ssDNA)anddouble-strandedDNA(dsDNA)insolutionscontaining0.01–1.0Msodiumacetate.ThemobilitiesofbothssDNAanddsDNAdecreasewithincreasingionicstrengthandapproachlimitingplateauvaluesathighionicstrengths.Hence,theDNAstrandsundergosimilarelectrostaticinteractionswiththeionsinthesolution.ThemobilitiespredictedbytheManningelectrophoresisequationfordsDNAarereasonablyclosetotheobservedmobilitiesatallionicstrengths.However,thepredictedmobilitiesofssDNAapproximatetheobservedvaluesonlyifthephosphate-phosphateseparationdistancedecreaseswithincreasingionicstrength.Hence,ssDNAstrandsappeartoexistasanensembleofcongurationsthatbecomemorecompactathighionicstrengths.BiophysicalJournal,2783–2789,June2,20202783https://doi.org/10.1016/j.bpj.2020.02.034 density(),andsolutionviscosity().Here,wehaveusedCEtodeterminethedependenceoftheelectro-phoreticmobilityofssDNAanddsDNAonionicstrengthinsolutionscontaininghighconcentrationsofNaions.Un-deridenticalsolventconditions,themobilityofdsDNAisgreaterthanthatofssDNA.ThemobilitiesofbothtypesofDNAdecreasewithincreasingionicstrength,approach-inglimitingplateaumobilitiesathighionicstrengths.Hence,bothssDNAanddsDNAappeartointeractinasimilarmannerwiththecationsandanionsinthesolution.FordsDNA,theobservedmobilitiesarereasonablywellpredictedbytheManningelectrophoresisequation()iftheaveragedistancebetweenphosphateresiduesisassumedtobe1.7A.However,themobilitiespredictedforssDNAagreewiththeobservedmobilitiesonlyiftheaveragedis-tancebetweenphosphateresiduesdecreaseswithincreasingionicstrength.TheresultssuggestthattheensembleofssDNAconformationsbecomesmorecompactwithincreasingionicstrength,decreasingthethrough-spacedis-tancebetweenphosphateresidues.MATERIALSANDMETHODSDNAsamplesThe422-bprestrictionfragmentusedinthesestudieswasobtainedfromtheIIdigestionoftheyeast2-circleandpuriedasdescribedpreviously).SmallDNAoligomersweresynthesizedbyIntegratedDNATechnol-ogies(Coralville,IA)andpuriedbypolyacrylamidegelelectrophoresis.Duplexeswerepreparedbymixingappropriatequantitiesofthedesiredoligomersin10mMTris-chloridebuffer(pH8.0),heatingto94Cfor5min,andslowlycoolingtoroomtemperature.TheconcentratedDNAstocksolutions(L)werestoredatCanddilutedwithwatertoconcentrationsof10–50ng/LfortheCEexperiments.ThesequencesoftheDNAstrandsandtheirshortacronymsareg

iveninTable1,alongwiththenumberofphosphateresiduesineachDNA.BuffersThebackgroundelectrolytes(BGEs)werepreparedfromstocksolutionscontaining1.0Msodiumacetate(ThermoFisherScientic,Waltham,MA)and0.005MTris-acetate(0.01MTrisbasetitratedtopH8.00.1withaceticacid).AppropriatevolumesofthetwostocksolutionsweremixedtoformBGEscontaining0.01–1.0Msodiumacetate(NaAc)plus0.005MTris-acetatebuffertokeepthepHofthesolutionconstant.NaAcwaschosenasthemajorcomponentoftheBGEbecausetheintrinsicconductivitiesofthecationandanionaresimilar(),leadingtowell-shapedpeaksintheelectropherograms.TheconductivitiesoftheTrisandNaionsarealsosimilar.Thefree-solutionmobilitiesoftheDNAstrandsweremeasuredusingaBeckmanCoulterP/ACESystemMDQCEsystem(Fullerton,CA)runinthereverse-polaritymode(theanodeonthedetectorside)withultravioletdetectionat254nm.Migrationtimesandpeakproleswereanalyzedusingthe32Karatsoftware