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Modeling of Interactions Between Nanoparticles and Cell Membranes

Permanent Link: http://ufdc.ufl.edu/UFE0041997/00001

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Title: Modeling of Interactions Between Nanoparticles and Cell Membranes
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Ban, Young
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: carbon, dppc, fullerene, lipid, membrane, molecular, nanoparticles, simulation, toxicity
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Modeling of interactions between nanoparticles and cell membranes Rapid development of nanotechnology and ability to manufacture materials and devices with nanometer feature size leads to exciting innovations in many areas including the medical and electronic fields. However, the possible health and environmental impacts of manufactured nanomaterials are not fully known. Recent experimental reports suggest that some of the manufactured nanomaterials, such as fullerenes and carbon nanotubes, are highly toxic even in small concentrations. The goal of the current work is to understand the mechanisms responsible for the toxicity of nanomaterials. In the current study coarse-grained molecular dynamics simulations are employed to investigate the interactions between NPs and cellular membranes at a molecular level. One of the possible toxicity mechanisms of the nanomaterials is membrane disruption. Possibility of membrane disruption exposed to the manufactured nanomaterials are examined by considering chemical reactions and non-reactive physical interactions as chemical as well as physical mechanisms. Mechanisms of transport of carbon-based nanoparticles (fullerene and its derivative) cross a phospholipid bilayer are investigated. The free energy profile is obtained using constrained simulations. It is shown that the considered nanoparticles are hydrophobic and therefore they tend to reside in the interior of the lipid bilayer. In addition, the dynamics of the membrane fluctuations is significantly affected by the nanoparticles at the bilayer-water interface. The hydrophobic interaction between the particles and membrane core induces the strong coupling between the nanoparticle motion and membrane deformation. It is observed that the considered nanoparticles affect several physical properties of the membrane. The nanoparticles embedded into the membrane interior lead to the membrane softening, which becomes more significant with increase in CNT length and concentration. The lateral pressure profile and membrane energy in the membrane containing the nanoparticles exhibit localized perturbation around the nanoparticle. The nanoparticles are not likely to affect membrane protein function by the weak perturbation of the internal stress in the membrane. Due to the short-ranged interactions between the nanoparticles, the nanoparticles would not form aggregates inside membranes. The effect of lipid peroxidation on cell membrane deformation is assessed. The peroxidized lipids introduce a perturbation to the internal structure of the membrane leading to higher amplitude of the membrane fluctuations. Higher concentration of the peroxidized lipids induces more significant perturbation. Cumulative effects of lipid peroxidation caused by nanoparticles are examined for the first time. The considered amphiphilic particle appears to reduce the perturbation of the membrane structure at its equilibrium position inside the peroxidized membrane. This suggests a possibility of antioxidant effect of the nanoparticle.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Young Ban.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Kopelevich, Dmitry I.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041997:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041997/00001

Material Information

Title: Modeling of Interactions Between Nanoparticles and Cell Membranes
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Ban, Young
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: carbon, dppc, fullerene, lipid, membrane, molecular, nanoparticles, simulation, toxicity
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Modeling of interactions between nanoparticles and cell membranes Rapid development of nanotechnology and ability to manufacture materials and devices with nanometer feature size leads to exciting innovations in many areas including the medical and electronic fields. However, the possible health and environmental impacts of manufactured nanomaterials are not fully known. Recent experimental reports suggest that some of the manufactured nanomaterials, such as fullerenes and carbon nanotubes, are highly toxic even in small concentrations. The goal of the current work is to understand the mechanisms responsible for the toxicity of nanomaterials. In the current study coarse-grained molecular dynamics simulations are employed to investigate the interactions between NPs and cellular membranes at a molecular level. One of the possible toxicity mechanisms of the nanomaterials is membrane disruption. Possibility of membrane disruption exposed to the manufactured nanomaterials are examined by considering chemical reactions and non-reactive physical interactions as chemical as well as physical mechanisms. Mechanisms of transport of carbon-based nanoparticles (fullerene and its derivative) cross a phospholipid bilayer are investigated. The free energy profile is obtained using constrained simulations. It is shown that the considered nanoparticles are hydrophobic and therefore they tend to reside in the interior of the lipid bilayer. In addition, the dynamics of the membrane fluctuations is significantly affected by the nanoparticles at the bilayer-water interface. The hydrophobic interaction between the particles and membrane core induces the strong coupling between the nanoparticle motion and membrane deformation. It is observed that the considered nanoparticles affect several physical properties of the membrane. The nanoparticles embedded into the membrane interior lead to the membrane softening, which becomes more significant with increase in CNT length and concentration. The lateral pressure profile and membrane energy in the membrane containing the nanoparticles exhibit localized perturbation around the nanoparticle. The nanoparticles are not likely to affect membrane protein function by the weak perturbation of the internal stress in the membrane. Due to the short-ranged interactions between the nanoparticles, the nanoparticles would not form aggregates inside membranes. The effect of lipid peroxidation on cell membrane deformation is assessed. The peroxidized lipids introduce a perturbation to the internal structure of the membrane leading to higher amplitude of the membrane fluctuations. Higher concentration of the peroxidized lipids induces more significant perturbation. Cumulative effects of lipid peroxidation caused by nanoparticles are examined for the first time. The considered amphiphilic particle appears to reduce the perturbation of the membrane structure at its equilibrium position inside the peroxidized membrane. This suggests a possibility of antioxidant effect of the nanoparticle.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Young Ban.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Kopelevich, Dmitry I.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041997:00001


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MODELINGOFINTERACTIONSBETWEENNANOPARTICLESANDCELL MEMBRANES By YOUNG-MINBAN ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2010

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c r 2010Young-MinBan 2

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Tomyencouragingparents;myprincess,Suh-Eu;andmylovin ghusband,Hyung-Seok 3

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ACKNOWLEDGMENTS Itisapleasuretothanktomyadvisor,Dr.DmitryI.Kopelevi ch,forinstillinginme thequalitiesofbeingaself-motivatedresearcher.Iowemy deepestgratitudetohim forgivingmetheopportunitytodevelopmyownindividualit yandself-sufciencyby beingallowedtoworkwithsuchindependence.Hisguidancea ndsupportfromthe preliminarytotheconcludinglevelenabledmetodevelopan understandingoftheeld ofmolecularmodeling.Hisconstantpatienceandencourage menthelpedmeovercome manycrisissituationsandnishthisdissertation.Ihopet hatonedayIwouldbecome asgoodanadvisortomystudentsasDr.Kopelevichhasbeento me.Iamalsodeeply gratefultothemembersofmycommittee,Dr.AravindAsthagi ri,Dr.YiiderTseng,and Dr.Bonzongofortheirvaluablesuggestionsandadvicerega rdingmyresearch. AveryspecialthankyoutomyfriendBeverlyHinojosaforgiv ingmevaluable advice.Iamthankfultoherforreadingmyreportsandcommen tingonmyviews.Ialso thankmyresearchgroupmembers,includingChia-YiChen,Gu njanMohan,Ashish Gupta,andYoung-NamAhnfortheirsupport. Mostimportantly,noneofthiswouldhavebeenpossiblewith outtheloveand patienceofmyhusbandHyung-Seok.Hissupport,encouragem ent,quietpatienceand unwaveringlovehaveshapedmetobethepersonIamtoday.Iwo uldliketoexpressmy heart-feltgratitudetohim. Finally,IappreciatethenancialsupportfromEnvironmen talProtectionAgencyand NationalScienceFoundationthatfundedtheresearchdiscu ssedinthisdissertation.I acknowledgeUniversityofFloridaHigh-PerformanceCompu tingCenterforproviding computationalresources. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTION ................................... 13 1.1Background ................................... 13 1.2SpecicAims .................................. 15 1.3OverviewofDissertation ............................ 15 2METHODS ...................................... 17 2.1MolecularDynamicsSimulations ....................... 17 2.2Coarse-GrainedMolecularModel ....................... 19 2.3StochasticModelandCMFMethod ...................... 24 2.4CalculationofElasticPropertiesofMembrane ............... 26 2.4.1EstimationofBendingandTiltModulus ............... 26 2.4.2StatisticalAnalysisofCorrelatedTimeSeries ............ 29 2.4.2.1Theory ............................ 29 2.4.2.2Numericalalgorithm ..................... 31 2.4.2.3Errorestimation ....................... 33 2.4.2.4Validation ........................... 34 2.4.3StressTensor .............................. 35 3TRANSPORTOFCARBON-BASEDNANOPARTICLESTHROUGHLIPID MEMBRANES .................................... 39 3.1Introduction ................................... 39 3.2FreeEnergyProles .............................. 40 3.3EffectofFullerenolOrientationonMembraneDeformati on ......... 46 3.4LocalMembraneEnergyandEffectiveInteractionPotent ial betweenNanoparticles .......................... 51 3.5Conclusions ................................... 53 4ASSESSMENTOFPOSSIBLENEGATIVEEFFECTSOFCNTSONLIPID MEMBRANES .................................... 55 4.1Introduction ................................... 55 4.2ModelandSimulationDetails ......................... 58 4.3SystemStructure ................................ 60 5

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4.4ElasticPropertiesofMembrane ........................ 62 4.5EffectofCNTonPressureDistributioninsideMembranes ......... 65 4.6MembraneEnergyaroundNanoparticles .................. 67 4.7Conclusions ................................... 69 5LIPIDPEROXIDATION ................................ 72 5.1Introduction ................................... 72 5.2ModelandSimulationDetails ......................... 74 5.3EffectofLipidPeroxidationonMembraneProperties ............ 75 5.4EffectofNanoparticlesonPeroxidizedLipidBilayers ............ 80 5.5Conclusions ................................... 84 6CONCLUSIONS ................................... 87 REFERENCES ....................................... 91 BIOGRAPHICALSKETCH ................................ 96 6

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LISTOFTABLES Table page 4-1Boxsizesofequilibratedsystems. ......................... 61 5-1Theaveragefractionoffoldedlipidsandtheaverageare aperlipidinbilayers withvariousconcentrationsofperoxidizedlipids. ................. 80 5-2TheaverageareaperlipidinDPPC-25%andDPPC-75%witha ndwithouta fullerenol. ....................................... 83 7

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LISTOFFIGURES Figure page 2-1CGmodelsofDPPClipidmolecule,fullerene(left)andfu llerenol(right),and CNT. .......................................... 23 2-2Self-assemblyofDPPCbilayer. ........................... 24 2-3Cross-sectionsofslabsandcolumnsinwhichthestresst ensorisaveraged. 37 3-1DensityproleoftheDPPCbilayerandfreeenergyprole sforfullerene(solid line)andfullerenol(dashed-dottedline). ...................... 42 3-2Dependenceofthediffusivityoffullereneonthenanopa rticlepositionwithin thebilayer. ...................................... 42 3-3Localdeformationofalipidmembranecontainingafulle reneorafullerenol. .. 43 3-4Averagedividingsurfacescorrespondingtothefullere nolconstrainedatz= -4.0nm(dash–dottedline,graycircle),z=-2.7nm(dashedline,hollowcircle) andz=0.0nm(solidline,blackcircle). ...................... 44 3-5DependenceoftheFouriermodewithwavenumberq=0.46nm 1of thedividingsurfaceoftheleaetcontainingthenanoparti cleonthenanoparticle positionz. ....................................... 45 3-6EnvelopsofACFoftherandomforceactingonthefulleren olconstrainedat z=-4.0nm(dashed-dottedline),z=-2.7nm(dashedline),an dz=0.0nm (solidline). ...................................... 46 3-7Correlationtimesoftheslowestuctuationsoftherand omforceactingon particles. ....................................... 46 3-8Denitionofthefullerenolorientation:anglebetween C60(OH)10director(d ) andthez-axisandcontributionofthefullerenolorientati ontothefreeenergy (kJ/mol). ........................................ 47 3-9Aschematicoffreeenergyproleforfullerenolanditso rientationalbehavior. 49 3-10Averageheightofdividingsurfacesofthebilayercont ainingafullerenollocated atthecenterorientedat0degreeand90degreeswithrespect toz-axis. .... 50 3-11Comparisonoflocalaverageheightsoflipidsaroundna noparticles. ...... 51 3-12EffectoffullerenolembeddedinaDPPCmembraneonuppe randlower membraneleaet. .................................. 53 3-13Energy(kJ/mol)ofmembranecontainingafullerenol. .............. 53 8

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4-1Lateralpressurewithinmembraneandcorrespondingdif ferentconformational statesofahypotheticalmembraneprotein. .................... 57 4-2MolecularmodelofaDPPClipidbilayercontainingacarb onnanotube. .... 58 4-3ProbabilitydistributionsofdistancezbetweenthebilayerandCNTcentersof massandorientationcos ofCNTwithrespecttothez-axis. .......... 61 4-4Spectralintensityofuctuationofmembraneundulatio nsandlipidtiltinpure DPPCmembrane,aswellasDPPCmembranescontainingCNTofva rious length(seelegend)atconcentration 0.01CNT/nm2. .............. 62 4-5DependenceoftheHKmodelparameters and tontheuppercut-off wavelengthq max. ................................... 65 4-6DistributionsoflateralpressurePjj indirectionnormaltothebilayersurface. .. 66 4-7DistributionsoflateralpressurePjj (inbar)inthebilayerplaneforbilayers containingCNT3,CNT4,andCNT6nanotubes. .................. 68 4-8EffectofCNT3embeddedinaDPPCmembraneonupperandlowermembrane leaet. ......................................... 70 4-9EffectofCNT4embeddedinaDPPCmembraneonupperandlowermembrane leaet. ......................................... 71 4-10EffectofCNT6embeddedinaDPPCmembraneonupperandlowermembrane leaet. ......................................... 71 5-1SimulationsnapshotsofDPPCbilayersat800ns0%(pureD PPClipidbilayer), DPPC-25%,andDPPC-50%,andDPPC-75%. .................. 76 5-2Spectralintensityofbilayersurfaceuctuationsofth epureDPPCbilayerand ofDPPC-25%,DPPC-50%,andDPPC-75%. ................... 77 5-3Densityprolesofheadandtailgroupsoflipidandwater inthepureDPPC bilayer,DPPC-25%,DPPC-50%,andDPPC-75%. ................ 78 5-4Densityprolesofthephosphatebeads(PO4,dotted)oftheheadgroup,the glycerol(dash-dotted),theterminalbeads(-CH3,dashed),and theperoxidizedterminalbeads(-COOH,solid)inDPPC-25%. .......... 79 5-5DensityprolesoftheperoxidizedterminalbeadsinDPP C-25%(dotted), DPPC-50%(dash-dotted),andDPPC-75%(solid). ................ 79 5-6PeroxidizedDPPClipidwithfoldedtails. ...................... 80 5-7Densityprolesofhead(thinlines)andtail(thickline s)groups inDPPC-25%andDPPC-75%withandwithoutfullerenol. ............ 82 9

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5-8Densityprolesofhead(thinlines)andtail(thickline s)groups inDPPC-25%andDPPC-75%withandwithoutfullerenol. ............ 82 5-9TimeevolutionoftheFouriermodesofDPPC-25%andDPPC75%. ...... 85 5-10Spectralintensityofbilayersurfaceuctuationsfor DPPC-25%andDPPC-75% withandwithoutfullerenol. ............................. 86 10

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AbstractofdissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy MODELINGOFINTERACTIONSBETWEENNANOPARTICLESANDCELL MEMBRANES By Young-MinBan August2010 Chair:DmitryI.KopelevichMajor:ChemicalEngineering Rapiddevelopmentofnanotechnologyandabilitytomanufac turematerials anddeviceswithnanometerfeaturesizeleadstoexcitingin novationsinmany areasincludingthemedicalandelectronicelds.However, thepossiblehealthand environmentalimpactsofmanufacturednanomaterialsaren otfullyknown.Recent experimentalreportssuggestthatsomeofthemanufactured nanomaterials,suchas fullerenesandcarbonnanotubes,arehighlytoxiceveninsm allconcentrations.The goalofthecurrentworkistounderstandthemechanismsresp onsibleforthetoxicity ofnanomaterials.Inthecurrentstudycoarse-grainedmole culardynamicssimulations areemployedtoinvestigatetheinteractionsbetweenNPsan dcellularmembranesata molecularlevel. Oneofthepossibletoxicitymechanismsofthenanomaterial sismembrane disruption.Possibilityofmembranedisruptionexposedto themanufacturednanomaterials areexaminedbyconsideringchemicalreactionsandnon-rea ctivephysicalinteractions aschemicalaswellasphysicalmechanisms.Mechanismsoftr ansportofcarbon-based nanoparticles(fullereneanditsderivative)acrossaphos pholipidbilayerareinvestigated. Thefreeenergyproleisobtainedusingconstrainedsimula tions.Itisshownthatthe considerednanoparticlesarehydrophobicandthereforeth eytendtoresideinthe interiorofthelipidbilayer.Inaddition,thedynamicsoft hemembraneuctuationsis signicantlyaffectedbythenanoparticlesatthebilayerwaterinterface.Thehydrophobic 11

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interactionbetweentheparticlesandmembranecoreinduce sthestrongcoupling betweenthenanoparticlemotionandmembranedeformation. Itisobservedthattheconsiderednanoparticlesaffectsev eralphysicalproperties ofthemembrane.Thenanoparticlesembeddedintothemembra neinteriorleadtothe membranesoftening,whichbecomesmoresignicantwithinc reaseinCNTlengthand concentration.Thelateralpressureproleandmembraneen ergyinthemembrane containingthenanoparticlesexhibitlocalizedperturbat ionaroundthenanoparticle.The nanoparticlesarenotlikelytoaffectmembraneproteinfun ctionbytheweakperturbation oftheinternalstressinthemembrane.Duetotheshort-rang edinteractionsbetweenthe nanoparticles,thenanoparticleswouldnotformaggregate sinsidemembranes. Theeffectoflipidperoxidationoncellmembranedeformati onisassessed.The peroxidizedlipidsintroduceaperturbationtotheinterna lstructureofthemembrane leadingtohigheramplitudeofthemembraneuctuations.Hi gherconcentrationofthe peroxidizedlipidsinducesmoresignicantperturbation. Cumulativeeffectsoflipid peroxidationcausedbynanoparticlesareexaminedforthe rsttime.Theconsidered amphiphilicparticleappearstoreducetheperturbationof themembranestructureat itsequilibriumpositioninsidetheperoxidizedmembrane. Thissuggestsapossibilityof antioxidanteffectofthenanoparticle. 12

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CHAPTER1 INTRODUCTION 1.1Background Nanoparticlesaredenedasmaterialswhoselengthislesst han100nanometers. Chemicalandphysicalpropertiesofnanoparticlesareofte ndifferentfromthoseof theirbulkcounterparts,whichpromotestheirapplication invariouselds.Onepossible applicationistheuseofnanoparticlesasadrugcarrier,si ncenanoparticlesaresimilar insizetobiologicalmolecules(proteins,DNA,andRNA)and arereadilytransported throughthebodyduetotheirsmallsize.Successfulprototy pesofdrugdeliveryvehicles weredevelopedusingvarioustypesofnanoparticles,inclu dingcarbonnanotubes (CNTs),fullerenes,andpolymericnanoparticles[ 17 55 ]. Becauseofthegrowingnumberofapplications,theproducti onofnanomaterials isexpectedtosignicantlyincrease.Largeamountsofmanu facturednanoparticles mightbereleasedintotheenvironmentpossiblyaffectingl ivingorganismsinavariety ofways.Inparticular,humansmaybeeasilyaffectedbynano particlesbecausehuman skinandlungsarealwaysindirectcontactwiththeenvironm ent.Adverseeffectsof variousnanoparticlesonlivingorganismshavebeendemons tratedbynumerousrecent studies.Forexample,pulmonaryexposureofmice[ 21 ]andrats[ 58 ]tosingle-wall carbonnanotubes(SWCNT)hasbeenshowntoleadtolunginam mation.Inaddition topulmonarytoxicity,SWCNTsmaycausedermaltoxicityasi ndicatedbystudiesof humanskincellcultureexposedtoSWCNTs[ 48 ]. Apparenttoxicityofothercarbon-basednanoparticlessuc hasfullereneshasalso beenobserved.Exposuretoanaqueoussolutionoflowconcen tration(0.5ppm)of uncoatedfullerenesleadstosignicantoxidativebrainda mageofshwithin48hours [ 36 ].Moreoever,thepresenceoffullerenesatconcentrations aslowas20ppbinduces membraneruptureandeventualdeathofhumandermalbrobla stcells[ 43 ]. 13

