1

Energyharvestingfromabiocell

Authors:L.Catacuzzeno1,F.Orfei2,A.DiMichele2,L.Sforna3,F.Franciolini1,L.Gammaitoni2

Affiliations:1Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia - viaPascoli,I-06123Perugia,Italy2NiPSLaboratory,DipartimentodiFisicaeGeologia,UniversitàdegliStudidiPerugia-viaPascoli,I-06123Perugia,Italy3DipartimentodiMedicinaSperimentale,UniversitàdegliStudidiPerugia-ViaGambuli,1,I-06132Perugia,Italy

Correspondingauthor:CorrespondenceandrequestsformaterialsshouldbeaddressedtoL. Catacuzzeno (luigi.catacuzzeno@unipg.it) and L. Gammaitoni(luca.gammaitoni@nipslab.org).

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Keywords

EnergyHarvestingBiologicalcellAutonomousdevicesNanojoule

Abstract

Thisworkshowsexperimentallyhowelectricalenergycanbeharvesteddirectly fromcell

membrane potential and used to power a wireless communication. The experiment is

performed by exploiting the membrane potential of Xenopus oocytes taken from female

frogs.Electricalpotentialenergyofthemembraneistransferredtoacapacitorconnectedto

thecellviaaproperelectricalcircuit.Oncethecapacitorhasreachedtheplannedamountof

energy, thecircuit isdisconnected fromthecelland thestoredenergy isused topowera

radiofrequencycommunicationthatcarriesbio-sensedinformationtoadistancedreceiving

circuit. Our result shows that electrical energy can be harvested directly from biological

cells and used for a number of purposes, including wireless communication of sensed

biologicalquantitiestoaremotereceivinghub.

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Introduction

In a popularmovie from the sixties (Fantastic voyage, 20th Century Fox), aminiaturized

submarine connects to human lung alveoli to replenish its accidentally emptied oxygen

reservoir,thusadvancingtheideathatuntetheredmicrodevicescouldnavigateinsidethe

bodywhilescavengingresourcesfrombiologicalcomponents.

In present day,micro robotics is considered tohave a potential impact in bioengineering

and in healthcare. Existing small-scale robots, however, still show limited mobility and

reduced communication capabilities due to a number of reasons, chief among them the

difficultytosolvethepoweringproblem.Themajorityofcentimetre-scalemedicalimplant

devices[1], considered for sensing and single-cell manipulation[2], targeted drug

delivery[3] and minimally invasive surgery[4], are powered by batteries[5] that have

severalunwantedfeatures,suchaslimitedlifetimeandenergycapacity,impactingsizeand

toxicityforthelivingorganism[6].Inthecaseofmicrorobots(sub-centimetre-scale),ifwe

exclude externally actuated and guided devices, self propelled devices for bioengineering

applicationshavebeendesignedtotakeadvantageoflocalchemicalgradients[7],parasitic

transport techniques[8] or bubble propulsions[9]. Exploiting cut-edge integrated circuit

technologyandoptimizingenergyharvestingprocesses[10],itmaybesoonpossibletoscale

downthepowerabsorbedbytheseimplanteddevicestothepointthattheycanbepowered

solely by the energy harvested from the biological environment[11]. Sources include

chemical energy (as generated by enzymatic reactions), mechanical energy (vibrations,

liquid flow) and thermal energy (exploiting temperature gradients). However, energy

harvestedfromthesesourcesisnotpromptlyavailableforcommunicationandtransduction

mechanismsare required toconvert it intoelectricalenergy for radiosignal transmission

purposes.Forthisreasonaninterestingenergysourcetopayattentionto,istheelectrical

potential existing in living organisms. Electrical potential energy in higher organisms has

beenrecentlyextractedfromthecochlea inthe innerearofguineapig,exploitingthe70–

100mVexistingacrossthethinwallbetweentheendolymphfluidinthecochlearductand

theperilymph[12].Thecochlearorganishoweverpresentonlyintheinnerear,sothata

more general approach topoweringmicrodevices from the environment requires amore

generallyavailablebodyenergysource.

Herewepropose tousea sourceofenergyubiquitouslypresent insidea livingorganism:

thepotentialdifferenceexistingacrosstheplasmamembraneofelectrically-polarizedcells.

