FORMATION OF SMALL UNILAMELLAR VESICLES AND APPLICATIONS TO TARGETED DRUG DELIVERY

PAGE 1

FORMATIONOFSMALLUNILAMELLAR VESICLESANDAPPLICATIONSTO TARGETEDDRUGDELIVERY BY SONALIGUPTA AThesis SubmittedtotheDivisionofNaturalSciences NewCollegeofFloridainpartialfulllmentoftherequirementsforthedegree BachelorofArts UnderthesponsorshipofDr.DonaldColladay,ProfessorofPhysics Sarasota,Florida May,2013

PAGE 2

Acknowledgements FirstlyIwouldliketothankmymotherforherunwaveringsupportand thefreedomshehasaordedmetoexploremyidentity,andpursuemy path.HerrstpriorityhasalwaysbeenmyeducationandforthatIam deeplygrateful.WithoutherIwouldnotbethepersonIamtoday.Sheis alsoaprofoundlyinteresting,caring,fun,andlovingperson,andaconstant sourceofinspirationtome.Iloveyou,mummy. Ialsowanttothankthemembersofmybaccalaureatecommittee: Dr.Colladay,forhisadvisingthroughouttheprocessofwritingthisthesis. WhenIlostdirectionandgotmiredindetails,youwereareorientingforce. Thankyouforyoureloquentlectures,andforyourpatiencewithme. Dr.Shipman,whohastaughtmethemeaningofhardworkandintegrity byexample.ThankyouforsomeofthebesttutorialsessionsIhavehad; yourlucidexplanationsofP.Chemconceptsleftmemoreinawethanyou know.Thankyouforbeingthekindofprofessorwhostaystill3a.m.ona Fridaybackingupthesisstudents'datawhenmasterkeysgomissing.After thelibraryclosedyourlabwasmyrefuge,withaconstantowofespresso. Mostofall,thankyouforrevealingtomethebeautyinP.Chemandfor inspiringmetowhollydedicatemylifetoscience. Dr.Clore,forbeingmyacademicadvisorthroughoutmostofmyundergraduatestudiesandservingonmybaccalaureatecommittee.Yourgreat lecturesincellbiologyandyourenthusiasmforthesubjectmovedmeto pursuebiophysics.Yourdisciplineandfocussetanexample,andIthank youforyourguidanceandyourpatiencetowardsme. Iamalsogratefulformyresearchmentor,Dr.Pai,forallhisguidance andinvaluablethesisadvice.Withouthimthisthesiswouldnotexist.I thankhimformakingmyrstresearchexperienceanincrediblypositive one,formotivatingme,andforteachingmethevalueofperserverancein doingresearch.

PAGE 3

IalsothankDr.BellamkondaforhiscounselandDr.AlbertoFernandezNievesforgenerouslyallowingmeuseoftheSoftCondensedMatterLabat GeorgiaTech. IespeciallywanttothankJohnS.HyattandAndreaScottifortheirinvaluablehelpwithDLSandfortakingtimeoutoftheirbusyschedulesto helpmerunexperiments.IalsowanttothankJohnHyattforwritingthe MATLABcodeIusedtoprocessmydata. FinallyIwouldliketothankmyfriendssimplyforbeingtheinteresting, awesomepeoplethattheyare.Thankyouforthewonderfultimewehave sharedtogether,forallthelaughs,andforallthelove.Ialsothankmy dog,Einstein,whohasbeenmyconstantcompanionandabundleofjoy.

PAGE 4

FORMATIONOFSMALLUNILAMELLARVESICLESAND APPLICATIONSTOTARGETEDDRUGDELIVERY SonaliGupta NewCollegeofFlorida,2013 Abstract Liposomes,ormembranousvesicles,witharadiuslessthan100nmarecalledSmall UnilamellarVesiclesSULVs.TheformationofstableSULVsisproblematicsincetensioninthemembraneduetoitshighcurvaturedestabilizestheparticles.Inthisstudy thespontaneousformationofSULVswasobservedthroughtwoseparatepathways, bothinvolvingstructuralprecursors.SULVsformedthroughthebicellarphasehave disk-likeprecursorswhosemorphologyisdictatedbythemolarratiooflongandshort chainphospholipidsinsolution.HereDMPCandDHPCwereusedina3.2:1ratioto createSULVsof34.3 0.24nmataconcentrationof0.75%lipidw/vand35.6 0.45 nmataconcentrationof1.0%lipidw/v.Ellipsoidalprecursorsyieldedliposomesrangingfromapproximately58to66nminradius,athighlydiluteconcentrations.03to 0.09%lipidw/vindicatingthatatlowconcentrationsthemolarratioofphospholipids incorporatedwithinthestructuresshiftsfromtheidealinputratio.Lamellarsheets werenotshowntoresultinSULVs,butmayhavemalleabilityatthresholdconcentrationswherethelamellaeareundergoingunbindingtransitions.Thedynamicsofdisk growthhintsatamechanismbywhichthemetastablemorphologiesofSULVswith structuralprecursorsaremaintainedforlongerperiodsthanSULVscreatedthrough high-energymethodssuchassonication.Thesevesicleswerecreatedforthepurpose ofoptimizinganti-tumordrugstoglioblastomamultiformecellsthroughtheenhanced permeabilityandretentioneect.SULVswerefoundtodiusethroughuniformporous mediaatrates50timesfasterthanthoseofLULVsLargeUnilamellarVesicles,indicatingthattheymaybeabletopenetratetumorstoagreaterextentthanLULVs, whicharealsohinderedbylowercirculationhalf-lives.Astudyofsizedependentleakageratesofencapsulatedagentsremainedinconclusive.Overall,stableSULVssuitable foruseintargeteddrugdeliveryweresuccessfullycreatedandshowpromiseforbiologicalapplicationsthatrequirepenetrationofsemi-permeablemembranes,tissues,or vasculatures. Dr.DonaldColladay,DepartmentofNaturalSciences iv

PAGE 5

Contents ListofFiguresix ListofTablesxi ListofAbbreviationsxiii 1Introduction1 1.1LiposomesinTargetedDrugDelivery...................1 1.2ModelSystem:GlioblastomaMultiforme..................2 1.3Motivations..................................4 2FormationofSmallUnilamellarVesicles7 2.1MembraneComposition...........................7 2.1.1PhospholipidStructure.......................7 2.1.1.1AcylChainLength....................8 2.1.1.2Phosphatidylcholines...................9 2.1.2PackingParameter..........................9 2.1.2.1DerivationandApplicability...............9 2.1.2.2Calculating P forComponentPhospholipids......11 2.1.2.3PredictingtheBicellarPhase...............12 2.1.3TheMolarRatio...........................13 2.1.3.1MolarRatiosforanIdealBicellePhase.........14 2.1.3.2OverallSignicanceoftheMolarRatio.........15 2.2ConcentrationandTemperaturePhaseDiagram.............17 3Methods21 3.1FormationofSmallUnilamellarVesicles..................21 3.1.1LipidCake..............................21 3.1.2Path1:DilutionAboveCriticalTemperature...........22 3.1.3Path2:Disk-likePrecursorsBelowCriticalTemperature....22 3.1.4Path3:EllipsoidalPrecursorsBelowCriticalTemperature...22 v

PAGE 6

CONTENTS 3.1.5Extrusion...............................23 3.1.6DLSMeasurements..........................23 3.2DependenceofBaselineLeakageonSizeofLiposomes..........24 3.2.1QuantifyingRhodamineConcentrationsthroughFluorescenceIntensity.................................24 3.2.2RhodamineLoadedLULVs.....................24 3.2.3RhodamineLoadedSULVs.....................25 3.2.4MembraneDialysis..........................25 3.2.5FluorescenceImaging........................25 3.3DiusionThroughaUniformGel......................25 3.3.1SettingtheSephadex.........................26 3.3.2SynthesisofLULVswithFluorescentMembranes.........26 3.3.3SynthesisofSULVswithFluorescentMembranes.........26 3.3.4DLSofLiposomeswithFluorescentMembranes..........26 3.3.5InjectionandFluorescentImaging.................27 4DataandAnalysis29 4.1FormationofSmallUnilamellarVesicles..................29 4.1.1ProcessingDLSData........................29 4.1.2Path1:DilutionAboveCriticalTemperature...........33 4.1.3Path2:Disk-likePrecursorsBelowCriticalTemperature....36 4.1.3.1 =0.75..........................36 4.1.3.2 =1.0...........................38 4.1.3.3 =1.5...........................39 4.1.3.4ComprehensiveDiscussionofSULVsFormedviatheBicellarPhase........................41 4.1.4Path2:EllipsoidalPrecursorsBelowCriticalTemperature...43 4.1.4.1 =0.3...........................43 4.1.4.2 =0.6...........................43 4.1.4.3 =0.9...........................45 4.1.4.4ComprehensiveDiscussionofLiposomesFormedviaEllipsoidalPrecursors....................45 4.1.5DiscussionofPreferredPathwayforSubsequentExperiments..46 4.2DependenceofVesicleLeakageonSize...................48 4.2.1QuantifyingRhodamineConcentrationsthroughFluorescenceIntensity.................................48 4.2.2DependenceofLeakageRateonVesicleSize............50 vi

PAGE 7

CONTENTS 4.3DiusionthroughaUniformMedium....................53 5Conclusions59 6Appendix61 6.1CurvatureEnergy...............................61 6.1.1CurvatureUsingMongeParametrizationinOneDimension...62 References67 vii

PAGE 8

CONTENTS viii

PAGE 9

ListofFigures 1.1EectofIBintheContainmentofGBMCells...............4 1.2SurvivalRatesofMiceUnderVariousGBMTreatments.........5 2.1DHPCandDMPC..............................8 2.2DHPCPhases.................................12 2.3TheDisk-likeBicelle.............................13 2.4Cross-SectionofDisk-likeBicelle......................14 2.5DependenceoftheHydrodynamicRadiusonMolarRatio........16 2.6PhaseDiagramofPhospholipidStructuresintheDMPC/DHPCSystem17 2.7GrowthbyCoalescenceandClosureofDisk-likeBicelles.........19 4.1SamplePlotofAutocorrelatedIntensityvs.DecayRate.........30 4.2ScalabilityoftheScatteringVector.....................32 4.3RelationshipbetweenIntensityandtheAngleofDetection........35 4.4LiposomesFormedviaBicellarPhaseat0.75%w/v............37 4.5LiposomesFormedviaBicellarPhaseat1%w/v-Uncorrected.....39 4.6LiposomesFormedviaBicellarPhaseat1%w/v.............40 4.7LiposomesFormedviaBicellarPhaseat1%w/v.............41 4.8LiposomesFormedviaEllipsoidalPrecursorsPhaseat0.3%w/v....44 4.9LiposomesFormedviaEllipsoidalPrecursorsPhaseat0.6%w/v....45 4.10LiposomesFormedviaEllipsoidalPrecursorsPhaseat0.9%w/v....47 4.11FluorescenceIntensitywithVaryingRhodamine-BConcentrations...48 4.12DependenceoftheQuantumYieldofRhodamine-BonConcentration.49 4.13FluorescenceIntensitywithVaryingRhodamine-BConcentrations...50 4.14FluorescenceIntensitywithVaryingRhodamine-BConcentrations...51 4.15FluorescenceIntensitywithVaryingRhodamine-BConcentrations...52 4.16Sephadex50GelMedium[31]........................53 4.17Diusionof50nmLiposomesAcrossa0.4 mSpace...........54 4.18Diusionof100nmLiposomesAcrossa0.4 mSpace..........55 ix

PAGE 10

LISTOFFIGURES 4.19Diusionof200nmLiposomesAcrossa0.4 mSpace..........56 x

PAGE 11

ListofTables 2.1ExperimentallydeterminedmolecularparametersforDMPCandDHPC.11 3.1MolecularWeightsforLiposomeIngredients................21 3.2PhospholipidConcentrationsforallPath1Solutions...........22 3.3PhospholipidConcentrationsforallPath2Solutions...........22 3.4PhospholipidConcentrationsforallPath3Solutions...........23 4.1Temperature,ViscosityandDiusionCoecientfor =0.75......38 4.2Temperature,ViscosityandDiusionCoecientfor =1.0.......39 4.3Temperature,ViscosityandDiusionCoecientfor =1.5.......42 4.4AverageHydrodynamicRadiiforallLiposomeswithDisk-likePrecursors42 4.5Temperature,ViscosityandDiusionCoecientfor =0.3.......43 4.6Temperature,ViscosityandDiusionCoecientfor =0.6.......46 4.7Temperature,ViscosityandDiusionCoecientfor =0.9.......46 4.8AverageHydrodynamicRadiiforallLiposomeswithEllipsoidalPrecursors48 xi

PAGE 12

GLOSSARY xii

PAGE 13

ListofAbbreviations SULVs -smallunilamellarvesicles;liposomes lessthan100nminradius. LULVs -largeunilamellarvesicles;liposomes greaterthan100nminradius. GBM -glioblastomamultiforme;themostcommonandthemostdeadlyformofbraincancer. BBB -bloodbrainbarrier;ltersbloodowto thebrain. IB -imipramineblue;anagentthatstuntsthe radialspreadoftumorsbyinhibitingactinpolymerization. DXR -doxorubicin;acommonchemotherapy drug. VEG-F -vascularendothelialgrowthfactor;its upregulationcausesangiogenesisandneovascularizationneartumors. PEG -polyethyleneglycol;usedasaliposomal coattoincreasecirculationhalf-lifeandincrease thenanoparticle'sstealthtothebody'sltration mechanisms. ECM -extracellularmatrix. DMPC -dimyristoylphosphatidylcholine;a phospholipidwithacholineheadgroupandtwo 14carbonlongacylchains. DHPC -dihexanoylphosphatidylcholine;aphospholipidwithacholineheadgroupandtwo6carbonlongacylchains. DLS -dynamiclightscattering;atechniqueused toindirectlyobservethesizeofvesiclesinsolutionbasedonhowtheparticlesscatterlaserlight. NBDDHPC -1-hexanoyl-2-6-[-nitro-2-1,3benzoxadiazol-4-ylamino]hexanoyl-sn-glycero-3phosphocholine-afattyacidlabeleduorescent phospholipidwithaphosphatidylcholineheadgroupandtwo6carbonlongacylchains. xiii

PAGE 14

0.LISTOFABBREVIATIONS xiv

PAGE 15

1 Introduction 1.1LiposomesinTargetedDrugDelivery Drugsareoftenintendedtotargetspecicregions,typesofcells,orparticularbiochemicalpathwaysinthebody.Commonmethodsofdrugadministration,likeoral uptakeorinjections,exposemanybodilysystemstothedrugsbeforetheydiuseto theirtargetsites.Drugsarealsosubjecttothebody'sltrationsystem;somemore thanothers,dependingontheirmolecularproperties.Ingeneralhowever,thedosage administeredisgreaterthantheeectivedoseinordertoaccountforlossduetoltration.Themetabolismofdrugs,orsimplytheirpassagethroughvariousorgansand tissues,contributessignicantlytosideeects.Thisisespeciallytrueforoftencytotoxicanti-cancerdrugs,orimmunosuppressantswhichgreatlyincreasetheriskof cancersandinfectionsoverall,evenwhentheinammationthedrugsaretryingto combatislocalized.Thegoaloftargeteddrugdeliveryistotransportdrugstotheir targetsiteswhileminimizingexposuretotherestofthebody,therebyreducingside eectsandincreasingtheiroverallecacy. Nanocarriersarenano-sizedstructuresusedtotransportdrugsinvivothatcan beengineeredinavarietyofways,andwithspecicpropertiesdependingontheir intendeduse.Onetypeofnanocarrierwithgreatversatilityareliposomes,whichare hollowstructureswithaphospholipidbilayermembrane.Liposomeshavebeenformed inavarietyofshapessuchasspheres,ellipsoids,anddisks.Sphericalliposomesarethe mostcommon,withthosegreaterthan100nminradiuscalledlargeunilamellarvesicles LULVs,andthosebelowthissizerangecalledsmallunilamellarvesiclesSULVs.[1] Thetherapeuticagentisencapsulatedwithintheliposomeduringformationandseveral techniquescanbeusedtoreleasetheliposomeloadatthetargetsite. Thetechniquesemployedfordrugreleasearehighlydependentuponthenatureof thetherapy.Forinstance,nanocarrierswouldbelargelyineectiveindeliveringsiRNA 1