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Themaingoalofthisworkistoinvestigatepossiblemechani smsofcellmembrane damagesduetoitsinteractionswithcarbon-basednanopart icles(suchasfullerenes andCNTs).Oneoftheproposedmechanismsofthecelldisrupt ioninvolvesthe particle-inducedoxidativestressandthecorrespondingl ipidperoxidation[ 36 43 44 47 ].Reactiveoxygenspecies(ROS),whichareprecursorstoth eperoxidation reactionwereobservedincellsexposedtoseveraltypesofn anoparticlesincluding SWCNTandfullerenes[ 43 ].TheROSproducesunstablelipidradicals,whichreactwit h otherlipidseventuallyresultinginthemembraneperoxida tion,followedbymembrane disruption. Inadditiontothischemicalmechanism,non-reactivephysi calinteractionsbetween nanoparticlesandbiologicalmembraneshavebeenconsider edasanalternative mechanismofmembraneinstability.Althoughdetailsofthi sphysicalmechanismis currentlynotclear,somecomputationalworkhasexploredt heinteractionsbetween nanoparticlesandcellmembranesatamolecularlevel.Mole culardynamicsstudies haveshowntranslocationofnanoparticlesthroughmembran es[ 5 ]andtheeffectsof theembeddednanoparticlesonthepropertiesofthemembran e[ 59 ].Itisobservedthat carbon-basednanoparticles,suchasfullerenesandsomeof fullerenederivativeshave caneasilypermeateintothemembraneinteriorandwillstay insidethemembranefor alongtime.Duringthestay,nanoparticlesmaysignicantl yperturbthemembraneand evendisruptthemembraneintegrity. Thisstudyrepresentsasteptowarddevelopmentofafundame ntalunderstanding ofthemolecularmechanismsofinteractionofmanufactured nanoparticleswithcellular membranes.Moleculardynamics(MD)simulationsareperfor medtoinvestigate trasportofnanoparticlesintothecellularmembraneinter ior,changesofthemembrane propertiesduetonanoparticlesabsorbedinsidethemembra neinterior,andbreakdown ofmembraneintegrityduetothelipidperoxidation. 14

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1.2SpecicAims Thegoalofthisstudyistounderstandinteractionsbetween nanoparticlesandcell membranesatamolecularlevel.Theinteractionbetweencar bon-basednanomaterials andmembranesarefocusedon,modeledasphospholipidbilay ers.Possibletoxic effectsofnanoparticleswithvariousphysicochemicalpro pertiesareinvestigated, namelytheirsize,shapeandfunctionalgroupsonthesurfac e.Thespecicaimsofthis researchare: Investigatethetransportmechanismofnanoparticleacros samembraneand evaluateofnanoparticlepartitioninthemembraneinterio r.Thefreeenergybarrier forthetransportofcarbon-basednanoparticlesacrossbil ayersarecomputed usingtheconstrainedmeanforcemethodandexaminethetran sportrateof carbon-basednanoparticlesforthecellmembranepermeati on. Examineeffectsofnanoparticlesonphysicalpropertiesof membranesand investigatepossibleimpactofnanoparticlesonmembranes tabilityand functionalityofmembraneproteins.Themembranephysical propertiesare characterizedbybendingandtiltmodulusandpressure. EvaluateinuenceofROSandresultantmembraneperoxidati oninducedby nanoparticles.Toexaminethedose-dependencyofnanopart iclesontoxicity,the concentrationofperoxidizedlipidsarealtered. 1.3OverviewofDissertation Inchapter2,methodsusedtosimulatebilayer-nanoparticl esystemsandanalyze thesimulationsarepresented.Coase-granedmolecularmod elisusedtomimic bilayer-nanoparticlesystems.Itisassumedthatanoparti cletransportcanbedescribed bytheLangevinequation.Simulationofnanoparticletrans portisperformedusingthe ConstrainedMeanForce(CMF)method.Calculationsofelast icpropertiesofmembrane andstresstensorinsidemembranearegiveninthischapter. Inchapter3,transportmechanismofnanoparticlethrougha lipidmembraneare discussedandeffectofthenanoparticleonmembranedeform ationduringthetransport areexamined.Theconsiderednanoparticlesarehydrophobi candthereforetheytendto 15

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resideintheinteriorofthelipidbilayer.Itisobservedth atnanoparticletransportthrough thebilayeraffectsthedynamicsofmembraneuctuations. Inchapter4,non-reactivephysicalmechanismsareconside redtoassesspossible inuenceofembeddednanoparticleintoamembraneondisrup tionofmembrane integrity.Itisobservedthatthesenanoparticlesmayaffe ctseveralphysicalpropertiesof themembrane,includingitsbendingmodulusandthelateral pressureprole. Inchapter5,Chemicalmechanismsareconsideredtoexamine effectsoflipid peroxidationonmembranedisruption.Changesininternals tructureofmembraneby thechemicalmechanismsaredemonstrated.Inaddition,eff ectsofnanoparticleonthe structureofmembraneareassessed. Inchapter6,thedissertationandpresentitsbroaderimpac tsareconcluded. 16

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CHAPTER2 METHODS 2.1MolecularDynamicsSimulations Thesystemcontainingalipidbilayerandcarbon-basednano particlesismodeled bymoleculardynamics(MD)simulation.MDsimulationisate chniqueforcomputingthe propertiesofamicroscopicsystembasedontheclassicalme chanics.Inprinciple,the purposeofusingMDsimulationistoobtainatrajectoryofal lmoleculesfromaninitial setofatompositionsandatomvelocities.Themotionofalla tomsisdescribedbythe Newton'sequationofmotion:m i@2 r i @t 2 = F i i = 1, ... N .(2–1) Theforcesarethenegativepartialderivativesofapotenti alfunctionU ( r 1 r 2 ..., r N ),F i = @U @r i .(2–2) Here,ireferstotheparticlenumber,ristheposition,misthemassoftheparticle,andFistheforceactingontheparticle.Thepotentialfunctionu sedinthisworkisdescribed insection 2.2 Theevolutionoftheatompositionsandvelocitiesisobtain edbynumerical integrationofEq. 2–1 usingtheVerletleap-frogalgorithm[ 1 ].Thisalgorithmuses theparticlepositionsrattimetandvelocitiesvattimet 4t 2toupdatethepositionatt +4tandvelocityattimet +4t 2usingtheforceF ( t )actingontheparticleattimet,vt +4t 2= vt 4t 2+ F ( t ) m4t (2–3) r ( t +4t ) = r ( t ) + vt +4t 2 4t (2–4) Newton'sequationsofmotionimplythatthetotalenergyoft hesystemremains constantbutthekineticenergyoftheparticleschanges,le adingtotemperature uctuations.Sincetemperatureisusuallyconstrainedine xperimentalsystems,itis 17

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desirabletomaintainconstanttemperatureinMDsimulatio ns.Severalthermostating techniquesareavailabletoaccomplishthisgoalandinthis worktheextended-ensemble approachrstproposedbyNos e[ 34 ]andlatermodiedbyHoover[ 14 ](Nos e-Hoover thermostat)isused.Theideaofthismethodistoextendthes ystembyintroducinga thermalreservoir.Africtionterm_ r iisintroducedintheequationsofmotion,d 2 r i dt 2 = F i m i dr i dt .(2–5) Thedynamicsofthefrictioncoefcient isgovernedbythefollwingequation:d dt = 1 Q ( TT 0 ).(2–6) Here,TandT 0arethecurrentandreferencetemperaturesofthesystem,re spectively andthereservoirmassparameterQdeterminesthestrengthofcouplingwiththe thermalreservoir. Thepressureinthesystemwithconstantvolumealsouctuat es.Inthissimualtion thepressureiskeptconstantbyParrinello-Rahmanpressur ecoupling[ 35 39 ],whichis similartotheNose-Hoovertemperaturecoupling,d 2 r i dt 2 = F i m iM dr i dt (2–7) M = b1hb d b0 dt + d b dt b0 ib01 (2–8) Here,Misthefrictioncoefcient,Visthevolumeofthesimulationbox,andthematrixbobeysthefollowingequationofmotiond 2 b dt 2 = V W1 b01 ( PP ref ).(2–9) Thecouplingstrengthisdeterminedbythemassparameterma trixW.ThematricesPandP refarethecurrentandreferencepressures,respectively. ImplementationoftheT-andP-couplingschemesrequiresca lculationof instantaneousTandP.TemperatureofanN-particlesystemi sgivenbyitstotalkinetic 18

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energy,3 2 k B T = E kin = 3 2 NXi =1 m i v 2 i (2–10) wherek BistheBoltzmannconstant,m iismassofi-thparticle,andv iisvelocityofi-th particle.Thepressureiscalculatedfromthedifferencebe tweenkineticenergyE kinand thevirial,P = 2 V ( E kin)(2–11) wherethevirialtensorisdenedas =1 2Xi
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andatomisticsimulationsforvariouslipidsystems[ 3 28 32 ].However,theCGmodel hassomelimitations.Whilesomevariables,suchasdensiti es,lengthscales,energies, temperatureandpressure,canbeaccuratelyreproducedbyt heCGmodel,thisisnot exactlytrueforthetimescale.TheeffectivetimeintheCGm odelis3-6timeslarger becausetheCGinteractionsaremuchsmoothercomparedtoat omisticinteractions.In addition,nechemicaldetailsareinaccessibleinanyCGap proach. Fourmaintypesofinteractionsitesareconsideredinthism odel:polar(P), nonpolar(N),apolar(C)andcharged(Q).Polarsitesrepresentneutralgroupsof atomsthatwouldeasilydissolveinwater,apolarsitesrepr esenthydrophobicmoieties, andnonpolargroupsareusedformixedgroupswhicharepartl ypolar,partlyapolar. Chargedsites(Q)arereservedforionizedgroups.Anumberofsubtypesforea ch particletypeisconsideredtoallowamoreaccuratereprese ntationofthechemical natureoftheunderlyingatomicstructure.Subtypeswithin eachmaintypeare distinguishedbytheirhydrogen-bondingcapabilities(d= donor,a=acceptor,da= both,0=none)andthedegreeofpolarity. ThenonbondedinteractionsbetweenCGbeadsiandjaredescribedbythe Lennard-Jones(LJ)potential,U LJ ( r ) = 4ij" ij r12 ij r6#.(2–13) Here, ijistheeffectiveminimumdistanceofapproachbetweentwopa rticlesand ijisthestrengthoftheirinteraction.Tenlevelsofinteract ionsaredenedandthe interactionstrength ofeachoftheinteractionlevelsisasfollows:themostpola r interaction(O, =5.6kJ/mol),attractiveinteractions(I, =5.0kJ/mol),semi-attractive interactionsinmorevolatileliquidssuchasethanolorace tone(II, =4.5kJ/mol,and III, =4.0kJ/mol),intermediateinteractioninaliphaticchain s(IV, =3.5kJ/mol),various degreesofhydrophobicrepulsionbetweenpolarandnonpola rbeads(V, =3.1kJ/mol, VI, =2.7kJ/mol,VII, =2.3kJ/mol,andVIII, =2.0kJ/mol),andtheinteractionbetween 20

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chargedparticlesandaveryapolarmedium(IX, =2.0kJ/molwith =0.62nm).Forall teninteractiontypesthesameeffectivesizeisassumed, ij=0.47nm,exceptforthethe levelIX( ij=0.62nm)andinspecialcase,namelyforringparticles.The ringparticles (labeled“S”)areintroducedtomodelmoleculescontaining rings.Themappingofatoms toringmoleculesis2or3to1.Theeffectiveminimumdistanc e fortheringparticles issetto0.43nmandthestrengthoftheirinteraction isscaledto75%oftheoriginal value.InthesimulationstheLJinteractionpotentialiscu t-offatadistancer cut=1.2nm, whichformostparticlepairscorrespondstoapproximately 2.5 InadditiontotheLJinteraction,themodeltakesintoaccou nttheelectrostatic interactionsbetweenchargedparticles.Inordertomimics creening,theCoulomb potentialenergy,U el ( r ) = q i q j 40r r ,(2–14) isshiftedbyaddingafunctionS(r)suchthattheeffectivep otentialU el ( r ) + S ( r )smoothlydecaystozeroasrapproachesthecut-offradiusof 1.2nm.Therelative dielectricconstant r=15isalsointroducedtomimicthescreening. Bondedinteractionbetweenchemicallyconnectedsitesare describedbyaweak harmonicpotentialU bond ( r )withanequilibriumdistancer bond=0.47nmforallparticles exceptforringparticles(r bond=0.43nm)andparticlesusedfortheglycerolbackbonein phospholipids(r bond=0.37nm),U bond ( r ) = 1 2 k bond ( rr bond ) 2(2–15) wherek bond=1250kJ/mol/nm2istheforceconstantandristheinstantaneousbond length.Thechainstiffnessismodeledbyaweakharmonicpot entialU angle ()forbond angles:U angle () = 1 2 k angle [cos()cos(0 )] 2(2–16) wherek angle=25kJ/mol/rad2istheforceconstantand 0istheequilibriumbondangle, whichdependsongeometryofthemolecule. 21

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Thecellmembraneismodeledbyadipalmitoylphosphatidylc holine(DPPC)lipid bilayer.TheDPPCmoleculeiscomprisedofthehydrophilich eadgroup,whichincludes esterbackbone,andtwohydrophobictails.TheCGmodelfort hismolecule,shown inFig. 2-1A ,containstwochargedbeads(Q)forthezwitterionicPCheadgroup,two non-polarbeads(N)fortheglycerolesterbackbone,andfourapolarbeads(C)foreach ofthetwotails. TheCGmodelforCNTsisbasedonthemodelproposedbyWallace andSansom (2007)[ 56 ].ThemodelCNTsarecomposedofthehydrophobicbeads,simi lartothe beadsusedforthelipidtail-groups.Open-endzigzag(6,0) SWCNTsisconsidered(see Fig. 2-1C ).Thediameterofthesenanotubesis1.56nmandlengthofthe irunitcells is1.3nm.Inordertoexamineeffectsofthenanotubelength, nanotubescontaining three,four,andsixunitcellswereconsidered.Inwhatfoll ows,thesenanotubesare denotedasCNT3,CNT4,andCNT6,respectively.Themodelnanotubesarecomposed ofhydrophobicbeadswhoseLJparametersarethesameasthos eofthetailbeads inaDPPClipid.Thebondandanglepotentialsareassumedtob eharmonic,andthe forceconstantsforthebondandanglepotentialswere2500k J/mol/nm2and10000 kJ/mol/rad2,respectively,chosentomaketheCNTsrigidenoughtomaint aintheir shapeagainstsurroundingmolecules.Itwasveriedthatth ebondlengthandangleare normallydistributedfromtheequilibriumlength(0.47nm) andangle(120degree)within 0.06nmand2.1degree,respectively,with95%condencelev el.Anintegrationtime stepwasreducedto0.02psfrom0.04ps,whichwasusedforsim ulationscontainingno CNTs,byconsideringthefastestfrequencyofbondvibratio ns. D'Rozarioetal.[ 5 ]isfollowedtoapproximatethestructureofthefullereneC60by20CGbeadsevenlyspacedonasphereofdiameter1.2nm.The forceconstants werethesameasthoseforCNTs.TheLJparametersofthesebea dsweretakento bethesameasthoseforCGmodelofbenzene[ 28 ].Inordertoinvestigateeffectsof functionalizationofcarbon-basednanoparticlesbyhydro philicgroups,aCGmodelofa 22

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fullerenol(functionalizedfullerene),C60(OH)10isconsidered.Thismodelwasobtained byreplacing10hydrophobicbeadsononeofthehemisphereso fC60by10hydrophilic beads.Theintegrationtimestep(0.02ps)wasused. A B C Figure2-1.CGmodelsof(A)DPPClipidmolecule,(B)fullere ne(left)andfullerenol (right),and(C)CNT. Acomputationalmodelforlipidbilayerispreparedthrough self-assembly.MD simulationsofaDPPClipidsolutioninwaterinasimulation cellofsize10 10 10nm3wereperformed.Thesystemcontained264DPPCmoleculesand 4832waterbeads. Theinitialconditionsforthissimulationwerechosentobe arandomdispersionoflipids inwater(Fig. 2-2A ).Itwasfoundthatlipidsself-assembledintoabilayersho wnin Fig. 2-2B withinafewnanoseconds.Temperatureandpressureweremai ntainedat323 Kand1bar.Afteralipidbilayerisprepared,semiisotropic pressurecouplingmethod isappliedtomaintainzerosurfacetensionofthebilayerme mbraneforallconsidered systems.Theboxsizechangedto9.169.1611.09nm3fromtheself-assembly 23

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simulationsinordertoensurezeromembranetension r and1barpressureP Ninthe normaldirection.Allsystemswererotatedsothatthebilay erisparalleltothex-yplane. A B Figure2-2.Self-assemblyofDPPCbilayer[ 50 ]:(A)initialrandomdispersionofDPPC beadsinwaterand(B)self-assembledDPPClipidbilayer.Fo rclarity,the watermoleculesarenotshown. 2.3StochasticModelandCMFMethod Transportofevensmallmoleculesacrossalipidbilayertak esplaceonatimescale thatisoutofreachofMDsimulations.Itisthereforenotpra cticaltostudythetransport effectsofnanoparticlesbydirectMDsimulations.Several techniqueshavebeen developedtoenableMDsimulationsofsuchrareevents[ 2 15 20 ].Inthisinvestigation theConstrainedMeanForce(CMF)method,whichhasbeenprev iouslyappliedto similarsystems[ 26 27 ]wasemployed. Themainassumptionunderlyingthisanalysisisthatnanopa rticletransportcanbe describedbythegeneralizedLangevinequation[ 7 ],m z ( t ) +Zt 0r 0( z t )_ z () d+ dG ( z ) dz = ( z t ).(2–17) Here,zisareactioncoordinate,misthemassofthenanoparticle, r 0 isthememory frictionkernel,Gisthefreeenergyandisthenormallydistributedrandomforcewith zeromeanandtheautocorrelationfunctionobeyingtheuct uation-dissipationtheorem, 24

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h( z t )i= 0,(2–18) h( z t )( z t +)i=r 0( z ,) k B T .(2–19) Thebracketsdenotetheensembleaverage,k BistheBoltzmannconstant,andTisthesystemtemperature.Theuctuation-dissipationthe oremallowsustocompute thefrictioncoefcientfromtherandomforceautocorrelat ionfunction,whichisreadily measurablefromMDsimulations. Ifthecorrelationtimeforisverysmallthenthefrictionwithmemorycanbe replacedbymemorylessfrictionwithcoefcient r .Inthiscase,Eqs. 2–17 and 2–19 simplifyto:m z ( t ) +r( z )_ z ( t ) + dG ( z ) dz = ( z t ), (2–20) h( z t )( z t +)i= 2r( z )() k B T (2–21) where istheDiracdelta-function.Further,theobtainedfrictio ncoefcientisdirectly relatedtolocaldiffusivity[ 7 ],D ( z ) = k B T=r( z ).(2–22) LetusnowdiscussthecomputationofthetermsofEq. 2–20 fromtheconstraint MDsimulations.Ifzisheldconstantbyapplicationofaconstraintforce,F,thentherst andsecondtermsofEq. 2–20 arezero.Further,theensembleaverageoftherandom forcetermiszero,seeEq. 2–18 .Therefore,theensembleaverageofEq. 2–20 yields thefollowingrelationshipbetweentheconstraintforce hFi andthefreeenergy: hF ( z 0 t )i= dG ( z 0 ) dz .(2–23) Inanalysisofthesimulationstheensembleaveragingisrep lacedbythetimeaveraging usingtheergodicassumption. 25

