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A classical electric paradigm of general superoxide dismutase function
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Title: A classical electric paradigm of general superoxide dismutase function
Physical Description: Journal Article
Creator: Workman, Aron S.
Publication Date: December 12, 2012
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Abstract: The free electron of superoxide ion radical has high mobility. Superoxide deionization to dioxygen and peroxide is catalyzed by superoxide dismutase enzymes, but mechanistic proposals to date have been strictly particulate without considering net continuum effects. The following communication begins to resolve this dissonance by modeling the free electron of superoxide as a current source and superoxide dismutase as an electric circuit. Oxygenated free electron flow current intensity was modeled as I=\mathrm{N_{A}}\mathrm{e}\mu\ce{O2^{\cdot-}}\iint_{\mathbf{S}}\mathbf{E\cdot\mathrm{d\mathbf{S}}} in the presence of a field of a superoxide sensor such as superoxide dismutase. A modeled black box superoxide dismutase network executes oxidation to dioxygen (anode) and reduction to peroxide (cathode) with a single reaction's terminal voltage of \mathrm{E}_{0'}=\num{1.05}\si{\volt}. Current intensity \mathrm{d}Q/\mathrm{d}t of the closed system model circuit was calculated from net rate constant \lambda as I=2\lambda\mathrm{F}\mathrm{V}\ce{O2^{\cdot-}}^{2}. This novel electrodynamic paradigm has immediate implications for superoxide dismutase mechanics.
Acquisition: Collected for University of Florida's Institutional Repository by the UFIR Self-Submittal tool. Submitted by Aron Workman.
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Aclassicalelectricparadigmofgeneralsuperoxidedismutasefunction AronScottWorkman Abstract Thefreeelectronofsuperoxideionradicalhashighmobility.Superoxidedeionizationtodioxygenand peroxideiscatalyzedbysuperoxidedismutaseenzymes,butmechanisticproposalstodatehavebeenstrictly particulatewithoutconsideringnetcontinuumeects.Thefollowingcommunicationbeginstoresolvethis dissonancebymodelingthefreeelectronofsuperoxideasacurrentsourceandsuperoxidedismutaseasan electriccircuit.Oxygenatedfreeelectronowcurrentintensitywasmodeledas I =N A e [O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] S E d S in thepresenceofaeldofasuperoxidesensorsuchassuperoxidedismutase.Amodeledblackboxsuperoxide dismutasenetworkexecutesoxidationtodioxygenanodeandreductiontoperoxidecathodewithasingle reaction'sterminalvoltageof E 0 0 =1 : 05 V.Currentintensity d Q= d t oftheclosedsystemmodelcircuitwas calculatedfromnetrateconstant as I =2 FV[O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] 2 .Thisnovelelectrodynamicparadigmhasimmediate implicationsforsuperoxidedismutasemechanics. Keywords: superoxidedismutase,superoxideionradical,enzymaticmechanism,bioelectrochemistry Introduction Theidenticationofanalogousframeworks acrossdisparatescienticdomainsisapowerful heuristictoolininterdisciplinarystudy[1,2],especiallyinthephysicalmodelingofbiologicalphenomena.TheparamountexampleisHodgkinand Huxley'sanalogicaluseofelectriccircuitdiagrams todescribetheelectrochemistryofaxonalaction potentials[3]workthatnucleatedaparadigmatic shiftinelectrophysiology[4]. Superoxidedismutaseisanenzymethatcatalyzes thedeionizationofsuperoxidetodioxygenandperoxideinareactionthatspontaneouslyproceedsentirelyviaradicalelectrontransferandsolvatedprotonation[5].Despitethisdependenceonthenature offreeelectrons,mechanisticinterpretationstodate havebeenstrictlyparticulatewithoutconsidering netcontinuumeectsviz.noworkhasyetbridged thenatureofmobileelectrontransfertothatof electriccurrentanditsaccompanyingelectromagneticframework. Oxygenatedfreeelectronow Dioxygen O 2 ,themoststableallotropeofoxygen,isthemostfrequentelectronacceptorinaerobicbiology.Itsreductionisoftencoupledwith URL: http://aronworkman.com AronScottWorkman protonationtogeneratewaterinterminalelectron transportation O 2 +4H + 4 e )]TJ/F25 9.9626 Tf -10.246 -8.654 Td [()274()275(! 