PAGE 16

1.INTRODUCTION tocellsinordertosilencecertaingenesunlesstheyaredesignedtoensureintracellular delivery.Nanoparticleswithprotonspongeexteriorscomposedofcarboxylicacidand tertiaryaminegroupsatavariableratiohavebeenusedtotransportdrugsinside cells.[2]Byadjustingtheratiothenanocarrierscanbedesignedtocauseabuild-upof osmoticpressurewhileinanacidicendosomeenvironment,causingtheendosomesto burstduringtransportintothecellthroughtheendocytoticpathway.[2]Thisisjust oneexampleofhowmodicationstoananocarrierscanenabletargeteddelivery,but moreover,itisdemonstrativeofhowtheymustbeengineeredwithpropertiesspecic tothetherapybeingimplemented. Whenaspecictypeofcellistobetargetedsurfaceligandscapableofdistinguishingthecelltypeareoftengraftedtothenanoparticlesurface.Anothercommon techniqueisdecoratingdrugcarrierswithchemicalgroupsthatcaninducethecarrier toreleasethedruguponexcitationwhenexposedtoexternalradiation.Chainsofiron oxidesthatoscillateinaradiofrequencyeldhavebeenusedtocauseburstreleaseof liposomesthroughthismechanism.[3]Theseareonlyafewselectexamplesofliposome applicationsindrugdelivery,buttheyillustratehowliposomescanbecustomizedto meetimportantstipulationsofsometherapiessuchasintracellulardelivery,pHdependentrelease,cell-specicdeliveryandtimedrelease.Sinceliposomesareengineered tomeetthedemandsofadesireddrugdeliveryscheme,itisnecessarytoestablisha modelsystembeforetheirfunctionalitycanbeoptimized. 1.2ModelSystem:GlioblastomaMultiforme GlioblastomamultiformeGBMisthemostcommon,andalsothemostdeadlyform ofbraincancer.Ithasamortalityrateof96%after5years,andamediansurvival timeof15months.[4]Thehighmortalityrateisexpectedasthebrainisvitalin regulatingthebody'sfunctions.However,theincorrigiblenatureofGBMisalsodue toseveralcomplicatingfactorsinitstreatment,thebiggestdicultybeingthehighly metastaticnatureofthecancer.Becausebraintissueissosoft,thetumoriseasilyable toproliferateoutwards,makingtherateandextentofmetastasismuchhigherthan cancersinharder,densertissues.Thiscomplicatesneurosurgerysincegreateramounts ofbraintissuehavetobeexcised,whichmaycausefurtherdisability.Still,chances thatthecancerhasmetastasizeddeeperintothebrainremainhigh,andtargetingthese cellswithchemotherapyandradiationalsoaectshealthybraincells.Moreover,neural cellregenerationisslowandoccurstoalimitedextent.ThebloodbrainbarrierBBB isalsoanobstacletoecientdrugdeliverytoGBMcells.Forthesereasons,notonlyis GBMhighlymalignantbuttreatmentonlyminimallyprolongsthelifeofthepatient. 2

PAGE 17

1.2ModelSystem:GlioblastomaMultiforme GBMisanappropriatemodelsystemtotestliposome-assisteddrugdeliverybecause liposomesareabletopermeatetheBBB.Previousstudieshavedemonstratedtheir ecacyindeliveringdrugstothebrain,especiallydrugsthathavelowcirculation times,orthosethatarelargemoleculesunabletotthroughthetightjunctionsbetween endothelialcellscomposingtheBBB.[5]Onepromisingstudythatusedliposomesto deliverdrugstoGBMcellsusedanovelcompoundcalledimipramineblueIB,followed bydoxorubicinDXR,acommonchemotherapydrug.IBwasfoundtohaveantimetastaticpropertiessinceitinhibitsthepolymerizationofactin,thelamentsalong whichcancercellsspread.[6]ThespreadofhumanGBMneurospheresinacollagen matrixwassignicantlymorecontainedupontreatmentwithIB,asshowninFigure1.1. Eventhoughtheirgrowthrateislargelyunaected,theircontainmentallowsGBMcells tobebettertargetedbythefollow-uptreatmentofliposomaldoxorubicinL-DXR. Anotherreasonliposomesareespeciallysuitedforuseinthisdrug-deliveryschemeis becausefreeIBhasaverylowcirculationtime,withahalf-lifeofonly11minutes. Thisfact,alongwithitslargemolecularsize,makesitvirtuallyimpossibleforIBto crosstheBBB.WhenencapsulatedwithinliposomesL-IB,thecirculatoryhalf-life increasesto18hours,andtheabilitytocrosstheBBBisgreatlyenhanced.[6] ThemostexpedientpartofthisschemeisthattheliposomesonlytargetGBM cells,sparinghealthybraincellsfromcytotoxiceects.Thisisduetotheenhanced permeabilityandretentioneectseeninthevasculaturesurroundingcancercells,especiallyduringmetastasis.Tumorcellsmaintaintheirnutritionalneedsbyreleasing certainangiogenicfactors,likevascularendothelialgrowthfactorVEGF,inexcessto createnewbloodvessels,therebyincreasingtheirsurfaceareacontacttovasculature. Duringmetastasis,connectionsareformedbetweenthenewandexistingvasculature, encouragingbothtumorgrowthandspread.[7]Vasculargrowthinhealthycellsdepends onatightbalanceandafeedbackbetweenpositiveandnegativeangiogenicfactors.A disruptioninthisbalancecausesthehaphazardgrowthofbloodvesselsincontrast tohealthyvasculaturewhichisuniformlyaligned.Thisrapid,disorderlygrowthis responsiblefortheincreasedporosityofthisneovasculature,causingporesrangingbetween100-300nminthebraintumorselsewhereinthebodyhaveneovasculatures rangingfrom200-780nm.[8,9]Sincehealthyvasculaturehasporesoflessthan10 nmonaverage,[10]liposomesgreaterthan25nminsizewillonlyexitthecirculatory systemwhentheyowthroughcancerousregions.Thispassivecollectionofliposomes inandaroundtumorcells,overtheirlongcirculatoryhalf-lives,minimizestheeect ofthedrugsontherestofthebrain.Thiswastestedinthesamestudy,onmice withGBMusingL-IBandL-DXRwithanaverageradiusof160nm,andcoatedwith polyethyleneglycolPEGwhichfurtherextendscirculationtime.[6]Asisevidentin 3

PAGE 18

1.INTRODUCTION Figure1.1: EectofIBintheContainmentofGBMCells PicturedaretwohumanGBMneurospheresinacollagenmatrix,treatedwithoutand with10 MIB,stainedwithrhodamineanduorescentlyimaged.[6]Thescalebar represents100 m. Figure1.2,micetreatedwithL-IBfollowedbyL-DOXhada100%survivalthroughout the200daylongstudy,whereasnoneoftheuntreatedmicesurvivedpast35days. 1.3Motivations OnewaytooptimizetheL-IB/L-DXRtreatmentforGBMistomaketheliposomes smaller.Withanaverageporediameteraround260nm,the160nmliposomesonly exitthecirculationthroughporesonthehighestendofthesizerange.Foraparticle tofreelydiusethroughthevascularjunctions,itsdiametershouldbe 1 3 to 1 5 the diameterofthepore.[11]Thelargestporesizesareduetoprolongedupregulationof VEGF,andreectthepathophysiologyoflatestagecancer.Toadministertargeted earlytreatment,withalesserextentofneovascularization,thedrugwillhavetobe incorporatedintoliposomeslessthan50nminradius. UponenteringtheendothelialjunctionsinthevasculaturetheLULVsusedinthe GBMstudyarelikelytoremainclosetovascularwalls,leakingsomeoftheircargo 4

PAGE 19

1.3Motivations Figure1.2: SurvivalRatesofMiceUnderVariousGBMTreatments Graphsshowingthesurvivalratetopandtumorvolumebottomofuntreatedmice andthosetreatedwithonlyL-IB,onlyL-DXR,andbothL-IBandL-DXR.[6] backintocirculation.SULVs,duetotheirsmallsize,arebetterabletodiusethrough theextracellularmatrixECMtotheperipheryofthetumor.Liposometreatments relyontheaccumulationofdrug-carryingliposomesintothevasculatureporeswith everypassthroughthecirculatorysystem.UsingSULVswouldincreasetheclearance aroundthepores,allowingmoreliposomestoaccumulatewitheachcirculationcycle. TheliposomesusedintheGBMstudyslowlyreleasetheirencapsulateddrugsthrough passivediusionacrossthemembrane.Afasterandmoreconcentratedpresenceof SULVsatthetumorsitewouldalsoensuremostoftheliposomalloadisreleasedat thetargetsite. Previousexamplesdemonstratehowliposomesweretailoredforspecicavenues oftreatment,buttheliposomesusedheredidnotneedanyornamentationbeyonda standardPEGcoating,especiallysinceasmooth,sphericalparticleisoptimalforprolongingcirculationtime.Surfaceligands,suchashumaninterleukin-13,couldincrease theliposomes'anitytoGBMcellsbutwouldalsolowerthepassiveaccumulationof liposomesattumorsduetostericdestabilizationandltrationbythekidneys.[12]Iron oxidechains,likeintheexampleabove,couldallowliposomestoreleasetheircargoat specictimesbuttheradiationcancausenerveablationinhealthytissue,anddamage 5

PAGE 20

1.INTRODUCTION bloodvessels.Liposomesareusedfortheirabilitytotargettherapyatacellularlevel, andexogenoustreatmentslikeradiationnegatethatbenet.Finally,iftherateof leakageofthedrugfromtheliposomecanbeapproximated,dosagecanbecontrolled toacheivesustainedreleaseratherthanburstrelease. Becausethistreatmentworkswellwithstandardliposomes,itcanbeusedtotest whetherintrinsicpropertiesofliposomessuchassizeandphospholipidcomposition canpredictthestabilityanddiusionofliposomes.SULVsshouldtheoreticallydiuse easilythroughboththeneovasculatureandtheECM,buthaveinherentinstabilitydue tohighmembranetension.SULVscreatedusingtraditionalmethodslikesonication havehighsurfacecurvature,oftencollapsingintolargeraggregates.[1]Thisstudyuses protocolsforthecreationofthermodynamicallystable,orkineticallytrappedSULVs fromstructuralprecursors.Testingwhetherthealteredsurfaceareatovolumeratioin SULVsaectsratesofpassivediusionofthedrugthroughtheliposomalmembraneis importantingauginghowthesizeofvesiclesinuencedosage.Leakageofthedrugfrom theliposomemightbeinuencedbythegreatertensionwithinSULVmembranes.The goalofthisstudyistoformstableSULVsusingstructuralprecursorsfordrugdelivery tobraintumorsandtesttheirleakageanddiusionagainsttheLULVsusedinthe GBMstudy. 6

PAGE 21

2 FormationofSmallUnilamellar Vesicles WhilevariousmethodsforSULVformationexist,liposomalsolutionsandtheconditionsofformationvarywidelybetweenprocedures.Thestability,permeability,and encapsulationeciencyoftheliposomesarehighlydependentontheirpathwayofformation.Thischapterisadiscussionofhowmembranecomposition,temperature,and concentrationdetermineliposomeproperties.IntheGBMdrugdeliveryscheme,stabilityandencapsulationeciencyarekeytothefunctionalityoftheSULVs.Hence thesecharacteristicswillbeprioritizedwhendeterminingtheoptimalprocessofSULV formation. 2.1MembraneComposition Therststepincreatinganyliposomeistocombinethecomponentsofitsmembrane intoalipidcake,ahomogenousmixtureoftheconstituentphospholipidsintheirrespectivemolarratios.Thestructureofeachphospholipid,itschargedistribution,and itsmolarratiohavealreadypreordainedmembranedynamicsthroughouttheprocess ofliposomeformation.Thissectiondetailstheconsiderationsthatgointomembrane composition,withanemphasisonfactorsthatfacilitateSULVformation. 2.1.1PhospholipidStructure Phospholipidsareamphiphilicmoleculeswithaphosphateheadandahydrophobicacyl chain.Inanaqueoussolutionthishydrophobictailrestrictsthenumberofpossible hydrogenbondsofthesurroundingwatermolecules,reducingthelocalentropy.The arrangementofphospholipidsintobilayerswiththeacylchainspointedinwardsis thereforeentropicallyfavoredsinceitminimizesthesurfaceareaofthehydrophobic 7

PAGE 22

2.FORMATIONOFSMALLUNILAMELLARVESICLES region,andincreaseshydrogenbondingbetweenwatermolecules.Thiseectalso explainswhybilayerstendtowraparoundattheedges,formingclosedstructuresand furthershieldinghydrophobicareas.Thepolarphosphategroupallowsthemembrane atlargetofreelytravelthroughaqueousmedia. 2.1.1.1AcylChainLength Thelengthofthephospholipids'acylchainsinuencesmembraneelasticityinseveral ways.Aphospholipidisconsideredtohavealongacylchainifithasmorethan14 carbons.Longerunsaturatedacylchainshavethegreatestamountofmolecularexibility,andthuscontributetooverallmembraneelasticity.However,iftheacylchain issaturated,itslengthonlycontributestoitstendencytoaggregatewithotherphospholipidswhichcanbeproblematicinmakingSULVswhichalreadyhaveatendency tofusetogether.[13]Whilelongeracylchainsareabletobendeasily,theyalsooccupy agreatervolumewithinthebilayer.Largerstructureswithlowercurvaturecanaord longacylchainstheirspace,butinSULVstheinnerbilayerbecomescramped,pushing theentirestructureapart. Inordertoretainexibilitybutminimizestrain,long-chainphospholipidscanbe attenuatedwithshort-chain,rigidphospholipids.Thesemoleculestypicallyhavefewer than8carbonsineachchain,andallowtheouterleaet'sheadgroupstoremainassociatedwhilestillallowingthelongacylchainsroomtouctuate.HenceforSULV synthesis,dimyristoylphosphatidylcholineDMPC,commonlyusedinliposomemembranes,willbethelong-chainphospholipidwithtwoacylchainof14carbonseach. TheshortchainphospholipidwillbedihexanoylphosphatidylcholineDHPC,with twoacylchainsof6carbons. Figure2.1: DHPCandDMPC 8

PAGE 23

2.1MembraneComposition 2.1.1.2Phosphatidylcholines DMPCandDHPCwerechosenbecausetheyarebothphosphatidylcholinesPCs,the mostnaturallyabundantclassofphospholipidsinthebody,comprisingapproximately 80%ofbiologicalmembranes.Theyarealsoeasilyextractedforlaboratorypurposes fromeggyolksorsoybeans,andareoneofthemostcommonlyusedphospholipids inliposomestudies.PCshaveanoverallneutralheadasthecationiccholinegroup neutralizesthenegativechargeonthephosphategroup.Otherclassesofphospholipids includephosphatidylglycerolPGandphosphatidylserinePS,bothwithnegatively chargedheadswhichcompose10-20%ofphospholipidsfoundthebody.Thechargeon aphospholipidcanaecttheliposome'sabilitytopenetratecertaintissuesandcells, andhencechargeisoneaspectofoptimizingdrugdelivery.Theinteractionsofcharged phospholipidsarecomplicatedandcanaectoverallmembranestability.Byonlyusing phospholipidswithneutralheadgroups,theseinteractionscanbeconsiderednegligibleandmembranestabilitycanbestudiedasdependentononlythephospholipids' structureandtheirrespectiveconcentrationswithinthemembrane.Theheadgroup's dimensionsalsovarywidelybetweenclassesofphospholipidssousingonlyoneclass, suchasPCs,minimizesthevariationinsurfaceareaandvolumeperphospholipid,and simpliescalculations. 2.1.2PackingParameter Theheadgroupsurfaceareaandvolumeofphospholipidscanbevaluableinpredicting thestructureoftheiraggregatesthroughthehighlysimpliedgeometricalconstruction ofapackingparameter, P .IntroducedbyIsraelachviliin1979toexplaingeometricalconstraintsinselfassembly,thepackingparameterisbasedontheideathatthe shapeofanaggregateplaceslimitationsonthestructuralparametersofitscomponent phospholipids.[14] 2.1.2.1DerivationandApplicability Considertheaggregationof N phospholipidsintoaspheremadeupofasinglelayered phospholipidmembrane,calledasphericalmicelle,andassumethatmostofitsvolume, V ,isoccupiedbythephospholipidtails.Thesurfaceareaandvolumeoftheaggregate willbethesumofthesurfaceareasandvolumesofthe N phospholipidscomposing theaggregate.Thisisexpressedinthefollowingequationsforthecaseofaspherical aggregate, 4 R 2 = N a .1 9

PAGE 24

2.FORMATIONOFSMALLUNILAMELLARVESICLES 4 3 R 3 = N v .2 where a isthesurfaceareaoftheheadgroupofonephospholipidand v isthevolume theentiremoleculeoccupies.Solvingbothequationsfor N andequatingthemyields, 1 3 = v Ra .3 Thus,usingapurelygeometricalargument,theaggregateofaphospholipidwill besphericalifthephospholipid'sdimensionssatisfytheaboverelation.Theradiusof theaggregate, R ,isdeterminedbythemaximumtaillength, l ,ofthephospholipid. Longertailscanalsocompressandfoldtoaccomodateasmallerradius,sothepacking parameterforaspherecanberewrittenintermsof l as, P v la 1 3 .4 Similarargumentsforpackingparametersofcylindricalaggregatesleadstothe condition, 1 3 P 1 2 .5 andforbilayersheets[15], 1 2 P 2.6 Above P =2aggregatesstarttoexhibitreversephasemorphologieswiththeir tailsorientedoutwards.[15]Itmustbenotedthatspanning P isnotrepresentativeof allpossibleaggregatestructuresforagivenphospholipid.However,whenaggregates areknowntoformundercertainconcentrationandtemperaturerangesinahomogenoussolutionofphospholipids,thepackingparametercanbeusefulinapproximating thestructure.Forinstance,atverylowconcentrationsDHPCandDMPCarefree moleculesinsolution,andatsucientlyhighconcentrationsallphospholipidswillarrangeintolamellarsheets.[16]Neitherofthesescenariosaredictatedbythepacking parametersincetheeectsofconcentrationandintermolecularandmolecule-solvent interactionsaredominant.However,bothphospholipidshaveaconcentrationrange wheremoleculesinsolutionareabletondandinteractwitheachother,andarrange intoenergeticallyfavorablestructuresdictated,inpart,bythemolecule'sdimensions. ThelowerboundofthisrangeiscalledthecriticalmicellarconcentrationCMCof whichDMPC'sis6nMandDHPC'sis15mM.[17]InspiteofbelongingtothesamePC 10