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TofullyreconstructEq. 2–20 itisnecessarytoobtainthefrictioncoefcient, r .To thisend,Eq. 2–21 isappliedtocalculatetherelationshipbetweenthetime-i ndependent frictioncoefcientandtheautocorrelationfunctionofth erandomforce,2r( z )() =h( z t )( z t +)i k B T .(2–24) Integratingbothsidesoftheequationfrom0toinnityyiel ds r( z ) =Z 10h( z t )( z t +)i k B T dt .(2–25) Therandomforce( z t )isobtainedbycomputingthedeviationoftheconstrainedfo rce fromitsmeanvalue,( z t ) = F ( z t )hF ( z t )i.(2–26) 2.4CalculationofElasticPropertiesofMembrane 2.4.1EstimationofBendingandTiltModulus Oneofthepossibleeffectsofnanoparticlesembeddediname mbraneisachange ofthemembraneelasticproperties,whichinturncanleadto amembraneinstabilityora failureofsomeofthemembranefunctions.Inthissection,t herelevantelasticproperties ofthemembraneandmethodsoftheircalculationarebrieyd iscussed. TheclassicalmembranemodelwasproposedbyHelfrich[ 11 ].Thismodel assumesthatthedominantcontributiontothemembraneener gyisassociatedwith themembranebending.Inthiscase,themembranefreeenergy canbeapproximated asF H =Z 2 ( JJ s ) 2 +KdA ,(2–27) whereJandKarethemeanandGaussiancurvaturesofthemembrane,respec tively,J sisthespontaneouscurvature, isthebendingmodulus, istheGaussianmodulus, andtheintegrationisperformedoverthemembranesurface. Thismodelapproximates themembraneasaninnitelythinelasticsheetandneglects themembraneinternal structure. 26

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However,interactionofthemembranewithnanoparticlesis likelytocauselocalized disturbancesintheneighborhoodofthenanoparticles.The refore,itisnecessaryto usethemodelwhichaccountsfortheinternalmembranestruc ture.Suchamodelwas proposedbyHammandKozlov[ 10 ].Toaccountfortheinternalmembranestructure, thismodelincludeseffectsoflipidtilt.Inordertoquanti tativelydenetilt,alipiddirector (n)isrstdenedasavectorpointingfromthecenterofmassof thelipidtailstothat ofthehead-group.Tilttisthendenedasthedeviationofthelipiddirectornfromthe normalNtothesurfaceofthemonolayercontainingthislipid[ 10 ],t = n nNN .(2–28) Here,vectorsNandnareofunitlength.TheHamm-Kozlovmodelapproximatesthe bilayerenergyasasumoffreeenergiesofthemonolayerscom prisingit.Themonolayer freeenergyisapproximatedasF HK =Z 1 2( ~ JJ s ) 2 + ~ K + 1 2 t 2dA .(2–29) Here,~ Jand~ KarethemeanandGaussiansplayswhichcontaincontribution ofboththe membranebendingandthelipidtiltand isthetiltmodulus. TheintegrationovertheGaussiansplaytermyieldsthesame resultforall membranescontainingnotearsordiscontinuities[ 30 ].Therefore,contributionof thistermtothemembranefreeenergycanbeneglectedandthe energyofamonolayer withvanishingspontaneoustotalcurvatureisF HK = 1 2Z h ~ J 2 ( x y ) + t 2 ( x y )idx dy .(2–30) ItfollowsfromtheEq. 2–30 andtheequipartitiontheorem[ 30 ]thatthemagnitudesof equilibriumuctuationsofthemonolayersurfaceh ( x y )andthemoleculartiltt ( x y )are 27

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givenby ^ h ( q )2= k B T1 jqj4 + 1 jqj2 (2–31) and D ^ t x ( q )2E=D ^ t y ( q )2E= k B T (2–32) Here,^ h ( q )and^ t ( q )aretheFouriertransformsofthemembranesurfaceh ( x y )andthe lipidtiltt ( x y )andqisthewavevector. Theinterfacecongurationofthemembraneisevaluatedbya nalyzingcontinuous approximationtotheinstantaneousdividingsurfaceateac htime-step.Thedividing surfaceattimetisdenedasasurfacepassingthroughthepivotpoints(xi(t),yi(t), zi(t)),i.e.mid-pointsofbondsconnectinglipidhead-andta il-groups.Inordertosmooth theinstantaneousdividingsurface,theleast-squaresti susedtoobtainitsFourier seriesexpansion,h ( x y ; t ) =Xqbh q ( t ) e i ( q x x + q y y ) (2–33) Xijz i ( t )h ( x i y i ; t )j2!min (2–34) NormalvectorNisobtainedfromtheobtainedinstantaneousinterfacecon guration necessaryforcalculationofthetiltvector(seeEq. 2–28 ),N = 1 p 1 + h 2 x + h 2 y (h x ,h y 1).(2–35) Here,h xandh yarethepartialderivativesofh ( x y )withrespecttoxandy,respectively. Eq. 2–31 indicatesthatthemagnitudeofthelongwavelengthuctuat ionsofthe monolayersurface(q! 0)scalesasq4,whereastheshortwavelengthuctuations scaleasq2.Thecross-overbetweenthesetworegimesdependsontheval uesofkandk andtypicallycorrespondstothewavelengthcomparablewit hthemembrane thickness(seesection 4.4 ). 28

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Eq. 2–31 enablesustoestimatethebendingandtiltmodulusfromsimu lations ofamembraneatequilibrium.Specically,kandk canbeobtainedbyperforminga least-squarestofthemagnitudeofthebendingandtiltuc tuationstoEq. 2–31 .Note thatk inuencestoboththebendingandtiltuctuations,whichal lowsustocheckthe self-consistencyofthevaluesofk obtainedfromEqs. 2–31 and 2–32 2.4.2StatisticalAnalysisofCorrelatedTimeSeries2.4.2.1Theory AsdiscussedinSection 4.4 ,relativelysmalldifferencesbetweenelasticitiesof thepurebilayersandbilayerscontainingnanoparticlesar eobserved.Itistherefore necessarytoruleoutapossibilitythatthesedifferencesc anbeattributedtostatistical uncertainties.Thebendingmodesmostrelevantinthecalcu lationofthebending moduluscorrespondtolongwavelengths( 10nm).Thetimescaleofuctuations ofthesemodesisrelativelyslow,O(102)–O(103)ns.Sincethesimulationtimescale istypicallyO(10 6)ns,itisnotpracticaltouseonlyuncorrelateddatainthea nalysis, sincethiswillnotprovideuswithsufcientlylargesample forstatisticalanalysis. Itisnecessarytoaccountforcorrelationinthisanalysis, sinceerrorestimates obtainedassumingzerocorrelationarenotappropriatefor datacorrelatedintime (seeSection 2.4.2.4 ). Assumethateachofthebendingandtiltmodesisindependent ofallothermodes. Consideroneofthesemodesanddenoteitbyz ( t )tosimplifythenotationinthis section.Assumefurthermorethatthedynamicsofz ( t )canbedescribedbyalinear Langevinequation rdz dt = ( zz 0 ) + ( t ).(2–36) Here, 2 R isthe“springconstant”, r 2 R isthefrictioncoefcient,and( t )2 C isthe Gaussianrandomforcewithzeromean.Therandomforceandth efrictioncoefcient 29

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arerelatedbytheuctuation-dissipationtheorem h j ( t ) j0( s )i= 2 k B Trj j0 ( ts ), j j0= re o r im .(2–37) Thelatterassumptionimpliesthat[ 7 ] 1. Realandimaginarypartsofz ( t )areindependentofeachother, h reimi= 0,(2–38) where ( t )z ( t )z 0isthedeviationofz ( t )fromitsmeanvaluez 0hzi and subscriptsreandimdenotetherealandimaginarypartsofacomplexvariable. 2. Autocorrelationfunctionsof re ( t )and im ( t )areidenticalanddecayexponentially, h j ( t )j ( s )i= Aejtsj =, j = re o r im .(2–39) AssumethatMDdataaresavedattimest n = ( n1) t,n = 1, ... N.Inorderto connectthesedatawiththetheoreticalmodel( 2–36 ),adiscretizedversionofthismodel isneededtoobtain.Forthis,integrateEq.( 2–36 )fromt n1tot n, ( t n ) =( t n1 ) +!n .(2–40) Here, !n2 C areindependentGaussianvariableswithzeromeanandvaria nce 2! Parametersofthediscreteequation( 2–40 )arerelatedtoparametersoftheLangevin equation( 2–36 )bythefollowingrelationships: = e t=,=r ,2!= k B T (1 2 ).(2–41) Moreover[ 46 ], 2= (1 2 )12!.(2–42) Oneoftheapproachestoobtaintheparametersofthestochas ticprocess( 2–40 ) istheYule-Walkermethod(see,e.g.Ref.[ 46 ]).Thisapproachinvolvesaleast-squares ttotheautocorrelationfunctionof ( t n ).However,thisapproachassumesthatthe 30

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stochasticprocesshasazeromeananddoesnotprovideasimp lewaytoestimatethe errorofz 0Sinceapplicationofthismethodisanticipatedtoanalyzes hapesofdeformed membranes,analternativeapproachischosen,whichwillal lowtoestimatez 0andits standarddeviation.Thisisamaximumlikelihood(ML)metho d[ 46 ],inwhichthevector ofthesystemparametersx( z 0, re z 0, im ,,2!)isobtainedbymaximizingthelikelihood functionL ( xjz ) = ln P ( zjx ) =N ln2!+ ln(1 2 )S 1 2! !max(2–43) foragivenrealizationoftimeseriesz = ( z 1 ..., z N ).Here,z nz ( t n ),P ( zjx )isthe probabilitytoobservetherealizationzofthetimeseriesifthevaluesofthesystem parametersarex,andS 1(1 2 )jz 1j2 + NXn =2jz n z n1j2 .(2–44) Notethatinthecaseofuncorrelatedtimeseries(i.e., = 0)andan apriori known 2! maximizationof( 2–43 )correspondstosolutionoftheusualleastsquaresproblem ,L =1 2!NXn =1jz nj2!max.(2–45) 2.4.2.2Numericalalgorithm Itwasfoundthatthestandardoptimizationalgorithms(suc hasthemethodsof conjugategradientsandsteepestdescent)donotalwayscon vergeorconvergevery slowlytothemaximumofthelikelihoodfunctionL.Theproblemisassociatedwiththe stiffnessofthisfunction,i.e.averynon-uniformdepende nceofLonitsparameters.To seethis,considerL (2!)atxedz 0and ,L (2!) =N ln2! S 1 2!+ const .(2–46) 31

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When 2! !1 ,thefunctionL (2!)isdominatedbythersttermofEq.( 2–46 ),i.e.this functionvariesslowlywhen 2! issufcientlylarge.Ontheotherhand,when 2! !0, thefunctionL (2!)isdominatedbythequicklyvaryingsecondtermofEq.( 2–46 ).This impliesthataniterationofastandardoptimizationmethod islikelyto“overshoot”when movingfromtheregionoftheslowvariationofL (2!)totheregionofthefastvariation. Therefore,analternativenumericalschemewhichtakesadv antageofthespecic structure( 2–43 )ofthelikelihoodfunctionisdeveloped.Acriticalpointo fLcorresponds tothesolutionofthefollowingsystemofequations @L @=2 1 2 + 2 2!( S 4 S 3 ) = 0, (2–47) @L @2!=N 2!+ S 1 4!= 0, (2–48) @L @z 0 = 2 2!S 2 (2–49) whereS 1isdenedbyEq.( 2–44 ),S 2 "(1 ) (1 +n ) +1 2N1Xn =2n#, (2–50) S 3N1Xn =2j nj2 S 4NXn =2 Re (n1 n ) andn = z nz 0 (2–51) Thesystemofequations( 2–47 )-( 2–49 )issolvedusingthefollowingiteration scheme: 1. Initialguessesforz 0and 2! aretakentobethevaluesofthemeanandstandard deviationsofz nobtainedassumingthezerocorrelationtime,i.e.z (0) 0 = 1 N NXn =1 z n 2! (0) = 1 N1 NXn =1 ( z nz (0) 0 ) 2 .(2–52) 2. Solveequation( 2–47 )for atxed 2! andz 0.ThisequationissolvedbyNewton's methodwiththeinitialguess = S 4=S 3. 3. Solveequation( 2–48 )for 2! 2!= S 1 N .(2–53) 32

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4. Solveequation( 2–49 )forz 0,z 0 = S 2 N (1 ) + 2,(2–54) atxed and 2! 5. Repeatsteps2-4untilconvergence. Steps2,3,and4yieldauniquemaximumofLasafunctionof 2! ,andz 0, respectively,withothervariablesheldconstant,since @2 L @2<0,@2 L @(2!) 2<0, and@2 L @z 2 0, j<0, j = re im fo r all 2[0, 1).(2–55) Therefore,thisalgorithmconvergestothemaximumoftheli kelihoodfunctionandthis maximumisuniquefor 2[0, 1). 2.4.2.3Errorestimation Let^ xbeasolutionof( 2–43 )foragiventimeseriesz,i.e. rL ( ^ xjz ) = 0and rrL ( ^ xjz )isanegative-denitematrix.Theprobabilitydistributio nofthesystem parametersxisP ( xjz )/e L (xjz)/exp1 2 ( x^ x )rrL ( ^ x )( x^ x ) + H O T.(2–56) Neglectingthehigherorderterms(H.O.T.)in( 2–56 ),itisobtainedthatthemaximum likelihoodsolutionisunbiased,i.e. hxi= ^ x,andthecovariancematrixofthemodel parametersisCh( x^ x )( x^ x )i=[rrL ( ^ x ) ]1 .(2–57) GeneralizingthederivationofRef.[ 12 ]tothecaseofcomplextimeseriesz,lim N!11 NrrL = lim N!11 NhrrLi=0BBBBBBB@ 2 z 0 0 0 0 0 2 z 0 0 0 0 0 20 0 0 0 4! 1CCCCCCCA (2–58) 33

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isobtained.Here, 2 z 0 =2! 2(1 )[(1 ) + 2=N ] (2–59) 2= (1 2 ) 2 2[(1 2 ) + (321)=N ] (2–60) Combine( 2–57 )with( 2–58 )toobtainlim N!1C = 1 N0BBBBBBB@ 2 z 0 0 0 0 02 z 0 0 0 0 020 0 0 04! 1CCCCCCCA.(2–61) Therefore,errorestimatesforz 0, j ( j = re im ), ,and 2! are z 0= p N = p N and2! = p N ,(2–62) respectively.2.4.2.4Validation InordertovalidatetheMaximumLikelihoodmethodandtodem onstrateits necessityforanalysisofthecorrelateddata,aseriesofsi mulationsoftheLangevin equation( 2–36 )fordifferentsetsofparameterscorrespondingtothecorr elationtimes = t = 1,10,40,and100isobtained.Thesimulationsforthesameset ofparametersxanumberoftimeswererepeatedinordertoobtainadistribut ionoftheestimated parameters^ x.Thestandarddeviationoftheestimatedsystemparameters computed fromthisdistributionrepresentsthetrueerrorofthisest imation.Ofcourse,inrealityitis necessarytoobtaintheerrorestimatesbasedonasinglerea lizationofthestochastic process( 2–36 ).Thelatterestimatesaretheestimates( 2–62 )providedbytheML method. ItwasfoundthatforallconsideredparametersoftheLangev inequation,the MLmethodyieldsanaccurateestimateofthesystemparamete rsandtheerror 34

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estimatesobtainedbytheMLmethodsareingoodagreementwi ththetrueerrors. Ontheotherhand,errorestimatesbasedontheassumptionof uncorrelatedtimeseries underestimatethetrueerrorsbyanorderofmagnitudefor = 40 t 100 tandafactor oftwofor = 10 t. 2.4.3StressTensor Inadditiontochangesinthemembranestability,theembedd ednanoparticlesmay affectthemembranefunctionbychangingactivityofmembra neproteins.Inparticular, someionchannelsaresensitivetothelateralpressurepro leinthemembrane [ 4 ].Therefore,nanoparticle-inducedchangesinthelateral pressuremayshiftthe equilibriumbalancebetweenopenandclosedstatesofthech annels. InordertostudyspatialvariationofthepressuretensorPwithinthemembrane, instantaneouslocalstresstensor ,P =h i,(2–63) isaveraged. Thestresstensoratthemicroscopiclevelconsistsoftwopa rts,namelythekinetic partduetomomentumtransportandapotentialpartarisingf romintermolecularforces [ 45 ], ( R t ) =1 VXi m i vi vi +Xi@ @ri U (fr jg)ZC 0 i dl ( Rl ). (2–64) Here, ,= x y ,orz,Visthevolume,m i,r i,andv iarethemass,velocity,andposition ofthei-thparticle,C 0 iisacontourconnectinganarbitrarypointR 0withthei-th,andUisthetotalpotentialenergy,whichcanbeexpressedasU (fr ig) =XaX U ( a ) ( r j 1 ..., r j a ). (2–65) 35

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Here,U ( a )area-bodypotentialsand ( j 1 ... j a )areparticleindices.Inthis system,a = 2correspondstoLennard-Jones,electrostatic,andbondlen gthpotentials anda = 3correspondstothebondanglepotential. AsdemonstratedinRef.[ 8 ],Eqs. 2–64 and 2–65 yieldthefollowingexpressionfor averageoftheinstantaneousstresstensoroversomedomainn: n ( t )1 V nZn ( R ; t ) d R (2–66) =1 V nXr i2n m i vi vi + 1 mV nXaX X @U ( a ) @rj k @U ( a ) @rj l!rj k j l f n ( r j k r j l ). (2–67) Here,r j k j lr j lr j kisthevectorpointingfromatomj ktoatomj landf n ( r j k r j l ) jr n ( r j k r j l )j jr j l j kj 2[0, 1](2–68) isaweightfunctionwhichspeciesthecontributionofinte ractionsbetweenatomsj kandj ltothestresstensorindomainn.r n ( r j k r j l )isthesegmentofr j l j kcontainedin domainn.TheintegrationcontourC j k j linEq. 2–68 isanarbitrarycontourconnecting atomsj kandj landf n ( r j k r j l )isthefractionofthiscontourcontainedindomainn.Inthis work,theIrving-Kirkwood(IK)contour[ 16 ]denedasastraightlineconnectingatomsj kandj l,R () = r j l +r j l j k 2[0, 1]isused.Inthiscase,assumingthattheinterval 2[in n ( r j k r j l ),out n ( r j k r j l )]correspondstothesegmentofthecontourC j k j linsidethe domainn,theweightfunctioncanbeexpressedasf n ( r j k r j l ) =j out n ( r j k r j l ) in n ( r j k r j l )j.(2–69) Inthecurrentwork,one-andtwo-dimensionalpressurepro lesarecomputedby averagingthestresstensoroverthefollowingdomains(see Fig. 2-3 ): 1. Slabsofthickness zparalleltothebilayerplane 2. Rectangularcolumnsnormaltothexyplane.Eachedgeofthesecolumnsis paralleltooneoftheaxesofcoordinatesandthecolumncros s-sectionis x y. 36

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A B Figure2-3.Cross-sectionsof(A)slabsand(B)columnsinwh ichthestresstensoris averaged.AnIKcontourconnectingatomsj kandj lisalsoshown. Contributionoftheinteractionbetweentheseatomstoapar ticulardomain (shownbylightgrey)correspondstothefractionofthecont ourcontained insidethedomain(shownbyathickerline). Whencomputingthetwo-dimensionalpressureproleofasys temcontainingan anisotropicnanoparticle(suchasacarbonnanotube),thes ystemofcoordinatesis rotatedsothatthenanoparticlepointsalongthex-axis.Thischangeofcoordinates isperformedateachtimestepafterthestresstensoriscomp uted.Therefore,itis necessarytoreectthecoordinatechangeinthetensorcomp onents.Ingeneral,ifnew andoldcoordinatesystemsarerelatedbyalinearorthogona ltransformationr new = T r old ,(2–70) thecorrespondingstresstensorsarerelatedby new = Told T1 .(2–71) 37

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Inthecurrentcase,thetransformationTistherotationaroundthezaxisbyangle betweenthenanoparticledirectionandtheoriginalx-axis,i.e.T =0BBBB@cossin0sincos0 0 0 11CCCCA.(2–72) 38