2H 2 O However,whenaberrantelectrontransportleaks arenotcoupledwithprotonation,theone-electron reductionofdioxygengeneratessuperoxide[6] O 2 e )]TJ/F25 9.9626 Tf -6.275 -8.654 Td [()474()473(! O )]TJ/F20 6.9738 Tf 0 -6.919 Td [(2 Exposinganoxygenatedsolutiontoabeamofacceleratedelectronspulseradiolysisgeneratessuperoxideviathesamenetreaction[7]. Oxygen'shighelectronegativityenablessuperoxide'srelativestabilityinbiologicalsolutionbecause thesuperoxideelectronwillonlyowtoacompatibleelectrophile.Self-exchangestudieshaveshown thatthesuperoxideelectronowsacrossdioxygen viaouterspheremechanismssc.therearenointermediatesortransitionstates[8,9] O 2 + O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 )459()460(! O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 + O 2 )459()459(! O 2 + O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 TheoutersphereelectronowofReaction2proceedsviathereversiblehalfReaction1. PreprintsubmittedtoInstitutionalRepositoryattheUniversityofFloridaDecember12,2012

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Generalsuperoxidedismutase Superoxideisatoxinwidelyimplicatedindisease andinammatorypathogenesis[10].Aerobiccells arethoughttomitigatesuperoxidewiththeubiquitousexpressionofsuperoxidedismutaseSOD metalloenzymes.AerobesthatlackSODorexpress dysfunctionalSODsuerdetrimentalandoftenfataleect[11];conversely,functionalSODisahistoricalexogenoustherapeutic[12].SODcatalyzes thedeionizationofsuperoxide 2O )]TJ/F20 6.9738 Tf 0 -6.919 Td [(2 +2H + )666(! O 2 +H 2 O 2 Netrateconstant atwhichSODdeionizessuperoxidevariesdependingontheenzymeandits milieu,butisgenerallyontheorderof10 9 m = 1 s = 1 over f 5 : 0 pH 9 : 5 g f 20 C T 40 C g ,and f 10 )]TJ/F20 6.9738 Tf 6.227 0 Td [(13 m [O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] 10 )]TJ/F20 6.9738 Tf 6.227 0 Td [(5 m g insolution[13,14]. ThetraditionalparticulatemodelofSODdescribesaboundtransitionmetal M assolefacilitatorofthesuperoxideelectrontransferinthe cyclicreaction O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 + M n +1+ 1 )276(! O 2 + M n + O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 +2H + + M n + 2 )276(! H 2 O 2 + M n +1+ Theactivityofwild-typeSODishistoricallydescribedasdiusionlimitedsc.strictBrownianmotion.However,certainperipheralmutations generateincreasedactivityseveraltimesthatof wild-typeperpart M [15,16].Additionally,what littledataexistsforanenzyme-substratecomplex O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 )]TJ/F39 9.9626 Tf 9.962 0 Td [(M n +1+ orevenabound M n + istheoreticalormimetic-based.Theseconditionsimplythe possibilityofacatalyticroleforSODthatisnot strictlyparticulaterelativeto M Models Oxygenatedfreeelectronowmodeledaselectric current Overcertainrangethereisapparentlyadirect linearcorrelationbetweenasuperoxidesensor's electriccurrentintensityandthesolutionconcentrationofsuperoxide 1 [2022]: I / [O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] 1 Describingsuperoxidesolelyintermsofsolutionconcentrationcf.thestandardforbiochemicalliteratureisan approximationbecauselikedioxygen,superoxideisprimarilygaseous[17].Whilegaseouspartialpressureisideally proportionaltosolutionconcentration[18],superoxidehasa shorterhalf-lifeasaliquidthanasagas[19]. Oxygenistheconductivemediumforthatelectriccharge[2123].Chargecarrierelectrondensityisthus n =N A [O )]TJ/F20 6.9738 Tf 0 -6.919 Td [(2 ] where N A isAvogadro's constant. SuperoxidefreeelectronsowacrossdioxygenaccordingtoReactions1and2[8,9].Thereforethe electricalconductivityamaterialconstantofoxygenatedelectronowis =e n where e isthe elementarychargeand isthemobilityofthesuperoxidefreeelectron. AcontinuumofOhm'slawstatesthatelectrical conductivityisproportionaltoelectriccurrentdensity J andelectriceld E by J = E ApproximatingReaction2asacontinuousloop withoutleakage,acontinuumofAmpre'slaw statesthat I maybewrittenastheuxintegralof J throughadioxygensurface S spanningtheloopsc. currentintensityisthesummationofcurrentdensityovertheregionwherecurrentowsaccording to I = S J d S ,yielding I = S E d S =N A e [O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] S E d S Thustheproportionalityconstantof I / [O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] canbedenedas k =N A e S E d S .Itfollows thatintheabsenceofaeldofanelectromagnet suchasasuperoxidesensor,theelectronswould diusewithoutalineofcurrent. Generalsuperoxidedismutasemodeledasanelectriccircuit ThemosttoplevelgeneralSODmodelisthe blackboxdiagramofFigure1describinginputand