PAGE 25

2.1MembraneComposition class,andbeingneutralmoleculeswithminimalelectrostaticinteractions,thethresholdconcentrationatwhichmicellesforminDHPCis6ordersofmagnitudegreater thanDMPC,indicatingthatdimensionalityhasalargeeectonaggregatestructure. Thus,withinamedianconcentrationrangethepackingparametercaninformaggregatestructureforeachphospholipid.Dimensionalitycanalsobeovershadowedbyhigh temperatureswherethekineticenergyofeachmoleculeistoogreatforittobeconstrainedwithinanaggregate.Thepackingparameterlosesmeaningforsolutionsheld abovethechain-meltingtemperatureofthephospholipid,whichisapproximately23 CforDMPCand45 CforDHPC.[1,18] 2.1.2.2Calculating P forComponentPhospholipids Quantity DMPC DHPC v A 3 1480 1126 a A 2 58.5 100 d A 25.3 23.9 P 1.182 0.471 Table2.1: ExperimentallydeterminedmolecularparametersforDMPCandDHPC. Table2.1displaysexperimentallydeterminedmolecularparametersofDMPCand DHPCalongwiththecalculatedvaluefor P .DMPCwitha P of1.18ispredicted tohaveplanarbilayeraggregates.Thisisconsistentwiththepreferenceforlower curvature,andhencelargervesiclesize,ofpureDMPCliposomesascomparedwith thosethatincludeDHPC.Asubtledistinctionistobemadeherebetweenthestacked bilayersoflamellarsheetsandthebilayeraggregatepredictedby P sinceconating thetwoimpliesthatconcentrationhasnoeectonDMPC'sfavoredstructure.In lamellarsheets,foundathighconcentrationsandminimalhydration,themoleculesare interdigitatedandhavegreaterintermolecularinteractions.[19]Thebilayersfoundat moredilutedconcentrationsareplanaruidmembranefragmentsthatariseinsolutions offreeDMPC,andarenotnecessarilyderivativeofthesheets.[1] The P valueforDHPCof0.471impliesformationofcylindricalmicelles.Sincethe DMPCexperimentaldatarepresentedafullyhydratedstate[20],theDHPCparametersforfullhydrationwerealsoselected.Figure2.2showsvariousphasesofDHPC andtheireectonmoleculardimensions.NotethatsinceDHPC'suidphaseistiedto atemperaturegreaterthanitschain-meltingthreshold,applyingitsuidphasedimensionstothepackingparameterwouldbeinappropriateforreasonsexplainedabove. SincetheDMPCdataaccountedfortheswellingofmembranewithwater,themaximummembranethicknessofahydratedDHPCmembranewashalvedinordertond 11

PAGE 26

2.FORMATIONOFSMALLUNILAMELLARVESICLES Figure2.2: DHPCPhases gel,interdigitatedfullyhydratedanduidfullyhydrated,T > 44 C.[18] thespaceoccupiedbythetail.Thisvalueisincloseagreementwiththe0.2nmlength approximatedby[21],whosedataforDHPCwillbeusedinalatersectiontorenea modelpredictingliposomesize.ThereisaninconsistencybetweentheDHPCsurface areafoundby[21]ofapproximately1nm 2 ,andthevalueof77.2A 2 givenin[18]. Theformervalueisemployedherenotonlybecauseofconsistencywithlatermodels, butbecause[18]displayshydratedDHPCasinterdigitated,whichistypicallynotthe caseinDHPCmicellesespeciallywhentheirheadgroupsareorientedoutwards,allowingspaceforwatermoleculesinbetween.Becauseswellingeectswereconsideredin membranethickness,theircontributiontotheheadgroupareawasalsoaccountedfor inusingtheheadgroupareadeterminedby[21]. 2.1.2.3PredictingtheBicellarPhase Thepurposeofusing P todeterminethepreferredstructuresofaggregatesinhomogenoussolutionswastwofold;itdemonstratedhoweventwoneutralphospholipidswith thesameheadgroupcanformdierentstructuresinthesamesolventandunderthe sameconditions,andwillnowbeusedtopredictstructuresinmixedphospholipidsolutions.ThisispossibleduetotheexistenceofabicellephaseinmixturesofDMPCand DHPCatparticulartemperaturesandconcentrations.Thedebateovertheconditions underwhichthebicellephaseemergeswillbeaddressedshortly,butNMRstudiesstate thatthebicellephaseischaracterizedbyloweredintermolecularinteractionsbetween DMPCandDHPCindicatinglimitedphysicalcontactbetweenthephospholipids.[22] Atthesametime,thebicellephaseemergesfrompreviousphaseswherethetwophospholipidsweremixedwithinaggregates,whetherthisbelamellarsheetswithDHPC linedpores,ormixedmicellesathighlydiluteconcentrations.[1]Thereforeinthebicel12

PAGE 27

2.1MembraneComposition larphasethespontaneousseparationofthetwoPCsoccurswithinthesamestructure allowingtheuseofthepackingparametertopredicttheindependentaggregationbehaviorofthePCsuponsegregation. P predictsthatDMPCwillformplanarbilayers andDHPCwilltendtowardscylindricalmicelles.Infact,thisispreciselythedisk-like structureassociatedwiththebicellarphase,withtheDMPCbilayersmakingupthe planarregionsofthediskandDHPCmoleculeslocalizingtothecurvedmicellarrimof thedisk.[1,22,23]ThecylindricalDHPCmicellepredictedby P canbeenvisionedas cutinhalfalongitslengthandwrappedaroundtheDMPCbilayer. Figure2.3: TheDisk-likeBicelle [24] Thepackingparameterisnotapplicablefortheentirespectrumofstructurescreated bymixturesofDMPCandDHPCsince,evenmorethantheabsenceofsegregation, thestructuresarehighlydependentontemperature,concentration,andmolarratiosof thePCs.Theireectswillbediscussedinturn,butsuccessfullyemployingthepacking parametertoexplainthedisk-likemorphologyofthebicellarphasehasdemonstrated howmoleculardimensionscandictateaggregatestructure. 2.1.3TheMolarRatio Theprevalenceofthedisk-likebicelle 1 inDMPCandDHPCmixtureshavenowbeen establishedbutyettobeaddressedistheirrelevancetotheformationofSULVs.When thetemperatureofthesolutioninbicellarphaseisraised,thediskscoalesceandundergo astructuralchangeintoSULVs.[1]Thismechanismwillbefurtherdiscussedinthe sectionofthischapterthatdiscussestemperatureeects.Themorphologyofthedisks willbeexploredfurtherherebecauseitisillustrativeoftheeectthemolarratiosof thephospholipidscanhaveonstructuresinsolution. 1 Theterm'bicelle'isamixtureoftheterms'micelle'and'bilayer'sincethedisk'splanesare attenedmicellebutitsend-statestructureresemblesabilayer. 13

PAGE 28

2.FORMATIONOFSMALLUNILAMELLARVESICLES 2.1.3.1MolarRatiosforanIdealBicellePhase Figure2.4: Cross-SectionofDisk-likeBicelle [25] Theplanarradiusofadisk, R ,tiesthesurfaceareaofDMPCbilayerstothedisk's perimeter,madeupofmicellarDHPCwithacross-sectionalradiusof r ,asshownin Figure2.4.HencelimitationsareplacedonthesizeofthediskbytheratioofDMPC toDHPC.IftheratioofDMPCtoDHPCistoohigh,disksinthebicellarphasewill havealoweraverageradiuscorrespondingtothesizeofdisksthatcanbefullyenclosed bythegivenconcentrationofDHPC.IftheDMPC:DHPCratioistoolowthesolution willcontainanexcessofDHPCmicellesandtheradiuswillbelimitedbythesizeofthe planarDMPCbilayers.Adistinctionthereforeneedstobemadebetweenthemolar ratio,denotedby q ,andtheeectivemolarratioofphospholipidsincorporatedwithin thedisk,calledq eff .Inanidealbicellesolutionq=q eff .[26]developedamodelfor themolarratioofdisksinanidealbicellesolutionbynotingthatifq=q eff theratio ofDMPCtoDHPCisgivenbytheratioofthesurfaceareasofthedisk'splanesA P tothesurfaceareaoftheircurvedrimsA C A P =2 R 2 .7 A C =2 r R +2 r .8 q = [ DMPC ] [ DHPC ] = A P A C = R 2 r R +2 r .9 Rearrangedintoaquadratic, R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(qrR )]TJ/F15 10.9091 Tf 10.909 0 Td [(2 r 2 q .10 14

PAGE 29

2.1MembraneComposition Usingthequadraticformulatosolvefor R intermsof q givestheidealbicelle equation, R = rq 2 [ + p 2 + =q ].11 Gloveret.al.renedthismodeltoaccountforthefactthattheDHPCheadgroup occupiesagreatersurfaceareapermoleculeinthecurvedrimthanDMPCoccupies inthebilayerplane.[25]ThiscorrectionwasaccountedforinTable2.1fromwhich k theratioofheadgroupsurfaceareaofDHPCtoDMPCisdeterminedtobe1.71.This parameterisincorporatedintothemodelbyGloverresultingintherelation, R = krq 2 [ + p 2 + k=q ].12 Thediameterofthediscs R canbeadjustedfrom5nmto40nmbyvarying q .[25]ThehydrodynamicradiioftheSULVsareconnectedtothecombinedradii, r 0 oftheplanarandthemicellarregionbythefollowingrelation.[25] r 0 = R + r .13 R H = 3 2 r 0 0 @ s 1+ t 2 r 0 2 + 2 r 0 t ln 2 4 t 2 r 0 + s 1+ t 2 r 0 2 3 5 )]TJ/F24 10.9091 Tf 16.872 7.38 Td [(t 2 r 0 1 A )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 .14 Figure2.5showsthataftera q ofapproximately3,thereexistsalinearrelationship between q and R H .Hence,themolarratioof3.2usedintheprotocolbyNiehet.al. increatingdisk-likebicellesasstructuralprecursorstoSULVswillbepreservedinthis study. 2.1.3.2OverallSignicanceoftheMolarRatio InthisstudySULVswillbecreatedfromdisk-likebicelleprecursorsandtheiraverage hydrodynamicradiuswillbecomparedtothevaluepredictedbyEquation2.14.The eectofthemolarratioonthesizeofthedisksisnotaseasilylegislatedforother shapes,butgeneralrulescanbestatedforspheresandellipsoids,theothertwomain structuresrelevanttothisstudy.Forspheresahigherq eff correspondstolargerradii andanincreaseinvesiclesizebecauseloweramountsofDHPCarepresenttostabilize themembrane'scurvature.Thedierencebetweenqandq eff forspheresdependson themethodofsynthesis;ifdisk-likebicellesformedunderidealmolarratiosareused asprecursorsthisdierencewillbenegligibleintheresultantSULVs. 15

PAGE 30

2.FORMATIONOFSMALLUNILAMELLARVESICLES Figure2.5: DependenceoftheHydrodynamicRadiusonMolarRatio Here r sph = R H .[26] Theeectsof q onellipsoidalvesiclesisverysimilartodisksexceptthatDMPC, undergoingachangefromauidbilayertogelphaseatdiluteconcentrations,becomes morerigidandorientsitselfsimilartothegelphasepicturedinFigure2.2.Thisshear eectintheplanarregioncauseswhatwouldbeadisktobecomeoblate.Thiseect isfurtherpronouncedwhenthedilutelipidconcentrationsfallbelowthehighCMC ofDHPC,causingittoloseitsmicelleshapeandinsteadbridgetheplanarDMPC gellayerswithfreemoleculesinstead.[1]Thusellipsoidalprecursorsfacesimilarsize limitationsdueto q becauseabalancingbetweenplanarsurfaceareaandthestructure's perimeterisstillatplay.Thedissolutionofthemicellarregionandphasechanges inDMPCmakeitdiculttorelate q tothesizesofSULVsresultingfromheated ellipsoids.Thelossofmicelleswithinthestructurehintstowardsalowerincorporation ofDHPCwithinthestructure,indicatingthatforellipsoidsq eff isgreaterthan q .The implicationsofthisonSULVradiiwillbeconsideredwhenanalyzingSULVdatafrom ellipsoidalprecursors. Thefactthatavarietyofstructurescanbeformedwiththesamephospholipids atthesamemolarratiosunderscoresanimportantprinciplethathasbeenalluded toseveraltimesthusfar;noonefactorlikethepackingparameter,themolarratio, theconcentration,nortemperaturecancompletelyaccountfortheemergenceofall structuresinsolution.Rather,atvariousphasesintheformationofSULVssomefactors 16

PAGE 31

2.2ConcentrationandTemperaturePhaseDiagram haveamoredominantroleindeterminingstructurethanothers.Ellipsoidsonlyemerge inanarrowrangeofverydilutelipidsolutionsasopposedtodiskswhichexistinvarious alignedornon-alignedstatesoveramuchbroaderrangeofconcentrations.[1,22,25] TheconversiontoSULVsfromprecursorsontheotherhandisentirelymediatedby temperaturechanges.Inthisspirit,thedatagleanedfromthisstudywillbeanalyzed mainlythroughthelensoftemperatureandconcentration,whicharethechiefvariables thatdictateconversionsbetweenstructuresinsolutionandinfactformanenergy surfacethattheparticlesnavigatetogettothermodynamicallystablestates.Other factors,suchasthemolarratioandsolvent,willbeheldconstantthroughoutallSULV solutionsandincludedintheanalysisonlyforthosestages,likeduringthebicellar phase,whentheybecomeprimaryinuencesonstructureorsize. 2.2ConcentrationandTemperaturePhaseDiagram Figure2.6: PhaseDiagramofPhospholipidStructuresintheDMPC/DHPCSystem [1] Becausethephospholipidsinsolutionandtheirmolarratiosarexed,concentrationandtemperaturebecomegoverningforcesbehindmorphologicaltransformations.Theconcentration, ,isdenedasthelipidweighttovolumepercent.Forthe DMPC/DHPCsystem,theemergentstructuresareoutlinedinFigure2.6.Thisdia17

PAGE 32

2.FORMATIONOFSMALLUNILAMELLARVESICLES gram,basedonthephasebehaviorofthephospholipidsandexperimentalNMRand SANSdata,isthebasisfortheprotocolfollowedinthisstudyforcreatingSULVs. Athighconcentrationsthemixturewillformporouslamellarsheets.Thepores arelinedwithDHPCmoleculesbecauseDHPC'sshorteracylchaincontributesto itsincreasedsolubility.[1]Figure2.6indicatesthatbicelledisksemergeatthesame concentrationsaslamellarsheets.ThisisrefutedbysomeNMRstudieswhichmeasured thepresenceofthebicellesbythealignmentoflipidbilayersinsolution,andfound magneticalignmentonlywithinanarrowrangeofafewdegreesabovechain-melting temperature.[22]Yetarguably,therapidtumblingofthebicellardisksprecludes theirmagneticalignment,andnumerousstudiesreportevidenceofdisk-likestructures acrossawiderangeoftemperaturesandconcentrations.[1,23,25].Infact,some studiesreportthatmagneticalignmentactuallyrepresentstheporouslamellarphase. [24,27]Thisstudyisbasedonthewidelyacceptedideathatbicellespopulateawide rangeofconcentrationsbelowthechain-meltingtemperature T c ,andissupportedby thepredictionofindividualphospholipidmorphologiesbythepackingparameter. Figure2.6showsthatpolydisperseULVcanforminsolutionregardlessoftemperature.When T>T c polydisperseULVemergeasproductsoftheunbindingtransition ofthelamellarphasewhichoccurswhen1.25 << 2.5.[1]PolydisperseULVarea kinetictrapthatindicateanon-idealmixingofphospholipidswithinthestructure,and requireahighenergyinput,suchassonication,tobreakupthevesicles.Evenifthe concentrationishighenoughthatcoolingyieldsbicellardisks,therewillstillexistin solutionexcludedDHPCmicelles,perturbingtheideal q eff .Thisstudydidnotemploy serialdilutionsinordertoreachadilutelipidconcentrationtoavoidfallingintothe trapofpolydisperseULVs.Insteadallsolutionswillbecreatedthroughaone-step dilutionfollowingbyrigorousvortexingandequilibrating. TheconversionofdiskstoSULVsismediatedentirelybytheincreaseintemperature beyondthechain-meltingtemperatureofthephospholipids.Raisingthetemperature increasesthekineticenergyofthedisks,whichatatrstseemstohintthatagreater diusioncoecientisresponsibleforthecoalescenceofdisksintoSULVs.Anyincrease indiusionwasshowntohaveanegligibleeectoncoalescenceinastudybyLeng et.al.whofoundthatexperimentallyobservedtime-scalesfordiskgrowthwere10 4 to10 6 timesslowerthanthetheoreticaltimescalculatedforcoalescencebydiusion. [23]Thisindicatesthatcoalescencedoesn'toccurimmediatelyuponcontact,andthat temperaturemediatestheconversiontoSULVsthroughanothermorepotentmechanism,specicallybyincreasingthemiscibilityofthetwophospholipids.[28]The DHPConthecurvatureoftherimmigrateintotheplanarbilayer,causingthedisk linetension,whichisthetensioncontainedintherimofthediskinholdingthedisk 18