Each cell of a living organism is surrounded by a plasma membrane bilayer selectively

permeable to ions, due to the presence of passive and active transport proteins for their

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passage.Someoftheseproteins(pumps)moveionsagainsttheirelectrochemicalgradient,

by using ATP (active transport). Others (channels) let ions flow passively through their

centralpore.The interplayof these transportsultimately results inanelectricalpotential

acrossthemembrane,whichinthecaseofneuronsandskeletalmusclefibresreachesthe

range70-90mV, negative inside[13]. Themembrane effectively acts as a biologic battery

whoseelectricalpotentialisactivelystabilizedbyionchannelsandNa/Kpumps.

5

Results

Here we present the results obtained according to the following scheme: we begin with

assessing themaximum power that can be extracted from a single cell. Subsequentlywe

showthatelectricalenergycanbeharvested fromacellandstored inapropercapacitor.

Finallyweshowthattheenergyharvestedfromthecellandstoredinthecapacitorcanbe

usedtotransmitaradiosignaltoanearbyreceiver.

Inordertoassessthemaximumelectricalpowerthatcanbeextractedfromabiocell,we

performed a number of simulations (see Supplementary material - “Model and

simulations”), which showed that, while cells with typical dimensions (5-20 µm in

diameter)werepredictedtoreleaseaverysmallpower(intheorderofpicowatts),cellsof

larger dimensions, such as skeletal muscle fibres, could provide a power of several

nanowatts(Supplementarymaterial-Fig.S1D,E),wellwithintherequirementofcurrently

availablewirelesssensornodes[14].

We verified experimentally this prediction using as test cell the large, round-shaped,

Xenopusoocyte(eggcellfromfrogXenopuslaevis),whichhasadiameterofabout1mm,and

expectedpoweroutputcomparabletotheskeletalmusclefibre(Supplementarymaterial-

Fig. S1F). The large dimension of these cells also allows to easily insert the harvesting

electrode and two voltage-clamp electrodes to record the electrical properties of the cell

(Fig. 1B) that areused to assess theharvestedpower. Initiallywemeasured the current-

voltage (I-V) relationship, with the harvesting electrode disconnected from ground, by

applyingvoltagesteps from-80to+60mV(in10mVsteps) fromaholdingpotentialof0

mV(squaresinFig.1C).Subsequently,theI-Vwasmeasuredaftertheharvestingelectrode

had been connected to ground, and the resulting current going through it (Ih) had

depolarizedtheoocytetoanewsteady-state level(Vm[g],circles inFig.1C).Thedifference

between the two I-Vsat the restingmembranepotential reachedby thegroundedoocyte

during energy delivery provides the current passing through the electrode, Ih[g] which

multipliedbyVm[g](Ih[g]*Vm[g])givesthepowerdeliveredbytheoocyte.Usingthisapproach

we obtained a mean harvested power of approximately 1.1 nW (Fig. 1D, left), well in

agreementwithourmodel(Supplementarymaterial-Fig.S1F).AsshowninFig.1D(right),

themembrane potential reached by the oocyte upon grounding the harvesting electrode,

which dictates the level of harvesting power, is relatively low (Vm[g] = ∼-20 mV) and

approximatelyhalftheinitialoocyterestingpotentialVm.

Thiselectricpotentialvalue,however, isexpectedtobesignificantlyhigher incellswitha

highrestingKpermeability.InoocytesoverexpressinginwardrectifierK(Kir4.1)channels,

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which displayed a resting membrane potential close to -90 mV, we obtained a ∼4-fold

workingpotentialanda∼20-foldharvestedpowerascompared tonaïveoocytes (Fig.1F,

insetand1G).

Given the relatively smallpower that canbeharvested froma single cell, energymustbe

accumulated over time in order to reach the amount needed to drive a

biosensor/transmittingdevice.Wethereforeperformedexperimentsaimedatdetermining

theabilityofXenopusoocytestoperformasapowersupply,tochargesmall-sizecapacitors

connectedinparalleltoit(Fig.2A).InFig.2Bwepresentatypicalvoltagetracewhere,after

theimpalementoftheoocyte(firstarrow),acapacitorwasinsertedinparallelwiththecell

(secondarrow).Rightaftertheconnectionofthecapacitor,thepotentialinstantlyreached

valuescloseto0mV,andthenslowlyhyperpolarizedwithexponentialtimecourse,during

thecapacitorchargingprocess.Fromthelevelofhyperpolarizationreachedandthevalueof

thecapacitance,weassessedtheenergystored inthecapacitorat theendof thecharging

process. This protocolwas implemented using capacitors of variable size (0.1, 0.2, and 1

mF). In addition, the charging ability of the 1 mF capacitor was assessed in control