.Thecapillarieswere40.0cminlength,withexternaldiametersof375mandinternaldiametersof75mmountedinaliquid-cooledcartridgethermostatedat20C.ThecapillarieswereinternallycoatedlinearpolyacrylamidecapillariesfromBio-RadLaboratories(Her-cules,CA).Thelinearpolyacrylamidecoatingminimizestheelectroos-moticow(EOF)ofthesolventwithoutaffectingthemobilityoftheanalyte().Thesampleswerehydrodynamicallyinjectedintothecapil-larybyapplyinglowpressure(0.5psi,0.0035MPa)for3s.Thesamplevol-umewas22nL;thelengthofthesampleplugwas0.51cm,1.3%ofthecapillarylength.Theappliedvoltagerangedfrom1.0to7.0kV,dependingontheionicstrengthoftheBGE.Exceptatthehighestionicstrengths,thecurrentwasalwayslessthan60.Undersuchconditions,heatingeffectsarenegligible,andtheobservedmobilitiesareindependentoftheappliedelectriceld(Theobservedelectrophoreticmobilities,,werecalculatedfromisthedistancefromtheinlettothedetector(incentimeters),theelectriceldstrength(involtspercentimeter),andisthetimerequiredforthesampletomigratefromtheinlettothedetector(inseconds).TheobservedmobilityisthealgebraicsumofthemobilityoftheDNA,andthemobilitycausedbytheEOFofthesolvent,.TheEOFwasmeasuredasafunctionof[NaAc]bythefastmethodofWilliamsandVigh()usingbenzylalcoholastheanalyte.TheEOFcorrectionwasonlynecessaryationicstrengthslessthan0.10M;for0.lM,theobservedmobilitieswereessentiallyindependentoftheEOF,allowingthemobilitiestobecalculateddirectlyfromEq..TheDNAmobilitiesmeasuredinsuccessiverunsonthesamedayusuallyagreedwithin0.01mobilityunits(m.u.;1m.u.).Themobilityofds26ain0.7MNaAc,measuredonthreedifferentdaysseparatedbyseveralmonths,was1.470.09m.u.Becausethesemobilityvariationsareapproximatelyequaltothesizesofthesymbolsintheguresbelow,er-rorbarsarenotshown.ElectrophoreticmobilityThefree-solutionelectrophoreticmobilityofapolyelectrolyteisdeter-minedprimarilybytheratioofthenumberofchargedresidues,,tothefrictionalcoefcient,,asshowninEq.Ifthepolyionisrigidandspherical,thelinearDebye-Huckeltheoryisvalid,andtheDebyescreeninglength()ismuchlargerthanthepolyionradius;theDebye-Huckel-OnsagertheorypredictsthatthemobilitycanbedescribedbyEq.istheviscosityofthesolventandisthepolyionradius(Forhighlychargedpolyions,thevalueofisoftentakentobetheeffec-tivechargeaftercounterioncondensation()ratherthanthenom-inalstructuralcharge.Inaddition,thepolyionmobilityisreducedbytwo TABLE1Acronyms,NumberofPhosphates,andSequencesofDNAAcronymNo.ofPhosphatesSequenceds442884IIdigestofyeast2-ds26a505-CGCAATTTTCAGCAATTTTCAGACAG-3ds26b505-CGCAAAGTGTCTATACATATCTATCG-3T2625TTTTTTTTTTTTTTTTTTTTTTTTTTT1615TTTTTTTTTTTTTTTTss076ACCTGATStellwagenandStellwagenBiophysicalJournal,2783–2789,June2,2020 solvent-relatedeffects,commonlyknownasthe‘‘relaxationeffect’’andthe‘‘electrophoreticeffect’’().Therelaxationeffectisduetotheseparationofthecentersofchargeofthecounterioncloudandthepoly-ion,creatinganinduceddipolethatopposesthedirectionoftheappliedelectriceld.Theelectrophoreticeffectiscausedbythemigrationofthesolvatedcount