PAGE 33

2.2ConcentrationandTemperaturePhaseDiagram Figure2.7: GrowthbyCoalescenceandClosureofDisk-likeBicelles [23] together,toincrease.Inordertostabilizetherim,thediskwillcoalescewithother disks.Thisoccursataratemuchslowerthanpredictedbycontactthroughdiusion becauseforthecoalescencetobeenergeticallyfavored,thedisksmustbealignedneck tonecksuchthattheDHPCrimisthecontactpointoffusion,aspicturedinFigure 2.7.[23]Plane-to-planecontactandplane-to-rimcontactbetweendisksareassociated withhigheractivationbarriersbecausetheywouldnecessitateanincreaseinareabeforestabilizationbyaddingDHPCtotherim.Theentirediskgrowsuntilthedisk-line tensionreachesitsthresholdatthediskradiusgivenby, R d = + G .15 where isthedisklinetension,and and G arethebendingandGaussianmoduli ofthebilayer.[1]TheULVcontainsbothanextrinsicandintrinsiccurvatureandboth areaccountedforintheHelfrichHamiltonian,whichgivesthetotalenergydueto curvature. R d istheradiusofthediskatthethresholdwheretheenergycontainedin therimtokeepthediskfromfallingapartisequaltotheenergyduetocurvatureof theULV.[29] Aderivationoftheintrinsicandextrinsiccurvaturesofasphericalvesicleusing MongeparameterizationisgivenintheAppendix.Notably,thecurvaturesarefound tobedependentonlyontheradiusoftheULV,indicatingthatallsphericalvesicles ofagivensizehavethesamecurvatureenergyregardlessoftheirformationpathway. WhythenwouldsonicatedSULVsbeinherentlymoreunstablethanthosecreated throughthebicellarorellipsoidalpathways?Thisquestionisnotonlyinterestingfrom abiophysicsperspective,butisrelevanttodrugdeliveryapplicationsofliposomes 19

PAGE 34

2.FORMATIONOFSMALLUNILAMELLARVESICLES sincetheirstabilitydictatesthecirculatoryhalf-lifeinsidethebody,drugstorage,and administration.ThisstudyaimstoidentifyuniquepropertiesofSULVsthatcontribute togreaterstabilitybyanalyzingdynamiclightscatteringdataofSULVsformedthrough themechanismsdetailedinthischapter. 20

PAGE 35

3 Methods 3.1FormationofSmallUnilamellarVesicles ThreepathwaysforSULVformationwillbetestedusingDMPCandDHPCatthesame molarratio,q,butatdierenttemperaturesaboveandbelowthecriticaltemperature, T c andatconcentrationsbelow2%. T c is25 C,thechainmeltingtemperatureofthe mixturesinceDMPChasachainmeltingtemperatureof23 CandDHPChasasmall positiveeectontheoverall T c ofthesolution.[19] 3.1.1LipidCake Thephospholipidsarerstcombinedwiththemolarratioofphospholipids3.2DMPC :1.0DHPC:0.043Tm 3+ inalipidcakealongwithsolventattheirmaximumhydratedconcentrationatabout25g/mLor25%w/vandhomogenizedthroughabrief vortexing. Molecule Mol.Wt.g/mol DHPC 453.507 DMPC 677.933 DPPC 734.039 Cholesterol 386.654 Fluor.DHPC 631.612 TmCl 204.3874 Table3.1: MolecularWeightsforLiposomeIngredients 25mgDHPCwasdissolvedin250 L1XPBSand12.1 Lofthissolutionwas combinedwith5.46mgDMPC.16.72mgTmCl H 2 Owasdissolvedin500 L1XPBS. 1.24 Lofthiswasaddedtothephospholipidmixture.Anadditional6.6 Lof1X 21

PAGE 36

3.METHODS PBSwasaddedtobringthesolutiontoavolumeof19.96 Lwitha25%lipidw/v ratio.Thissolutionwasmixedthoroughlybypipettingandvortexing. 3.1.2Path1:DilutionAboveCriticalTemperature Thispathwayattemptstotakethephospholipidmixturefromitsmaximumconcentration,withlamellarsheetsinsolution,toverydiluteconcentrationsofSULVsinasfew dilutionsaspossibleatT > T c .Thephospholipidandsolventamountsfortherangeof concentrationstestedarelistedinTable3.2.Thelipidcakeand1XPBSwereheated to45 C,combined,andimmediatelyvortexedonthehighestsettingfor5minutes. Immediatelyfollowingvortexingthesolutionswereheatedtoandmaintainedat45 C forextrusion. Concentration 2.5%1.25%0.5%0.25%0.1% 25%PC L 52.52.52.51.25 1XPBS L 4547.5122.5247.5311.25 Table3.2: PhospholipidConcentrationsforallPath1Solutions 3.1.3Path2:Disk-likePrecursorsBelowCriticalTemperature Whenlamellarsheetsarecooledbelowtheircriticaltemperaturedisk-likemicellesform insolutionwhich,whenreheated,coalesceintoSULVs.The25%w/vphospholipid solutionwascooledto4 Calongwithaaskof1XPBS.Thesewerecombinedin threeseparatesolutionsaccordingtotheamountsinTable3.3.Thesolutionswere vortexedfor5minutesimmediatelyaftermixing,placedina45 Cheatblock,and subsequentlyextruded. Concentration 0.75%1.0%1.5% 25%PC L 13.51827 1XPBS L 436.5432423 Table3.3: PhospholipidConcentrationsforallPath2Solutions 3.1.4Path3:EllipsoidalPrecursorsBelowCriticalTemperature BelowT c atverydiluteconcentrations,oblateellipsoidsemergeinsolutionandbecome SULVsuponheating.Table3.4belowshowstheamountsof25%w/vphospholipid solutionand1XPBSthatwerecombinedtoproduceliposomalsolutionsatthese concentrations.ThephospholipidsandPBSwereonceagaincooledto4 Cbefore combining,vortexedfor5minutesandallowedtoequilibrateat45 Cforextrusion. 22

PAGE 37

3.1FormationofSmallUnilamellarVesicles Concentration 0.03%0.06%0.09% 25%PC L 0.541.081.62 1XPBS L 449.46448.92448.38 Table3.4: PhospholipidConcentrationsforallPath3Solutions 3.1.5Extrusion Aminisyringeextruderwasusedtoltertheliposomalsolutionstoparticlesizesbelow 50nm.Theextrusionchamberwasrstloadedwitha200nmnanoporemembrane. Eachliposomesolutionat45 Cwasforcedfromoneextrudingsyringe,intothechamber,andoutintothesecondsyringe.10suchpasseswereperformedforeachsolution afterwhichthesolutionwasreturnedtothe45 Cheatblock.Theentireapparatus wasthoroughlycleanedandloadedwitha50nmnanoporemembrane.Theliposome solutionspreviouslypassedthroughthe200nmmembraneweresimilarlyextruded throughthe50nmmembrane. 3.1.6DLSMeasurements AllextrudedsolutionsweretransferredtoanNMRtubeandallowedtoequilibrateina 37.5 CbathbeforeDLSmeasurements.100nmpolystyrenespheresinasolutionwith lowopacitywereusedasacontrolbeforeeachDLSruntoensurethesetupwasworking correctly.EachNMRtubecontainingasolutionwasimmersedina37.5 Cdecylene baththroughwhichlaserlighttravelledduringthecourseofDLSmeasurements.The decyleneensurestherefractiveindexoftheglassisthesameasthetube'ssurroundings. Forsomesolutionstherewassignicantvolumelossduringextrusion,so1XPBSat 37.5 CwasaddedtotheNMRtubeimmediatelyprecedingmeasurementstobringthe solutionlevelapproximately2cmfromthebottomofthetubesothatthelasercrosssectionwassafelybelowtheminiscusofthesolution.WhileDLScanbedonewith onlyonelaser,usingtwoinacross-sectionreducesmultiple-scatteringeects.Before eachmeasurement,3DSpec,theprogramusedtocontroltheDLS,wassettoread cross-sectionallaserdata,andtheintensityofthelaserwassettoapproximately3500 Hzat20 .Quickreadingswerecollectedat20 and140 todetermineifthesignal tonoiseratiowastoolowattheseextremeanglesduetoscatteringeects.Weak signalsattheseanglesweretypicallyfoundindensersolutionsandthosewithhigher polydispersity;hereangleswereadjustedin5 incrementsuntiltheygaveconsistent readings.Thenewanglesthendenedtherangeofthedatacollectionset-up.The programwassettorecordtheintensityateachdetectorover2minutesforeachangle, 23

PAGE 38

3.METHODS progressingwithastepsizeof5 ,andrepeatingthemeasurementfortwodatapoints foreachangle. 3.2DependenceofBaselineLeakageonSizeofLiposomes Inordertotestwhetherahighsurfacecurvaturecontributestotheleakinessofthe liposome,thebaselineleakageofvarioussizedliposomesloadedwithrhodamine-B,a uorescentmolecule,wasmeasuredinthisexperimentusingmembranedialysis.The largerliposomeswerecreatedusingprotocolsfromearlierGBMstudies.TheseformulationsdonotincludeDHPCandinsteadincorporatecholesterolandDPPC.The SULVswererecreatedusingthemostsuccessfulpathwayfromtheprevioussection. 3.2.1QuantifyingRhodamineConcentrationsthroughFluorescence Intensity Measuringliposomeleakageinthisexperimentreliesontranslatingtheuorescenceof thesamplestotheconcentrationofrhodamine.Todothistheuorescenceofknown concentrationsofrhodaminewillbemeasuredandplottedagainstthepercentsaturation.Themaximumsaturationofrhodamineinwateris50mg/mL.Therefore50mg rhodamine-Bwasaddedto1mL1XPBSandvortexeduntilitwasdissolved.200 L ofthiswasdepositedintoonewellofa96wellplate.Theremainingvolumeof800 L wasthendoubledwith800 L1XPBS,resultingina50%saturatedsolution.After abriefvortexing200 Lofthiswascollectedanddepositedintoasecondwell.These serialdilutionswererepeated,halvingthepercentsaturationeachtime,untilapercent saturationof0.0061 3.2.2RhodamineLoadedLULVs TomaketheLULVs201.8mgDPPCand77.4mgcholesterolwerecombinedin1 mLof100%ethanolandheatedto65 Cuntilthesolutionwasclear.Arhodamine concentrationofapproximately12.5%itssaturationinwaterwasused,at6.25mg/mL ofrhodamine.Hence56.25mgofrhodaminewasdissolvedin9mLwaterandheated to65 C.Thephospholipidsolutionwascombinedwiththerhodamineandstirred at65 Conalowspeedfor1hr.Thesolutionwascentrifugedat15000rcffor20 minutes,afterwhichthepelletwasresuspendedin10mL1XPBS.Theliposomes weresonicatedonhighfor1hr.Halfofthesolutionwasextrudedthrougha400nm nanoporemembrane,andtheotherhalfthrougha200nmnanoporemembrane. 24

PAGE 39

3.3DiusionThroughaUniformGel 3.2.3RhodamineLoadedSULVs A25%w/vlipidcakewascreatedusingtheprocedureintheprevioussectionand cooledto4 C.Then6.88mgofrhodaminewasaddedto1067 L1XPBSandcooled to4C.33 Lofthe25%w/vsolutionwasaddedtotherhodamine,resultingina solutionof0.75%lipidw/v.Thiswasimmediatelyvortexedfor5minutesandheated to45 C.Theliposomeswereextrudedthrougha200nmmembrane,andthenthrough a50nmmembrane.1XPBSwasheatedto45 Candaddedtothesolutiontobring thevolumeupto3mLbeforeDLSandmembranedialysis. 3.2.4MembraneDialysis 3Thermo-Scienticmembranedialysiscasettesof10000MCWwithacapacityofup to3mLswereimmersedinabeakerof1XPBSfor2minutes.Usinga20gauge syringeonevalveofeachcasettewaspuncturedandinjectedwithliposomesofeach size,removingasmuchexcessairfromthechamberaspossible.Thesecasetteswere onceagainimmersedin1XPBSfor2hours,afterwhichthebuerwasonceagain exchangedfor20mLoffresh1XPBSat37.5 C.Thecasettesweremaintainedatthis temperatureoveraperiodof36hours,with200 Lsamplescollectedfromthesolvent every3hours,andreplacedwith200 Loffresh1XPBS. 3.2.5FluorescenceImaging TherhodamineloadedliposomeswerenotmeasuredwithDLSduetotimeconstraints. FluorescenceimagingwasdoneusingaBiotekSynergy4Reader.Allsampleswere collectedandimagedina96wellblackplatewithaclearbottom.Theuorometer wassettoanexcitationwavelengthof544nm,andanemissionwavelengthof627nm. Twolterswereused,onewithagainsettingof50andtheotherwithagainof100 themaximumgainbeing200. 3.3DiusionThroughaUniformGel Forthisexperiment,liposomesofthesamesizerangeastheprevioussectionwere injectedintoauniformgelcalledSephadexG-50whichconsistsofcross-linkeddextran withepichlorohydrinresultinginparticlesizesof40to160 mwhichformalattice oncethegelisprepared.Iftheliposomes'abilitytopenetratethisgelmediumissize dependent,itstandstoreasonthatthepassivediusionofliposomesoutoftumorous vasculatureisalsosizedependent. 25

PAGE 40

3.METHODS 3.3.1SettingtheSephadex Tosetthegel1.5gofSephadexG-50wascombinedwith17.5mL1XPBSinasmall cellculturedish.Threesuchdisheswerepreparedandlefttosetforthreehours.Excess waterwasdecantedandallowedtoevaporateresultinginagelwithavolumebetween 13.5mLto16.5mL. 3.3.2SynthesisofLULVswithFluorescentMembranes LULVsweremadebycombining50.45mgDPPCwith17.98mgcholesteroland1.37 mgBodipyCholesterolin250 Lof100%ethanolandheatingto65C.Next2.25mLof 1XPBSwasalsoheatedto65C,combinedwiththephospholipidsolution,andstirred onlowspeedfor1hour.Thesolutionwascentrifugedat15000rcffor20minutes,after whichthepelletwasresuspendedin2.5mL1XPBS.Theliposomesweresonicatedon highfor1hr.Halfofthesolutionwasextrudedthrougha400nmnanoporemembrane, andtheotherhalfthrougha200nmnanoporemembrane.Theliposomeswerestored at4 C. 3.3.3SynthesisofSULVswithFluorescentMembranes 43.02 LoftheDHPCsolutionmadeinsection4.1.1wascombinedwith21.84mg DMPC.2mgNBDDHPCuorescentlylabeledDHPCwasdissolvedin100 L1X PBSand27.1 Lofthissolutionwasaddedtothephospholipidmixture,alongwith 4.96 LoftheTmClsolutionalsofrom4.1.1.Anadditional4.76 Lof1XPBSwas addedtobringthesolutiontoavolumeof79.84 Lwitha25%lipidw/vratio.This solutionwasmixedthoroughlybypipettingandvortexing,resultinginahomogenized lipidcake.SULVswerethencreatedusingPath2,andextrudedto50nmasdetailed insection4.1.5.Theliposomeswerestoredat4 C. 3.3.4DLSofLiposomeswithFluorescentMembranes TheexcitationwavelengthofNBDDHPCis464nm,sothescatteringoftheDLS laserlightat632.8nmwillnotbeaectedbyabsorptionandemissionoflightby theuorescentliposomes.300 LoftheextrudedLULVsolutionsweretransferred toanNMRtubeandallowedtoequilibrateto37.5 C.Afterensuringthe100nm polystyrenespheresgaveappropriatereadings,theNMRtubeswereimmersedinthe 37.5 Cdecylenebath.Theintensityofthelaserwassettoapproximately3500Hzat 20 and3DSpecwassettorecordtheintensityateachdetectorover2minutesfor eachangle,progressingwithastepsizeof5 26

PAGE 41

3.3DiusionThroughaUniformGel 3.3.5InjectionandFluorescentImaging Approximately8weeksaftertheliposomeswerecreated,thegelswererehydratedand lefttositagainfor3hours.Theliposomes,whichhadbeenstoredat4 Cwereheated to37.5 C.0.5mLwereinjectedintothecenterofthegelplateusinga20gauge syringe.Theliposomeswereallowedtodiusefor2minutes,afterwhichtheplatewas placedundera4Xobjectivelensofauorescencelightmicroscope.Themicroscope wassetatagaintotheFITClter,whichexcitesat495nmanddetectsemittanceat 519nm,andthesoftwarewassettorecordimagesatagainof1000withamaximum gainof2000.Theplacementofthegelplatewasadjustedusingthestand'scontrol knobsuntiltheuorescentparticleswerebarelyvisibleontheborderofthescreen. Thisimagewasrecordedandtheexcitationlightwasturnedotoavoidquenchingthe liposomemembranes.After30secondsthelightwasturnedonagaintogaugetherate atwhichtheliposomeswerediusingthroughthegel.At30secondstheSULVshad diusednoticeablysosubsequentimageswererecordedat30secondintervalswithout movingthegelplateuntiltheliposomeshaddiusedacrossthescreen.Signicant diusionwasnoticedforthe100nmliposomesafterthree30secondintervals,setting theintervalforthefollowingrecordedimagesto90seconds.The200nmliposomesdid notshowsignicantdiusionevenafter3minutes.Fortheseliposomesimageswere recordedevery5minutesuntiltheliposomesreachedtheendofthescreen. 27