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CHAPTER3 TRANSPORTOFCARBON-BASEDNANOPARTICLESTHROUGHLIPID MEMBRANES 3.1Introduction Asdiscussedinthepreviouschapter,thesmallsizeofnanop articlesmakesthem promisingcandidatesfornewgenerationofdrugdeliveryve hiclesanddiagnostictools. However,possibilityofharmfuleffectsofnanoparticleso ncellularmembranesisof increasingconcern.Someexperimentshaveshowntoxicityo fnanoparticlessuchas deathofculturedcellsexposedtomulti-wallcarbonnanotu bes,carbonnanobers, andcarbonblack[ 25 ].Althoughexactmechanismsofcytotoxicityarenotclear, it hasbeenshownthatcelldeathtakesplaceafterthenanopart iclescontactwithcell membranesoraftertheyareinternalizedbycell.Rothen-Ru tishauser etal .[ 42 ] haveshownthatpolystyrene,goldandTiO2nanoparticlescanenterredbloodcells byanunknownmechanismdifferentfromendocytosis(acommo nmechanismof internalizationofmolecules,whichinvolvesinteraction ofthemoleculeswithspecic bindingproteinsinthecellmembrane).Therefore,underst andingnanoparticletoxicity requiresunderstandingofthemechanismsofnanoparticlep ermeationintocytoplasm. Inadditiontoexperments,molecularmodelingoftheintera ctionsofnanoparticles withcellmembranemayprovideinsightintotoxicitymechan ismsofnanoparticles. Computersimulationshavebeenusedtoexploretheinteract ionsbetweennanoparticles andbiologicalmembranes.Inparticular,MDsimulationisa usefultoolforinvestigation ofthepermeationofnanoparticlesintolipidmembranes.Th eyprovidespatialand temporalresolutioninaccessiblebyexperiments.Molecul ardynamicsstudieshave showntranslocationofC60fullereneanditsderivativesthroughlipidmembranes. Fullereneaggregatesformedinwaterpenetratedintoalipi dmembraneandstayed asmonomericfullereneinthemembraneinterior[ 59 ].Ontheotherhand,fullerene derivativesabsorbedtothebilayersurfaceandremainedat thebilayer-waterinterface [ 5 41 ],whichwassaidtomakefullerenederivativeslesstoxicth anpristinefullerenes. 39

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Inadditiontothenanoparticlepartitionsinlipidbilayer s,effortshavebeenmadein examiningchangesofmembranepropertiescausedbythepart icles.MDsimulationsof Wong-Ekkabut etal .[ 59 ]showedthathighfullereneconcentrationinalipidmembra ne affectsitselasticandstructuralproperties.Fullerenes inducedanincreaseinboththe projectedareaandthethicknessofthebilayerbutdecrease inthebendingmodulus. Inaddition,fullereneandsomefullerenederivativeshave beenshowntoexperiencea smallenergybarrierfortheirentryintoalipidbilayer[ 5 ].Inthisstudy,itisdemonstrated thatnotonlythenanoparticlesmaycausethemembranedefor mationbutthatthe deformationitselfplaysasignicantroleinthenanoparti cletransport. Inthecurrentchapter,interactionsbetweenfullerenesan dalipidmembraneduring theirtransportacrossthelipidmembraneareevaluated.Th epermeationprocessinto aatlipidbilayerisconsideredneglectingthecurvaturee ffectsofacell.Thisisagood approximationsincethetypicalcellsizeismuchlargertha nthenanoparticlesofinterest. Inaddition,lipidbilayersaresimulatedbyneglectingthe presenceofthemembrane proteinsbasedontheexperimentalevidencethatnanoparti cletransportmayoccurbya processdifferentfromendocytosis.Similarmembraneswit houtthemembraneproteins wereusedinresearchoftransportofcarbon-basednanopart icles[ 51 ]andfattyacids acrossmembranes[ 53 ]. 3.2FreeEnergyProles Toputtheobtainedresultsinperspective,inFig. 3-1A thedensityproleofthelipid bilayerisshown.Thefreeenergyprolesobtainedfortheco nsiderednanoparticles areshowninFig. 3-1B .Recallthatthesystemofcoordinatesisorientedsothatth ez-axispointsalongthebilayernormalandthebilayercenter ofmassislocatedatz = 0nm.Asexpected,thefullereneexperiencesasignicantdec reaseofthefree energyinthebilayerinterior,i.e.for-2nm
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watermolecules.Thesestrongattractiveinteractionspro videadrivingforceforthe nanoparticletoremaininthebilayerinteriorforaverylon gtime.Theshiftoftheenergy minimaofC60occursinthesoftpolymerregionofthelipidbilayer[ 27 ]characterized bythehighdensityoforderedtailgroups.Ascanbeseenfrom Fig. 3-1B ,thisregion correspondsto0.5nm < jzj < 1.0nmforC60.Thenanoparticleislikelytobelocated atthebilayercenterduetothefreevolumecausedbythedecr easeddensityofthe tailregionat0nm < jzj < 0.5nm(seeFig. 3-1A ).However,strongatractivevander Waalsinteractionbetweentheparticleandthelipidtailsi nthehighestdensityregion (0.5nm < jzj < 1.0nm)appearstopulltheparticleslightlyawayfromthepo intof thelowesttaildensity.Incontrast,thefreeenergyprole ofC60(OH)10exhibitsthe energyminimaat1.5nm < jzj < 2.0nm.AsshowninFig. 3-1A ,lipidhead-groups arepresentat1.5nm < jzj < 2.0nm.Theyattractthefunctionalgroupsoftheparticle towardthewaterphase.Therepulsionbetweenthehydrophil icgroupsoftheparticle andtail-groupsinducesthehighenergybarrieratthebilay ercenter.Thepreferential locationofhydrophobicC60andamphiphilicC60(OH)10areintheneighborhoodof themembranecenterandattheboundarybetweenthehead-and tail-groupsofthe membrane,respectively. BothC60andC60(OH)10experiencerelativelysmallenergybarrier( 4kJ/mol)to enterthemembrane.Thiscanbeexplainedbythefollowingob servation.Thestrength ofnanoparticleinteractionwithhydrophiliclipidhead-g roupisverysimilartothatofthe interactionwithwater.Further,theinteractionsofthehy drophobicnanoparticlewiththe glycerolesterbackboneareslightlymoreattractiveandth einteractionswithlipidtail beadsaresignicantlymoreattractivethantheinteractio nswithwater.Ofcourse,the energyrequiredtomoveapartthelipidhead-groupsthatare chemicallybondedwith relativelybulkytail-groupsisgreaterthantheenergyreq uiredtomoveapartsmallwater molecules.However,asthedensityproleinFig. 3-1A illustrates,thebilayerinterface containsalargeproportionofwaterbeads,whichmitigates theneed,atleastinthis 41

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-4 -2 0 2 4 0 2 4 6 8 10 z (nm)Density (beads/nm 3 ) Total Water Head Group Tail Group A -4 -2 0 2 4 -80 -60 -40 -20 0 20 40 60 z (nm)G (kJ/mol) C 60 C 60 (OH) 10 B Figure3-1.(A)DensityproleoftheDPPCbilayer.Thesolid lineshowstheaverage numberofbeadspercubicnanometer,whiletheremaininglin esindicatethe densityofwater,headgroupandtailgroupbeads.(B)Freeen ergyproles forfullerene(solidline)andfullerenol(dashed-dottedl ine). region,tomovetheDPPCbeadsapart.Oncethenanoparticlei swithintherangeof theglycerolesterbackbone,thedrivetowardsmorefavorab leinteractionsbecomes signicant.Thisdriveisfurthermagniedasthenanoparti cleapproachesthetailregion. -8 -6 -4 -2 0 0 0.5 1 1.5 2 2.5 3 3.5 x 10 -10 z (nm)D (m 2 /s) Figure3-2.Dependenceofthediffusivityoffullereneonth enanoparticlepositionwithin thebilayer. AscanbeseeninFig. 3-2 ,thenanoparticlediffusivityishighlyinhomogeneous insidethebilayer.Moreover,alloftheconsiderednanopar ticlesexperienceasharp decreaseofdiffusivityneartheentrypointintothemembra ne.Ithasbeenrecently 42

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demonstrated[ 9 ]thatsuchdecreasecharacterizesstrongcouplingbetween the nanoparticletransportandthemembraneundulation.Inpar ticular,themembrane shapeisexpectedtobesignicantlyperturbed.Suchmembra nedeformationisindeed observedwhenananoparticleislocatednearthemembraneen trypoints.InFig. 3-3 averagedividingsurfacesoftheupperandlowermembranele aetsareshownwhen thenanoparticleislocatedinthelowerleaetandthenanop articlelocationcorresponds totheminimumofthediffusioncoefcientD.Thelowerleae tsharplyprotrudes towardthenanoparticleinitsdirectneighborhood.Thispr otrusionisfollowedbyaslow decaytowardstheequilibriumstateasthedistancefromthe nanoparticleincreases. Theupperleaetdeformstowardthebilayercenteraroundth efullereneandslowly returnstotheequilibriumstateasthedistancefromthenan oparticleincreases.The hydrophobicgroupsofC60andC60(OH)10attractthehydrophobictailsoflipids,which resultsinthedeformationofthelowerleaettowardsthena noparticle.This,inturnpulls theupperleaetinthesamedirection. 0 1 2 3 4 5 -4 -3 -2 -1 0 1 2 3 4 r (nm)< h > (nm) C 60 C 60 (OH) 10 Figure3-3.Localdeformationofalipidmembranecontainin gafullereneorafullerenol: Averagedividingsurfacesofthetopandbottomleaetsofth emembrane whenthefullerene(solidline,blackcircle)isconstraine datz=-3.1nmand thefullerenol(dashedline,hollowcircle)isconstrained atz=-2.7nm;rdenotesthedistancefromthenanoparticlecenterofmass. Fig. 3-4 showsthedividingsurfacesofthebilayercorrespondingto several nanoparticlepositions.Whenthenanoparticleisawayfrom thebilayer,theaverage 43

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surfacesofbilayerareatforbothtypesoffullerenes.How ever,themembrane deformationisextremelysensitivetothenanoparticlepos itionasitapproachesthe membrane,ThiscanbeseenfurtherfromFig. 3-5 ,whichshowsthedependenceofone oftheFouriermodesintheexpansion 2–33 ofthedividingsurfaceonthenanoparticle position.TheleaetscontainingC60andC60(OH)10undergothelargeshapechangesat jzj =3.1nmand jzj =2.7nm,respectively.Thereisasteepincreaseofthemembr ane deformationatthemembraneentrypointscorrespondingtos malldiffusioncoefcientD. Thisimpliesthatasmallchangeinthenanoparticlepositio ncausessubstantialchanges inthemembraneundulations. 0 1 2 3 4 5 -4 -2 0 2 4 6 r (nm)< h > (nm) z = -4.0 nm z = -2.7 nm z = 0.0 nm Figure3-4.Averagedividingsurfacescorrespondingtothe fullerenolconstrainedatz= -4.0nm(dash–dottedline,graycircle),z=-2.7nm(dashedline,hollow circle)andz=0.0nm(solidline,blackcircle). Suchsharpchangesleadtoastrongcouplingbetweenmembran euctuationsand nanoparticlemotion[ 9 ].Thecouplingiscausedbyanattractiveinteractionbetwe enlipid tailsandhydrophobicgroupsoftheparticles.Sincethetim escaleofthedeformation ismuchlongerthanthatofthenanoparticlediffusion,thed eformationleadstoalong correlationtimeoftherandomforceactingontheparticle. Indeed,theforceauto correlationfunction(ACF)exhibitsaslowdecaywhenthena noparticleisconstrained nearthepointscorrespondingtostrongmembranedeformati onasshownFig. 3-6 Forallnanoparticlepositions,theforceACFexhibitsfast initialdecay.Forpositions 44

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-6 -4 -2 0 2 4 6 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 z (nm)Re (nm) C 60 C 60 (OH) 10 Figure3-5.DependenceoftheFouriermodewithwavenumberq=0.46nm 1of thedividingsurfaceoftheleaetcontainingthenanoparti cleonthe nanoparticlepositionz. insidethemembrane,theACFalsoexhibitsfastoscillation s.Theseoscillationsand fastdecayoccurduetointeractionsbetweenindividualato ms.Theinteractionsof theslow collective membranedegreesoffreedomwiththenanoparticlecorrespo nd totheslowdecayofACF,whichisobservedonlyforspeciclo cationsinsidethe membrane.Inordertoestimatetherateoftheslowdecay,the envelopoftheACFtoa double-exponentialfunctionistted.Theenvelopisobtai nedbytracinglocalmaxima andminimaoftheACF,asillustratedintheinsetofFig. 3-6 Dependenceoftheobtainedcorrelationtimeonthefulleren epositionisshownin Fig. 3-7 .Thecorrelationtimeoftherandomforceisfairlysmallatm ostnanoparticle locationsbutisratherlargeattheentrypointsintothebil ayer,whichcorrespondtothe sharpchangesofthemembranedeformation(seeFig. 3-7 ). C60andC60(OH)10havedifferenteffectsonthemembranedeformationasthey movefurthertowardsthemembranecenter.Thebilayerconta iningC60returnsback totheundeformedatstatewhenthenanoparticleislocated atthebilayercenter.On theotherhand,C60(OH)10increasesthemembranedeformationasitmovescloser tothemembranecenter(seeFig. 3-5 ).Thisdeformationiscausedbythehydrophilic functionalgroups,-OH,ofC60(OH)10,whichattractthebilayerheadgroups. 45

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0 50 100 150 200 10 -2 10 -1 10 0 t (ps)C( t )(b) (c) (a) 0 5 10 0 0.2 0.4 0.6 0.8 1 t (ps)C( t ) Figure3-6.EnvelopsofACFoftherandomforceactingonthef ullerenolconstrainedat (A)z=-4.0nm(dashed-dottedline),(B)z=-2.7nm(dashedli ne),and(C)z =0.0nm(solidline).InthisplotACFsarenormalizedsothat C( )=1.The insetshowsC( )(solidline)andttedenvelops(dashedline)forsmall -8 -6 -4 -2 0 0 100 200 300 400 500 z (nm)t (ps) C 60 C 60 (OH) 10 Figure3-7.Correlationtimesoftheslowestuctuationsof therandomforceactingon particles. 3.3EffectofFullerenolOrientationonMembraneDeformati on Inthissection,aneffectoforientationoffullerenolC60(OH)10onthemembrane deformationandfreeenergyproleisconsidered.Theorien tationoftheamphiphilic fullerenolisdenedasthecosineofangle betweenthez-axisandafullerenoldirector. Thelatterisavectorpointingfromthecenterofmassoftheh ydrophilicgroupstothat ofthehydrophobicgroupsasshowninFig. 3-8A .Thez-axisisorientedsothatthez coordinateoftheparticlecenterofmassispositive.Thenc os =1indicatesthatthe 46

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hydrophilicpartofC60(OH)10pointsdownwardandtheplaneseparatingthehydrophilic andhydrophobicpartisexactlyparalleltothebilayersurf ace.Inordertoobtaina relationshipbetweenC60(OH)10positionandorientationinsidebilayer,thecontribution ofoftheorientationtothefreeenergy bG ( cos; z )iscomputed. bG ( cos; z )isobtained fromMDsimulationswithconstrainedz.Thesesimulationsa llowustocomputethe probabilityP ( cos; z )ofthenanoparticleorientationwhenitisconstrainedatpo sitionz.SincethesystemobeystheBoltzmanndistribution,thefol lowingcontributionofthe nanoparticleorientationtothesystemfreeenergy bG ( cos; z )isconsidered: bG ( cos; z ) =k B TlnP ( cos; z ).(3–1) A B Figure3-8.(A)Denitionofthefullerenolorientation:an glebetweenC60(OH)10director (d )andthez-axis.Grayandwhitespheresindicatehydrophili cand hydrophobicbeadsoffullerenol,respectively.(B)Contri butionofthe fullerenolorientationtothefreeenergy(kJ/mol). Fig. 3-8B showstheobtainedtwo-dimensionalproleof bG ( cos; z ).Asexpected, theparticleorientationisuniformlydistributedawayfro mthebilayer.Astheparticle approachesthebilayer,thefunctionalgroupbecomesorien tedtowardthehydrophilic headgroupsduetoattractionbetweenthefunctionalgroups oftheparticleandthelipid head-groups.Theparticleorientationremainsinanarrowr angeasthenanoparticle 47

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entersthemembrane.Therangeoforientationsbecomeswide rnearthebilayercenter. Thistrendisexplainedbyastrongerattractionbetweenthe hydrophilicgroupsofthe particleandlipidhead-groupsattheentryregionthanatth ebilayercenter.Itwasfound thattheminimumenergypathobtainedfromthetheenergypro leissonoisythata correctpathcannotbedeterminedfollowedbythenanoparti cle.Therefore,apossible energypathisapproximated,referredtoasthedashedarrow ,followedbytheparticle whenitcrossesthebilayer.Assumethataparticlestartsto movefromapointofz=-6 nmandcos =1.Theparticlepreferstomaintainorientationofcos =1asitmoves towardsthebilayercenter,butitchangesitsorientationt ocos =-1whenitpasses throughthecenterandmaintainsthisorientationuntilitl eavesthebilayeratz=3nm.It isexpectedthatthenanoparticlewouldfollowasmoothtran sitionoforientationinreality ratherthanthesharpchangeinthedashedlineduringitstra nsprot. Thedependenceofthenanoparticlebehavioronitsposition andorientationcan bebetterunderstoodbyconsideringa3-dimensionalfreeen ergyproleschematically showninFig. 3-9 .Theschematicproleaddstheobservedorientationindica tedas cos tothefreeenergyproleshowninFig. 3-1B .Whenaparticleentersthebilayer withorientationofcos =1,itfollowsthefreeenergyproleonthefrontplane(1)at cos =1.Theparticlehasorientationofthecartoonontheplane( a)attheminimum freeenergyandmaintainstheorientationasitapproachest hebilayercenter.Asthe particlemovestowardtheothermonolayerpassingthrought hecentermarkedas(*),it experiencesanenergybarrierhigherthanisevidentfromth e1-dimensionalprolein Fig. 3-1B .Thisisexplainedbythenecessityofthechangeoforientat ion(notcaptured by1-dimensionalprole).Sincethechangeoftheparticleo rientationfromplane(1)to (2)takesplacecontinuously,theparticlefollowsthethic kerdottedlineinrealtransport ratherthanpassingthroughaunrealisticsharppointobser vedinFig. 3-1B Inwhatfollows,arelationshipbetweenthefullerenolorie ntationandtheinterface shapeisanalyzed.Tothisend,boththepositionandorienta tionofthenanoparticleare 48

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Figure3-9.Aschematicoffreeenergyproleforfullerenol anditsorientationalbehavior. Thedarkpartofasphereindicatesahydrophilicpartoffull erenol. constrained.Thedistancebetweenthecenterofmassofthef ullerenolandthebilayer inthedirectionperpendiculartothebilayersurfaceandth enanoparticleorientation isconstrained.Thelatterisconstrainedbykeepingaconst antdistancebetweenthe centerofmassofthefullerenolhydrophilicbeadsandthebi layercenter.Adetailed investigationwasperformedforthenanoparticleconstrai nedatthebilayercenter.In Fig. 3-10 theaverageheightofdividingsurfacesofthebilayerconta iningafullerenol locatedatthebilayercenterfortheconsideredorientatio ns,0and90degrees,is shown.AscanbeseenfromFig. 3-10A ,theupperlayerissignicantlydeformedwhen thefunctionalgroupoftheparticleispointingupward.The upperlayerisattracted towardthehydrophilicpartofthefullerenol.Deformation ofthislayerinturncausesthe deformationofthelowerlayer. 49

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A B Figure3-10.Averageheightofdividingsurfacesofthebila yercontainingafullerenol locatedatthecenterandorientedat(A)0degreeand(B)90de greeswith respecttoz-axis. Adifferentmembranedeformationisobservedwhencos= 0,i.e.theplane separatingthehydrophilicandhydrophobicpartofthepart icleisperpendicularto thebilayersurface.AsshowninFig. 3-10B ,thisparticleorientationleadstoan asymmetricbilayerdeformation.Whilethefunctionalgrou pattractsneighboringlipid headgroupsclosetoit,thehead-groupsofotherlipidsinth esameleaetbutonthe oppositesideofthenanoparticleareoutoftheattractionr angeofthefunctionalgroup. Theunbalancedinteractionwithlipidsoneachsidefromthe boundaryresultsinthe asymmetricdeformedmembrane. Themembranedeformationwasalsoconsideredforotherpart icleorientations, namely30,45,and60degrees.Thesedeformationsshowthetr ansitionbetweenthe membraneshapesobservedatthe0degreeto90degreenanopar ticleorientations. Astheparticleorientationincreasesfrom0to90degrees,t heasymmetrywithrespect totheplanenormaltothebilayersurfacealsoincreases,wh ereastheasymmetrywith respecttothebilayerplanedecreases.Theasymmetrywithr especttotheverticalplane tothebilayerofthedeformationiscomparedbycomputingad ifferenceoftheaverage heightofthemembranesurfaceforvariousnanoparticleori entations.betweentwo 50