conditions(NormalFrogRingerasextracellularsolution)or inpresenceofaNormalFrog

Ringer inwhichweadded10mMglucose.Undertheseconditionsweexpectedthecell to

metabolize the available glucose through the glycolytic pathway and increase its energy

content in terms of available ATP. As a consequence, the cell should display a stronger

ability to preserve the intracellular vs extracellular ionic gradients, and maintain a

hyperpolarized membrane potential during energy harvesting. As shown in Fig. 2C, on

increasing the capacitance value, the measured voltage across the capacitor tends to

decrease,thusindicatingthattheoocytecellbehaviourdepartsfromthatofanidealpower

supply. This is likely caused by the limited nutrient supply to the cell in our recording

conditions, given that a higher voltage is reached when 10 mM extracellular glucose is

added. In Fig. 2D we present the accumulated energy for the different cases. We finally

inspected the ability of the oocyte to charge a capacitor several times in temporal

succession, and found that theenergystoreddecreasedduring repeatedcharging rounds,

eveninpresenceofextracellularglucose(Fig.2E,F).

Finally,wedemonstratethattheenergyextractedfromasingleXenopusoocyteandstored

inthecapacitorcanbeusedtotransmitaradiosignaltoanearbyreceiver.Morespecifically

weusedtheharvestedenergytogenerateacurrentthroughanLRCcircuit,whosemagnetic

fieldwasabletoinduceanelectromotiveforceinanearby(fewcentimetres)coil/antenna

connected to an oscilloscope (Fig. 3A). As shown in Fig. 3B, at the beginning of the

experiment themicroelectrodewas inserted intoanoocytebathed inNormalFrogRinger

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plus10mMglucose,andanegativerestingpotentialofabout-60mVcouldberead.A1mF

capacitor was then connected to the oocyte and after the charging process, it was

disconnected from the cell and connected to an LRC circuit, where it induced a damped

sinusoidal current, capableofgeneratinga clearlydetectable signal in thecoil/antennaof

the receiver (Fig. 3C). The resulting signal was fitted with an exponentially decaying

sinusoidal function (Fig. 3D) and the best fit parameters, obtained from eleven repeated

experiments,arepresentedinFig.3Easafunctionofthecapacitorvoltageattheendofthe

chargingprocess.Asexpected,whilethefrequency(ω)andthedampingfactor(γ)remained

constant,theinitialamplitudeofthesignal(As)showsanapproximatelylinearrelationwith

thecapacitorvoltage,thusconveninginformationofthecellrestingpotential.

Conclusions

Webelievethatthedemonstratedpossibilitytoharvestelectricalenergydirectlyfrombio

cells anduse it topowerwireless communications represents anewenabling technology

thatwillfosterthedesignofanovelclassofmicrodevicesaimedatinteractingdirectlywith

biological components inside living organisms, with endless possibility for future

biotechnologicalapplications.

ExperimentalMethods

Electrophysiology.Xenopusoocyteswereeitherpreparedaspreviouslydescribed[16]or

purchasedbyEcocyteBioscience(Dortmund,Germany).Twoelectrodevoltage-clamp

(TEVC)recordingswereperformedfromoocytesatRT(22 °C),1–10daysafterisolation,by

usingaGeneClamp500amplifier(AxonInstruments,FosterCity,CA)interfacedtoaPC

withanITC-16interface(InstrutechCorporation,Longmont,CO).Membranepotential

measurementswereperformedbyusinganEPC-10patch-clampamplifier(HEKA

Instruments,Lambrecht/Pfalz,Germany)interfacedtoaPC,usingasingleintracellular

electrode.IntracellularelectrodesalwaysconsistedinAg/AgClwiresinsertedintoheat-

pulledglasscapillariescontaining3MKCl,havingaresistancehigherthan1MΩwhen

testedinNormalRingersolution.Thecorrectrecordingconfigurationwasachievedby

usingmicromanipulators(Narishige,Cambridge,UnitedKingdom).Thestandardrecording

solution(NormalRinger)waspurchasedfromEcocyteBioscience.Recordingswerefiltered

at2 kHzandacquiredat5 kHzwithPulsesoftwareandanalysedwithPulseFit(HEKA,

Germany).

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ExpressionofKir4.1channels.Oocyteswereinjectedwith50 nlhumanKir4.1mRNAsand

storedat16 °CinfreshND96mediumcontaining(inmmol/L):NaCl96,KCl2,MgCl21,

CaCl21.8,Hepes5,gentamicin50 μg/ml(Sigma,Italy).mRNAconcentrationswere

quantifiedbyelectrophoresisandethidiumbromidestainingandbyspectrophotometric

analysis.