erionsandthepolyioninoppositedirections,increasingtheviscousdragonthepolyion.Asaresult,theobservedmobilityofagivenpolyionisacomplicatedfunctionofthenumberofchargedresidues,thesizeofthepolyion,counterioncondensation,andthecompositionofthesurroundingionicmedium(ManningelectrophoresisequationManningusedcounterioncondensationtheory()andlinearDebye-uckelstatisticstoderiveanequationforDNAelectrophoreticmobilitythatincludestherelaxationandretardationeffectsjustdescribed(TheDNAismodeledasaninnitelylongwire(noendeffects)withpointchargesseparatedbytheaveragedistancebetweenthemalongtheDNAchain,termedthefactor.Theresultingequation,whichcontainsnoadjust-ableparameters,canbewrittenasfollows:
kBT3o½jlnðkbÞj;(4b)a¼1 n13ðn1þn2Þ z21z22z1z2;(4c)b¼1þ 108n1ðn1þn2Þ ð300mÞjz1þz2j z21lo1þ isthepredictedmobility;arethecounterionandcoionvalencies,respectively;isthedielectricconstantofthesolvent;Boltzmann’sconstant;istheabsolutetemperature;istheviscosityofthesolvent;istheinverseDebyelength;istheelementarycharge;arethenumbersofcounterionsandcoionsintheBGE;andaretheequivalentconductancesofthecounterionsandcoions.AllparametersinEqs.c,anddareknownphysicalconstantsorcanbecalculatedfromthecompositionofthesolutionanddataintheliter-ature.ThechargeseparationparametercanbeestimatedfordsDNAbydividingthelengthoftheoligomer(numberofbasepairsriseperbase-pair,3.4A)bythenumberofphosphateresiduesintheDNA.TheofssDNAwillbediscussedbelow.RESULTSANDDISCUSSIONdsDNAThefree-solutionmobilitiesofds442,ds26a,andds26bareplottedinFig.1asafunctionofionicstrength,denotedas[NaAc]forsimplicity.ThemobilitiesofallthreedsDNAstrandsdecreasedwithincreasingionicstrengthuntiltheybegantoleveloffationicstrengthsabove0.6M.Theamplitudeofthemobilityofds442waslargerthanobservedforthesmalleroligomers,asexpectedfrompreviousstudiesshowingthatDNAmobilitiesincreasewithincreasingmolecularweightuntiltheyreachaplateauvalueathighmolecularweights().Toemphasizethegeneralityoftheresults,themobilitiesofthethreedsDNAstrandswereanalyzedtogether.ThesolidcurveinFig.1correspondstoathree-parameterexponentialdecayofthecombinedmo-bilitiesofthethreedsDNAstrandsasafunctionofNaAcconcentration.Similarresultswereobtainedfromathree-parameterhyperbolictofthecombinedmobilitiesasafunctionofionicstrength(datanotshown).ThedashedcurveinFig.1correspondstothemobilitypredictedfordsDNAfromtheManningelectrophoresisequation()usingavalueof,theaverageseparationbe-tweenchargedphosphateresidues,equalto1.7A.Theobservedandpredictedmobilitiesarereasonablycloseovertheentirerangeofionicstrengths.However,thepre-dictedmobilitiesarehigherthantheobservedmobilitiesatlowionicstrengths(0.2M),asobservedpreviously),anddonotapproachaplateauvalueathighionicstrengths.Asaresult,thecurvesdescribingthedependenceofthepredictedandobservedmobilitiesonionicstrengthhavedifferentshapesandcrossat0.6MNaAc.ssDNAThefree-solutionmobilitiesofssDNAstrandscontaining7,16,and26nucleotidesareplottedasafunctionofionicstrengthinFig.2.ThemobilitiesofthessDNAstrandsdecreasedwithincreasingionicstrengthatlowionicstrengthsandapproachedlimitingplateauvaluesationicstrengthsgreaterthan0.6M.AsobservedwithdsDNA,themobilitiesofthessDNAstrandsincreasedinmagnitudewithincreasingmolecularweight,asexpectedfromprevi-ousstudies().Again,toemphasizethegeneralityoftheresults,themobilitiesofthethreessDNAstrandswere FIGURE1Dependenceofthefree-solutionmobilityofdsDNAonthesodiumacetateconcentration([NaAc]).Thesymbolsrepresentthefollowing:solidcircle(),ds442;opencircle(),ds26a;andopentrian-gle(),ds26b.Thesolidlinecorrespondstoathree-parameterexponentialdecayofthecombinedmobilitiesofthethreedsDNAstrandsasafunctionofionicstrength.ThedashedlinecorrespondstothemobilitypredictedbytheManningelectrophoresisequation(),assuming1.7ADNAMobilityandIonicStrengthBiophysicalJournal,2783–2789,June2,20202785 analyzedtogether.ThesolidcurveinF