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dividedregionsfromthefullerenolcenteralongxdirectio n.Thelocalaverageheights oflipidsarecomputedineachregion(region1and2)denedi nFig. 3-11A .x=0 correspondstothecenteroftheparticle.Theheightsareav eragedovertheregion1(-2 nm
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decreaseofthedistancebetweenthemleadstoadecreaseint hetotalstresswithinthe membrane.Inthecurrentsection,themembranedeformation andthecorresponding energypenaltycausedbynanoparticleslocatedattheirpre ferredpositionswithinthe membraneareassessed.Themembraneenergyisestimatedusi ngtheHamm-Kozlov (HK)model[ 10 ].TheHKmodeldescribeselasticmembranedeformationbyac counting forenergiesofbendingandlipidtailtilt.Toapplythismod el,themeandividingsurface h(x,y)andlipidtiltt(x,y)denedinchapter 2.4.1 areobtainedineachofthebilayer leaets.Thelipiddirectorisdenedasavectorpointingfr omthecenterofmassof tailstothatofheads.Thesystemofcoordinatesusedinthes ecalculationswaschosen sothat(i)theorigincoincideswiththeprojectionofthena noparticlecenterofmass ontothex-yplaneand(ii)thex-axiscoincideswithadirectorpointingfromacenterof hydrophilicgroupstothatofhydrophobicgroups. AscanbeseenfromFig. 3-12A ,thefullerenolcreatesamembraneprotrusion aroundtheparticle.Inaddition,arelativelylargedeviat ionoflipidtiltisobservedaround thehydrophilicpartoftheparticlefromitsbulk(zero)val ue,seeFig. 3-12B .Sincelipids onthehydrophilicsidearedisruptedduetothehydrophilic attraction,lipidtailsarelikely tobetiltedtoavoidarepulsionbetweenthetailsandthehyd rophilicpartoftheparticle. ParametersintheHKmodelareobtainedusingthemethodprop osedbyMayetal [ 30 ].Thebendingandtiltmoduliareestimatedfromthespectra lintensityofmembrane uctuations(seeEq. 2–31 )aleast-squarest.Thecorrespondingmembraneenergy isshowninFig. 3-13 .Theperturbationofthemembraneenergyisrelativelysmal land islocalizedaroundthenanoparticle.Therefore,interact ionsbetweenthenanoparticle andothermembraneinclusionsareratherweakandshort-ran ged.Theshort-ranged interactionisnotlikelytocauseaggregationofthenanopa rticles,whichisconsistent withresultsshowninotherMDsimulations[ 23 59 ]. 52

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A B Figure3-12.EffectoffullerenolembeddedinaDPPCmembran eon(A)upperand(B) lowermembraneleaet.SeeFig. 4-8 fordetails. Figure3-13.Energy(kJ/mol)ofmembranecontainingafulle renol. 3.5Conclusions Thecalculatedfreeenergyprolesdemonstratethattherei snosignicantenergy barriertoenterthebilayerforanyofthenanoparticlesstu died.Thissuggeststhatthese nanoparticlesmayenterthebilayerrelativelyquickly.On theotherhand,nanoparticles spendlongtimeinsidethebilayerduetoadeepenergywellin thebilayerinterior. Therefore,thehydrophobicinteriorofalipidbilayeracts asatrapforhydrophobic 53

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particles.Sincetheconsiderednanoparticleswillspenda signicantamountoftime withinthecellmembrane,theywillhavetheopportunitytoi mpactthemembraneinterior. Itwasobservedthatthereisastrongcouplingbetweentheco nsiderednanoparticle transportandthemembraneundulation.Themembranewassig nicantlyperturbed neartheentrypointsofthenanoparticleintothemembrane, whichimpliesthatthe nanoparticlesmaydamagethemembraneduringtheirpermeat ionintothemembrane. Effectsoforientationoftheamphiphilicnanoparticleont hemembraneperturbation wereexamined.Themembranedeformationwasaffectedbythe orientationofthe nanoparticleinsidethebilayerduetothehydrophilicattr actionbetweenfunctionalized groupsofthenanoparticleandlipidhead-groups.Moreover ,considerationofthe orientationallowsustobetterunderstandthetransportme chanismofthenanoparticle acrossthebilayer,sincethetransportinvolvesparticler eorientation.Aspredictedbythe orientation-dependentfreeenergyprole,thenanopartic leisexpectedtoexperience ahigherenergybarrierthanthatpredictedbythefreeenerg yproledependingon positiononly. Theamphiphilicparticleinducesasmallandlocalizedpert urbationofthe membraneenergywhenitislocatedatitsequilibriumpositi on.Thisimpliesthatthe rangeofinteractionbetweennanoparticlesisshort.Thewe akandshort-ranged interactionsbetweentheparticlesareunlikelytocausepa rticleaggregationinsidethe membrane. 54

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CHAPTER4 ASSESSMENTOFPOSSIBLENEGATIVEEFFECTSOFCNTSONLIPID MEMBRANES 4.1Introduction Asitwasdiscussedinthepreviouschapter,thesmallsizeof nanoparticles enablesthemtoeasilypenetratecellmembranes.Onceinsid eamembranethe nanoparticlesmayspendlongtimeinteractingwithitscomp onents.Anumberof experimentsdemonstratedchangesinmembranestructurein ducedbynanoparticles. E.g.,membranesofhumanepidermalkeratinocytescellshav ebeenshownto undergomorphologicalchangesuponexposuretoSWCNTs[ 47 ].Furthermore,some nanoparticleshavebeenshowntocausebreaksincellmembra nes[ 38 ].Oneofthe proposedmechanismsoftheobservedmembraneinstabilityi slipidperoxidationcaused bychemicalreactionsbetweennanoparticle-inducedROSsa ndlipids.Inaddition, recentstudieshaveshownanalternativemechanismduetoan on-reactivephysical interactionbetweennanoparticlesandmembranes.Forexam ple,positivelycharged generation7polyamidoamine(PAMAM)dendrimerswereshown tocreatenanoscale holesindimyristoylphosphatidylcholine(DMPC)bilayerd uetoaphysicalinteraction ofthenanoparticleswiththemembrane[ 31 ].Amine-terminatedgroupswereattached toPAMAMdendrimersandelectrostaticinteractionbetween thepositivechargeson thedendrimersurfaceandlipidscausedformationofthehol es.Ontheotherhand, electricallyneutralgeneration5PAMAMdendrimersdidnot createanyholes[ 13 ], therebyindicatingthatmodicationofananoparticlesurf aceplaysanimportantrole intheinteractionbetweennanoparticlesandcells.Moreov er,studyofpolycationic nanoparticlesdemonstratedthatbothnanoparticlesizean dchargecontributedtothe degreeofdisruption[ 22 ]. MDsimulationshaveshownthatcarbon-basednanoparticles ,suchasfullerenes andsomeoffullerenederivativesexperiencearelativelys mallenergybarriertoenter thelipidbilayerandtheirenergydecreasessignicantlyo ncetheyareinsidethebilayer 55

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[ 5 41 59 ].Thisimpliesthatthesenanoparticleswilleasilypermea teintothemembrane interiorandwillresideinsidethemembraneforalongtime. Duringtheirresidence, nanoparticlesmaysignicantlyperturbthemembraneandev endisruptthemembrane integrity.Possiblesourcesofinstabilityincludelipidmediatednanoparticleaggregation, changesofthemembraneelasticproperties,andformationo fnon-bilayerphases RecentMDinvestigations[ 59 ]ofthechangesofmembranepropertiesdueto embeddednanoparticles(fullerenes)reportthatthemembr anelipidsstretchinthe neighborhoodofthenanoparticle,whichleadstothedecrea seofthemembranearea perlipid.Moreover,itwasalsoobservedthatthefullerene saffectelasticpropertiesof themembrane.However,thelatterchangesareobservedonly atveryhighfullerene concentrations. Inthischapterthephyscialmechanismsofnanoparticletox icityarefocusedon,i.e. itisassumedthatnoreactiontakesplaceandthedamagetoth emembraneiscaused bysucheffectsaschangesofmembraneelasticproperites.C hangesinmembrane elasticpropertiescanoccurfromchangesinmembranecompo sitionandforcesacting onthemembrane.Stabilityofcellmembraneismaintainedth roughabalanceofforces actingontheinterfacialregionandhydrophobiccore.Nano particlesembeddedinto membranemaycausevariationinmembranecompositionprol e,leadingtomembrane instability.Moreover,interactionbetweenembeddednano particlesandmembranemay affecttheforcesactingonthemembraneandresultinmembra nedeformation. Inadditiontothemembranedeformation,nanoparticlesmay affectfunctionalityof membraneproteins.Animportantclassofmembraneproteins isionchannelswhich regulatetheowofionsacrossthemembraneinresponsetova riousstimuli.The stimuliincludeelectricalsignalsforvoltage-gatedionc hannelsorchemicalsinexternal environmentforligand-gatedionchannels.Thechannelsta te(openorclosed)also dependsonlateralpressureprole.Variationofthepressu redistributionwithinthe membranemayshiftequilibriumbalancebetweenopenandclo sedstates(Fig. 4-1 ). 56

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Nanoparticlesembeddedintothemembranemayaffectthepre ssureproleand,hence, theionchannelfunctionality. A B Figure4-1.Lateralpressurewithinmembraneandcorrespon dingdifferent conformationalstatesofahypotheticalmembraneprotein[ 6 ].Arrows representthedirectionandmagnitudeoflateralpressure. Evenifindividualnanoparticlesintroducearelativelywe akperturbationtothe membrane,itispossiblethataggregatesofthesenanoparti cleswillsignicantlydisrupt themembrane.Inordertoassessthispossibility,thetende ncyofCNTstoaggregate insidethemembrane isestimated.Thisaggregationcanbefacilitatedbyalongrange attractionbetweennanoparticlesembeddedintothemembra ne.Intheabsenceof long-rangeelectrostaticinteractionsbetweenthenanopa rticles(whichisthecasein thecurrentwork),thedominantcontributiontolong-range interactionsbetweenthe nanoparticlesisexpectedtobemediatedbythemembrane.Sp ecically,embedding aCNTintoamembranecreatesaperturbationofthemembranee lasticenergyin someneighborhoodofthenanoparticle.Thisperturbationw illbemodiedifanother nanoparticleisembeddednearby.Themembrane-mediatedna noparticle-nanoparticle interactionwillbeattractiveifdecreasingthedistanceb etweenthenanoparticles reducestheelasticenergyofthemembrane. Inthischapter,effectsofnanoparticlesonelasticproper tiesofthemembrane, namely,bending,tilt,andstretchingmoduli,andonthelat eralpressureproleare investigatedinordertoconsiderbothdirectandindirecte ffectsofnanoparticleson 57

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themembranefunction.SWCNTsarefocusedon,andthreediff erentlengthsofthe SWCNTsareusedtoassesstheeffectofnanoparticlesizeont heelasticproperties. 4.2ModelandSimulationDetails CNTarehydrophobicand,therefore,experienceastrongdri vingforcetoward thehydrocarbon-lledbilayercenter.Moreover,theenerg ybarrierforentryofthese nanoparticlesintothemembraneisverysmall.Thispropert yisusedtoprepare equilibriumbilayerscontainingCNT.Specically,nanotu beswereplacedintoabilayer insize9.169.1611.09nm3bypushingthemwithaconstantaccelerationof1m/s2towardthebilayerinthedirectionperpendiculartothebil ayersurface.Thenanotubes werereleasedbeforetheytouchedheadgroupsofthebilayer lipidstopreventbilayer disruptionduetothepushingforce.Nanotubewasreleasedw henthedistancebetween thenanotubeendandthehead-groupwascloseto0.25nm.Ther eleasednanotube enteredthebilayerwithinafewnanoseconds.Thebilayerco ntainingthecarbon nanotubeisshowninFig. 4-2 .InordertoperformthisprocedurefornanotubesCNT4andCNT6,itwasnecessarytoincreasetheboxheightto16and21nm,re spectively, toaccomodatethesenanotubeswhentheyareperpendiculart othebilayer.Thiswas accomplishedbyaddingwatermoleculestothesimulationbo x. Figure4-2.MolecularmodelofaDPPClipidbilayercontaini ngacarbonnanotube. 58

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The99nm2bilayersystemsdescribedwillbereferredtointhesection 2.2 asthe smallsystems .Thesimulationsofthesesystemswereusedtoassesslocalp erfurbation ofthebilayerstructure,stress,andenergyaroundtheembe ddednanotube.However, inordertoassesselasticpropertiesofthemembrane,itisn ecessarytoconsider membraneundulationsofsufcientlylargewavelength.Tot hisend,simulationsoflarger272721nm3systemswereperformed.Thesesystemswillbereferredtoas the large systems. Thesesystemswereobtainedbycopyinglaterallythesmalls ystemsand,if necessary,addingwatermoleculestoensurethattheheight allofthelargesystemsis thesame,21nm. InordertoinvestigateeffectsoftheCNTconcentrationont hemembrane properties,bilayerscontainingtwoorveCNT6arealsoconsidered.Thesesystems wereobtrainedbyremovingsevenorfournanotubes,respect ively,fromalargesystem containingnineCNT6. Inordertoinvestigateinuenceofembeddednanotubesonth ecriticaltension r necessarytorupturethemembrane,aseriesofsimulationso fapuremembraneis performedinNPNr Tensembles.ANPNr TensemblecorrespondstoconstantN,PN, r andT,whereNisanumberofmolecules,PNthethepressureinthedirectionnormalto themembranesurface, r isthetensioninthedirectionparalleltothemembranesurf ace, andTisthetemperature.TheBerendsenbarostatandtheNos e-Hooverthermostat wereemployed.ThevalueofthenormalpressureP Nwasmaintainedat1barandthe valueofthelateraltension r wasmaintainedataxedvaluebetweenof60mN/mand70mN/m.Thesesimulationswereperformedforthesmallsystem s.Initialconditionsfor thesimulationswiththeappliedtensionwasanequilibrate dtensionlessmembrane.The simulationswiththetensionwereperformedfor100nsunles sthemembraneruptured withinashorterperiodoftime. 59

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4.3SystemStructure Sincethenanotubesarehydrophobic,theirpreferredlocat ionisnearthebilayer center.Thebilayerdensityminimumatz = 0providesanadditionaldrivingforce forCNTtowardsthebilayercenter.Thisisconrmedbytheco mputedprobability distributionsofthedistancezbetweenthenanotubeandthebilayercentersofmass andthenanotubeorientationcos withrespecttothez-axisshowninFig. 4-3 .Ascan beseen,themostlikelypositionoftheCNTcentersofmassis atorveryclosetothe bilayercenter.Moreover,themostlikelynanotubeorienta tionsarealmostparalleltothe bilayersurface. Surprisingly,themostlikelyCNTorientationsarenotexac tlyparalleltothebilayer plane,whichwouldminimizethesystementhalpy.Thedeviat ionfromtheparallel locationcanbeexplainedbytheentropiccontributionstot hefreeenergyofthesystem. Asthenanotubelengthdecreases,theenthalpygainedbyCNT alignmentwiththez = 0planealsodecreases,whiletheentropiccontributiontoth efreeenergyremainsroughly thesame.Therefore,themostlikelyorientationofCNTbeco meslessalignedwiththe bilayerplaneandtheuctuationsofCNTorientationbecome largerasthenanotubes becomeshorter. Theboxsizes,L x,L z,andaverageareaperlipid,a 0,aresummarizedinTable 4-1 Ascanbeseen,additionofthenanotubetothesystemincreas estheareaperlipidand thisincreasebecomeslargerforlongernanotubesandhighe rnanotubeconcentration. Itisinterestingtocomparetheareaperlipidinthesystems ofdifferentsizescontaining thesamenanotubesatthesameconcentration.Thevaluesofa 0arealmostthesame inthesmallandlargesystemsunderthesameconditions.How ever,thelargersystem typicallyhasaslightlysmallervalueofa 0,whichcanbeexplainedbylargermagnitude ofthebilayerundulationsinlargersystems.Themagnitude ofthebilayerundulations increaseswiththewavelength(seeSection 4.4 ).Therefore,thearea(perlipid)of 60

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0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 z (nm)P CNT 3 CNT 4 CNT 6 A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 1 2 3 4 5 6 7 8 9 cosP B Figure4-3.Probabilitydistributionsof(A)distancezbetweenthebilayerandCNT centersofmassand(B)orientationcos ofCNTwithrespecttothez-axis. thebilayerprojectionbecomesslightlysmallerinlargers ystems.Theonlyobserved exceptionisthebilayercontainingCNT6. Table4-1.Boxsizesofequilibratedsystems.N CNTdenotesthenumberofCNTinthe system,L x = L yisthelengthoftheboxsideparalleltothebilayer,L zisthe boxheight,anda 0istheareaperlipid.Statisticalerrorsoftheseaveragesa re negligiblysmall,O (105 )nmforL xandO (103 )nmforL z. CNTN CNT L x(nm)L z(nm)a 0(nm2) –09.1611.090.636 CNT319.2510.860.648 CNT419.2916.430.654 CNT619.3420.690.661 –027.4521.600.634 CNT3927.7221.160.647 CNT4927.8420.980.652 CNT6227.6221.330.642 CNT6527.8720.940.654 CNT6928.0820.610.664 Theobservedincreaseofa 0withadditionofnanoparticlesisqualitativelydifferent fromobservationsofRef.[ 59 ].Thelatterstudyshowedthatadditionoffullerenestoa lipidbilayerdecreasestheareaperlipid. 61

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4.4ElasticPropertiesofMembrane Thespectralintensitiesofthemembraneundulationsandli pidtiltuctuations obtainedforapureDPPCmembraneandDPPCmembranescontain ingCNTofvarious lengthareshowninFigure 4-4 .Overall,theobtainedresultsareingoodagreement withthetheoreticalpredictionEqs.( 2–31 ),( 2–32 ).However,thefollowingqualitative differencesareobserved: 1. Themagnitudeoftiltuctuations, hj^ t ( q )j2i ,exhibitsaweakdependenceonthe wavenumberq,whereasEq.( 2–32 )predictsthat hj^ t ( q )j2i isindependentofq. 2. Themagnitudeoftheshort-wavelengthuctuationsofthebe ndingmodesscales decaysslowerasq!1 thanpredictedbythemodel.Specically,aleast-squares tof hj^ h ( q )j2i forsufcientlylargeqtoapowerlawq resultsin <2,whereas themodelpredictsthat = 2. 0.2 0.4 0.6 0.8 1 10 -1 10 0 10 1 q (nm -1 )hj ^ h ( q ) j 2 i Pure DPPC DPPC+CNT 3 DPPC+CNT 4 DPPC+CNT 6 10 0 10 -2 10 -1 10 0 10 1 q (nm -1 )hj ^ h ( q ) j 2 i A 0 0.5 1 1.5 2 2.5 3 3.5 4 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 q (nm -1 )hj ^ t ( q ) j 2 i B Figure4-4.Spectralintensityofuctuationof(A)membran eundulationsand(B)lipidtilt inpureDPPCmembrane,aswellasDPPCmembranescontainingC NTof variouslength(seelegend)atconcentration 0.01CNT/nm2(i.e.nineCNT perlargesimulationbox).In(A),themainplotshowsdetail forthelong wavelengthlimitandtheinsetshowsthespectralintensity forallconsidered wavenumbers.ResultsobtainedusingFouriersumsoftwodif ferentlengths (withveandelevenharmonics)areshown.Thedashedliness howresults ofthettotheHKmodelwiththecut-offwavenumberq max = 1.6nm 1. Thereisasystematicdependenceofthespectralintensity hj^ h ( q )j2i ofthebending modesonthelengthandconcentrationofnanotubescontaine dinthemembrane. 62