PAGE 42

3.METHODS 28

PAGE 43

4 DataandAnalysis Theoveralloutlineofthisstudywastorstdetermineareliablepathwaytocreate stableSULVs,andthentestthemagainststandardLULVs,likethoseusedinthe GBMstudy,fordiusivityandpermeability.ThischapterbeginsbypresentingDLS dataforSULVscreatedusingthethreepathwaysoutlinedinChapter2.Themost reliablepathwayisthenusedtocreateSULVswhicharecomparedwithLULVsused intheGBMstudiesforleakageratesanddiusionthroughuniformmedia. 4.1FormationofSmallUnilamellarVesicles ThethreeSULVformationpathwaysstudiedweremadeusingformulationswithidenticalmembranecompositions,phospholipidratios,andsolvents.Theonlyvariables thatdierentiateonepathwayfromanotherarethelipidweighttovolumepercentage andthetemperatureatwhichthesolutionswereallowedtoequilibrateafter vortexing.DLSmeasurementsofeachsolution,alsoperformedunderidenticalconditions,measuredtheintensityoflaserlightateachdetectorovertime.Thissection rstdemonstrateshowtheaverageradiusofparticlesinsolutionisgleanedfromthis rawintensitydataandsubsequentsectionspresenttheprocessedDLSdataforvarious solutions.Fromthisdataboththesizeandstructureofvesiclesinsolutionwillbe discussedandexplainedintermsofconcentrationandtemperaturemodulation. 4.1.1ProcessingDLSData OneinterestingaspectofDLSisthatthewavelengthoflaserlightusedis632.8nm,yet theradiiofparticlesinsolutioncanbedeterminedtoaresolutionthatislessthana tenthofthewavelength.Atrstglancethisseemstoviolatetheuncertaintyprinciple, accordingtowhichthewavelengthoflightusedtoobservetheparticlesdetermines theprecisionofthemeasurement.DLShoweverevadestheproblemposedbythe 29

PAGE 44

4.DATAANDANALYSIS uncertaintyprinciplebecauseratherthanmeasuringanindividualparticle,itmeasures theintensitydistributionoveraspaceasafunctionoftherelativeorientationofall particlesinthespace.Aparticulardistributionofparticlesatagivenmomenthasan eectonincidentlightsimilartoaseriesofslits;thelightisscatteredandaninterference patternofspecklesisdetected.Thisinterferencepatternshiftsastheparticlesdiuse, makingtheintensityofonepointickerwithtime.Ratherthanadirectmeasurement, cumulantanalysisoftheickeringintensityoflightautocorrelatedintimeprovidesthe decayratefromwhichthediusionconstantoftheparticlesinsolutioniscalculated. Therateofdiusionisthenrelatedtothesizeoftheparticlesinsolutionbythe Einstein-Stokesrelation. Figure4.1: SamplePlotofAutocorrelatedIntensityvs.DecayRate Intensityuctuationsareautocorrelatedintimeastheyaremeasuredforeachangle,therebygivingameasureoftheextenttowhichthescatteringintensityatonetime pointisrelatedtothatatanothertimepoint.TheintensitywasautomaticallycorrelatedbytheDLSsoftwareasitwasmeasuredresultinginacharacteristicexponential decayplotseeninFigure4.1.Thedecayrate, denesthetimeittakesforscattered lightdatatakentaparttolosecorrelation.AMATLABcodethendeterminesthe electriceldcorrelationfunctionusingtherelation, g 1 = Z 1 0 e i )]TJ/F25 7.9701 Tf 5.289 0 Td [( P\051d)]TJ0 g 0 G [-11526(.1 whereP\051istheintensity-weightedsumofeachparticlesize,dependentuponthe decayrateoftheirindividualintensities.Therelativeorientationoftheparticleswill 30

PAGE 45

4.1FormationofSmallUnilamellarVesicles maketheelectriceldinterfereconstructivelyatsomepointsanddestructivelyatothers.Theelectriceldcorrelationfunction,givenby g 1 takestheseinterferenceeects intoaccount.Thus g 1 describescorrelatedparticlemovementasgleanedfromthe uctuatingintensity.Theelectriceldcorrelationfunctionandtheintensitycorrelation functionarerelatedtoeachotherthroughtheSiegertrelation,givenby g 2 =1+ g 1 2 .2 whereg 2 istheintensitycorrelationfunction.TheMATLABcodeusestheintensity datatottheSiegertrelation,nding values,andperformsacumulantexpansion ong 1 tondthedecayconstantofthesumofalltheparticles,.Cumulantanalysisis beyondthescopeofthisstudy,andhereitwillsucetosaythatthedecayconstantis obtainedfromtheintensitydataforeveryangleatwhichameasurementisperformed. Astheangleofthedetectorschanges,dierentscatteringvectorsarepickedup. Thescatteringvector, q ,isafunctionoftheangleofthedetector, ,thewavelength oflaserlight, ,andtherefractiveindexofthesample, ,thelattertwoofwhichare constants. q = 4 sin 2 .3 Itisevidentthat q hasdimensionsofm )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 .Thereforethequantity l = 2 q .4 hasdimensionsofmanddeterminesthesizeofparticlespickedupinthesolution. Thisquantitymustbeonthescaleoftheparticlesbeingmeasured;hencethewavelengthoflightandtheangleofdetectionarewhatdeterminetheresolutionoftheDLS measurement.Since l isdependentupon ,changingtheangleallowsthedetection ofparticleswithradiispanningdierentlengthscalesasdepictedinFigure4.2.As theangleofthedetectorincreases,radiionsmallerlengthscalesarebetterdetected. Maximizingtherangeof isoptimalbecauseitallowsdetectionofawidersizerange ofparticles.Thisalsomeansthattheanglescanbeadjustedtoonlypickupcertain speciesofparticlesinsolution,asinthecaseofbimodalsizedistributions.Thevariationinsizewith q canalsogiveasenseoftheextentofpolydispersityinthesolution, andwillbediscussedforeachSULVpathwayinlatersections. Thedecayconstant,,isrelatedtothediusioncoecient, D ,by )-278(= )]TJ/F24 10.9091 Tf 8.485 0 Td [(D q 2 .5 31

PAGE 46

4.DATAANDANALYSIS Figure4.2: ScalabilityoftheScatteringVector Thedimensionallinesrepresentthevaryingscaleof l .Justasonewouldn'tusea metersticktomeasurethesizeofacellorthelengthofaskyscraper,thesizeofthe particlesbeingmeasuredmustbeonthesamescaleas l Plottingthe)-232(valuesinthedata'sMATLABcodeoutputagainst q 2 yieldsastraight line,theslopeofwhichgivesthediusioncoecient.Iftheliposomesareassumedto besphericalparticles,theEinstein-Stokesequationgivestheaveragehydrodynamic radius, R H oftheliposomesfrom D ,whichhasunitsm 2 /s. D = k B T 6 R H .6 Thehydrodynamicradiusreferstotheradiusofahardspherethatdiusesatthe samerateasD.Thediusionoftheliposomesareinrealityaectedbytheirhydration andglobularshapeeects.Since1XPBSwasusedassolvent,theviscosity, ,isclosely approximatedbytheviscosityofwater,whichhasatemperaturedependenceaccording totherelation, = : 414 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 247 : 8 = T )]TJ/F22 7.9701 Tf 6.586 0 Td [(140 .7 whereTistheaveragetemperatureofthesolutionduringmeasurementinKelvins. 32

PAGE 47

4.1FormationofSmallUnilamellarVesicles 4.1.2Path1:DilutionAboveCriticalTemperature CoherentDLSdatadoesnotexistforliposomescreatedusingPath1sincenoneofthe samplescreatedabovethecriticaltemperatureresultedinamonodispersesolutionof SULVs,evenafterextrusion.AtlowanglestheDLSdatawashighlyerratic,jumping betweenanundenedradiusto5000nm.Thesenonsensereadingsindicatedthatthe detectorwasnotmakingmeasurementsappropriatetothescaleof l andthereforethe anglewasadjustedtoanarrowerrange.Betweenapproximately50 and110 the readingsconvergedtoarangebetween950nmand2900nmforthe2.5%solution. Theremainingsolutionsdidnotstabilizeeventothisdegreeatmedianangles.For lowangles,theradiuspredictionwasonceagaininniteandhighlyerratic,moving momentarilytopredictionsapproximating100nm.Thevolatilesizereadingsimply thattherewasmorenoisethansignalevenatnerscaleresolutions. Toensurethesampleswerenotfaultyorgiventoomuchtimetoaggregate,the procedurewasrepeatedagainforasecondbatchofliposomesthatwereDLStested withinhoursofextrusion.DLSmeasurementsonceagainwerenotrecordedbecause themoredilutesolutionsdidnotproducestablereadingsatanyangle,andthe1.25% and2.5%solutionsgavesomewhatstablereadingsonlywithinaverysmallrangeof angles.The1.25%solutioninthissecondtrialvariedbetween3000and9000nmfrom 45 to110 ,andthe2.5%solutionconsistentlygavereadingsbetween600and1500 nmfromapproximately40 to80 DLSmeasurementsontherstbatchoccurreddaysaftertheparticleswereextruded whereasthesecondbatchonlysatundisturbedforapproximately2hoursbeforetesting. Perhapsbecauselittletimewasaordedforsolutionsfromthesecondtrialtoaggregate, the1.25%solutionfromthesecondtrialstabilizedwithina6000nmrange.The2.5% solutionalsostabilizedtosmallersizeswithinasmallerrangeofanglesinthesecond trial.Thereforeaggregationdidhaveasmallcontributiontothesizesofthe2.5% solutionfromthersttrial,indicatingthatPath1liposomesareunstableandcan coalesceoverthespanofafewdays.ThePath1solutionswerehypothesizedtoyield smallerliposomesasthedilutionofthephospholipidsincreased,butthelargeraverage radiusofthe1.25%solutionthanofthe2.5%solutionindicatestheopposite. ThepossibilitywasstillconsideredthatSULVsmaybepresentinPath1solutions,butundetectablebytheDLSeitherduetothenatureofthesolutionordueto systematicerrorintheDLSsetup.OnepossiblereasontheSULVsinthesesolutions couldbeoverlookedisduetorogueLULVsinsolutionformedduringthehighpressure conditionsofextrusion.Tearingofthenanoporemembraneisaknownriskofhigh pressureextrusion,buttheextentoftearingisoftenunknown.Becausethevolumeof 33

PAGE 48

4.DATAANDANALYSIS asphereincreasescubicallywiththeradius,onlyafewliposomesoneorderofmagnitudegreaterinradiuscouldhaveasignicanteectonthewaylightscattersthrough thesolution.EvenifLULVsmakeup5%oftheparticlesinsolution,theytogethercan occupyalargervolumethantheremainingSULVS.Sinceparticlesofgreatervolume willscattermorelight,thescatteringeectsofjustafewLULVscanmakeSULVs weaklydetectableonlythroughmultiplescatteringeects,ifatall.Thiswouldresult inaveryweaksignalforsmallparticles,andisoneexplanationforwhySULVsmight notbedetectedatsmallerangleseveniftheyarepresentinsolution.TheLULVsalso contributetopolydispersity,increasingthenoiseinthesignalandcausinginstability inthecontinuousrstorderreadingoftheradiusdisplayedbythesoftware,makingit diculttotakeascriptedmeasurement.TheLULVsalsodiusemoreslowlythanthe smallerparticlesandthesporadicjumpsinradiusintheDLSreadingsarelikelydue toanLULVdiusingataslowerratethroughthespaceilluminatedbythelaserlight. Extrusioninthiscasewasineectiveinlteringoutlargeparticlessincethehigh pressureenvironmentduringextrusioncanactuallycreateLULVs.AsPath2andPath 3datawillshow,extrusionwashighlyeectiveatlteringoutlargeparticlesinthe othersolutionswhichdidnotrequireasmuchpressure.Thereasonsforthisaredue tophospholipidconcentration;becausePath1solutionscalledforhigherconcentrationsthesolutionsbeingextrudedwerenotasdiluteandhencemorelikelytotearthe nanoporemembrane.ThehighpressureextrusionalsoindicatesthatthelteringprocessisheavilyreliedupontosizetheparticlesforPath1,ratherthantheaggregates spontaneouslyequilibratingintoSULVsaswillbedemonstratedfortheotherpathways.SinceDLSfunctionwascheckedbeforeeverysampleusing100nmpolystyrene beads,andbecausemultipletrialsofPath1solutionsgavesimilardata,thepresenceof LULVsinsolutionisacertainty.Thegoalofthisportionofthestudywastotestthe formationofSULVs,andsincethepresenceofafewLULVsconfoundstheDLSdata, analternatemethodisneededtotestwhetherSULVsarepresentinPath1samples. Thisalternatemethodreliesonthescalabilityofthemeasurementby q ,which reliesontheangleofdetection.ThelightscatteringotheLULVscanberendered largelyundetectableif ishighenoughsuchthatthevalueof l ismuchlessthanthe radiusofthelargerparticles,andcomparabletothatofSULVs.Thisessentiallymeans thatathighanglesmostofthedetectedlightwillbeduetosmallparticlescattering,so observinghowtheintensityoflightvarieswith canprovideinformationoftherelative concentrationsofdierentsizedparticles.EventhoughDLSdatadidnotstabilizelong enoughtorecordascriptedmeasurementforthe2.5%solutioninthesecondtrial,the softwarewasusedtoproduceaplotofhowtheintensityvarieswiththeangle.Thisis showninFigure4.3below. 34

PAGE 49

4.1FormationofSmallUnilamellarVesicles Figure4.3: RelationshipbetweenIntensityandtheAngleofDetection Thenon-linearityoftherelationshipindicatestheabsenceofsmallparticlesas l scalesdownatgreaterangles. Theplotshowsthatbelowa of80 theintensitywasverylowandconstant.At smallangleswhere l islonger,theintensityishigh,onceagainconrmingthepresence ofLULVs.Ifthereexistedanormaldistributionofliposomeswithinthesizerange of l takenfromthelargesttosmallestangles,theintensitywoulddroplinearlywith theangleofthescatteringvector.Theplotaboveinsteadshowsanexponentialdecay. Thismeansthatas l decreasesandthescaleofthemeasurementshrinkstodetectthe smallerparticles,intensityrapidlydecaysandverylittlemeaningfulsignalisobserved. Athighangles,thereadingsoftenremainedundenedindicatingthatonlyparticles signicantlylargerthanthescaleof l werebeingobserved.Theplotabovethusconrms thatthelackofDLSdetectionofSULVsforPath1solutionsisduetotheirabsence insolution,andnotbecausemultiplescatteringeectsorothersystematicerrorsare interferingwithaproperreading. UltimatelyPath1solutionsdidnotyieldamonodispersesolutionofSULVs,and wasinsteadfoundtobeapolydispersesolutionofLULVs.Thiswasananticipated stageofPath1solutionsasSANSstudiesbyNiehetal.demonstratethatatconcentrationsaslowas0.1%polydisperseULVsareformedaboveT c .[1]However,thisstudy aimedtoreducethatpolydispersitythroughtheaddedstepofextrusiontoeitherlter outLULVsorsizethembyforcingthemthroughsmallerpores.Tostillretainadecent SULVyieldafterltrationhigherconcentrationswereusedwiththispathway.The solutionswithconcentrationslessthan0.5%likelygavenonsensedataduetothehigh 35

PAGE 50

4.DATAANDANALYSIS pressureextrusionsinwhichtheULVswereeithercompletelyltered,orcompromised theintegrityofthenanoporemembrane,andonlyresultedinmoreaggregatesdueto shearstressthroughtearsinthemembrane.Inthislightitisparticularlyinteresting thatthesolutionsofhighestconcentrationgavemorestablereadingsthantheother solutionsbecausetheconcentrationof2.5%isapproximatelythethresholdatwhich thelamellartoULVtransitionoccursatanytemperature.[1]ExtrudingintheneighborhoodofthisconcentrationactuallyfacilitatedtheformationofULVsfromlamellar sheets.Thiswasstillahigh-pressureextrusion,butthe2.5%solutionstabilizedthe mostbecausenewlydissociatedsheetswereconveredtoULVsintheprocessofbeing pushedthroughandtearingthepores. Asanalnote,thispathwayisverysimilartotheprocessofmakinglargerliposomesusedintheGBMstudies.Themaindierencesbetweenthispathwayandthe IBandDXRloadedliposomesaretheinclusionofcholesterolratherthanDHPCas astabilizingagent,andtheabsenceofsonicationorcentrifugationtosizedownthe liposomes.SimplyusingDHPCdoesnotautomaticallylowermembranecurvature, orSULVswouldhavespontaneouslyformedinthispathway.Toachievethesizing downofliposomesusingDHPC,itmustberstincorporatedintothestructure,as willbeexploredintheotherpathways.Path1alsoindicatesthatliposomesformed abovechain-meltingtemperaturesrequireasizingdownmechanismwithoutwhichthe solutionwillremainhighlypolydisperse.Italsoshowsthatextrusionisnotaneectivemeansofsizingparticles,butmayoeranovelmeansofaectingthestructures aroundthresholdparameters.Anotheravenueforfurtherexplorationwouldbecreating DMPC/DHPCSULVsthroughtypicalsonicationmethodstotestwhetherincorporationofDHPCintoSULVstructurecanoccuraboveT c 4.1.3Path2:Disk-likePrecursorsBelowCriticalTemperature Path2solutionswereformedbydilutingtolowconcentrationsat4 C,equilibrating aboveT c ,andthenextruding.Figures4.4-4.7showthedecayrateofcorrelatedintensityplottedagainstthescatteringvectorforeachSULVsolutionmadeviathebicellar phase.Theslopesofthelinesdenotethediusioncoecient, D ,whichisthenusedin Equation4.6todeterminetheaverageradiusofthevesiclesineachsolution. 4.1.3.1 =0.75 Figure4.4displaystheDLSdataforliposomeswithdisk-likeprecursorsmadeata concentrationof =0.75%.Thedatapointsfallneatlyalongthetrendlineshowing thatthedecayrateincreasedproportionallywiththedetectionofsmallerparticles. Sincesmallerparticlesdiusefastertheirdecayrateshouldbehigherthanthedecay 36