ig.2describesathree-parameterexponentialdecayofthecombinedmobil-itiesasafunctionofionicstrength.TocomparetheobservedmobilitiesofthessDNAstrandswiththemobilitiespredictedbytheManningelectropho-resisequation,itisnecessarytorstestimatethevalueof,theaveragedistancebetweenchargedphosphateresiduesalongthecontourlengthofthechain().Thedis-tancebetweenadjacentnucleotidesinprotein-DNAcrystalshasbeenfoundtobe6.3A),closetothemaximumseparationbetweenphosphateresiduesinstretchedpolynu-cleotides().However,muchshorterseparationdistancesaretypicallyobservedforpolynucleotidesandssDNAinsolution.Earlybiophysicalstudiesshowedthatsingle-strandedpolynucleotidesarewelldescribedasworm-likecoilswith-valuesbetween3and4ARecentdeterminationsofthe-valuesofsmallssDNAstrands,withandwithoutintrinsicbasestacking,aresimilar).Somewhatlarger-values,between4.0and4.5Ahavebeendeterminedforsmall(dT)oligomersusingensembleandsingle-moleculeuorescenceresonanceen-ergytransfer(FRET)methods().Finally,aconforma-tionalenergyanalysisofsingle-strandedrandomlycoilingpolynucleotidechainsfoundthattheparameteronlyweaklyreectsthespatialcongurationoftheindividualchainsegmentsandcannotbeusedtoinfertheoverallconformationofthechain(Giventheuncertaintiesabouttheappropriate-valuetouseforssDNA,wechosetocomparetheobservedmobil-itiesofthessDNAstrandsinFig.2withthemobilitiespredictedbytheManningelectrophoresisequationusingtwoarbitraryvaluesof,4.1and2.3A.Otherfactorspri-marilyshiftthepredictedmobilitiesupordownonthemobilityscale(datanotshown).ThelowerdashedcurveFig.2correspondstothepredictedmobilitiesif4.1A.Thepredictedandobservedmobilitiesarereasonablycloseatlowionicstrengths(0.1M),suggestingthatthis-valuecorrespondstotheaverageseparationbetweenssDNAphosphateswhentheionicstrengthisverylow.Similarresultshavebeenobservedinsingle-moleculeFRETstudies(Ationicstrengths0.1MNaAc,thepredictedmobilitiesofthessDNAstrandsaresignicantlylowerthantheobservedmobilitieswhenthe-valueisassumedtobe4.1A,asshownbycomparingthelowerdashedcurveinFig.2withthesolidcurvedescribingtheobservedmobilities.Thediscrepancycanprobablybeattributedtoanincreaseinexibilityand/oradecreaseintheoverallextensionofthessDNAmoleculeswithincreasingionicstrengthbecausethepersistencelengthdecreasesinasimilarmannerwithincreasingionicstrength(TheupperdashedcurveinFig.2correspondstothepre-dictedmobilityofssDNAifthevalueofisassumedtobe2.3A.Inthiscase,thepredictedandobservedmobilitiesarereasonablycloseathighionicstrengths(0.3M)butdivergeatlowionicstrengths(0.2M).Theresultssug-gestthattheensembleofssDNAconformationsinsolutionmayundergoatransitionfromrod-likeextendedstructuresinsolutionscontaininglessthan0.1MNaActomorecompactbutstillsomewhatextendedconformationsinBGEscontainingmorethan0.3MNaAc.The-valuesofthesemorecompact,‘‘crumpled’’ssDNAconformationscouldcorrespondtocomparativelyshortphosphate-phos-phatedistancesthroughspaceinsteadoftracingapathalongthecontourlengthofthechain(TopredictssDNAmobilitiesoverawiderangeofionicstrengthsusingtheManningelectrophoresisequation,itwouldseemnecessarytouse-valuesthatdecreasewithincreasingionicstrength.Recentsmall-anglex-rayscat-tering()anduorescencespectroscopy()measure-mentsofsmallssDNAstrandsshowedthatthepersistencelengthdecreased45–50%whentheionicstrengthoftheso-lutionincreasedfrom0.1to1.0M[Na).Thisper-centagedecreaseissimilarinmagnitudetothe78%decreasein-valuesusedtocalculatethepredictedssDNAmobilitiesinFig.2.Hence,itmightbeusefultothinkofthe-valuesofssDNAasphenomenologicalparametersdescribingtheaveragedistancebetweenphosphateresiduesthroughspaceunderagivensetofexperimentalconditionsratherthantheaverageseparationofphosphateresiduesalongthecontourlengthofthechain.TheconformationalensembleofssDNAstrandsinhighionicstrengthsolutionscouldthenbethoughtofasthessDNAequivalentofthemoltenglobulesobservedduringproteinfolding(e.g.,))orthecomp

actrandom-walkstructuresobserved FIGURE2Dependenceofthefree-solutionmobilityofthreessDNAstrandsonionicstrength.Thesymbolsrepresentthefollowing:solidcircle),T26;opencircle(),T16;andopentriangle(),ss07.Thesolidcurvecorrespondstoathree-parameterexponentialdecayofthecombinedmobilitiesofthessDNAstrandsasafunctionofionicstrength.ThedashedcurvescorrespondtothemobilitiespredictedfromtheManningelectropho-resisequationusing4.1Alowerdashedcurve)or2.3AupperdashedStellwagenandStellwagenBiophysicalJournal,2783–2789,June2,2020 forvariouspolymersbyelasticitymeasurements(e.g.,ComparisonofthemobilitiesofssDNAanddsDNAThefree-solutionmobilitiesobservedforssDNAanddsDNAinsolutionsofdifferentionicstrengthsarecomparedinFig.3usingthettedmobilitycurvestakenFigs.1tomoreeasilyvisualizetheresults.ThemobilitiesofssDNAanddsDNAdecreaserapidlywithincreasingionicstrengthuntilreachinglimitingplateauvaluesationicstrengths0.6M.ThemobilitiesofdsDNAarelargerthanthoseofssDNAatallionicstrengthsbecauseofthegreaterchargedensityofdsDNA(ThenearlyparallelmobilitycurvesobservedforssDNAanddsDNAinsolutionsofdifferentNaAcconcentrationsFig.3)suggestthatbothssDNAanddsDNAundergosimilarinteractionswiththecounterionsandcoionsintheBGE.Theunexpectedmobilityplateausobservedathighionicstrengths(0.6M)suggestthatcoun-terion-counterioncorrelationeffects(55–57),coun-terion-phosphateinteractions(),and/orcation-anioninteractionsintheBGEmaycontributetothemobilityplateausobservedforssDNAanddsDNAathighionicstrengths.Variationsinthecompositionoftheionatmosphereatdifferentionicstrengthsmayalsocontributetothemobilityplateaus.RecentioncountingexperimentshavesuggestedthatthenumberofcationsclosetotheDNAsurfacede-creaseswithincreasingionicstrength,whereasthenumberofanionsexcludedfromtheionatmosphereincreases(TheresultcouldbeagradualincreaseintheeffectivenetchargeoftheDNAwithincreasingionicstrength,increasingtheobservedmobilityandinpartcounteractingtheusualdecreaseinDNAmobilitywithincreasingionicstrengthFinally,thedistinctionbetweenthecondensedcationsintheionatmospherearoundtheDNA,theconcentrationofcationsintheadjacentDebyelayer,andthecationsinthebulksolutionmaybecomeblurredwhentheDebyelayerisverythin,asistrueforthehighionicstrengthbuffersusedhere.Furtherstudieswillbeneededtoclarifytheseissues.CONCLUSIONSThefree-solutionmobilitiesofssDNAanddsDNAdecreasewithincreasingionicstrengthandapproachlimitingplateauvaluesat0.6M.Whetherthemobilityplateausareduetoion-ionand/orDNA-ioninteractionsthatbecomeimportantathighionicstrengthsremainstobedetermined.TheManningelectrophoresisequation,whichcontainsnoadjustableparame-ters,providesareasonableestimateofthefree-solutionmobilityofdsDNAinsolutionsofdifferentionicstrengths,usinga-value(lineardistancebe-tweenchargedphosphateresidues)of1.7A.ForssDNA,theappropriatevalueappearstodecreasewithincreasingionicstrength,suggestingthatssDNAstrandsexistasanensembleofcrumpledconformationsthatbecomemorecompactathighionicstrengths.Neithertheaveragedimen-sionsofindividualmoleculesintheensemblenorthecontourlengthsofin-dividualssDNAchainscanbedeterminedwithoutfurtherexperimentalinformation(AUTHORCONTRIBUTIONSE.S.andN.C.S.designedexperiments.E.S.carriedoutexperiments.E.S.andN.C.S.analyzedthedataandwrotethearticle.ACKNOWLEDGMENTSHelpfulcommentsfromthereviewersaregratefullyacknowledged.REFERENCESLipfert,J.,S.Doniach,,D.Herschlag.2014.Understandingnucleicacid-ioninteractions.Annu.Rev.Biochem.Haran,T.E.,andU.Mohanty.2009.TheuniquestructureofA-tractsandintrinsicDNAbending.Q.Rev.Biophys.Saenger,W.1984.PrinciplesofNucleicAcidStructure.Springer-Ver-lag,NewYorkLu,Y.,B.Weers,andN.C.Stellwagen.2001-2002.DNApersistencelengthrevisited.Biopolymers.61:261–275Brunet,A.,C.Tardin,,M.Manghi.2015.DependenceofDNApersistencelengthonionicstrengthofsolutionswithmonovalentanddivalentsalts:ajointtheory-experimentstudy.Macromolecules.48:3641–36

52Savelyev,A.2012.DomonovalentmobileionsaffectDNA’sexibilityathighsaltcontent?Phys.Chem.Chem.Phys.Yuan,C.,H.Chen,,L.A.Archer.2008.DNAbendingstiffnessonsmalllengthscales.Phys.Rev.Lett.Garai,A.,S.Saurabh,,P.K.Maiti.2015.DNAelasticityfromshortDNAtonucleosomalDNA.J.Phys.Chem.B.119:11146–11156Wu,Y.-Y.,L.Bao,,Z.-J.Tan.2015.FlexibilityofshortDNAheliceswithnite-lengtheffect:frombasepairstotensofbasepairs.J.Chem. FIGURE3ComparisonofthemobilitiesobservedfordsDNA()andssDNA(lowercurve)asafunctionofNaAcconcentration.Themobilitycurvescorrespondtothettedmobilitycurves(solidlinesFigs.1,respectively.DNAMobilityandIonicStrengthBiophysicalJournal,2783–2789,June2,20202787 McIntosh,D.B.,G.Duggan,,O.A.Saleh.2014.Sequence-depen-dentelasticityandelectrostaticsofsingle-strandedDNA:signaturesofbase-stacking.Biophys.J.106:659–666Chen,H.,S.P.Meisburger,,L.Pollack.2012.Ionicstrength-depen-dentpersistencelengthsofsingle-strandedRNAandDNA.Proc.Natl.Acad.Sci.USA.109:799–804Murphy,M.C.,I.Rasnik,,T.Ha.2004.Probingsingle-strandedDNAconformationalexibilityusinguorescencespectroscopy.phys.J.86:2530–2537Laurence,T.A.,X.Kong,,S.Weiss.2005.Probingstructuralhet-erogeneitiesanductuationsofnucleicacidsanddenaturedproteins.Proc.Natl.Acad.Sci.USA.102:17348–17353Bosco,A.,J.Camunas-Soler,andF.Ritort.2014.Elasticpropertiesandsecondarystructureformationofsingle-strandedDNAatmonovalentanddivalentsaltconditions.NucleicAcidsRes.42:2064–2074Zhang,Y.,H.Zhou,andZ.