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Sincethisdependenceisrelativelyweak,itisnecessaryto obtainaccurateestimates ofstatisticalerrorsincomputed hj^ h ( q )j2i toruleoutthepossibilitythattheobserved differencescanbeattributedtostatisticaluncertaintie s.Sincethemembrane uctuationsareslowincomparisonwiththesamplingfreque ncyofthisMDsimulations, theinstantaneousnormalmodesusedintheaveragingarecor relatedintime.The autocorrelationfunctionsofthenormalmodesdecayexpone ntiallywhichindicatesthat evolutionofeachofthemodescanbedescribedbyarstorder stochasticdifferential equation.TheMaximumLikelihood(ML)method[ 46 ]isused,toobtaintheparameters ofthisequationand,inparticular,themagnitudeofthemem braneuctuationsandthe errorestimatesofthismagnitude.ThedetailsoftheMLmeth odappliedtothecurrent systemarediscussedinSection 2.4.2 TheobtainederrorestimatesareshowninFig. 4-4 byerrorbars.Thestatistical errorsareverysmallandsomeoftheerrorbarsaresmallerth anthesymbolsusedto plotthedata.Therefore,theobserveddifferencesinthema gnitudeofthemembrane uctuationsaresignicantlylargerthanthestatisticale rrors. Anotherpossiblesourceoftheobserveddifferencesinthe uctuationmagnitudes issensitivityofthecomputedFouriercoefcientstothenu mberofharmonicsNused intheFouriersum.Sincethesecoefcientsareobtainedusi ngleast-squareststo MDdata,thevaluesof^ h ( q )and^ t ( q )leadingtothebesttmaybedifferentfordifferent numberoftermsincludedintothesums( 2–33 ). ToassesspossibleeffectofNontheFouriermodes,Fouriercoefcients correspondingtoNrangingfrom5to11wereobtained.Itisobservedthat instantaneousvaluesoftheFouriermodes^ h ( q ; t )and^ t ( q ; t )arerelativelyinsensitive toN.TheeffectofNontheaveragespectralintensities hj^ h ( q )j2i and hj^ t ( q )j2i canbe gaugedfromFig. 4-4 .Inthisgure,thespectralintensitiescorrespondingtoN = 5andN = 11areplotted.Thedifferencebetweenthe bending modesobtainedwithdifferentNisinvisibleintheplot,whichimpliesthattheobserveddep endenceofthespectral 63

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intensities hj^ h ( q )j2i onthelengthandconcentrationofCNTembeddedinthebilaye r cannotbeattributedtothedetailsofthisnumericalproced ure. Ontheotherhand,thedifferencebetweenthe tilt modesofthesamesystembut computedwithdifferentNislargerthanthedifferencebetweenthesemodescomputed fordifferentsystemsbutwiththesameN.Therefore,withintheresolutionofthecurrent model,themagnitudeofthetiltuctuationsappearstobein sensitivetothepresenceof CNT. Asitwasdiscussedearlier,thereisasystematicdeviation oftheobservedMDdata fromtheHKmodelpredictionsforshort-wavelengthbending modes, hj^ h ( q )j2i/q <2asq!1 .Thisimpliesthatthebendingandtiltmoduliobtainedbyt tingtheMD datatoEq.( 2–31 )aresensitivetotheupperlimitq maxofthewavenumbersoverwhich thettingisperformed.ThisisevidentfromFig. 4-5 whichshowsthedependenceof and tonq max.Clearly,dependenceoftheelasticmodulionq maxismuchstrongerthan theirdependenceonthepresenceandlengthofCNT. However,itisobservesthatforthesamevalueofq max,thebendingmoduli ( q max )increasewithCNTlength.Moreover, ( q max )appearstohaveanasymptoteasq max!0andthereforethelimitof ( q max )inasufcientlylargesystemiswelldened. ThevalidityofHKmodelcanbealsoassessedbycomputing tusingthe magnitudeofthetiltuctuations,seeEq. 2–32 .Asitwasdiscussedearlier,thevalues of hj^ t ( q )j2i obtainedfromMDsimulationsshowasystematicdependenceo nq,whereas HKmodelpredictsthatthemagnitudeoftiltuctuationsisi ndependentofq.Sincethe dependenceof hj^ t ( q )j2i onqisrelativelymild(seeFig. 4-4 ),itiscomputed tusingthe magnitudeof hj^ t ( q )j2i averagedovertheentirerangeofwavenumbersqq max. AsFig. 4-5 shows,thevaluesof tobtainedusingthismethodaresomewhatlarger thanthoseobtainedfromthebendingmodes.Thisimpliestha tthemagnitudeofthetilt uctuationsinferredfromthebendingmodesislargerthan hj^ t ( q )j2i measureddirectly. Thiscanbeexplainedbyadditionalcontributionsofthepro trusiontension[ 30 ]tothe 64

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1.5 2 2.5 3 3.5 1 2 3 4 5 6 7 x 10 -19 q max (nm -1 ) (J) Pure DPPC DPPC+CNT 3 DPPC+CNT 4 DPPC+CNT 6 A 1.5 2 2.5 3 3.5 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 q max (nm -1 ) t (N/m) B Figure4-5.DependenceoftheHKmodelparameters(A) and(B) tontheupper cut-offwavelengthq max.Thesolidlinesandlledsymbolsshowthemoduli obtainedfromthebendingmodes,seeEq.( 2–31 )andthedashedlinesand unlledsymbolsshowthetiltmoduliestimatedfromthetilt modes,seeEq. ( 2–32 ). bendingmodesatshortwavelength.Sincetheprotrusionten sionisassociatedwiththe motionofthelipidmoleculesinthedirectionnormaltotheb ilayersurface,thismotion doesnotcontributetothetiltuctuations.Itisalsonoted that t ( q max )obtainedfromthe tiltmodesapproachesanasymptoteasq max!0,whereas t ( q max )obtainedfromthe bendingmodesdoesnotappeartoapproachalimit. 4.5EffectofCNTonPressureDistributioninsideMembranes Inadditiontochangesinthemembraneelasticity,nanopart iclesembeddedin amembranemayaffectthemembranefunctionbychangingacti vityofmembrane proteins.Thiscanbeachieved,e.g.,bymodicationofthel ateralpressureinsidethe membrane,sincesomemembraneproteins,suchasionchannel s,aresensitiveto changesinthispressure.[ 4 29 52 ].Therefore,nanoparticle-inducedchangesinthe lateralpressuremayshifttheequilibriumbalancebetween openandclosedstatesofthe channels. 65

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Pressuretensorisanisotropicinsidethemembrane.Normal componentofthe pressuretensor,P?= P zz,isposition-independentandcoincideswiththepressure inbulkwatertoensuremechanicalstabilityofthemembrane .However,thelateral componentofthepressuretensor,Pjj= ( P xx + P yy )=2,undergoessignicantvariations insidethemembrane.Thiscanbeseenfromtheprolesofthel ateralpressurealong thedirectionnormaltothebilayershowninFig. 4-6 .Pjj isnegativeattheinterface betweenthehydrophilicheadgroupsandhydrophobictailgr oups(z1.8nm)dueto interfacialtensionbetweenthehead-andtail-groups.Pjj ispositiveinthehydrophobic coreandthehead-groupregionofthemembrane.Thepositive pressureiscausedby excludedvolumerepulsionand,inthehead-groupregion,by electrostaticinteractions. Thebalancebetweenthetensionandrepulsionmaintainszer onetsurfacetensionof themembrane. -4 -2 0 2 4 -500 -400 -300 -200 -100 0 100 200 300 z (nm)P (bar) Pure DPPC DPPC + CNT 3 DPPC + CNT 4 DPPC + CNT 6 Figure4-6.DistributionsoflateralpressurePjj indirectionnormaltothebilayersurface. PressureprolesinsideapureDPPCbilayerandinsidebilay erscontaining CNTofvariouslengthsareshown. Theobtainedlateralpressureproleforthepurebilayeris verysimilartothat obtainedbyMarrink etal [ 28 ]usingthesamecoarsegrainedmodelasinthis simulations.However,therearesomedifferencesbetweent heseresultsandRef.[ 28 ]. Specically,themagnitudeoftheminimumpressureatthehe ad-tailinterfacecomputed 66

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inthecurrentworkisapproximately120barlargerthanthat computedinRef.[ 28 ]. Inaddition,thepressuremaximuminthebilayercentercomp utedinthisworkis approximately40barsmaller.Thesediscrepanciesareattr ibutedtothedifference inmethodsofcalculationofthestressprole.Marrink etal. haveusedthemethod describedinRef.[ 24 ].Inthismethod,theassignmentoftheweightfunctionfforaslab containingoneoftheend-pointsoftheIKcontourisperform edlessaccuratelythan inthecurrentwork.Specically,in[ 24 ]locationofthebeadcontainedintheslabis approximatedaslocatedexactlyhalfwaybetweentheslabbo undaries.Inthecurrent work,precisebeadlocationsinthecalculationoftheweigh tfunctionareused.Although thedifferenceofmethodsisrelativelysmall,thegradient ofthestressproleisvery largearoundthestressextrema.Therefore,itispossiblet hatthisdifferenceaccountsfor thequantitativediscrepancybetweenthisresultandthato fRef.[ 28 ]. AdditionofCNTtothemembranedoesnotchangethequalitati veshapeofthe pressureprolebutdoesleadtoquantitativechangesinthe lateralpressureprole, ascanbeseenfromFig. 4-6 .Pressurebecomeslargerinthebilayercenterdueto excluded-volumeinteractionsbetweenthelipidtail-grou psandCNT.IncreasingtheCNT lengthleadstoanincreaseddeviationofthepressureprol efromthatinaCNT-free membrane.However,thedistributionofthelateralpressur einthemembraneplane showninFig. 4-7 demonstratesthatthechangesinthelateralpressurearelo calized totheimmediateneighborhoodoftheembeddedCNT.Therefor e,thesenanotubesare unlikelytohavesignicantimpactonthemembraneproteinf unction. 4.6MembraneEnergyaroundNanoparticles Whenthenanoparticleislocalizedatitsfavorablepositio ninsidethemembrane, themembraneremainsdeformed.Mechanicalstresscreatedb ythesemembrane deformationsisdirectlyresponsibleformembrane-mediat edinteractionsbetweenthe membraneinclusions(suchasnanoparticlesandproteins). Forexample,twomembrane 67

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-4 -2 0 2 4 -4 -3 -2 -1 0 1 2 3 4 x (nm)y (nm) 100 150 200 250 300 A -4 -2 0 2 4 -4 -3 -2 -1 0 1 2 3 4 x (nm)y (nm) 200 220 240 260 280 300 320 B -4 -2 0 2 4 -4 -3 -2 -1 0 1 2 3 4 x (nm)y (nm) 200 220 240 260 280 300 320 340 360 C Figure4-7.DistributionsoflateralpressurePjj (inbar)inthebilayerplaneforbilayers containing(A)CNT3,(B)CNT4,and(C)CNT6nanotubes.Theoriginofthe systemofcoordinatescoincideswiththelocationoftheCNT centerofmass andthex-axisisalignedalongthenanotube. inclusionswouldbeattractedtoeachotherifdecreaseofth edistancebetweenthem leadstoadecreaseinthetotalstresswithinthemembrane. Inthecurrentsection,themembranedeformationandthecor respondingenergy penaltycausedbynanoparticleslocatedattheirpreferred positionswithinthe membraneareassessed.Themembraneenergyisestimatedusi ngtheHamm-Kozlov model( 2–30 ).Toapplythismodel,themeandividingsurfaceh ( x y )andlipidtiltt ( x y ) 68

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foreachofthebilayerleaetsareobtained.Resultsofthes ecalculationforbilayers containingvariousnanotubesareshowninFig. 4-8 4-9 ,and 4-10 .Thesystemof coordinatesusedinthesecalculationswaschosensothat(i )theorigincoincideswith theprojectionoftheCNTcenterofmassonthexyplane;(ii)theCNTcenterof massislocatedintheupperhalf-space,(iii)thex-axiscoincideswiththeCNTaxisof symmetry,and(iv)CNTpointsupwardinthepositivedirecti onofthex-axis.Ascanbe seenfromFig. 4-8 4-9 4-10 ,nanotubescreatesamembraneprotrusionaroundthe CNTendpointingtowardsthedividingsurface.Inaddition, arelativelysmalldeviationof lipidtiltfromitsbulk(zero)valueisobserved.Thelarges tmagnitudesofthetiltvectors are ForCNT3:0.26(upperleaet)and0.17(lowerleaet), ForCNT4:0.19(upperleaet)and0.15(lowerleaet), ForCNT6:0.20(upperleaet)and0.16(lowerleaet), Sincetheperturbationstoboththemembraneshapeandlipid tiltarelocalizedto theimmediateneighborhoodofthenanotubes,theperturbat ionoftheelasticenergy ofthemembranewillalsobelocalized.Thisresultisconsis tentwiththelocalized perturbationtothelateralpressurediscussedintheprevi oussection.Therefore, interactionsbetweenCNTandothermembraneinclusionsare expectedtoberather weakandshort-ranged. 4.7Conclusions Thefollowingeffectsofnanoparticlesonthemembraneswer eobserved: Carbonnanotubesembeddedinlipidmembranesleadtothemem branesoftening, whichbecomesmoresignicantwithincreaseoftheCNTlengt handconcentration. Inclusionofcarbonnanotubesintoamembraneleadstopertu rbationofthelateral pressureprolewithinthemembrane.However,thisperturb ationislocalizedandis unlikelytoaffectfunctionofmembraneproteins. 69

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A B Figure4-8.EffectofCNT3embeddedinaDPPCmembraneon(A)upperand(B)lower membraneleaet.Theheightofthedividingsurfaceisshown bythecolor plot(innm);thelipidtiltareshownbythearrows.Thearrow sarescaledto haveconsistentscalingbetweeneachother;otherwisethel engthofthe arrowsintheplotisarbitrary. Carbonnanotubeslocatedattheirequilibriumpositionsin sidealipidmembrane introducerelativelysmallandlocalizedperturbationsto themembraneenergy.This impliesthatinteractionsbetweenthesenanoparticlesand othermembraneinclusions (suchasmembraneproteins)arerelativelyweakwhenthenan oparticlesarelocatedat theirequilibriumpositions.Theinteractionsofthenanop articleareoutofreachtoother nanoparticles,whichisconsistentwithothersimulations showingthatfullerenesdonot formstableaggregatesinsidethebilayer[ 59 ]. 70

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A B Figure4-9.EffectofCNT4embeddedinaDPPCmembraneon(A)upperand(B)lower membraneleaet.SeeFig. 4-8 fordetails. A B Figure4-10.EffectofCNT6embeddedinaDPPCmembraneon(A)upperand(B) lowermembraneleaet.SeeFig. 4-8 fordetails. 71

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CHAPTER5 LIPIDPEROXIDATION 5.1Introduction Inbiologicalcells,oxidativestressoccursduetoanimbal ancebetweenreactive oxygenspecies(ROS)producedbynormalaerobicmetabolism andtheabilityofcellsto recoverfromtheresultingdamage.TheproducedROSmaydama gesuchbiomolecules asnucleicacids,proteins,andlipids[ 37 ].Inparticular,thelipidperoxidationisthe processoftheoxidativedegradationoflipidsandoccurswh enfreeROSradicals takeelectronsfromthelipidsincellmembranes.Oneofthem echanismsofthelipid peroxidationinwhichlipidmoleculesareattackedbyfreer adicalswasproposedby Wang etal .[ 57 ].LH +_ OH!_ L + H 2 O (5–1) L + O 2!LOO (5–2) L OO + LH!_ L + LOOH (5–3) Here,LHdenoteslipidwithhydrocarbonchain(-CH2)andhydrogen(H)andLOOHdenotesalipidperoxide.Ifthelipidperoxidationreactio nisnotterminatedfastenough, thecellmembranewillbedamaged[ 18 ]. Severalgroupshavearguedthatthenanoparticletoxicityc anbeattributedtothe oxidativestressandthelipidperoxidation.E.g.thepione eringworkofOberd ¨ rster reportedtheoxidativestressandlipidperoxidationinthe brainofalargemouth bassfollowingexposuretofullerenes[ 36 ].Inaddition,Sayes etal .[ 43 ]observedthe disruptionofcellmembraneexposedtoC60.ItwasshownthatC60inducesproduction ofthesuperoxideanion(O_2)incell-freeaqueoussolutions.Thesuperoxideanionscan generateahydroxylradical(_ OH)asaproductofthereactionbetweenthesuperoxide anionsandhydrogenperoxide(H2O2)asfollows:O _2 + H 2 O 2!_ OH + OH+ O 2 .(5–4) 72

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Theproducedhydroxylradicalacceleratestheproductiono fperoxidizedlipidsas showninthereactions( 5–1 ),( 5–2 ),and( 5–3 ).Althoughthefullerenesdonot directlyparticipateintheshownlipidperoxidationreact ions,itwasdemonstrated experimentallythattheyincreaseconcentrationofROSinw aterandinducedisruption ofcellmembranes.CNTsmayalsobeabletoinducethelipidpe roxidation.Electron spinresonanceofSWCNT-stimulatedhumanepidermalkerati nocytescellsprovides evidenceofaccumulationofperoxidationproductsandadec reaseofintracellular levelsofglutathione,amajornaturalantioxidant[ 47 ].Transmissionelectronmicroscopy imagesofthecellmembranesexposedtoSWCNTshowmorpholog icalchanges. Incontrastwiththelargenumberofexperimentalstudiesof peroxidation oflipidmembranes,thereiscurrentlyaverylimitednumber ofcomputational studiesofthisphenomenon.TherstMDstudyofeffectoflip idoxidationonthe structuralproperitiesofmodelmembraneswasperformedby Wong-Ekkabut etal.[ 60 ].Theauthorsinvestigatedeffectoffourdifferentproduc tsof 1-palmitoyl-2-linoleoyl-sn-glyceero-3-phosphatidylc holine(PLPC)peroxidationonPLPC bilayersatveconcentrations,rangingfrom2.8%to50%usi nganatomisticmodel.Itis observedthatoxidizedfunctionalgroupsinthelipidtails causethetailstobendtoward theaqueousphaseandformhydrogenbondswithwaterandthel ipidheadgroups.This internalstructuralchangeofthebilayerresultsintheinc reaseoftheaverageareaper lipidandthedecreaseofthebilayerthicknessinagreement withexperimentalresults [ 40 49 ].Moreover,thetendencyoftheoxidizedlipidtailstobend towardthewater phaseincreasesthemembranepermeabilitybywater.Thestu dyshowsnotonlythe signicantchangesinthestructureofmembranebutalsothe possibilityofmembrane ruptureindicatedbyformationofwaterpores. Possibleimpactsofoxidizedlipidsonmembrane-associate dbiologicalprocesshave beenexaminedbyMDsimulationsofKhandeliaandMouritsen[ 19 ].Theyevaluated structuralchangesinthepalmitoyloleoylphosphatidylch oline(POPC)lipidbilayerdueto 73

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thepresenceoftwotypesofoxidizedlipids,zwittterionic PoxnoPCandanionicPazePC. Itwasobservedthattheanionicfunctionalgroupspreferto resideintheaqueousphase andtheirnegativechargewouldattractpositivelycharged peptides,ions,drugs,and hormones. Whilecomputationalstudiesofthelipidperoxidationhave focusedonchangesof structureofoxidizedmembranes,tothebestoftheknowledg e,effectsofthepresence ofnanoparticlesontheperoxidizedmembraneshaveneverbe eninvestigatedusing computationalmethods.Inthecurrentstudy,membraneinst abilityduetoacombination oflipidperoxidationandananoparticlepresentinthememb raneisinvestigated. 5.2ModelandSimulationDetails TheperoxidizedlipidLOOHinreaction( 5–3 )ismodeledbyreplacingthe hydrophobicbeadattheendofoneofthelipidtailsbyahydro philicbeadwithpolarity lowerthanthatofwater.Thehydrophilicperoxidizedbeadh asastrongpolarinteraction withthenegativelychargedbead( =5.0kJ/mol)andlesspolarinteractionwiththe positivelychargedbead( =4.0kJ/mol)andglycerolsandwater(4.5kJ/mol).Ithasa hydrophobicrepulsionwithcarbonbeadsintails( =2.7kJ/mol).Thebondandangle potentialsfortheperoxidizedlipidarethesameasthosefo rDPPClipids. Reaction( 5–3 )suggeststhatbothofthelipidtailsareequallylikelyto randomlyreplacetheirendbeadbyahydroperoxidegroup(-O OH).Therefore,the systemispreparedasfollows.Randomlipidmoleculesinthe pureDPPCbilayer (9.169.1611.09nm3)arereplacedbytheperoxidizedlipidsatthreeconcentrat ions (25%,50%,and75%),keepingthenumberoftheperoxidizedli pidsequalinboth lipidmonolayers.Theneachsystemiscopiedlaterallytocr eateanewbilayersystem of30 30 20nm3.Theobtainedsystemsareequilibratedfor50nsthensimula ted for800ns.Inwhatfollows,theseperoxidizedbilayerscont aining25%,50%,and 75%peroxidizedlipidsaredenotedasDPPC-25%,DPPC-50%,a ndDPPC-75%, respectively.Inaddition,simulationofperoxidizedbila yerscontainigafullerenolis 74