References

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2. Ceylan,H.,Giltinan,J.,Kozielski,K.&Sitti,M.Mobilemicrorobotsforbioengineeringapplications.Lab.Chip17,1705–1724(2017).

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8. Carlsen,R.W.&Sitti,M.Bio-hybridcell-basedactuatorsformicrosystems.Small10,3831–3851(2014).

9. Li,J.,Rozen,I.&Wang,J.RocketScienceattheNanoscale.ACSNano10,5619–5634(2016).

10. Gammaitoni, L., Chiuchiú, D., Madami, M. & Carlotti, G. Towards zero-power ICT.Nanotechnology26,319501(2015).

11. Piguet,C.inLow-powerelectronicsdesignChapter45(CRCPress,2005).

12. Mercier,P.P., Lysaght,A.C.,Bandyopadhyay, S., Chandrakasan,A.P., Stankovic,K.M.Energy extraction from the biologic battery in the inner ear. Nat. Biotechnol. 30, 1240-12433(2012).

13. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K. & Walter, P. inMolecularbiologyofthecellChapter11(GarlandScience,2002).

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15. XPPAUTSoftwarecode.Seehttp://www.math.pitt.edu/~bard/xpp/xpp.html.

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16 Sforna,L.,D'Adamo,M.C.,Servettini,I.,Guglielmi,L.,Pessia,M.,Franciolini,F.,Catacuzzeno,L.ExpressionandfunctionofaCP339,818-sensitiveK⁺currentinasubpopulationofputativenociceptiveneuronsfromadultmousetrigeminalganglia.JNeurophysiol.113:2653-65(2015).

Acknowledgements

The authors gratefully acknowledge financial support from the European Commission(H2020, Grant agreement no: 611004, ICT- Energy) and ONRG grant N00014-11-1-0695andDr.M.C.D’AdamoforprovidingthehumanKir4.1mRNA.

Dataavailabilitystatement

The data that support the findings of this study are available from the correspondingauthorsuponrequest.

CompetingFinancialIntereststatement

Theauthorsdeclarenocompetingfinancialinterests.

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Figure1.A)SchematicdrawingofacellexpressingNa,K,andClchannelsandNa/KATPases.Thecellhasbeenimpaledwithaharvestingelectrodeconnectedtoaloadresistanceandgroundedinthesame bath containing the cell. B) Photograph showing a Xenopus oocyte impaled with two glasselectrodes used to voltage clamp the cell and a third one to extract energy from the cell whenconnectedtoground.C)Currentvoltagerelationsobtainedbefore(black)andafter(red)groundingtheharvestingelectrode.D)Meanharvestedpower(left),andmembranepotential(right)assessedin fouroocytesbefore(gray)andaftergrounding(red).Thepowerwasassessedas theproductofthesteady-statemembranepotentialreadaftergroundingtheharvestingelectrodeandthecurrentthroughtheharvestingelectrodeatthispotential.E)FamiliesofmembranecurrentsrecordedfromaXenopus oocyte expressing Kir4.1 channels, in response to voltage steps from -120 to +20 mV(step=10 mV) from a holding potential of -80 mV, before and after grounding the harvestingelectrode.F)Currentvoltagerelationships(I-V)obtainedfromthecurrenttracesshowninpanelE.Inset:Meanmembranepotential fromsixKir4.1-expressingoocytesbeforeandaftergrounding.G)Meanharvestedpowerassessedinsixoocytesastheproductoftherestingmembranepotentialreadaftergroundingand thecurrent through theharvestingelectrodeat thispotential.Forcomparisonthemeanpowerharvestedinuninjected(endogenous)oocytes(frompanelD)isalsoshown.