-C.Ou-Yang.2001.Stretchingsingle-strandedDNA:interplayofelectrostatic,base-pairing,andbase-pairstackinginteractions.Biophys.J.81:1133–1143Sarkar,S.,A.Maity,,R.Chakrabarti.2019.Saltinducedstructuralcollapse,swelling,andsignatureofaggregationoftwossDNAstrands:insightsfrommoleculardynamicssimulation.J.Phys.Chem.B.Vesnaver,G.,andK.J.Breslauer.1991.ThecontributionofDNAsin-gle-strandedordertothethermodynamicsofduplexformation.Proc.Natl.Acad.Sci.USA.Zhou,J.,S.K.Gregurick,,F.P.Schwarz.2006.Conformationalchangesinsingle-strandDNAasafunctionoftemperaturebyBiophys.J.Isaksson,J.,S.Acharya,,J.Chattopadhyaya.2004.Single-strandedadenine-richDNAandRNAretainstructuralcharacteristicsoftheirrespectivedouble-strandedconformationsandshowdirectionaldiffer-encesinstackingpattern.Biochemistry.43:15996–16010Ramprakash,J.,B.Lang,andF.P.Schwarz.2008.ThermodynamicsofsinglestrandDNAbasestacking.Capobianco,A.,A.Velardo,andA.Peluso.2018.Single-strandedDNAoligonucleotidesretainrisecoordinatescharacteristicofdoubleJ.Phys.Chem.B.Stellwagen,N.C.,C.Gel,andP.G.Righetti.1997.ThefreesolutionmobilityofDNA.Biopolymers.Dong,Q.,E.Stellwagen,,N.C.Stellwagen.2003.Freesolutionmobilityofsmallsingle-strandedoligonucleotideswithvariablechargeElectrophoresis.Stellwagen,E.,Y.Lu,andN.C.Stellwagen.2003.UnieddescriptionofelectrophoresisanddiffusionforDNAandotherpolyions.Biochem-istry.42:11745–11750Stellwagen,E.,andN.C.Stellwagen.2003.ProbingtheelectrostaticshieldingofDNAwithcapillaryelectrophoresis.Biophys.J.84:1855–1866Stellwagen,E.,andN.C.Stellwagen.2002.ThefreesolutionmobilityofDNAinTris-acetate-EDTAbuffersofdifferentconcentrations,withandwithoutaddedNaCl.Electrophoresis.Stellwagen,E.,Y.Lu,andN.C.Stellwagen.2005.CurvedDNAmol-eculesmigrateanomalouslyslowlyinfreesolution.NucleicAcidsRes.33:4425–4432Dong,Q.,E.Stellwagen,andN.C.Stellwagen.2009.MonovalentcationbindingintheminorgrooveofDNAA-tracts.Biochemistry.48:1047–1055Stellwagen,E.,Q.Dong,andN.C.Stellwagen.2015.FlankingAbasepairsdestabilizetheB(*)conformationofDNAA-tracts.108:2291–2299Stellwagen,E.,J.P.Peters,,N.C.Stellwagen.2013.DNAA-tractsarenotcurvedinsolutionscontaininghighconcentrationsofmonova-lentcations.Biochemistry.52:4138–4148Stellwagen,N.C.,J.P.Peters,,E.Stellwagen.2014.Thefreesolu-tionmobilityofDNAandotheranalytesvariesasthelogarithmofthefractionalnegativecharge.Electrophoresis.Stellwagen,N.C.2017.Electrophoreticmobilitiesofthechargevar

i-antsofDNAandotherpolyelectrolytes:similarities,differences,andcomparisonwiththeory.J.Phys.Chem.B.121:2015–2026Stellwagen,N.C.,andE.Stellwagen.2019.DNAthermalstabilityde-pendsonsolventviscosity.J.Phys.Chem.B.123:3649–3657Manning,G.S.1981.Limitinglawsandcounterioncondensationinpolyelectrolytesolutions.7.Electrophoreticmobilityandconductance.J.Phys.Chem.Stellwagen,N.C.,A.Bossi,,P.G.Righetti.2001.Doorientationef-fectscontributetothemolecularweightdependenceofthefreesolutionmobilityofDNA?Electrophoresis.Vanysek,P.1996–1997.IonicconductivityanddiffusionatinniteHandbookofChemistryandPhysics,77thEdition.D.R.Lide,ed.CRCPress,Inc.:598–100Williams,B.A.,andG.Vigh.1996.Fast