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performedinordertoinvestigateifthenanoparticleprese ncechangesthestabilityof theperoxidizedmembrane.ApureDPPCbilayercontainingaf ullerenolinasimulation boxof15 15 15nm3(592DPPCmoleculesand19896waterbeads)isprepared. Thenrandomlipidmoleculesarereplacedbytheperoxidized lipidsinthepurebilayer containingtheparticle.Thesystemswasequilibratedfor1 00nsfollowedbyaproduction runfor200ns. 5.3EffectofLipidPeroxidationonMembraneProperties Structuralchangesareobservedinbilayerscontainingper oxidizedlipids. Snapshotsofthebilayerscontainingperoxidizedandnon-p eroxidizedlipidsat equilibriumareshowninFig. 5-1 .Theperoxidizedbilayersundergouctuationsof highermagnitudeincomparisonwiththepurebilayer.Thedi fferencebetweenthe uctuationsintheperoxidizedbilayersandpurebilayersi ncreasesastheconcentration ofperoxidizedlipidsincreases.Inaddition,thebilayerw iththelargestconcentration ofperoxidizedlipids(DPPC-75%)undergoeslocalperturba tionofitssurface.The dependenceofthespectralintensityofthebilayerbending modesonthewavevector qisshowninFig. 5-2 .Thisplotconrmsthattheuctuationmagnitudeincreases as theconcentrationofperoxidizedlipidsincreases.Thisre ferslipidperoxidationleadsto moreexiblemembranes.Moreover,thedependenceoftheuc tuationmagnitudeon thewavenumberinthebilayerscontaininghighconcentrati onofperoxidizedlipidsis qualitativelydifferentfromthatofthepurebilayer.Theq -dependenceoftheuctuations oftheperoxidizedbilayersexhibitsasharptransitionbet weenthelongandshort wavelengthmodeswhereasthatofthepurebilayershowsasmo othtransitionbetween themodesofallwavelengths.Thetransitionisalsosmoothi nthebilayerwiththelowest consideredconcentrationofperoxidizedlipids(DPPC-25% ).Inordertoexaminethe structuralchangesindetail,anumberofpropertiesofaDPP Cbilayerisinvestigated. Thedensityprolesofthepureandperoxidizedbilayersare showninFig. 3-1A .As showninFig. 5-3A and 5-3B ,densitiesofthehead-andtail-groupsintheperoxidized 75

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A B C D Figure5-1.SimulationsnapshotsofDPPCbilayersat800ns( A)0%(pureDPPClipid bilayer),(B)DPPC-25%,and(C)DPPC-50%,and(D)DPPC-75%. bilayershavebroaderdistributionsthanthoseinthepureb ilayer.Afractionofthehead groupsinperoxidizedbilayersislocatedatthebilayercen ter,andsometailgroupsin thesebilayersarelocatedinthewaterphase.Theperoxidiz edbeadsareattractedto head-groupsoflipids,andhencesomeofthehead-groupsper meateintothebilayer coreduetothisattraction.Wateralsopenetratestheperox idizedbilayerasshownin Fig. 5-3C .Non-negligibleamountsofwaterarepresentinthetail-ri chregionofthe bilayerandinparticular,waterispresentatthecenteroft heDPPC-75%bilayer.Itis possiblethattheperoxidizedlipidsinduceaformationofw aterpores.Thedisruptionof thebilayerismorepronouncedwhentheperoxidizedlipidco ncentrationishigher. Itisobservedthatsomeofthewater-solubleterminalbeads ofperoxidizedlipids alignattheinterface.Attractionbetweentheperoxidized terminalbeadsandwater causesalipidtail-chaincontainingtheperoxidizedbeadt oreorientitselfsothatthe hydroperoxidegrouppointsoutintotheaqueousphase.This canbeseenfromFig. 5-4 whichshowsthedensitydistributionoftheperoxidizedter minalbeadsinthebilayer. Thesebeadsaredistributedfromthecenterofthebilayerup totheinterface(-3nmand 76

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10 0 10 -2 10 -1 10 0 10 1 10 2 q (nm -1 )j ^ h ( q ) j 2 0% 25% 50% 75% Figure5-2.Spectralintensityofbilayersurfaceuctuati onsofthepureDPPCbilayer andofDPPC-25%,DPPC-50%,andDPPC-75%. 3nm)betweenhead-groupsoflipidsandwater.Thisindicate sthataperoxidizedtail foldstowardtheaqueousphase,resultingininternalstruc turalchangesinthebilayer. ItisshowninFig. 5-5 thatthehigherconcentrationofperoxidizedlipidsleadst oa broaderdistributionandhigherdensityoftheperoxidized lipidsatthebilayercenter. Thedistributionbecomesbroaderbecausethebilayerinthe higherperoxidizedlipid concentrationismoreuctuatinganddisrupted. Togainfurtherinsight,thefractionofperoxidizedDPPCli pidswithtailsfolded towardsthewaterphaseisobtained.Atailtobefoldediscon sideredifthepositionof thereplacedperoxidizedbead(P)isfurtherawayfromthebi layercenterthanthetail bead(C1orC5)connectedtoGL1orGL2(seeFig. 5-6 ).Table 5-1 showsdependence oftheaveragefractionofthefoldedlipidsontheconcentra tionofperoxidizedlipids inthebilayers.Sincethepolarityoftheperoxidegroupsis lowerthanwater,notall ofthetailsarefoldedtowardwater(seeFig. 5-5 ).Thefractionofthefoldedlipids 77

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-4 -2 0 2 4 0 1 2 3 4 5 6 7 z (nm)Bead density (beads/nm 3 ) 0% 25% 50% 75% A -4 -2 0 2 4 0 2 4 6 8 10 z (nm)Bead density (beads/nm 3 ) 0% 25% 50% 75% B -4 -2 0 2 4 0 2 4 6 8 10 z (nm)Bead density (beads/nm 3 ) 0% 25% 50% 75% C Figure5-3.Densityprolesofheadandtailgroupsoflipida ndwaterinthepureDPPC bilayer,DPPC-25%,DPPC-50%,andDPPC-75%. decreasesastheconcentrationofperoxidizedlipidsincre ases.Whentheperoxidized lipidconcentrationislow,therearefewerhydroperoxideb eadsinanimmediate neighborhoodofeachoftheperoxidizedlipid,i.e.peroxid izedtailsarelikelytobe surroundedbyhydrophobictailgroupsunlesstheyfoldtowa rdstheheadgroup.On theotherhand,whentheconcentrationofperoxidizedlipid sincreases,aperoxidized lipidislikelytobeincontactwithanotherperoxidizedlip id.Therefore,theperoxidized beadswillattracteachotherinthecoreofthebilayerandth edrivingforcetowardstail 78

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-4 -2 0 2 4 0 0.5 1 1.5 2 z (nm)Bead density (beads/nm 3 ) PO 4 Glycerol -CH 3 -COOH Figure5-4.Densityprolesofthephosphatebeads(PO4,dotted)oftheheadgroup,the glycerol(dash-dotted),theterminalbeads(-CH3,dashed),and theperoxidizedterminalbeads(-COOH,solid)inDPPC-25%. -4 -2 0 2 4 0 0.1 0.2 0.3 0.4 0.5 0.6 z (nm)Bead density (beads/nm 3 ) 25% 50% 75% Figure5-5.Densityprolesoftheperoxidizedterminalbea dsinDPPC-25%(dotted), DPPC-50%(dash-dotted),andDPPC-75%(solid). foldingwilldecrease.Thus,thefractionoffoldedtailsin thecaseofhighconcentrationis smallerthaninthecaseoflowconcentrationofperoxidized lipids. Thechangesinthetailconformationsleadtochangesinthea verageareaperlipid inbilayercontainingperoxidizedlipids.Theareasperlip idintheperoxidizedbilayers inTable 5-1 arelargerthanthatinthepurebilayer(0.6356nm2/lipid),andafurther 79

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deviationfromthepurebilayerisobservedastheconcentra tionoftheperoxidized lipidsincreases.Thepresenceofperoxidizedterminalbea dsattheinterfaceinthe peroxidizedlipidbilayercausesarepulsionbetweenthepe roxidizedbeadsand head-groupsduetotheexcludedvolumeinteractions,which leadstotheincreasein thesurfaceareaperlipid.Moreterminalbeadsathigherper oxidizedlipidconcentration inducesmoreexcludedvolume. Figure5-6.PeroxidizedDPPClipidwithfoldedtails.NC3andPO4refertoapositively andnegativelychargedbeads,respectively.GL1andGL2ref ertoglycerols. CandPrefertohydrophobiccarbonbeadandaperoxidizedbea d. Table5-1.Theaveragefractionoffoldedlipidsandtheaver ageareaperlipidinbilayers withvariousconcentrationsofperoxidizedlipids. ConcentrationFractionoffoldedtailsAreaperlipid(nm2/lipid) 25%0.61990.669950%0.57310.719375%0.55610.7741 5.4EffectofNanoparticlesonPeroxidizedLipidBilayers AsdiscussedinChapter 3.2 ,morphologicalchangesmaybecausedinbilayer containingnanoparticlesduetophysicalinteractionbetw eenthenanoparticlesandthe 80

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bilayer.Tothebestoftheknowledge,therehasbeennoworko nexaminingeffectsof nanoparticleontheperoxidizedbilayer.Inthissection,t heeffectsofnanoparticleson propertiesofperoxidizedbilayerareinvestigated.Itisc heckedthatthereisacumulative effectoflipidperoxidationandstresswithinthemembrane imposedbynanoparticles. Inparticular,afullerenolC60OH10isofinterestduetoitsamphiphilicproperty.Since ahydrophilicgroupofafullerenolisattractedbyhydroper oxidebeadswhereasa hydrophobicgroupismorelikelytointeractwithhydrophob ictails,theinterplayof theinteractionsbetweenafullerenolandperoxidizedlipi dsisexpectedtoinuence peroxidizedmembranes.Effectsoffullerenolsontheperox idizedmembranesare examined. Theinteractionbetweenafullerenolandperoxidizedlipid sislikelytobeaffected bythelocationofthefullerenolintheperoxidizedbilayer .Inthestudythefullerenol isconstrainedatthecenterofthebilayer(z=z0=0nm)andneartheinterface(z= zmin=-1.78nm).Thelatterpositioncorrespondstothefulleren olenergyminimumin unperturbedbilayer(seesection 3.2 ). Inordertoexamineeffectsoflocationoffullerenolintheb ilayeronthechangeson thebilayerstructure,theaveragedensityoftheperoxidiz edlipidsaroundafullerenol locatedatz=z0andz=zminisconsidered.AsshowninFig. 5-7A ,thefullerenollocated atthebilayercenteressentiallydoesnotinuencethedens ityprolesofthehead andtailgroupsinDPPC-25%.Ontheotherhand,thedensitydi stributionsofheadandtail-groupsbecomenarrowerthanthoseoftheunperturb edbilayerinDPPC-75% asshowninFig. 5-7B .Whenthefullerenolislocatedatz=zmin,theheadandtail groupsbecomemorenarrowlydistributedandthedensitypro lebecomessimilar totheunperturbedbilayerinbothDPPC-25%andDPPC-75%.It isremarkablethat thedensityofhead-groupsandwaterdecreaseatthebilayer centerdecreaseofthe DPPC-75%bilayer.Thishappensbecausewhenthefullerenol islocatedatz=zmin, thehydrophilicpartofthefullerenolattractsheadgroups oftheneighboringlipidsto 81

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theinterface,therebythewaterdensitydecreasesatthebi layercenterbutincreases neartheinterface.Inaddition,thehydrophilicpartofthe fullerenolattheinterfacealso attractstheperoxidizedterminalbeadstobefoldedtoward stheinterface.Fig. 5-8B showsthatthenanoparticleattractsmoreperoxidizedbead stowardstheinterface. -4 -2 0 2 4 0 2 4 6 8 10 z (nm)Bead density (beads/nm 3 ) 0% 25% 25% + C 60 OH 10 (z = z 0 ) 25% + C 60 OH 10 (z = z min ) A -4 -2 0 2 4 0 2 4 6 8 10 z (nm)Bead density (beads/nm 3 ) 0% 75% 75% + C 60 OH 10 (z = z 0 ) 75% + C 60 OH 10 (z = z min ) B Figure5-7.Densityprolesofhead(thinlines)andtail(th icklines)groupsin(A) DPPC-25%and(B)DPPC-75%withandwithoutfullerenol.Thed ottedlines refertoheadgroupsinthepureDPPCbilayer. -4 -2 0 2 4 0 2 4 6 8 10 z (nm)Bead density (beads/nm 3 ) 25% 25% + C 60 OH 10 (z = z 0 ) 25% + C 60 OH 10 (z = z min ) 75% 75% + C 60 OH 10 (z = z 0 ) 75% + C 60 OH 10 (z = z min ) A -4 -2 0 2 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 z (nm)Bead density (beads/nm 3 ) 25% 25% + C 60 OH 10 (z = z 0 ) 25% + C 60 OH 10 (z = z min ) 75% 75% + C 60 OH 10 (z = z 0 ) 75% + C 60 OH 10 (z = z min ) B Figure5-8.Densityprolesof(A)waterand(B)peroxidized terminalbead(-COOH)in DPPC-25%(thinlines)andDPPC-75%(thicklines)withandwi thout fullerenol. Theeffectofthenanoparticlepresenceinsidethemembrane onthemembrane stretchingisconsidered.Asdiscussedinsection 3.2 ,fullerenolsarelikelytostaylong 82

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timeatthewater-lipidinterface.Theirstayattheinterfa ceinducestheexcludedvolume interactionsandleadstoincreaseinthesurfaceareaperli pidfollowedbystretching inthebilayer.Theincreaseinthesurfaceareaperlipidena bleswatermoleculesto permeateintothemembraneinterior.Thewaterpermeationm ayformwaterpores inthemembrane,therebyleadingtomembranedisruptionorr upture.Thisbecomes remarkablewhenthenanoparticleclusterstransportthrou ghthebilayer. Afullerenollocatedateitherz=z0orz=zmininthebilayerwithDPPC-25%leads toalmostnegligiblestretchingofthemembrane,seeTable 5-2 .Incontrast,theareaper lipidinDPPC-75%containingthefullerenolatz=zminslightlyincreaseswhencompared tothatintheperoxidizedbilayerwithouttheparticleorwh entheparticleislocatedat thecenter.Theincreaseintheareaperlipidmaybecausedby thepresenceofthe peroxidizedterminalbeadsattheinterfaceattractedbyth ehydrophilicgroupsofthe particle.Theperoxidizedterminalbeadsinducetheexclud edvolumeinteractionsatthe interfaceleadingtostretchinginthelateraldirection.F ig. 5-8B showsthehigherdensity oftheperoxidizedterminalbeadsinbothDPPC-25%andDPPC75%whentheparticle islocatedattheinterface.Sincetherearemoreperoxidize dbeadsinDPPC-75%than DPPC-25%aroundthefullerenol,theincreaseintheareaper lipidismorepronounced inDPPC-75%. Table5-2.TheaverageareaperlipidinDPPC-25%andDPPC-75 %withandwithouta fullerenol.Thefullerenollocationsz0andzmincorrespondtothecenterofthe bilayerandtheminimumfreeenergyinanunperturbedbilaye r. SystemsAreaperlipid(nm2/lipid) DPPC-25%(z=z0)0.6713 DPPC-25%(z=zmin)0.6754 DPPC-75%(z=z0)0.7745 DPPC-75%(z=zmin)0.7836 Inaddition,effectsoffullerenolembeddedinperoxidized lipidbilayersonthe membraneelasticpropertiesareexamined.Inordertoensur ethatthemembrane uctuationsoftheperoxidizedbilayerhavereachedthetim escaleofthesimulations,the 83

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timeevolutionofFouriermodesofthebilayersurfacesisch ecked.Fig. 5-9 showsan exampleofsuchanevolutionofseveralFouriermodesinDPPC -25%andDPPC-75% bilayerswithandwithoutthenanoparticle.Itisobservedt hatmembraneuctuationsin alloftheconsideredbilayersareatsteadystate,whichind icatesthattheconsidered systemsareindeedatequilibrium. Themagnitudeofthemembraneuctuationsisessentiallyin dependentofthe presenceofthefullerenolintheconsideredperoxidizedbi layersasshowninFig. 5-10 Thisindicatesthatbendingmoduliintheperoxidizedbilay erarenotsensitivetothe presenceofthefullerenol.However,sincethesizeofthebi layer-fullerenolsystemsis relativelysmallandthemagnitudeofthelong-waveuctuat ionsisnotassessedforas widerangeofqasforthenanoparticle-freesystems.Furthe rinvestigationsareneeded toevaluatetheeffectofthenanoparticleonmembranestabi litymoreaccurately. 5.5Conclusions Itwasobservedthatlipidperoxidationleadstosofteningo fthemembranedue toperturbationofthemembranestructure.Themaindriving forceforthisisthe hydrophilicinteractionoftheperoxidizedlipidswithhea dgroupsoflipidsleading tothetailfoldingtowardsthewaterphase.Thisenableswat erpermeationinto themembraneinterior,whichisexpectedinduceleakagethr oughthemembrane observedinexperiments[ 43 ].Thechangeinthemembranesstructurebecomesmore pronouncedathigherconcentrationofperoxidizedlipids, whichisconsistentwithresults showingdose-dependenceofnanoparticletoxicityinexper iments. Inaddition,effectsofnanoparticlesonperoxidizedlipid bilayerswereinvestigated. Theconsideredamphiphilicnanoparticleisobservedtosta bilizethemembrane structurewhenitislocatedatitsequilibriumposition(ne artheinterfacebetween lipidtail-andhead-groups).Thehydrophilicpartofthepa rticlefacingthewaterphase encouragesheadgroupslocatedinthemembraneinteriortom ovebacktotheinterface. 84

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0 0.5 1 1.5 2 x 10 5 1.65 1.7 1.75 1.8 1.85 t (ps)^ h k ( t ) 25% 25% + C 60 OH 10 (z = z 0 ) 25% + C 60 OH 10 (z = z min ) A 0 0.5 1 1.5 2 x 10 5 1.4 1.45 1.5 1.55 1.6 t (ps)^ h k ( t ) 75% 75% + C 60 OH 10 (z = z 0 ) 75% + C 60 OH 10 (z = z min ) B Figure5-9.TimeevolutionoftheFouriermodesof(A)DPPC-2 5%and(B)DPPC-75% bilayers.TheshownFouriermodescorrespondtowavenumber q=0.22 nm 1(DPPC-25%),0.45nm 1(DPPC-25%+fullerenol),0.21nm 1(DPPC-75%),and0.42nm 1(DPPC-75%+fullerenol). However,despitethisstabilizationofthemembranestruct ure,themembranebending andstretchingwerenotstronglyaffectedbythenanopartic le. 85

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10 0 10 -2 10 -1 10 0 10 1 10 2 q (nm -1 )< j ^ h ( q ) j 2 > 25% 25% + C 60 OH 10 (z = z 0 ) 25% + C 60 OH 10 (z = z min ) 75% 75% + C 60 OH 10 (z = z 0 ) 75% + C 60 OH 10 (z = z min ) Figure5-10.Spectralintensityofbilayersurfaceuctuat ionsforDPPC-25%and DPPC-75%withandwithoutfullerenol. 86