outputwithoutconsideringinternalcircuitry.Terminal A acceptselectricchargethatowsacross thecircuittoterminal B ,generatingdirectelectric current I .Thesuperoxidereactionsatterminals A and B generatedioxygenandperoxide,respectively. Inaqueousconditionsat pH 7thestandardoxidationpotentialforareactionatterminal A anodeisapproximately E o 0 =0 : 16 Vandthestandardreductionpotentialforareactionatterminal B cathodewiththeadditionoftwohydrogenionstogeneratehydrogenperoxideisapproximately E r 0 0 =0 : 89 V[24,25].Thusthestandardpotentialforasinglenetreactiontohydrogenperoxidesc.thevoltageacrosstheterminalsis E 0 0 =1 : 05 V. 2

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Figure1:BlackboxdiagramofageneralSODcircuitin electronownotation. EmpiricallydeterminedSODrateconstantsenableacertaincurrentintensitycalculationofthe circuitmodel.Inthetraditionalparticulatemodel ofReaction4, 1 = 2 thus isconsideredempiricallyequivalentto 1 [26],despite beingpseudosecond-orderand 1 beingpseudo-rst.ForReaction3inaclosedsystemofconstantvolume,the reactionrate r = )]TJ/F19 9.9626 Tf 7.749 0 Td [(d[O )]TJ/F20 6.9738 Tf 0 -6.919 Td [(2 ] = d t =2 [O )]TJ/F20 6.9738 Tf 0 -6.919 Td [(2 ] 2 .Treatingsuperoxideasitselectron[8,9,2023]:charge carrierdensity n =N A [O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] ,Faraday'sconstant F=eN A ,andchargedensity = )]TJ/F19 9.9626 Tf 7.748 0 Td [(e n ;yielding r =2 )]TJ/F22 9.9626 Tf 7.749 0 Td [(= F 2 .Averagechargedensitywithconstantcontainervolume V yieldsthecurrentintensityexpression I = d Q d t =2 FV[O )]TJ/F20 6.9738 Tf 0 -6.918 Td [(2 ] 2 isconstantover f 10 )]TJ/F20 6.9738 Tf 6.227 0 Td [(13 m [O )]TJ/F20 6.9738 Tf 0 -6.919 Td [(2 ] 10 )]TJ/F20 6.9738 Tf 6.227 0 Td [(5 m g Ina 100 fLhumancellwhere 2 10 9 m = 1 s = 1 byEquation2humanintracellularSODhasacurrentintensity I ontheorderofyAtonA.The SODcircuithasamagneticeldassociatedwith itselectriccurrent. Figure2:NortonequivalentdiagramofageneralSODcircuit inelectronownotation. Ifcurrentintensitywereinsteadcalculatedwith theunknowntraditionalparticulatemodelrate constant 1 ,Equation2wouldbe I = 1 FV[O )]TJ/F20 6.9738 Tf 0 -6.919 Td [(2 ] concurringwithprecedentasalinearcorrelation betweenthesuperoxidesensor'selectriccurrentintensityandthesolutionconcentrationofsuperoxide [21,22]. AccordingtothetheoremsofNortonand Thvenin,theblackboxmodelofFigure1simpliedtocontainonlycurrentsource,voltagesource, andresistorelementsmaybeequivalentlydescribed asasinglecurrentsourceinparallelwithasingle resistorandasinglevoltagesourceinserieswitha singleresistor,respectively.TheNortonequivalent isdiagrammedinFigure2toshowcontinuityof currentsourcealthoughaconstantcurrentintensityistheexpectedbehavioronlyatmaximumsaturation.Undervariablecurrentintensity,constant voltageappliesviz.giventheThveninequivalent, electrictension V=E 0 0 Discussion Thiscommunicationrequirednumerousassumptionsandsimplications.SODisonlyabout 3 : 5 to 6 : 0 nmhighwithadiameterofabout 2 : 0 to 5 : 5 nm sothemostprominentdissonancemaybethatthis isaclassicaldescriptionofwhatislikelypredominantlyquantumphenomena.Classicalmodelsdo howeverhaveheuristicutilityasquantumbiological systemsremaininaccessible. Oxygenatedfreeelectronowmodeledaselectriccurrentenablesanenergeticviewofoxidative stress.Anoxidativemilieumaybeviewedasan electromagneticdysfunctionviz.aberrantelectron owisthetoxicagentwhereastheiraliatedreducedspeciesaresimplyablecarriers.UnlikecircuitSOD,thisisnotanentirelynovelmodel. SOD'sroleasabiologicalcircuit,oratleastthe capabilitytomodelitasone,isintuitiveconsidering itsknownreactionissolelyelectrontransfer.The SODmodelingresultsareontheorderofwhatis expectedforananometerscaledevice. Althoughthemagneticcomponentisnotthesubjectofthiscommunication,mostSODisoforms haveawindingcylindricalbackbone -barreland arehollowexceptingcoretransitionmetalssc.an analogicalsolenoid.Bothdioxygenandsuperoxide areconsiderablyparamagnetic.SOD'selectromagneticpropertiesmayaccountforitsgreaterthan diusionlimitedactivity. Theelectrodynamicparadigmcommunicatedhas immediatemechanisticimplicationsforSOD'sactivityasabiologicalsuperoxidebuer.Thetraditionalparticulatemodeldoesnotsucientlydescribethisactivity.IncontrasttheSODcircuit 3

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