PAGE 51

4.1FormationofSmallUnilamellarVesicles Figure4.4: LiposomesFormedviaBicellarPhaseat0.75%w/v rateoftheintensitycorrelationoflargerparticles.Ifthereexistapproximatelyasmany smallparticlesaslargerones,thedecayratewillhaveacloselylinearrelationshipwith q 2 asdepictedinFigure4.4,indicatinganunskewednormaldistributionofparticlesize. Thediusioncoecient,theaveragetemperature,andviscosityareneededinorder toaccuratelydeterminetheaveragehydrodynamic R H .Theaveragetemperatureand itsstandarddeviationwasdeterminedfromtherecordedtemperatureateachangle. Equation4.7wasusedtocalculate withthevariancein givenby, var = @ @T 2 dT 2 .8 var = : 414 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(5 247 : 8 = T )]TJ/F22 7.9701 Tf 6.587 0 Td [(140 ln 247 : 8 T )]TJ/F15 10.9091 Tf 10.909 0 Td [(140 )]TJ/F15 10.9091 Tf 8.485 0 Td [(247 : 8 T )]TJ/F15 10.9091 Tf 10.909 0 Td [(140 2 2 dT 2 .9 TheaveragevalueforTandthestandarddeviationintemperaturedTforthe =0.75solutionaregiveninTable4.1.BysubstitutingthesevaluesintoEquations4.7 and4.9thevaluesanduncertaintiesfor werecalculatedandarealsolistedinTable 4.1. 37

PAGE 52

4.DATAANDANALYSIS Quantity Units ValueStd.Dev.Variance T K 310.6450.3140.099 Pa s 6.837 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 6.82 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(7 4.64 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 D m 2 /s 9.714 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(12 6.87 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(14 4.72 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(27 Table4.1: Temperature,ViscosityandDiusionCoecientfor =0.75 TheradiusoftheseliposomesisdeterminedbyrearrangingEquation4.6, R H = k B T 6 D = : 380648810 )]TJ/F22 7.9701 Tf 6.587 0 Td [(23 : 6453 : 837 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(4 : 714 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(12 .10 andtheuncertaintyinliposomesizeisgivenbytheformula, var R H = @R H @T 2 dT 2 + @R H @ 2 d 2 + @R H @D 2 dD 2 .11 var R H = k B 6 D 2 dT 2 + )]TJ/F24 10.9091 Tf 8.485 0 Td [(k B T 6 2 D 2 d 2 + )]TJ/F24 10.9091 Tf 8.485 0 Td [(k B T 6 D 2 2 dD 2 .12 Asimpleunitanalysisfor R H showsthat, R H = k B T 6 D = J K s K Pa s m 2 = kg m 2 m s 2 s 2 kg m 2 = m .13 Thehydrodynamicradius,R H ,anditsvarianceandstandarddeviationwerecalculated inmetersfromtheaboveformulasandarelistedinTable4.4. 4.1.3.2 =1.0 Figure4.5displaysDLSdataforSULVsformedviabicelleprecursorsataconcentration of =1.0.Notably,thissolutiondisplaysaclearoutlierforthetwodatapointstaken at =135degrees.Becausetherestofthedatafollowsawell-denedlineartrend, theoutlierslikelyoccurredduetointerferencewiththelaserlightbyanobject,which couldbeadustparticleorsmudgeatthewallofthedecylenecontaineratthisangle.A noisysignalforsuchreasonswouldresultinamuchhigherdecayrateastheintensity wouldnotcorrelatewelltoitself.Ifthetwomisplacedpointswereduetoajumpin theamountofsmallervesicles,thesurroundingpointswouldalsoshowsomedeviation fromthetrend.Sincetheseoutliersmostlikelydonotholdanymeaningwithregards tothesizeofvesiclesdetectedatthatangle,theywereomittedandinterpolatedusing thetrendlineinthecorrectedplotdisplayedinFigure4.6. 38

PAGE 53

4.1FormationofSmallUnilamellarVesicles Figure4.5: LiposomesFormedviaBicellarPhaseat1%w/v-Uncorrected Thetemperature,viscosity,anddiusioncoecientforthissolutionarelistedin Table4.2.Thevarianceformulasandtheunitanalysiswereprovidedassamplecalculationsfortherstsolutionandwillnotbereproducedhere.Justasforthe = 0.75solution,thevaluesinTable4.2weresubstitutedintotheformulastocalculate thevalueanduncertaintyof R H ,listedinTable4.4. Quantity Units ValueStd.Dev.Variance T K 311.9750.2790.078 Pa s 6.663 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 5.69 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(7 3.24 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 D m 2 /s 9.674 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(12 1.29 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 1.66 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(26 Table4.2: Temperature,ViscosityandDiusionCoecientfor =1.0 4.1.3.3 =1.5 Finally,SULVsinthelastbicellardisksolutionwitha of1.5weremeasured,giving theplotshowninFigure4.7andvalueslistedinTable4.3.Itisevidentfromthe 39

PAGE 54

4.DATAANDANALYSIS Figure4.6: LiposomesFormedviaBicellarPhaseat1%w/v plotthatthissolutionwasnotasuniforminparticlesizeastheotheronesmadewith thesamepathway.Outliersareseenthroughoutarangeoflengthsofthescattering vectorindicatingthatratherthanthenormaldistributionofparticlesizesthereis polydispersity.Ifthesolutionwaspolydisperseinsizetherewouldbeanincreasein randomerroraroundthetrendlineduetogreateramountsofnoiseateachscattering anglefromparticlesoutsideofthescale, l .Howeverthepointsontheplotdonotshow increasedrandomnessofallpointsaroundtheline,ratherafewpointsaresignicantly shifted,andallmeasuredalowerdecayrate.Thelowereddecayrateofafewof thepointsindicatesthatthemajorityoftheparticlesinsolutionareSULVbutthat somethinginsolutionisdiusingmuchslower,resultinginhighcorrelationofscattered lightwithtime. Thiscanbeexplainedbyreferringtotheexpectedmorphologyofthesolution accordingtoFigure2.6.Atconcentrationsbetween1.25%and2.5%Niehet.al.observe theunbindingtransitionofthebicelledisksintolamellarsheets.Aconcentrationon thethresholdofthebicellephasewaschosentoobservetheeectonSULVsize.The 40

PAGE 55

4.1FormationofSmallUnilamellarVesicles Figure4.7: LiposomesFormedviaBicellarPhaseat1%w/v plotisnotaccuratelydescribedasanincreaseinSULVsize,butrathertheemergence oflamellaeinsolution.ThesesheetsareDHPC-pore-linedaggregatesofaDMPC bilayeraboveT c andthereforediusemuchslowerthroughsolution,resultinginthe lowerdecayrate.Theyalsointroduceslightanisotropytothesolution,seenbythe curvingofthedatapointsatthehighestandlowestscatteringvectors.Thiswillbe furtherexplainedinanalyzingtheDLSdataforSULVswithellisoidalprecursorssince theeectwillbecomemorepronounced.Interestingly,theverypresenceoflamellaein the =1.5solutioncausedasignicantincreaseintheaveragehydrodynamicradius oftheSULVs.Fromthisitcanbeinferredthattheproliferationoflamellaeisnotjust limitedtothesheetsbutisseeninthebicellarphaseaswell,withtheplanesofthe disksexcludingDHPCfromthestructure,resultinginlargerSULVs. 4.1.3.4ComprehensiveDiscussionofSULVsFormedviatheBicellarPhase Table4.4showstheaveragehydrodynamicradiusandtheuncertaintyinthevaluesof allSULVsolutionstakenthroughthebicellarphase.Themolarratio, q ,ofDMPCand 41

PAGE 56

4.DATAANDANALYSIS Quantity Units ValueStd.Dev.Variance T K 312.0100.3110.096 Pa s 6.658 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 5.68 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(7 3.23 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 D m 2 /s 5.952 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(12 2.19 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 4.80 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(26 Table4.3: Temperature,ViscosityandDiusionCoecientfor =1.5 R H mStd.Dev.Variance 0.75 3.426 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(8 2.423 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(10 5.871 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(20 1.0 3.545 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(8 4.469 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(10 1.997 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(19 1.5 5.767 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(8 2.406 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(9 5.790 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(18 Table4.4: AverageHydrodynamicRadiiforallLiposomeswithDisk-likePrecursors DHPCinthesesolutionswas3.2,whichaccordingtorenedbicelletheory,detailedin Chapter2,shouldresultinbicellediskswithaplanarradiusof, R = krq 2 [ + p 2 + k=q ].14 Table2.1showsthattheratiooftheheadgroupsofDHPCtoDMPC, k ,is1.71and thevalueof r is2.39nmleadingtoaplanarradiusof, R = : 71 : 39 : 2 2 [ + p 2 + : 71 = : 2]=45 : 14nm.15 Withaplanarradiusof45.14nmandacross-sectionalrimradiusof2.39nmthe lengthofaDHPCmolecule,alsogiveninTable2.1,thecombinedradius r 0 is r 0 = R + r =45 : 14+2 : 39=47 : 53 nm .16 allowingcalculationofthetheoreticalhydrodynamicradiusforSULVswithdisk-like precursorsusingEquation2.14,reproducedhere, R H = 3 2 r 0 0 @ s 1+ t 2 r 0 2 + 2 r 0 t ln 2 4 t 2 r 0 + s 1+ t 2 r 0 2 3 5 )]TJ/F24 10.9091 Tf 16.872 7.38 Td [(t 2 r 0 1 A )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 .17 Thethicknessofthebilayerdisk, t ,isdoublethelengthofaDMPCtail.Referring toTable2.1 t isfoundtobe5.06nm.SubstitutingintoEquation4.17gives R H =36 : 60nm.18 UsingthisvalueasthetheoreticalradiusofSULVsformedthroughthebicellar phase,thepercenterrorintheaverageradiusforSULVsinthe =0.75solutionis6.4% 42

PAGE 57

4.1FormationofSmallUnilamellarVesicles andtheerrorinSULVsizeinthe =1.0solutionis2.9%.Thelowpercenterrorsof thesesolutionsindicatethatbicelleswereformedunderlargelyidealconditions,with q verycloseto q eff .ThusbyfollowingPath2,andmodulatingthemolarratiowithinthe rangeshowninFigure2.5,SULVscanbecreatedwithinaverynarrow,predetermined sizerange.Thiscouldbeparticularlyusefulintargeteddrugdeliveryapplications wherethedrughastopenetratetissuesorsemipermeablemembranesthatonlyallow particleswithinanarrowsizerangetodiusethrough.Theprimarymotivationfor creatingtheseSULVswastocreatestabledrug-carriersthatcouldpenetratefenestrae intheinterendothelialjunctionsoftheneovasculatureinGBMtumors.Atabout35 nm,theSULVscreatedthroughthebicellarphaseareabletofreelydiusethrough poresinneovasculature.[11] 4.1.4Path2:EllipsoidalPrecursorsBelowCriticalTemperature Path3solutionswerehighlydilutedat4 CandequilibratedaboveT c .Becausethe precursorsareellipsoidsandincorporatefreeDHPCmoleculesratherthanmicellar DHPCastherim,idealbicelletheoryisnotapplicable.ThesignicantlylowerconcentrationsinducedagelphaseinDMPC,andlossofmicellarDHPC.Thedatafrom thispathwaywillthusfocusontheeectofconcentrationonSULVsize. 4.1.4.1 =0.3 Figure4.8showsDLSdataofthe =0.3solutionandTable4.5listsitstemperature, viscosity,andmeasureddiusioncoecient. Quantity Units ValueStd.Dev.Variance T K 311.0590.2920.085 Pa s 6.782 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 6.22 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(7 3.86 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 D m 2 /s 5.056 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(12 1.18 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 1.39 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(26 Table4.5: Temperature,ViscosityandDiusionCoecientfor =0.3 TheaveragehydrodynamicradiusofthissolutionisgiveninTable4.8. 4.1.4.2 =0.6 Figure4.9showsDLSdataforthe =0.6solution. Notethatthedatapointsexhibitaconcavityinthemiddleandshiftupwards towardstheends.Theupswingindecayratesatthehighestandlowestanglesindicates polydispersityastheintensitylosesitscorrelationataratethatdoesn'ttthediusion oftheSULVs.Sincethescaleofmeasurementvariesinverselywith q ,thepolydispersity 43

PAGE 58

4.DATAANDANALYSIS Figure4.8: LiposomesFormedviaEllipsoidalPrecursorsPhaseat0.3%w/v iscomingbothfromareasofhighandlowcurvature.Thiscanbeexplainedbythe presenceofellipsoidsremaininginsolutionastheirrimsscatterlightaswellastheir planes,meaningthatellipsoidswouldbebetterdetectedatextremeangles.Dueto theiranisotropicdiusionandbecauseoftumbling,whichisnegligibleforspheres,the decayrateofellipsoidswouldbehigherthanSULVs. CallingthestructuresresponsibleforthestructuralpolydispersityseeninFigure4.9 ellipsoidsisnottechnicallycorrect.Forone,thetemperatureduringdatacollectionwas higherthanthechain-meltingtemperatureofDMPC,causingaphasechangetoliquidcrystallinewithintheellipsoid.TheellipsoidsthatdidconverttoSULVsunderwent thisphasechangeastheycoalescedwithotherellipsoids,allowingthedisk-linetension causedbyDHPCtotakeover.Duetothehighlydiluteconcentrations,notallellipsoids mayhaveinteractedwithotherellipsoidsasthesolutionequilibratedto45 C.These loneellipsoidsmostlikelydesegregatedDMPCandDHPCwithinthestructureand adoptedmorphologiesrangingfrommicellestouidbicellesbasedonstudiesbySternin et.al.[22]ThesestructuresaremostlikelyanisotropicasindicatedbytheDLS 44

PAGE 59

4.1FormationofSmallUnilamellarVesicles Figure4.9: LiposomesFormedviaEllipsoidalPrecursorsPhaseat0.6%w/v data,andnotsignicantlyhighinconcentrationrelativetoSULVs,otherwiseagreater variationwouldbeseenaboutthetrendlineortheconcavityoftheplotwouldbemore pronounced.Heretheconcavityissmallenoughthattheerrorbarsremainclosetothe trendline. 4.1.4.3 =0.9 Finally,Figure4.10showstheplotofthe =0.9solution. Thissolutionalsoexhibitstheslightconcavityindicatingpolydispersityinstructure forreasonsexplainedabove.Theaveragehydrodynamicradiusofthissolutionisgiven inTable4.8. 4.1.4.4ComprehensiveDiscussionofLiposomesFormedviaEllipsoidal Precursors OveralltheSULVsmadethroughtheellipsoidalpathwayaresignicantlylargerinsize thanthosethatwereformedthroughthebicellarphase.Thisisbecausetheellipsoids 45

PAGE 60

4.DATAANDANALYSIS Quantity Units ValueStd.Dev.Variance T K 311.0350.3080.095 Pa s 6.785 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 6.57 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(7 4.31 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(13 D m 2 /s 5.771 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(12 9.54 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(14 9.10 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(27 Table4.6: Temperature,ViscosityandDiusionCoecientfor =0.6 Quantity Units ValueStd.Dev.Variance T K 311.0110.3000.090 Pa s 6.788 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(4 1.31 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(6 1.73 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(12 D m 2 /s 5.237 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(12 8.74 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(14 4.64 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(27 Table4.7: Temperature,ViscosityandDiusionCoecientfor =0.9 useDHPCmoleculesratherthanaDHPCmicelletostabilizetherim,incorporating lessDHPCintotheSULV q>q eff ,increasingthebendingmodulusofthemembrane, resultinginaspherewithlowercurvature. AlloftheSULVsolutionsmadeat < 0.9demonstratedaslightconcavity,linked topolydispersityinstructure.Specically,structuresofbothhighandlowcurvature areindicatedinsolution.Thesizeofthesestructuresdoesnotseemtobeoutsidethe scalabilityof l sinceotherwisethedatawould'vebeensignicantlynoisier.Sincethe upperandlowerboundanglesareknowntobe140 and20 ,respectively,thebounds of l canbecalculated.UsingEquations4.3and4.4, l wascalculatedtobebetween 1.37 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(6 mat =20 and2.53 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(7 mat =140 4.1.5DiscussionofPreferredPathwayforSubsequentExperiments BecausethebicellepathwayreliablyproducedSULVswithaverageradiilessthan50 nm,liposomeswithdisk-likeprecursorswillbeusedtotestdiusivityandleakagerates againstLULVs.TheseSULVshavebeenexperimentallyshowntobemorerobustthan SULVscreatedthroughsonicationbutjustifyingthisfactisnotatrivialmatter.[23] Thedependenceon q eff inthebicellarphaseandthewayconcentrationdictatesthe divergenceof q eff from q intheellipsoidalpathwayareindicationsthatthesizeof theresultantULVisdictatedlargelybytheamountofDHPCthatwasincorporated intothestructure.IftheamountincorporatedisclosetotheamountofDHPCused whilemakingthesolution,renedbicelletheorycanaccuratelypredictparticlesize. Sonicationusesultrasoundtotransferenergyintothesystem,breakinguplargerparticles,andcausingDHPCandDMPCtomix,makingSULVs.Theend-statesofboth processesrepresentnonequilibriumsystems.Insonication,theenergytransferredto themoleculestoassumetheSULVmorphologyallowedthemtotemporarilyovercome 46