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CHAPTER6 CONCLUSIONS InthisstudyMDsimulationswereusedtoinvestigateintera ctionsbetween nanoparticlesandcellmembranesatamolecularlevel.Thei nteractionbetween carbon-basednanoparticlesandamodelmembrane,aphospho lipidbilayer,was focusedon.Themainmotivationforthisworkwastoundersta ndoriginsofobserved toxicityofthenanoparticles.Apossibilityofananoparti cle-inducedmembrane disruptionduetoeitherchemicalreactionsornon-reactiv ephysicalinteractionswas examined. Theinitialstepinthisworkwasmodelingthenanoparticlet ransportacross membrane.Theconstrainedsimulationsareusedtoobtainth efreeenergyproleofthe nanoparticleinsidethemembrane.Itwasobservedthatthec onsideredhydrophobicand amphiphilicnanoparticlescaneasilypenetrateintotheme mbraneduetoattractionto thehydrophobiclipidtails.Theirchemicalnatureofthena noparticleandthemembrane interiorallowstheparticletospendasignicantamountof timeinsidethemembrane, whichbringsapossibilityofanegativeimpactofthenanopa rticleonbiologicalsystems. Astrongcouplingbetweenthetransportofananoparticle(f ullereneanditsderivative) andthemembranedeformationcausedbythehydrophobicinte ractionbetweenthe nanoparticleandthelipidtailswasobserved.Itwasobserv edthattheparticleinduces themembranedeformationevenbeforeitreachesthecorereg ionofmembrane,which indicatesthattheparticlemaydamagethemembraneduringi tspermeationintothe membrane. Anadditionaldegreeoffreedom,orientationoffunctional izedamphiphilic nanoparticle,wasconsideredinordertostudyitsinuence onthemembrane deformation.Itwasfoundthatorientationofthefunctiona lizedamphiphilicnanoparticle affectsthemembranedeformationbyinteractionofthefunc tionalgroupsofthe 87

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nanoparticlewithlipidsatbilayercenter.Thisimpliesth atorientationofthenanoparticle introducesanadditionalenergybarriertonanoparticletr ansport. Anothertypeofnanoparticlesconsideredinthisworkiscar bonnanotubes.Effects ofthecarbonnanotubesonthemembranestabilityandchange sinelasticproperties ofmembranewereevaluated.Itwasobservedthattheparticl esembeddedintothe membraneinteriorleadtothemembranesoftening,whichbec omesmoresignicant forlongerCNTandhigherCNTconcentration.Thelateralpre ssureprolewithinthe membranewereobtainedinordertoexamineeffectsofnanopa rticlesonfunctionality ofmembraneproteins.Localizedperturbationinthelatera lpressureproleand membraneenergywasalsoobserved.Sincetheperturbationi sshort-ranged,itcan beconcludedthattheparticlesarenotlikelytoaffectmemb raneproteinfunctionthrough theperturbationoftheinternalstressinthemembrane. Itwasdemonstratedthatthenon-reactivephysicalinterac tionbetween nanoparticlesandmembraneisofimportanceinthedisrupti onofthemembrane integrity.Thephysicalinteractionsofnanoparticleswit hmembranescanbeaffected bysuchmodicationsaschargesandlocationoffunctionalg roupsontheparticle. RealCNTsusedinexperimentscontainimpuritiessuchasoxy gen,therebyleadingto negativesurfacecharge[ 33 ]whereasthemodeledCNTinthestudyishydrophobicand hasnochargesonitssurface.Thelong-rangedelectrostati cinteractionofCNTwith lipidsmayperturbthemembraneenergyinabroaderregion. Lipidperoxidationwasinvestigatedtoassesspossibility ofcelldamagebychemical reactions.Itwasobservedthattheperoxidizedlipidslead toaperturbationofthe internalstructureofthemembrane.Theperoxidizedlipids alsocausedthemembrane softeningleadingtohigheramplitudeofthemembraneuctu ations.Theseeffects becamemoresignicantwithincreaseofconcentrationofpe roxidizedlipids.More peroxidizedlipidsaroundthenanoparticleinhigherconce ntrationofperoxidizedlipids 88

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aremorelikelytoattractperoxidizedterminalbeadstowar dthewaterphaseleadingto moredisruptionofthemembraneinterior. Cumulativeeffectsoflipidperoxidationandnanoparticle adsorptionintothe membranewasexaminedforthersttime.Thefunctionalized amphiphilicparticle locatedatitsequilibriumpositioninsidetheperoxidized membraneappearstoreduce theperturbationofthemembranestructurebystabilizingt heperturbedbilayer.This suggestsapossibilityofantioxidanteffectofthenanopar ticle.Incontrast,effectofthe particleonthemembranestretchingandbendingwasalmostn egligible. Toxicityofwater-soluble(functionalized)fullerenesha sbeencontroversialwhereas thatofpurefullerenehasbeenapparent.Thecurrentworkpr oposesamechanismfor bothdestabilizationofthemembrane(throughlipidperoxi dation)andremediationofthe lipidperoxidation(throughthenanoparticlepresentinth eperoxidizedbilayer).However, theprecisebalanceofthesetwoeffectsisstillnotwellund erstood.Incontrast,itis notexpectedtoobservethelatterfromperoxidizedbilayer scontainingpurefullerenes. Sincearepulsionbetweentheparticleandthelipidhead-gr oupsencouragesthe nanoparticletopushthehead-groupsnotonlytowardsthewa terphasebutalsoto thelateraldirection,theinternalstructureofthemembra newouldbemoredisrupted. Furtherinvestigationofvariouspropertiesofperoxidize dmembraneisneededinorder tobetterunderstandtoxicityoffunctionalizedparticles .Theseinvestigationwould involvevaryingthenanoparticlefunctionalizationandde velopmentofamoreprecise modelforperoxidizedbeads. Inconclusion,theinvestigationofinteractionofnanopar ticlewithcellmembrane isanimportantsteptoassesstherisksrelatedtonanomater ialexposuretohumans andtheenvironment.Considerationofeffectsofthephysic ochemicalpropertiesofthe nanoparticleontheirtoxicityisakeyfactorindrugdelive rytoolsinthebiomedicaleld. Inaddition,understandingthemechanismsofnegativeimpa ctsofnanoparticleson 89

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cellularmembranesenablesustohandlepotentiallytoxicn anomaterialssafelyanduse nanomaterialsforvariousapplicationsineffectiveways. 90

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REFERENCES [1] Allen,M.P.andTildesley,D.J. ComputerSimulationofLiquids .NewYork:Oxford UniversityPress,1987. [2] Berendsen,H.J.C.“Sloweventsincomplexsystems:potenti alsofmeanforceand theSmoluchowskilimitinbiologicalsystems.” SIMUNewsletter 3(2001):33–50. [3] Bond,P.J.,Parton,D.L.,Clark,J.F.,andSansom,M.S.P.“C oarse–grained simulationsofthemembrane–activeantimicrobialpeptide maculatin1.1.” Biophys. J. 95(2008):3802–3815. [4] Cantor,R.S.“Lateralpressuresincellmembranes:amechan ismformodulationof proteinfunction.” J.Phys.Chem.B 101(1997):1723–1725. [5] D'Rozario,R.S.G.,Wee,C.L.,Wallace,E.J.,andSansom,M. S.P.“The interactionofC60anditsderivativeswithalipidbilayerviamoleculardynam ics simulation.” Nanotechnology 20(2009):115102. [6] Eckenhoff,R.G.“Promiscuousligandsandattractivecauit ies:howdotheinhaled anestheticswork?” MolecularInterventions 1(2001):258–268. [7] Gardiner,C.W. HandbookofStochasticMethodsforPhysics,Chemistryandt he NaturalSciences .Berlin:Springer,2004. [8] Goetz,R.andLipowsky,R.“Computersimulationsofbilayer membranes: Self-assemblyandinterfacialtension.” J.Chem.Phys. 108(1998).17:7397–7409. [9] Gupta,A.,Chauhan,A.,andKopelevich,D.I.“Moleculartra nsportacrossuid interfaces:couplingbetweensolutedynamicsandinterfac euctuations.” Phys. Rev.E 78(2008):041605. [10] Hamm,M.andKozlov,M.M.“Elasticenergyoftiltandbending ofuidmembranes.” Eur.Phys.J.E 3(2000):323–335. [11] Helfrich,W.“Elasticpropertiesoflipidbilayers:theory andpossibleexperiments.” Z.Naturforsch.C 28(1973):693–703. [12] Hildreth,C.“Asymptoticdistributionofmaximumlikeliho odestimatorsinalinear modelwithautoregressivedisturbances.” Ann.Math.Statist. 40(1969):583–594. [13] Hong,S.,Hessleer,J.A.,Holl,M.M.Banaszak,Leroueil,P. ,Mecke,A.,andOrr, B.G.“Physiccalinteractionsofnanoparticleswithbiolog icalmembranes:the observationofnanoscaleholeformation.” Chem.HealthSaf. 13(2006):16–20. [14] Hoover,W.G.“Canonicaldynamics:equilibriumphase-spac edistribution.” Phys. Rev.A 31(1985):1695–1697. 91

PAGE 92

[15] Hummer,G.andKevrekidis,I.G.“Coarsemoleculardynamics ofapeptide fragment:Freeenergy,kinetics,andlong-timedynamicsco mputations.” J.Chem. Phys. 118(2003).23:10762–10773. [16] Irving,J.H.andKirkwood,J.G.“Thestatistalmechanicalt heoryoftransport processes.IV.theequationsofhydrodynamics.” J.Chem.Phys. 18(1950): 817–829. [17] Johnson,C.M.,Pandey,R.,Sharma,S.,Khuller,G.K.,Basar aba,R.J.,Orme, I.M.,andLenaerts,A.J.“Oraltherapyusingnanoparticleencapsulated antituberculosisdrugsinguineapigsinffectedwith Mycobacteriumtubersulosis .” Antimicrob.AgentsChemother. 49(2005):4335–4338. [18] Jr.,En.M.Ostrea,Cepeda,E.E.,Fleury,C.A.,andBalun,J. E.“Redcell membranelipidperoxidationandhemolysissecondarytopho totherapy.” Acta Paediatr. 74(2008):378–381. [19] Khndelia,H.andMouritsen,O.G.“Lipidgymnastics:eviden ceofcompleteacyl chainreversalinoxidizedphospholipidsfrommolecularsi mulations.” Biophys.J. 96 (2009):2734–2743. [20] Kopelevich,D.I.,Panagiotopoulos,A.Z.,andKevrekidis, I.G.“Coarse-grained kieticcomputationsforrareevents:applicationtomicell eformation.” J.Chem. Phys. 122(2005):044908–1–044908–13. [21] Lam,W.,James,J.T.,McCluskey,R.,andHunter,R.L.“Pulmo narytoxicityof single–wallcarbonnanotubesinmice7and90daysfaterintr atrachealinstillation.” Toxicol.Sci. 77(2004):126–134. [22] Leroueil,P.R.,S.Hong,A.Mecke,Baker,J.R.,Orr,Jr.B.G. ,andHoll,M. M.Banaszak.“Nanoparticleinteractionwithbiologicalme mbranes:Does nanotechnologypresentajanusface?” Acc.Chem.Res. 40(2007):335–342. [23] Li,L.,Davande,H.,Bedrov,D.,andSmith,G.D.“Amolecular dynamicssimulation studyofC60fullerenesinsideadimyristoylphosphatidylcholinelipi dbilayer.” J.Phys. Chem.B 111(2007):4067–4072. [24] Lindahl,E.andEdholm,O.“Spatialandenergetic-entropic decompositionof surfacetensioninlipidbilayersfrommoleculardynamicss imulations.” J.Chem. Phys. 113(2000):3882–3893. [25] Magrez,A.,Kasas,S.,Salicio,V.,Pasquier,N.,Seo,J.W., Celio,M.,Catsicas,S., Schwaller,B.,andForro,L.“Cellulartoxicityofcarbon-b asednanomaterials.” Nano Lett. 6(2006):1121–1125. [26] Marrink,S.J.andBerendsen,H.J.C.“Simulationofwatertr ansportthroughalipid membrane.” J.Phys.Chem. 98(1994):4155–4168. 92

PAGE 93

[27] ———.“Permeationprocessofsmallmoleculesacrosslipidme mbranesstudiedby moleculardynamicssimulations.” J.Phys.Chem. 100(1996):16729–16738. [28] Marrink,S.J.,Risselada,H.J.,Yemov,S.,Tieleman,D.P. ,anddeVries,A.H. “TheMARTINIforceeld:coarsegrainedmodelforbiomolecu larsimulations.” J. Phys.Chem.B 111(2007):7812–7824. [29] Marsh,D.“Lateralpressureinmembranes.” Biochim.Biophys.Acta 1286(1996): 183–223. [30] May,E.R.,Narang,A.,andKopelevich,D.I.“Molecularmode lingofkeyelastic propertiesforinhomogeneouslipidbilayers.” MolecularSimulation 33(2007).9–10: 15–30. [31] Mecke,A.,Uppuluri,S.,Sassanella,T.M.,Lee,D.-K.,Rama moorthy,A.,Jr.,J. R.Baker,Orr,B.G.,andHoll,M.M.Banaszak.“Directobserv ationoflipidbilayer disruptionbypoly(amidoamine)dendrimers.” Chem.Phys.Lipids 132(2004): 3–14. [32] Monticelli,L.,Kandasamy,S.K.,Periole,X.,Larson,R.G. ,Tieleman,D.P.,and Marrink,S.“TheMARTINIcoarse–grainedforceeld:extens iontoproteins.” J. Chem.TheoryandComput. 4(2008):819–834. [33] Monticelli,L.,Salinen,E.,Ke,P.C.,andVattulainen,I.“ Effectsofcarbon nanoparticlesonlipidmembranes:amolecularsimulationp erspective.” Soft Matter 5(2009):4433–4445. [34] Nose,S.“Amoleculardynamicsmethodforsimulationsinthe canonicalensemble.” Mol.Phys. 52(1984):255–268. [35] Nose,S.andKlein,M.L.“Constantpressuremoleculardynam icsformolecular systems.” Mol.Phys. 50(1983):1055–1076. [36] Oberdorster,E.“Manufacturenanomaterials(fullerens,C60)induceoxidativestress inthebrainofJuvenilelargemouthbass.” Environ.HealthPerspect. 112(2004): 1058–1062. [37] Pacici,R.E.andDavies,J.A.“Protein,lipidandDNArepai rsystemsinoxidative stress:thefreeradicaltheoryofagingrevisited.” Gerontoloty 37(1991):166–180. [38] Panessa-Warren,B.J.,Warren,J.B.,Wong,S.S.,andMisewi ch,J.A.“Biological celluarresponsetocarbonnanoparticletoxicity.” J.Phys.:Condens.Matter 18 (2006):2185–2201. [39] Parrinello,M.andRahman,A.“Polymorphictransitionsins inglecrystals:anew moleculardynamicsmethod.” J.Appl.Phys. 52(1981):7182–7190. [40] Porter,N.A.,Caldwell,S.E.,andMills,K.A.“Mechanismso ffreeradicaloxidation ofunsaturatedlipids.” Lipids 30(1995):277–290. 93

PAGE 94

[41] Qiao,R.,Roberts,A.P.,Mount,A.S.,Klaine,S.J.,andKe,P .C.“Translocationof C60anditsderivativesacrossalipidbilayer.” NanoLett. 7(2007):614–619. [42] Rothen-Rutishauser,B.M.,Schurch,S.,Haenni,B.,Kapp,N .,andGehr,P. “Interactionofneparticlesandnanoparticleswithredbl oodcellsvisualizedwith advancedmicroscopictechniques.” Environ.Sci.Technol. 40(2006):4353–4359. [43] Sayes,C.M.,Fortner,J.D.,Guo,W.,Lyon,D.,Boyd,A.M.,Au sman,K.D.,Tao, Y.J.,Sitharaman,B.,Wilson,L.J.,Hughes,J.B.,West,J.L .,andColvin,V.L. “Thedifferentialcytotoxicityofwater-solublefulleren es.” NanoLetters 4(2004): 1881–1887. [44] Sayes,C.M.,Gobin,A.M.,Ausman,K.D.,Mendez,J.,West,J. L.,andColvin, V.L.“Nano-C60cytotoxicityisduetolipidperoxidation.” Biomaterials 26(2005): 7587–7595. [45] Schoeld,P.andHenderson,J.R.“Statistalmechanicsofin homogeneousluids.” Proc.R.Soc.Lond.A 379(1982):231–246. [46] Seber,G.A.F.andWild,C.J. Nonlinearregression .NewYork:Wiley,1989. [47] Shvedova,A.A.,Castranova,V.,Kisin,E.R.,Schwegler-Be rry,D.,Murray,A.R., Gandelsman,V.Z.,Maynard,A.,andBaron,P.“Exposuretoca rbonnanotube material:assessmentofnanotubecytotoxicityusinghuman keratinocytecells.” J. Toxicol.Environ.Health,PartA 66(2003):1909–1926. [48] Shvedova,A.A.,Kisin,E.R.,Mercer,R.,Murray,A.R.,John son,V.J.,Potapovich, A.I.,Tyurina,Y.Y.,Gorelik,O.,Arepalli,S.,SchweglerBerry,D.,Hubbs,A.F., Antonini,J.,Evans,D.E.,Ku,B.,Ramsey,D.,Maynard,A.,K agan,V.E., Castranova,V.,andBaron,P.“Unusualinammatoryandbro genicpulmonary responsetosingle-walledcarbonnanotubesinmice.” Am.J.Physiol.Lung.Cell. Physiol. 289(2005):698–708. [49] Stark,G.“Theeffectofionizingradiationonlipidmembran es.” Biochim.Biophys. Acta. 1071(1991):103–122. [50] Tasseff,R.A.“Molecularmodelingofnanoparticletranspo rtacrosslipidbilayers.” JournalofUndergraduateResearch 7(2006):3. [51] Tieleman,D.P.,Marrink,S.J.,andBerendsen,H.J.C.“Acom puterperspective ofmembranes:moleculardynamicsstudiesoflipidbilayers ystems.” Biochim. Biophys.Acta 1331(1997):235–270. [52] Traikia,M.,Warschawski,D.E.,Lambert,O.,Rigaud,J.,an dDevaux,P.F. “Asymmetricalmembranesandsurfacetension.” Biophys.J. 83(2002):1443–1454. [53] Ulander,J.andHaymet,A.D.J.“Permeationacrosshydrated DPPClipidbilayers: simulationofthetitrableamphiphilicdrugvalproicacid. ” Biophys.J. 85(2003): 3475–3484. 94

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[54] vanderSpoel,D.,Lindahl,E.,Hess,B.,Groenhof,G.,Mark, A.E.,andBerendsen, H.J.C.“GROMACS:fast,exible,andfree.” J.Comput.Chem. 26(2005): 1701–1718. [55] Venkatesan,N.,Yochimitsu,J.,Ito,Y.,Shibata,N.,andTa kada,K.“Liquidlled nanoparticlesasadrugdeliverytoolforproteintherpeuti cs.” Biomaterials 26 (2005):7154–7163. [56] Wallace,E.J.andSansom,M.S.P.“CarbonNanotube/Deterge ntInteractionsvia Coarse-GrainedMolecularDynamics.” NanoLett. 7(2007):1923–1928. [57] Wang,I.C.,Tai,L.A.,Lee,D.D.,Kanakamma,P.P.,Shen,C.K .F.,Luh,T.,Cheng, C.H.,andHwang,K.C.“C60andwater-solublefullerenederivativesasantioxidants againstradical-initiatedlipidperoxidation.” J.Med.Chem 42(1999):4614–4620. [58] Warheit,D.B.,Laurence,B.R.,Reed,K.L.,Roach,D.H.,Rey nolds,G.A.M.,and Webb,T.R.“Comparativepulmonarytoxicityassessmentofs ingle-wallcarbon nanotubesinrats.” Toxicol.Sci. 77(2004):117–125. [59] Wong-Ekkabut,J.,Baoukina,S.,Triampo,W.,Tang,I.,Tiel eman,D.P.,and Monticelli,L.“Computersimulationstudyoffullerenetra nslocationthrough lipidmembranes.” Nat.Nanotechnol. 3(2008):363–368. [60] Wong-ekkabut,J.,Xu,Z.,Triampo,W.,Tang,I-M.,andTiele man,D.P.“Effectof lipidperoxidationonthepropertiesoflipidlipidbilayer s:amoleculardynamics study.” Biophys.J. 93(2007):4225–4236. 95

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BIOGRAPHICALSKETCH Young-MinBanreceivedherBachelorofScienceinchemicale ngineeringfrom YonseiUniversity,Seoul,Koreain2002.Shecompletedherm aster'sdegreeinchemical engineeringfromYonseiUniversity,Seoul,Koreain2004.S hejoinedtheDepartment ofChemicalEngineeringattheUniversityofFloridainAugu st2005.Shereceivedher Ph.D.fromtheUniversityofFloridainthesummerof2010.Du ringhergraduatestudies, sheworkedunderthesupervisionofDr.DmitryKopelevich.H erresearchinterestsare modelingofinteractionsbetweennanoparticlesandcellme mbrane. 96