,accuratemobilitydeterminationmethodforcapillaryelectrophoresis.Anal.Chem.68:1174–1180Grossman,P.D.1992.Chapter4:Free-solutioncapillaryelec-trophoresis.CapillaryElectrophoresis:TheoryandPractice.P.D.GrossmanandJ.C.Colburn,eds.AcademicPress,pp.111–132Bockris,J.O.’M.,andA.K.N.Reddy.1998.ModernElectrochem-istry:Vol.1,Ionics,SecondEdition.PlenumPress,NewYorkWiersema,P.H.,A.L.Loeb,andJ.T.G.Overbeek.1966.Calculationoftheelectrophoreticmobilityofasphericalcolloidparticle.J.ColloidInterfaceSci.O’Brien,R.,andL.R.White.1978.Electrophoreticmobilityofasphericalcolloidalparticle.J.Chem.Soc.,FaradayTrans.II.74:1607–1626Viovy,J.-L.2000.ElectrophoresisofDNAandotherpolyelectrolytes:physicalmechanisms.Rev.Mod.Phys.72:813–872Manning,G.S.1978.Themoleculartheoryofpolyelectrolytesolutionswithapplicationstotheelectrostaticpropertiesofpolynucleotides.Q.Rev.Biophys.Record,M.T.,Jr.,C.F.Anderson,andT.M.Lohman.1978.Thermo-dynamicanalysisofioneffectsonthebindingandconformationalequilibriaofproteinsandnucleicacids:therolesofionassociationorrelease,screening,andioneffectsonwateractivity.Q.Rev.Biophys.11:103–178Chatterji,A.,andJ.Horbach.2007.Electrophoreticpropertiesofhigh-lychargedcolloids:ahybridmoleculardynamics/latticeBoltzmannsimulationstudy.J.Chem.Phys.Jumppanen,J.H.,andM.-L.Riekkola.1995.Inuenceofelectrolytecompositionontheeffectiveelectriceldstrengthincapillaryzoneelectrophoresis.Electrophoresis.Gulik,A.,H.Inoue,andV.Luzzati.1970.Conformationofsingle-strandedpolynucleotides:small-anglex-rayscatteringandspec-troscopicstudyofpolyribocytidylicacidinwaterandinwater-alcoholsolutions.J.Mol.Biol.Manning,G.S.1976.Theapplicationofpolyelectrolytelimitinglawstothehelix-coiltransitionofDNA.VI.Thenumericalvalueoftheaxialphosphatespacingforthecoilform.Olson,W.K.,andG.S.Manning.1976.Acongurationalinterpreta-tionoftheaxialphosphatespacinginpolynucleotidehelicesandrandomcoils.15:2391–2405Sim,A.Y.L.,J.Lipfert,,S.Doniach.2012.Saltdependenceoftheradiusofgyrationandexibilityofsingle-strandedDNAinsolutionprobedbysmall-anglex-rayscattering.Phys.Rev.EStat.Nonlin.SoftMatterPhys.Baldwin,R.L.,andG.D.Rose.2013.Moltenglobules,entropy-drivenconformationalchangeandproteinfolding.Curr.Opin.Struct.Biol.23:4–10Christensen,H.,andR.H.Pain.1991.Moltenglobuleintermediatesandproteinfolding.Eur.Biophys.J.19:221–229StellwagenandStellwagenBiophysicalJournal,2783–2789,June2,2020 Saleh,O.A.,D.B.McIntosh,,N.Ribeck.2009.Nonlinearlow-forceelasticityofsingle-strandedDNAmolecules.Phys.Rev.Lett.McIntosh,D.B.,andO.A.Saleh.2011.Saltspecies-dependentelectro-staticeffectsonssDNAelasticity.Macromolecules.Tan,Z.-J.,andS.-J.Chen.2005.Electrostaticcorrelationsanductua-tionsforionbindingtoanitelengthpolyelectrolyte.J.Chem.Phys.Xi,K.,F.H.Wang,,Z.J.Tan.2018.CompetitivebindingofMgandNaionstonucleicacids:fromhelicestotertiarystructures.phys.J.114:1776–1790Hayes,R.L.,J.K.Noel,,J.N.Onuchic.2015.GeneralizedManningcondensationmodelcapturestheRNAionatmosphere.Phys.Rev.Lett.114:258105Gebala,M.,G.M.Giambas,D.Herschlag.2015.Cation-anionin-teractionswithinthenucleicacidionatmosphererevealedbyionJ.Am.Chem.Soc.137:14705–14715DNAMobilityandIonicStrengthBiophysicalJournal,2783–2789,June2,2020