PAGE 61

4.1FormationofSmallUnilamellarVesicles Figure4.10: LiposomesFormedviaEllipsoidalPrecursorsPhaseat0.9%w/v theenergybarrierofthemembrane'scurvatureenergy.Furthermore,insonication notallvesicleshavethesamemolarratiosofDHPCandDMPC,leadingtoawide variationinSULVsize.Interestingly,thisvariationspeedsupthecoalescenceofthe vesiclesasthosewithlittleDHPCseektostabilizetheirmembranecurvatureandfuse withothervesicles.Thiseectalsoexistsintheend-stateSULVscreatedthroughthe bicellephase,buttheseSULVswereprecludedbydiskswhichplacedtightconstraints onthemolarratio,onlyself-foldingintoSULVswhenthethresholddisklinetension wascrossed.Thecrossingofthisboundaryisadiscretestepmarkedbythefusionofthe growingdiskbyjustonemorebicelle.Thismeansthatthevariationin q eff isminimal acrossSULVsformedfromdiskprecursors.WhileSULVsmadethroughbicelledisks arestillnonequilibriummorphologiesthatseektoaggregatetorelievethecurvature energiesintheirmembranes,itisnotimmediatelyfavorableforthemtocoalescewith mostotherSULVsinsolution.Theendresultisasolutionofmetastablestructures thatdegenerateataratefarslowerthansonicatedSULVs. 47

PAGE 62

4.DATAANDANALYSIS R H mStd.Dev.Variance 0.03 6.640 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(8 8.813 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(11 7.767 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(21 0.06 5.818 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(8 9.651 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(10 9.314 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(19 0.09 6.408 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(8 8.450 10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(10 7.140 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(19 Table4.8: AverageHydrodynamicRadiiforallLiposomeswithEllipsoidalPrecursors 4.2DependenceofVesicleLeakageonSize Thisportionofthestudymeasuredtheconcentrationoffreerhodamine-Bovertimein solutionsof200nm,100nm,and35nmSULVsusingmembranedialysistoseparate liposomesfromtheuorescentdye. 4.2.1QuantifyingRhodamineConcentrationsthroughFluorescence Intensity Figure4.11belowplotsthemeasureduorescenceintensitytotheconcentrationofdye in1XPBS. Figure4.11: FluorescenceIntensitywithVaryingRhodamine-BConcentrations 48

PAGE 63

4.2DependenceofVesicleLeakageonSize Theexpectationwasaproportionalrelationshipbetweenthepercentsaturationof rhodamineandtheintensity,butasFigure4.11shows,afterasaturationofapproximately0.5%intensitybeginstodecrease.Thelowintensityreadingsofsaturation percentagesabove20 = photonsemitted photonsabsorbed .19 AstudyofthequantumyieldofrhodamineBbyBindhuet.al.demonstratedthe dependenceofthequantumyieldonconcentration,showninFigure4.12.[30] Figure4.12: DependenceoftheQuantumYieldofRhodamine-BonConcentration [30] At1 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 Mthequantumyieldisalreadyatabout80%,decreasingtolessthan 10%atconcentrationsabove1 10 )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 M.Theseeectsareduetonon-radiativeprocessesduetotheformationofdimersandotherhigherorderaggregates.Notonlycan anexcitedrhodamineBmoleculeconvertfromthesinglettotripletstate,therebylosinguorescence,butdimerizationalsoresultsinForster-typeenergytransfersbetween dimers,signicantlyloweringthequantumyield.[30]Theregionfrom0.5%to12.5% isexpandedinaplotofintensityagainstmolarconcentrationshowninFigure4.13. Thedataistwithanexponentialdecayfunctionshowingtheplateauinintensity towardshigherconcentrations. 49

PAGE 64

4.DATAANDANALYSIS Figure4.13: FluorescenceIntensitywithVaryingRhodamine-BConcentrations Finally,theregionofthegraphshowingincreasingintensitywithincreasingrhodamineconcentrationisalsoexpandedintermsofmolarconcentrationandshownin Figure4.14below.Theexponentialrelationshipgivenbyttingthetrendlineoughtto havebeenusedtogaugetheconcentrationofrhodamineusedinliposomalsolutionsfor encapsulation.However,duetologisticalconstraintstheserhodaminesolutionswere imagedatthesametimeasthesamplestestingrhodamineleakagefromliposomes,so theinitialconcentrationusedinencapsulationdoesnotreecttheoptimalvaluesas willbecomeevidentinthefollowingsection. 4.2.2DependenceofLeakageRateonVesicleSize Figure4.15showstheuorescenceintensityofthe200 Lsamplestakenfromsolutions inwhichtheliposomes,connedtoamembranedialysiscassette,wereimmersed. TheplotdoesnotshowacleartrendintheleakageratesbetweenSULVsand LULVs.Thiscouldbeduetoseveraldierentreasons,includingtheuseofinappropriate 50

PAGE 65

4.2DependenceofVesicleLeakageonSize Figure4.14: FluorescenceIntensitywithVaryingRhodamine-BConcentrations concentrationsofrhodamine,theeectrhodaminemayhavehadontheformationof theliposomes,orsimplybecausesizedoesnotaectrateofleakage. Theinitialamountofrhodamineaddedwas12.5%,andFigure4.11showsthat thisamounthasaverylowquantumyield.Thisconcentrationofrhodaminewas chosentoensurethatSULVformationwouldencapsulateahighenoughconcentration ofrhodaminesuchthatevensmallpercentagesleakingintothe20mLbuerwouldbe detectablebyuorescence.Theliposomeswerewashedwithbuerinordertowashall thefreerhodamineoutofsolution,buttheconcentrationofrhodaminewerelikelyhigh enoughthatlongerbuerwasheswereneededtoridthesolutionoffreerhodamine. Sinceleakageofthedyeoutoftheliposomebeginsimmediately,withoutestimates forthetimescalesforleakagetherewasnowaytogaugeatwhichpointtheexcess rhodamineinthebuerincludedrhodamineleakingfromtheparticles.Thereforedata wascollectedimmediatelyafterthersthour-longbuerwashwiththeassumption thattheinitialrhodamineconcentrationscouldbenormalizedfor,andthechangein rhodamineconcentrationovertimeforeachsolutionwouldstillyieldeectiveleakage 51

PAGE 66

4.DATAANDANALYSIS Figure4.15: FluorescenceIntensitywithVaryingRhodamine-BConcentrations rates. AsisevidentinFigure4.15therewasverylittlechangeinintensityduetorhodamineconcentrationaftertherst5hours.Thisindicatestheassumptionmade abovedidnothold,mostlikelybecausetheamountofrhodaminediusingoutofthe liposomeswasnegligiblecomparedtothefreerhodamineinsolution.Theliposomes composed0.75%w/voftheapproximately1.5mLsinjectedintothemembranedialysis cassettesandtheconcentrationofrhodaminewassignicantevenfora20mLbuer solution.Theleakageofrhodaminefromtheliposomesdidnotcontributesignicantly totheoverallconcentrationoffreerhodamine.Finally,becausethesampleswerecollectedoveraperiodof36hours,quenchingeectsoftherhodamineduetolightand oxygenexposurenegativelyaectedtheuorescenceintensityovertimebyanunknown amount.Thislossofuorescenceintensitymayhavealsocounteredthesmallincrease inrhodamineinsolutionduetoleakage.ThesequenchingeectsareindicatedbyFigure4.15sincetheintensityindicatestheconcentrationofrhodamineinallsolutions decreasedovertime,whenitoughttohaveincreased. 52

PAGE 67

4.3DiusionthroughaUniformMedium Thehighrhodamineconcentrationalsomayhaveaectedtheformationofbicellesin solution,whicharehighlydependentontherespectivemolarratiosofphospholipidsas discussedintheprevioussection.BecauseDLSdatawasnottakenforthesesolutions, theexactsizesoftheseliposomesareunknown,andtheporesizeoftheextrusionlters areusedasestimates.Togainexperimentallysoundinformationaboutthedependence ofleakageratesonliposomesize,DLSshouldbeusedtoaccuratelysizetheparticles, andtheinitialconcentrationofrhodamineshouldbeadjustedtobeataconcenration ofapproximately10 )]TJ/F22 7.9701 Tf 6.587 0 Td [(4 M.Theuorescenceimagingshouldalsobeperformedasthe samplesarecollected,usingahighgainifnecessarytodetectevensmallamountsof rhodamineleakage. 4.3DiusionthroughaUniformMedium SULVswithanaverageradiusof34.95nmandLULVswithaverageradiusof120nm and211nmwereinjectedintoagelmediuminordertoobservetheirdiusionacross a0.4 mspace.Thegelmedium,Sephadex50,formsarelativelyuniformnetworkof pores,aspicturedinFigure4.16.Figures4.17-4.19showthediusionoftheliposomes. Figure4.16: Sephadex50GelMedium[31] Itisimmediatelyevidentfromobservingthetimescales,measuredinseconds,that theSULVsdiusedmuchfasterthantheLULVs,coveringthe0.4 mspacein330s. The120nmliposomestook1260sandthe211nmliposomestook6600stocoverthe samedistance.Becausetheimagesshowthatthediusionprogressedforeachsolution atarelativelyconstantrate,thedistancecoveredovertimeforeachsolutioncanbe takentobeanaveragerateofdiusion.TheSULVsthusdiusedatarateof1.21nm persecond,the120nmdiusedat0.32nmpersecondandnallythe211nmliposomes diusedatarateof0.06nmpersecond. ThisdemonstratesthatSULVscanpenetrateporesduetopassivediusionmuch fasterthanLULVscan.Theliposomesusedindrugdeliveryrelyonpassivediusion andrecirculationoftheliposomestodeliverthedrugtotumorregions.Thecirculatory 53

PAGE 68

4.DATAANDANALYSIS Figure4.17: Diusionof50nmLiposomesAcrossa0.4 mSpace 54

PAGE 69

4.3DiusionthroughaUniformMedium Figure4.18: Diusionof100nmLiposomesAcrossa0.4 mSpace 55

PAGE 70

4.DATAANDANALYSIS Figure4.19: Diusionof200nmLiposomesAcrossa0.4 mSpace 56

PAGE 71

4.3DiusionthroughaUniformMedium owisinthiscasemimickedbytheminimalhydrationofthegel,causingtheaqueous mediumtoowoutwardsrehydratingtheSephadexbeads.Thelevelofhydration wasestimatedtobeasdryaspossiblewithoutintroducingcracksinthegel,andthe variationsinhydrationlevelsbetweentheplatesisaprimarysourceofuncertainty inthisexperimentasitcausesdierentowpressuresintheowoftheliposomal solutions.Thisportionofthestudyismeanttobelargelyqualitative,andthelarge dierencesindiusionrateswithliposomesizearemorethantheslightvariationin gelhydrationcanaccountfor. TheSULVsdiusedataratenearly50timesfasterthanthe211nmliposomes. AppliedtoabiologicalcontextthismeansthatLULVswouldneedtohave50timesthe circulatoryhalf-lifeofSULVstopenetratetissuestothesameextentasSULVs.LULVs infacthavealowercirculatoryhalf-lifeaslargerparticlesaremoreeasilytargetedby clearancemechanismsandlteredbythekidneys.Thisisassumingthatthetissues targetedfordrugdeliveryhaveporesthatallowLULVstoeasilydiusethrough.As discussedintheIntroduction,GBMneovasculaturehasporesapproximately260nm indiameter.[9]Thesearetoosmallforthe211nmliposomestopenetrate,andeven the120nmliposomesarenotabletofreelydiusethrough.Therefore,basedon thisdiusionstudy,SULVswouldbemosteectiveindeliveringdrugsusingpassive diusionthroughGBMvasculature. 57

PAGE 72

4.DATAANDANALYSIS 58

PAGE 73

5 Conclusions Thisstudyvalidatedthespontaneousformationofsmallunilamellarvesiclesthrough thestructuralprecursorsofbicelledisksandellipsoidsusinga3.2:1DMPC/DHPC formulation.SULVswerenotdetectedforsolutionscreatedoverarangeofconcentrationsaboveT c ,evenutilizingone-stepdilutionsandtwo-stepextrusions.These solutionsindicatedthatwhilelamellarphasesarenotconvertibleintoSULVsthrough highpressure,thresholdconcentrationswherelamellarsheetsarebeginningunbinding transitionsmaybeusedtocreateULVsorotherstructures.Thebicellediskpathway wasfoundtoreliablyproduceSULVswithanaverageradiusofapproximately35nm 0.3nm.Bystudyingthedisk'sgrowthbycoalescenceanditsconversiontoaSULV, itwasdeterminedthatthemolarratioisabletoaccuratelypredictthehydrodynamic SULVradiuswithintheboundsoutlinedbyidealbicelletheory.Theproximityofthe averageradiustotheradiuspredictedbyrenedbicelletheoryalsoindicatesverylow polydispersityinsolution.Thiswasevenfurthercorroboratedbythegrowthmodel ofthediskswhichproceedindiscretesteps,immediatelyfoldingintoaSULVwhen thethresholddisklinetensionovercomesthemembrane'scurvatureenergy.Anideal bicellephasewillthereforegiverisetometastableSULVsthatapproachequilibriumat aratemuchslowerthanSULVsmadethroughothermethods.Theellipsoidalpathway yieldedliposomesbetweenapproximately56and68nminradius,alongwithindicationsofotherstructuresinsolution,possiblyanisotropicmicellesormixedbilayers. Thehighlydiluteconditionsunderwhichtheellipsoidswereformedweredeterminedto excludefreeDHPCmoleculesfromthestructure,alteringthemolarratio,andresulting inlargerliposomesthanthosemadethroughthebicellepathway. ThemetastableSULVscreatedthroughthebicellarphasewerecomparedindiffusivityandleakagetoLULVssimilartothoseusedintheGBMstudy.Theleakage studieswereinconclusiveduetooversaturationofthesolutionswithrhodamine.The diusionstudiesdemonstratedthat35nmvesiclesdiusedatarate50timesthatof 59

PAGE 74

5.CONCLUSIONS 211nmvesicles.NotonlywillSULVsfreelydiusethroughGBMneovascualturethat theLULVsmaynotbeabletopenetrate,buttheresultsofthisstudyindicatethat SULVswillpenetratethetumorstoamuchgreaterextent. TheGBMtargeteddrugdeliveryschemeusingstealthSULVsallowstargetingof thecanceratitsearlystageswhenneovasculatureinthebrainhasn'treacheditspeak size.ByloadingwithIBandDXR,SULVsmaybeabletodeeplypenetratetumorous regions,especiallylocalizingwherethecancerismostmetastatic.Futurestudiesshould testtheleakageofSULVswiththesespecicanti-cancerdrugs,eventuallytestingthe eectsofSULVsinvivo. 60

PAGE 75

6 Appendix 6.1CurvatureEnergy Deformationstothemembranesuchasstretches,bends,andtwistscostthemembrane someamountoffreeenergy.Suchappliedforcescanchangethemembrane'ssurface area,thickness,anddensity,allofwhichcontributetothefreeenergydierence.When abilayerisbent,theinnerlayeriscompressedandtheouterlayer'ssurfaceareais expanded.Betweenthelayersthereexistsaneutralsurfacethatexperiencesnochange inintermembranousforces,andhasafreeenergychangeonlycorrespondingtothe curvatureofthestructure.Thisneutralsurfacewillbeusedtocalculatethecurvature ofthesurfaceateachpoint,fromwhichthecurvatureenergydensitycanbecalculated forvariousstructures. Consideranarbitrarycurvedsurface F x;y withanormalvector n ij x i ;y j and atangentplane F 0 ij x i ;y j .Atanygivenpoint,thetangentplanecontainsallpossible tangentvectorsatthatpoint.Thusthereexists,ateverypointonthesurface,aset ofpossibleplaneseachofwhichcontains n ij x i ;y j andonepossibletangentvector in F 0 ij x i ;y j .Eachplaneintersects F x;y togiveacurve f ij x i ;y j withaspecic curvature at x i ;y j .Dependingonthesymmetryofthesurface, f ij x i ;y j ,and therefore ,canvaryacrossallpossibleplanesat x i ;y j Specically, isthecurvatureofthelargestcircletotthecurveat x i ;y j ,and canbeexpressedintermsoftheradius,whichisinverselyproportionaltotheextentof curvature.Thegoalistodeterminetheprincipalcurvatures max and min fromall possible of f ij x i ;y j at x i ;y j .Theaverageofthesevaluesisthemean-curvatureof thesurfaceat x i ;y j ,andmultiplyingthevaluestogetheryieldstheGaussiancurvature atthatpoint.ThemeanandGaussiancurvaturescanthenbeusedtoconstructthe HelfrichHamiltonian,whichhaseigenvaluescorrespondingtotheenergyofonlythe curvatureoftheneutralsurfaceofthestructure.Formationpathwaysestablished 61