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Figure 2. A) Schematic representation of the circuit used to charge a capacitor with the energyderiving from the oocyte membrane potential. B) Representative trace showing the oocytemembranepotentialuponcellimpalement(firstarrow)andfollowingconnectiontoa1mFcapacitorin parallelwith the cell (second arrow). The charging process of the capacitor and its exponentialtimecoursearealsoillustrated.C)Plotofthechargingvoltage(VC)acrossthecapacitorasafunctionofitscapacitance.Noticethatthe1mFcapacitancehasbeentestedineitherNormalRinger(white)orNormal Ringer plus 10mM glucose (grey).D) Energy stored in the capacitor at the end of thechargingprocess,assessedforthefourdifferentconditionstested.ThestoredenergywasassessedasE=½C⋅V2.Thetimesrequiredtochargethecapacitortohalf-maximalvoltageamplitudewere:0.1mF,193±49s;0.2mF,300±45s;1mFinNormalRinger,432±152s;1mFinNormalRingerplus10mMglucose,285±139s.E)Representativevoltage trace showing the impalementof a cell and thechargeofa0.2mFcapacitor5timesinsuccession.F)Plotofthemeanchargingvoltagereachedinthe5successivechargingprocessesinexperimentssimilartothatshowninA(n=5).Thefirstvoltagevaluerepresentstherestingmembranepotentialoftheoocytesoonaftertheimpalement.

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Figure 3. A) Schematic representation of the circuit used to charge a capacitor with the energyderivingfromtheoocytemembranepotential,andtransmitawirelesssignal.B)Timecourseoftheoocyte membrane potential upon cell impalement, connection to a 1 mF capacitor, capacitordischargeandsignalemissionthatiscapturedviaelectromagneticinductionbythereceiver.Noticethattheseexperimentswereperformedwith10mMglucoseaddedtotheNormalRinger.C)Typicalsignaldetectedatfewcentimetredistancebyanelectromagneticinductionsensor.D)Representativequantitativeanalysisof thesignalsdetected.Theexponentially-dampedsinewavesignalwas fittedwiththegeneralequationVs=As·exp(-γt)·sin(ωt),whereAsistheamplitudeoftheoscillatingpart,γis thedecay constantof theexponential, andω is theangular frequencyof the sinewave.E)Plotsillustrating the relation between the fitting parameters and voltage. As expected, the decay timeconstant,γ,andtheangularfrequencyofthesinewave,ω,arebothvoltageindependent,whereastheamplitudeofthesinewaveattimezerodisplaysalineardependenceonvoltage.

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SupplementarymaterialModelandsimulations

OurmodelconsideredacellexpressingNa/KATPasesandionchannelsselectiveforNa,K

andClions(Fig.S1A).Aharvestingelectrodewasinsertedintothecell,andgroundedinthe

samesolutionbathingtheextracellularmembrane. Inserieswiththeharvestingelectrode

was a load resistance RL. The extracellular solution contained Na, K, and Cl ions at their

physiological concentrations [Na]o, [K]o, and [Cl]o, respectively, and the electroneutrality

condition implied that 𝑁𝑎 ! + 𝐾 ! = 𝐶𝑙 ! . The intracellular solution contained Na, K,

and Cl ions, in addition to impermeant monovalent anions A, mostly representing

macromolecularanionicgroups,atconcentration[Na]i,[K]i,[Cl]i,and[A]i,respectively.In

the intracellular compartment the electroneutrality conditionwas also respected: 𝑁𝑎 ! +

𝐾 ! = 𝐶𝑙 ! + 𝐴 ! .Theelectricalbehaviourofthecellmayberepresentedasanelectrical

circuitwherea capacitor is inparallelwith several resistances anda current source (Fig.

S1B).Thecapacitor represents thephospholipidmembrane, theresistancesrepresent the

variouspathwaysforionpassagethroughionchannelsandforcurrentpassagethroughthe

loadresistance,andthecurrentsourceisgeneratedbytheactivityoftheNa/KATPases.As

for the above described electrical circuit, also in the cellmembrane the sum of the ionic

currents passing through the various pathways must cancel out (principle of charge

conservation).

𝑖!" + 𝑖! + 𝑖!" + 𝑖! + 𝑖!" + 𝑖!" = 0 (1)

Here𝑖!" ,𝑖! ,and𝑖!" representthecurrentsgeneratedbyNa,K,andClionspassingthrough

their respective ion channels. These currents may be modeled through the Goldman-

Hodgkin-Katzrelationship:

𝑖! = !!!

(!!!)!

! ! 𝑉! [!]!! ! ! !!

!!! !!! !

!! !!!!! !!! !

; 𝑛 = 𝑁𝑎,𝐾,𝐶𝑙 (2)

thatinthephysiologicalcondition,where!!! !!! !

≪ 1,maybeapproximatedto:

𝑖! = 𝑔! [𝑛]! (𝑉! − 𝐸!); 𝑛 = 𝑁𝑎,𝐾,𝐶𝑙 (3)

Here𝑃! is the channel permeability to ion n,𝑧! is the ion n valence, F is the Faraday

constant,Ristheuniversalgasconstant,Tistheabsolutetemperature,𝑉!isthemembrane

potential difference (inside minus outside), [n]i/o are the intracellular/extracellular

concentrationsofionn,𝑔! = !!!