PAGE 76

6.APPENDIX inpreviousstudiesshowthatcertaintemperaturesandconcentrationsgiveriseto structureswithcharacteristiccurvatures.TheprimarygoalindevelopingtheHelfrich Hamiltonianistotestwhetherminimizationofthefreeenergyofcurvatureunder variousconditionscanpredictthestructuresoutlinedintheformationpathways. 6.1.1CurvatureUsingMongeParametrizationinOneDimension Thecurvature, ,willbeformulatedforthecurve f i x i inonedimension,andlater extendedtohigherdimensions.Thiscurverepresentsapossiblecross-sectionofan arbitrarysurfaceat x 0 ;f x 0 ,wheretosimplifynotation, f x 0 = f 0 .Thenormal, n 1 ,at x 0 ;f 0 willintersectthecenterofthecirclewhosecurvaturematchesthelocal curvatureof f 0 .Thecenterofthecircle, x c ;y c ,isdenedasthepointofintersection of n 1 ,withthenormal, n 2 ,at x 0 + dx .Thedistancebetween x 0 ;f 0 and x c ;y c isthe radius. Figure3.1 Thetangentat x 0 ;f 0 hastheslope f 0 0 .Hence,theslopeof n 1 is )]TJ/F22 7.9701 Tf 11.673 4.296 Td [(1 f 0 0 .Bysubstitutingtheslopeandthepoint x 0 ;f 0 intothelineequation y = mx + b for n 1 f 0 = )]TJ/F24 10.9091 Tf 9.68 7.38 Td [(x 0 f 0 0 + b andcalculatingforthey-intercept, b = x 0 f 0 0 + f 0 theequationfor n 1 isdeterminedtobe, n 1 x = x 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x f 0 0 + f 0 Theequationfor n 2 isthen 62

PAGE 77

6.1CurvatureEnergy n 2 x = x 0 + dx )]TJ/F24 10.9091 Tf 10.909 0 Td [(x f 0 x 0 + dx + f x 0 + dx f x 0 + dx and f 0 x 0 + dx canbeexpandedusingtheTaylorseries, f x 0 + dx f x 0 + f 0 x 0 dx + 1 2! f 00 x 0 dx 2 + ::: n 2 x x 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x + dx f 0 0 + f 00 0 dx + f 0 + f 0 0 dx Since n 1 and n 2 intersectat x c x 0 )]TJ/F24 10.9091 Tf 10.91 0 Td [(x c f 0 0 + f 0 = x 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c + dx f 0 0 + f 00 0 dx + f 0 + f 0 0 dx x 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c f 0 0 = x 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c + dx f 0 0 + f 00 0 dx + f 0 0 dx x 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c f 0 0 + f 00 0 dx = f 0 0 x 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c + dx + f 0 2 0 f 0 0 + f 00 0 dx dx x 0 f 0 0 + x 0 f 00 0 dx )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c f 0 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c f 00 0 dx = x 0 f 0 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c f 0 0 + f 0 0 dx + f 0 3 0 dx + f 0 2 0 f 00 0 dx 2 x 0 f 00 0 dx )]TJ/F24 10.9091 Tf 10.909 0 Td [(x c f 00 0 dx = f 0 0 dx + f 0 3 0 dx + f 0 2 0 f 00 0 dx 2 x c f 00 0 dx = )]TJ/F24 10.9091 Tf 8.485 0 Td [(f 0 0 dx )]TJ/F24 10.9091 Tf 10.91 0 Td [(f 0 3 0 dx )]TJ/F24 10.9091 Tf 10.909 0 Td [(f 0 2 0 f 00 0 dx 2 + x 0 f 00 0 dx x c = )]TJ/F24 10.9091 Tf 10.447 7.38 Td [(f 0 0 f 00 0 )]TJ/F24 10.9091 Tf 12.104 7.38 Td [(f 0 3 0 f 00 0 )]TJ/F24 10.9091 Tf 10.91 0 Td [(f 0 2 0 dx + x 0 Asdxgoestozero, x c = )]TJ/F24 10.9091 Tf 8.485 0 Td [(f 0 0 1+ f 0 2 0 f 00 0 + x 0 y c = n 1 x c y c = x 0 )]TJ/F15 10.9091 Tf 10.909 0 Td [( )]TJ/F24 10.9091 Tf 8.485 0 Td [(f 0 0 1+ f 0 2 0 f 00 0 + x 0 f 0 0 + f 0 y c = x 0 + f 0 0 1+ f 0 2 0 f 00 0 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 0 f 0 0 + f 0 63

PAGE 78

6.APPENDIX y c = 1+ f 0 2 0 f 00 0 + f 0 R = p x c )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 0 2 + y c )]TJ/F24 10.9091 Tf 10.909 0 Td [(f 0 2 R = s )]TJ/F24 10.9091 Tf 8.485 0 Td [(f 0 0 1+ f 0 2 0 f 00 0 2 + 1+ f 0 2 0 f 00 0 2 R = p + f 0 2 0 3 f 00 0 Thecurvature, K ,istherefore, K = 1 R = f 00 0 p + f 0 2 0 3 = f 0 0 p 1+ f 0 2 0 0 Thistechnique,Mongeparameterization,wasuseddetailedforonedimensionto demonstratehowexpressionsforcurvaturecanbederivedintermsoffx.When extrapolatedtohigherdimensionstheformulaforcurvaturelookssimilar: K = r r h r p 1+ r h r 2 Liposomeshapewillbeexpressedasaheightfunction, h r ,where r isavectorin twodimensions, ^x and ^y .Thecurvatureisthen: K = r 0 @ h x ^x + h y ^y q 1+ h 2 x + h 2 y 1 A where h x = @h @x and h y = @h @y K = @ h x + h 2 x + h 2 y )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 = 2 @x + @ h y + h 2 x + h 2 y )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 = 2 @y K = h xx + h 2 y )]TJ/F24 10.9091 Tf 10.909 0 Td [(h x h y h xy + h 2 x + h 2 y 3 = 2 + h yy + h 2 x )]TJ/F24 10.9091 Tf 10.909 0 Td [(h x h y h xy + h 2 x + h 2 y 3 = 2 K = h xx + h 2 y )]TJ/F15 10.9091 Tf 10.909 0 Td [(2 h x h y h xy + h yy + h 2 x + h 2 x + h 2 y 3 = 2 Theequationabovereferstothemeancurvatureofasurface,andisequivalentto theaverageoftheprincipalcurvaturesofthesurface h x;y .Themeancurvatureisan 64

PAGE 79

6.1CurvatureEnergy extrinsicpropertyofthesurface,meaningthatitisdependentuponthespaceinwhich itisembedded.Whileextrinsiccurvatureonlyexistswithrespecttoaspaceseparate fromthecurvedsurface,theintrinsic,orGaussian,curvatureisaninherentpropertyof thesurface,andwouldbeinvisibletoanyofitsinhabitants.Gaussiancurvatureisthe productoftheprincipalcurvatures,andcanbedeterminedforasurface h x;y using thefollowingformula: G = h xx h yy )]TJ/F24 10.9091 Tf 10.909 0 Td [(h 2 xy + h 2 x + h 2 y 2 BothmeanandGaussiancurvaturesaecttheenergyofastructure,andneedtobe explicitlycalculatedtodeterminethecurvaturecontributiontotheoverallfreeenergy. Thecurvatureenergydensityofaspherewillnowbedeterminedusingtheformulations above.Theheightfunctionforasphereis h x;y = p R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 h x = )]TJ/F24 10.9091 Tf 8.485 0 Td [(x p R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 h y = )]TJ/F24 10.9091 Tf 8.485 0 Td [(y p R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 h xx = y 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 h yy = x 2 )]TJ/F24 10.9091 Tf 10.91 0 Td [(R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 h xy = h yx = )]TJ/F24 10.9091 Tf 8.485 0 Td [(xy R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 h xx + h 2 y = y 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 1+ y 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 = )]TJ/F24 10.9091 Tf 8.485 0 Td [(R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 y 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 5 = 2 h yy + h 2 x = x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 1+ x 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 = )]TJ/F24 10.9091 Tf 8.485 0 Td [(R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 y 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 5 = 2 )]TJ/F15 10.9091 Tf 8.485 0 Td [(2 h x h y h xy = )]TJ/F15 10.9091 Tf 8.485 0 Td [(2 xy R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 )]TJ/F24 10.9091 Tf 8.485 0 Td [(xy R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 = 2 x 2 y 2 R 2 )]TJ/F24 10.9091 Tf 10.91 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 5 = 2 + h 2 x + h 2 y )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 = 2 = 1+ x 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 + y 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 )]TJ/F22 7.9701 Tf 6.587 0 Td [(3 = 2 = R )]TJ/F22 7.9701 Tf 6.587 0 Td [(3 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 Themeancurvatureisthen, K = )]TJ/F15 10.9091 Tf 8.485 0 Td [(2 R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F15 10.9091 Tf 10.909 0 Td [(2 x 2 y 2 +2 x 2 y 2 R 3 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 5 = 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = 2 = 2 R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 R 3 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.91 0 Td [(y 2 65

PAGE 80

6.APPENDIX K = 2 R h xx h yy )]TJ/F24 10.9091 Tf 10.909 0 Td [(h 2 xy = R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 + x 2 y 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 )]TJ/F24 10.9091 Tf 38.597 7.38 Td [(x 2 y 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 3 = R 2 R 2 )]TJ/F24 10.9091 Tf 10.91 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 2 + h 2 x + h 2 y 2 = 1+ x 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 + y 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 2 = R 4 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 2 G = R 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.91 0 Td [(y 2 2 R 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(x 2 )]TJ/F24 10.9091 Tf 10.909 0 Td [(y 2 2 R 4 = 1 R 2 TheHelfrichHamiltonianisdescribedby E bend = Z membrane dA 0 + 0 K )]TJ/F15 10.9091 Tf 10.909 0 Td [(2 c 0 2 2 + 0 K G Usingthevaluesderivedfor K and K G ,theHelfrichHamiltonianforasphereis E bend = Z membrane dA 0 + 0 2 2 R )]TJ/F15 10.9091 Tf 10.909 0 Td [(2 c 0 2 + 0 1 R 2 E bend = Z membrane dA 0 +2 0 1 R )]TJ/F24 10.9091 Tf 10.909 0 Td [(c 0 2 + 0 1 R 2 E bend = Z membrane dA 0 +2 0 1 R 2 )]TJ/F15 10.9091 Tf 12.105 7.38 Td [(2 c 0 R + c 2 0 + 0 1 R 2 66

PAGE 81

References [1] Mu-PingNieh,VelayudhanA.Raghunathan,SteveR. Kline,ThadA.Harroun,Chien-YuehHuang,andJohn Katsaras SpontaneouslyFormedUnilamellarVesicleswithPath-DependentSizeDistribution Langmuir 21 ,2005.1,6,11,12,13,16,17,18,19,35, 36 [2] MaksymV.Yezhelyev,LifengQi,RuthM.O'Regan,ShumingNie,andXiaohuGao Proton-Sponge-Coated QuantumDotsforsiRNADeliveryandIntracellularImaging JAmChemSoc. 130 :9006{9012, 2008.2 [3] PubuduM.Peiris,ErikSchmidt,MichaelCalabrese,and EfstathiosKarathanasis AssemblyofLinearNanoChainsfromIronOxideNanosphereswithAsymmetricSurfaceChemistry PLoSONE 6 ,2011. 2 [4] NationalBrainTumorSociety GlioblastomaMultiformeGBM ,2013.2 [5] KathleenMcNeeleyKristinLoomisandRaviV.Bellamkonda Nanoparticleswithtargeting,triggered release,andimagingfunctionalityforcancerapplications SoftMatter 7 :839{856,2011.3 [6] JenniferM.Munson,LeviFried,SydneyA.Rowson, MichaelY.Bonner,LohitashKarumbaiah,BegoaDiaz, SaraA.Courtneidge,UllaG.Knaus,DanielJ.Brat, JackL.Arbiser,andRaviV.Bellamkonda AntiInvasiveAdjuvantTherapywithImipramineBlue EnhancesChemotherapeuticEcacyAgainst Glioma SciTranslMed 4 ,2012.3,4,5 [7] BruceI.TermanandKonstantinV.Stoletov VEGF andtumorangiogenesis EinsteinQuart.J.Biol.and Med. 18 :59{66,2001.3 [8] W.GregoryRoberts,JoanDelaat,MotooNagane, SuHuang,WebsterK.Cavenee,andGeorgeE.Palade HostMicrovasculatureInuenceonTumorVascularMorphologyandEndothelialGeneExpression AmericanJournalofPathology 153 ,1998.3 [9] W.GregoryRobertsandGeorgeE.Palade NeovasculatureInducedbyVascularEndothelialGrowth FactorIsFenestrated CancerRes 57 :765{772,1997. 3,57 [10] C.C.MICHELandF.E.CURRY MicrovascularPermeability PhysiologicalReviews 79 ,1999.3 [11] RaziaNoreen,RaphaelPineau,Chia-ChiChien,MariangelaCestelli-Guidi,YeukuangHwu,AugustoMarcelli, MichelMoenner,andCyrilPetibois FunctionalhistologyofgliomavasculaturebyFTIRimaging Anal BioanalChem 401 :795{801,2011.4,43 [12] A.B.Madhankumar,BeckySlagle-Webb,AkivaMintz, JonasM.Sheehan,andJamesR.Connor Interleukin13receptor?targetednanovesiclesareapotential therapyforglioblastomamultiforme MolCancer Ther 5 :3162{3169,2006.5 [13] AnneS.Ulrich BiophysicalAspectsofUsingLiposomesasDeliveryVehicles BioscienceReports 22 ,2002.8 [14] J.N.Israelachvili,D.J.Mitchell,andB.W.Ninham Theoryofself-assemblyofhydrocarbonamphiphiles intomicellesandbilayers. J.Chem.Soc.,Faraday Trans. 2 ,1976.9 [15] JohnTexter ReactionsAndSynthesisInSurfactantSystems .CRCPress;1edition,2001.10 [16] AvantiPolarLipids PreparationofLiposomes ,2013. 10 [17] AvantiPolarLipids CriticalMicelleConcentrations CMCs ,2013.10 [18] S.DerenGulera,D.DiponGhoshb,JianjunPana,JohnC. Mathaic,MarkL.Zeidelc,JohnF.Naglea,andStephanie Tristram-Naglea Eectsofethervs.esterlinkage onlipidbilayerstructureandwaterpermeability ChemistryandPhysicsofLipids 160 :33{44,2009.11,12 [19] NelsonS.Haas,P.K.Sripada,andG.GrahamShipley Eectofchain-linkageonthestructureofphosphatidylcholinebilayers;Hydration studiesof1-hexadecyl2-palmitoyl-sn-glycero-3phosphocholine Biophys.J. 57 :117{124,1990.11, 21 [20] M.A.Kiselev,E.V.Zemlyanaya,andV.K.Aswal SANS STUDYOFTHEUNILAMELLARDMPCVESICLES.THEFLUCTUATIONMODELOFLIPID BILAYER. 2009.11 [21] N.E.GabrielandM.F.Roberts. Spontaneousformationofstableunilamellarvesicles. Biochemistry. 23 :4011{4015,1990.12 [22] EdwardSternin,DavidNizza,andKlausGawrisch TemperatureDependenceofDMPC/DHPCMixing inaBicellarSolutionandItsStructuralImplications Langmuir 17 ,2001.12,13,17,18,44 [23] J.Leng,S.U.Egelhaaf,andM.E.Cates StructuralEvaluationofPhospholipidBicellesfor Solution-StateStudiesofMembrane-Associated Biomolecules. BiophysicalJournal 85 :1624{1646, 2003.13,18,19,46 [24] Mu-PingNieh,CharlesJ.Glinka,SusanKrueger,R.Scott Prosser,andJohnKatsaras SANSStudyontheEffectofLanthanideIonsandChargedLipidsonthe MorphologyofPhospholipidMixtures. Biophysical Journal 82 :2487{2498,2002.13,18 [25] KerneyJ.Glover,JenniferA.Whiles,GuohuaWu,Nan junYu,RaymondDeems,JochemO.Struppe,RuthE. Stark,ElizabethA.Komives,andRegitzeR.Vold StructuralEvaluationofPhospholipidBicellesfor Solution-StateStudiesofMembrane-Associated Biomolecules. BiophysicalJournal 81 :2163{2171, 2001.14,15,17,18 [26] R.R.VoldandR.S.Prosser Magneticallyorientedphospholipidbilayeredmicellesforstructuralstudiesofpolypeptides.Doestheidealbicelleexist? J.Magn.Reson.B. 113 :267{271,1996. 14,16 [27] J.ChungandJ.H.Prestegard Characterizationof eld-orientedaqueousliquidcrystalsbyNMRdiffusionmeasurements. J.Phys.Chem. 97 :9837{9843, 1993.18 [28] M.-P.Nieh,V.A.Raghunathan,G.Pabst,T.A.Harroun, K.Nagashima,H.Morales,J.Katsaras,andP.M.MacDonald Temperaturedrivenannealingofperforations inbicellarmodelmembranes Langmuir 27 :4838{ 4847,2011.18 67

PAGE 82

REFERENCES [29] EugeneMachlin AnIntroductiontoAspectsofThermodynamicsandKineticsRelevanttoMaterialsScience:3rd Edition .Elsevier;3rdEdition,2010.19 [30] C.V.Bindhu,S.S.Harilal,GeethaK.Varier,RijuC.Issac,V.P.N.Nampoori,andC.P.G.Vallabhan Measurementoftheabsoluteuorescencequantumyield ofrhodamineBsolutionusingadual-beamthermallenstechnique J.Phys.D:Appl.Phys. 29 :1074{ 1079,1996.49 [31] AmershamBiosciences GelFiltration:Principlesand Methods .AmershamBiosciences.ix,53 68