(!!!)!

! ! isthemacroscopicconductanceoftheionchannel

selective to ion n,𝐴 is the cell model membrane surface and𝐸! =! !!! !

𝑙𝑛 [!]![!]!

is the

equilibriumpotentialforionn.

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Fig.S1.A)SchematicdrawingofacellexpressingNa,K,andClchannelsandNa/KATPases.Thecellhas been impaledwith a harvesting electrode connected to a load resistance and grounded in thesamebathcontainingthecell.B)Equivalentelectricalcircuitof thecellshownonthe left.gNa,gK,andgCl represent the conductancesprovidedby the respective ion channels, each in serieswithabatterysetattheequilibriumpotentialoftheion.TheNa/KATPasecontributesasacurrentsource,and themembranephospholipidbilayerof themembranewill contributeasa capacitanceCm.Theenergy harvesting pathway is here represented by the load resistance RL. C) Simulation of themembrane voltage and harvested power dynamics when the load resistance associated to theharvestingelectrodechangesfrom1000to3GΩ.Parameterswereasintheneuronmodel(Table1).D)Plotsof thesteadystatevoltage,harvestedpowerand intracellular ionicconcentrationsvs load

15

resistance, obtained from simulations similar to that shown in panel A.E) Simulations performedwithcelldimensionstypicalofskeletalmusclecells(diameterof100µmandlengthof0.5to2cm).Thepanelsshowplotsofthemembranevoltage(top)orharvestedpower(bottom)asafunctionoftheloadresistanceconnectedtotheharvestingelectrode.Theeffectofvaryingthemusclelengthisalso shown.F) Simulationsof thepowerharvestedwithcelldimensionsandparameters typicalofXenopusoocytes.TheeffectofvaryingtheKconductanceanddensityofNa/Kpumpsisshown.

𝑖!representsthenetcurrentpassingthroughtheNa/KATPases.Thistransporter,ateach

cycle, promotes the passage of three Na ions outside and 2 K ions inside the cell, thus

generating a current equivalent to the passage of one positive charge outside. For our

purposes𝑖!maybemodeledbythefollowingequation:

𝑖! =!

!!!!

!" !

! (4)

where𝜌is the maximal Na/K ATPase pump current density, and𝑘!is the affinity of the

pumpforintracellularNaions.

𝑖!" representthecurrentpassingthroughtheharvestingelectrode,obeyingtoOhm’s law

𝑖!" =!!!! !

. Finally 𝑖!" represents the current charging the capacitor and creating an

electricalpotentialdifference

𝑖!" = !! !!!!"

(5)

Where𝐶! isthespecificmembranecapacitanceofthecellmembrane.Substitutingeqn.(2)-

(5) into eqn (1), and making the quasi steady-state assumption for membrane potential

relaxation !!!!"

= 0, validbecause the relaxation time for themembranepotential ismuch

shorterthantheionequilibrationtime(seebelow),weobtainthefollowingequationforthe

membranepotentialdifference:

𝑉! = !!" !" ! !!"!!! ! !!!!!!" !" ! !!"!!!!!" !" ! !!! ! !!!!" !" !!

!! !!

(6)

InourmodeltheintracellularconcentrationsofNa,K,andClvarywithtimebecauseofthe

passage of these ions through ion channels and transporters expressed in the cell

plasmamembrane.Inaddition,itisassumedthattheharvestingelectrode,whileinjectinga

current insidethecell, increasesthe intracellularprotonconcentration(thiswilloccurfor

electrodes such as platinum or iridium, that catalyze the reaction 2H2O-> 4e + 4H++O2).

Excess protons will then be exchanged for external Na ions by the activity of the Na/H

counter-transporter. This processwill result in an increase of a Na ion for each electron

passingthroughtheharvestingelectrode.

16

Taking intoaccountall theabovesourcesof intracellular ionchanges,wecanwritedown

thefollowingdifferentialequationsfortheintracellularmolesofions:

𝑑𝑛!"𝑑𝑡

= 𝛾 −𝐼!" − 3 𝐼! − 𝐼!"

!!!!"

= 𝛾 −𝐼! + 2 𝐼! (7)

𝑑𝑛!"𝑑𝑡

= 𝛾 𝐼!"

Where𝛾 = 𝐴𝐹,𝑛!" ,𝑛! ,and𝑛!" aretheintracellularmolesofNa,K,andCl,respectively.

Finally,sincetheplasmamembraneishighlypermeabletowater(muchmorethantoions),

thecellwilladjustitsvolumeinordertopreservetheiso-osmolaritycondition

𝑂𝑠𝑚! = 𝑂𝑠𝑚!" (8)

Where𝑂𝑠𝑚! =𝑛!" + 𝑛! + 𝑛!" + 𝑛!

𝑉𝑜𝑙 is the intracellular osmlolarity,𝑉𝑜𝑙 is the cell

volume,𝑂𝑠𝑚! = [𝑁𝑎]! + [𝐾]! + [𝐶𝑙]! istheextracellularosmolarity,giving

𝑉𝑜𝑙 = 𝑛!" + 𝑛! + 𝑛!" + 𝑛!𝑂𝑠𝑚!"

(9)

Fromtheintracellularionmolesandcellvolumewecanfinallyassesstheintracellularion

concentrationsas:

[𝑁𝑎]! =𝑛!"

𝑉𝑜𝑙 , [𝐾]! =𝑛!

𝑉𝑜𝑙 , [𝐶𝑙]! =𝑛!"

𝑉𝑜𝑙 (10)

ParametersusedforthethreecellmodelsaregiveninTable1andthesolutionofthesetof

differentialequations(7)wasobtainedwithxppaut[15].

Wefirstperformedsimulationsusingparameterstypicalofaneuron,whosecellbodywas

assumedtobesphericalwitharadiusof7µm.Asyoucanseefromtheresultspresentedin

Fig.4C,whentheloadresistanceisloweredfromaverylargevalue(>100GΩ)tofewGΩ

(from1000GΩ to 3 GΩ), a current began to pass through the harvesting electrode, thus

generatingapower.Thiscurrent,however,tendstodepolarizetherestingpotentialofthe

cellandchangetheinternalionconcentrations(thislatterrelevantonlyinsmallsizecells),

processesthatlimitthepowerrecoveredatsteadystate.Forthisreasontherelationshipof

theharvestedpowerasafunctionoftheloadresistancehadabellshape,withamaximum

power of 1 pW at around 2 GΩ of load resistance. Although the trend is towards a

continuous reduction in the energy required to power biosensors, 1 pW appears to be a

valuetoolowtoevenhypothesizethataneuronmayinthenearfuturebecomeaplausible

sourceofenergy,evenforultralowpowerdevices.

17

Table1-Modelparameters

Parameter Description Neuronmodel SkeletalMusclemodel Oocytemodel

Dimension Cellradius(R) R=7µm(1) R=50µm,variablelength(7) R=0.5mm(11)

CS Specificmembranecapacitance 0.01pF/µm2(6) 0.01pF/µm2(6) 0.01pF/µm2(6)gKS SpecificKchannelconductance 3.8*10-6nS/(mMµm2)(1) 2.33*10-5nS/(mMµm2)(5) 2.2*10-6nS/(mMµm2)

(9)

gNaS SpecificNachannelconductance 2.5*10-5nS/(mMµm2)(1) 8*10-7nS/(mMµm2)(5) 2*10-5nS/(mMµm2)(9)gClS SpecificClchannelconductance 1*10-4nS/(mMµm2)(1) 1*10-4nS/(mMµm2)(5) 5.4*10-7nS/(mMµm2)

(10)

RL Loadresistance variable variable variableρ MaximalturnoverrateofNa/K

ATPase0.018pA/µm2(1) 0.07pA/µm2(4) 0.024pA/µm2(8)

[K]O ExtracellularKconcentration 3mM(2) 3mM(2) 3mM(12)

[Na]O ExtracellularNaconcentration 142mM(2) 142mM(2) 118mM(12)[Cl]O ExtracellularClconcentration 145mM(2) 145mM(2) 120mM(12)nAAi Intracellularimpermeableanions 0.189pmol(3) 10,140pmol(3) 7.41*104pmol(3)

(1)FromWeietal.,2004;reasonablestartingvaluesof[Na]i=10mM,[Cl]i=10mM,and[K]i=132mMwereconsideredintheparameterconversionsofconductances(2)Typicalextracellularsolutionforamammaliancell(3) Chosen to neutralize the intracellular solutions, by considering the starting values used forintracellularionconcentrationsinthesimulation([Na]i=10mM,[Cl]i=10mM,and[K]i=132mMinthemammaliancellmodel)(4)BasedonPlesnerandPlesner,1981,andClausen,2003.(5)BasedonPedersenetal.,1981,andDulhunty,1979(6) Hille, B. (2001) Ion Channels of Excitable Membranes. 3rd Edition, Sinauer Associates Inc.,Sunderland.(7)BasedonHegartyandHooper,1971(8)BasedontheestimatedNa/Kpumpcurrentof34nA(Costaetal.,1989)andconsideringa[Na]Iof10mM(Sobczaketal.,2010)(9)SettledbyconsideringthatinourmodelINaandIKshouldbeequalto3and2timestheNa/Kpumpcurrent,atarestingmembranepotentialof-45mV(Kusanoetal.,1982)(10)BasedonCostaetal.,1989)(11)BasedonSobczaketal.,2010)(12)Typicalextracellularsolutionforamphibiancells

ReferencesreportedintheTable:

PlesnerL,PlesnerIW.Thesteady-statekineticmechanismofATPhydrolysiscatalyzedbymembrane-bound(Na++K+)-ATPasefromoxbrain.I.Substrateidentity.BiochimBiophysActa.1981May6;643(2):449-62.

ClausenT.Na+-K+pumpregulationandskeletalmusclecontractility.PhysiolRev.2003Oct;83(4):1269-324.

HegartyPVandHooperAC.Sarcomerelengthandfibrediameterdistributionsinfourdifferentmouseskeletalmuscles.J.Anat.1971.110,2,pp.249-257

SobczakK,Bangel-RulandN,LeierG,WeberWM.EndogenoustransportsystemsintheXenopuslaevisoocyteplasmamembrane.Methods.2010May;51(1):183-9.

CostaPF,EmilioMG,FernandesPL,FerreiraHG,FerreiraKG.DeterminationofionicpermeabilitycoefficientsoftheplasmamembraneofXenopuslaevisoocytesundervoltageclamp.JPhysiol.1989Jun;413:199-211.

KusanoK,MilediR,StinnakreJ.CholinergicandcatecholaminergicreceptorsintheXenopusoocytemembrane.JPhysiol.1982Jul;328:143-70.

18

Wethenturnedourattentiontothelarge,cylinder-shapedskeletalmusclecells,witha100

µmdiameterandlengththatmayreachseveralcentimetres–thatis,avolume3-5ordersof

magnitudeof neuronal cells. The largedimensionsof these cells confer a larger electrical

capacitance(i.e.thecapacitanceisproportionaltothesurfaceoftheplasmamembrane)and

thusahigherabilitytoaccumulateenergy,since𝐸𝑛𝑒𝑟𝑔𝑦 = !!

𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑥 (𝑉𝑜𝑙𝑡𝑎𝑔𝑒)!.

Otherpropertiesmakethesecellsappropriateasenergyharvester:theirdiffusepresencein

the human body, their large ATP content they use to contract, and their high

transmembranepotential.AsshowninFig4E,oursimulationresultsindicatethataskeletal

muscle cell is able to provide an electrical power of several nanowatts, and linearly

dependentonthelengthofthemusclefibre.

In thisstudyweexperimentally testedthepredictionthatabiologicalcellmaybeusedto

harvestelectricalenergybyusingascellmodelthelargeXenopusoocytesthatcanbeeasily

takenfromfemalefrogs.Thesecellsareroundshapedwithaverylargediameter(about1

mm), and a plasma membrane area approximately corresponding to that of a skeletal

musclefibreof5cmlength.ThesecellsdonothavethesamesurfacedensityofNa/Kpumps

and hyperpolarized membrane potential of a skeletal muscle fibre, yet a relatively high

harvestedpowerisexpected.ThisisshownbytheblacktraceinFig.S1FofSupplementary

material,showingthatanoocytewith itsendogenouschannelsandtransportersmaygive

backapowerofabout1nW. Xenopus oocyteshave theadditionaladvantage tobeeasily

used to express ion channels and transporters, to verify whether the harvested power

increasesaccordingly.ThecolouredcurvesinFig.S1FofSupplementarymaterialshowthat

the simulated harvested power may increase several folds for model oocytes

overexpressing K channels or Na/K pumps. The increase in harvested power in oocytes

expressing more K channels may be explained by considering that K efflux results in

increased membrane potential difference (i.e. the membrane potential becomes more

hyperpolarized), and the squared power dependence of the accumulated energy on

membranepotential.