Contribution of proton leak to oxygen consumption in skeletal muscle during intense exercise is very low despite large contribution at rest

PLOSONE|https://doi.o r g/10.13 7 1/journal.p o ne.0185 9 9 1 Octobe r18,2017 1^/14

2

RESEARCHARTICLE

Contributionofprotonleaktooxygenconsump tioninskeletalmuscleduringintenseexercisei sverylowdespitelargecontributionatrest

BernardKorzeniewski*

FacultyofBiochemistry,BiophysicsandBiotechnology,JagiellonianUniversity,Krako´w,Poland

*bernard. k orzeniewski @ gmail.com

Abstract

Acomputermodelwasusedtosimulatethedependenceofprotonmotiveforce(Δp),proton leakandphenomenological(involvingprotonleak)ATP/O2ratioonworkintensityinskeletal

muscle.Δp,NADHandprotonleakdecreasedwithworkintensity.Thecontributionofproton OPENACCESS

Citation:KorzeniewskiB(2017)Contributionofpro tonleaktooxygenconsumptioninskeletalmuscledu ringintenseexerciseisverylowdespitelargecontrib utionatrest.PLoSONE12(10):e0185991.https:// d oi.org/10.1371/ j ournal. pone.01859 9 1

Editor:AndrewPhilp,UniversityofBirmingham, UNITEDKINGDOM

Received:February27,2017 Accepted:September22,2017

leaktooxygenconsumption(V_O₂)decreasedfromabout60%atresttoabout3and1%atmo derateandheavy/severeexercise,respectively,whiletheATP/O2ratioincreasedfrom2.1to 5.5and5.7.Atwo-foldincreaseinprotonleakactivityoritsdecreasetozero

decreased/increasedtheATP/O2ratiobyonlyabout3and1%duringmoderateandheavy/severeexer cise,respectively.ThelowcontributionofprotonleaktoV_O2inintensivelywork-

ingskeletalmusclewasmostlycausedbyahugeincreaseinATPusageintensityduringrest-to- worktransition,whileOXPHOS,andthusoxidativeATPsupplyandV_O₂relatedtoit,wasmostlystimul atedbyhigheach-

stepactivation(ESA)ofOXPHOScomplexes.ThecontributionofprotonleaktoV_O₂andATP/O²ratioi nisolatedmitochondriashouldnotbedirectlyextrapolatedtoworkingmuscle,asmitochondrialackES A,atleastintheabsence

Published:October18,2017 ofCa²⁺,andthereforeV_O cannotbeelevatedasmuchasinintactmuscle.

Copyright:©2017BernardKorzeniewski.Thisisa nopenaccessarticledistributedunderthetermsofth eCreativeCommons Attribut i onLicense ,whichper mitsunrestricteduse,distribution,andreproductioni nanymedium,providedtheoriginalauthorandsourc earecredited.

DataAvailabilityStatement:Alldataarepresented withinthemanuscript.

Funding:ThisstudywasfundedbytheKNOWprogr am,whichsupportstheFacultyofBiochemistry,Biop hysicsandBiotechnologyofJagiellonianUniversity.

Thefundershadnoroleinstudydesign,datacollectio nandanalysis,decisiontopublish,orpreparationofth emanuscript.

Competinginterests:Theauthorshavedeclaredth atnocompetinginterestsexist.

Introduction

Protonleakacrosstheinnermitochondrialmembrane[1–4]leadstodissipationoftheproto- nmotiveforce(Δp)thatisnotcoupledwithATPsynthesisorATP,ADPandPitransportacrossthisme mbrane.ThemechanismofH^+ionsflowacrossthemembraneisstillnotfully

understood[1–4].Theintensityoftheprotonleakthroughtheinnermitochondrialmem- brane(vLK)dependssteeply(non-ohmicdependence)ontheprotonmotiveforceΔp[5–

9].Protonleakcanbeconstitutive(basalprotonconductance)andregulated(inducibleprotonco nductancecatalyzedbyuncouplingproteins,UCPs)[1–

4].Thyroidhormoneselevatetheconstitutiveprotonleak[10].BasalvLKisinverselyproportional tobodymass[11]andishigherinwarm-bloodedanimalsthanincold-

bloodedanimalsofthesamemass[12].Protonleakcanbeinducedbyreactiveoxygenspecies(R OS)actingthroughUCPs[2,13].

LK

Protonleakatrestandduringexerciseinskeletalmuscle

ThecontributionofprotonleaktoV_O_2inperfusedrestingratskeletalmusclewasesti- matedbyRolfeandBrandtobeabout60%at37˚C[8].Ontheotherhand,Marcinekandco- workers[14]estimated,onthebasisofinvivospectroscopicmeasurements,thatthereisessen- tiallynoprotonleakinrestingskeletalmuscle.

Ithasbeenproposedthattheso-calledeach-

stepactivation(ESA)mechanismisamajormechanismoftheregulationofOXPHOSduringworktra nsitions[15–

21].Accordingtothismechanism,NADHsupply,glycolysisandallOXPHOScomplexes(complexI, complexIII,complexIV,ATPsynthase,ATP/ADPcarrierandPicarrier)aredirectlyactivatedbysome cytosolicfactor(s)/mechanism(s)inparallelwiththeactivationofATPusagebyCa²⁺.

ThepresentstudyisaimedtoinvestigateinthetheoreticalwaythecontributionofvLK-

relatedV_O_2tototalV_O_2andthephenomenological(involvingprotonleak)ATP/O2ratioatdifferentworki ntensitiesinskeletalmuscle.Theeffectoftheprotonleakactivityonthesevari-

ablevaluesisalsostudied.ThedependenceoftotalV_O2,ATPsynthesis- relatedV_O2,Δp,NADHandprotonleak-

relatedV_O_2onworkintensityissimulated.ItishypothesizedthatthetotalV_O_2andATPsupply-

relatedV_O_2willriselinearlywithATPdemandactivity(workintensity),whileΔpand,consequently,leak- relatedV_O_2willdrop.Asaresult,thecontribu-tionofvLK-

relatedV_O2tooveralloxygenconsumptionwilldecreaseverysignificantly,whilethephenomenologic alATP/O2ratiowillincrease.Itisalsoexpectedthatanincreaseinprotonleakactivity(rateconstant)willinc reasethecontributionofvLK-

relatedV_O_2tototalV_O₂,decreasethephenomenologicalATP/O2ratioandΔp,whilereductionofthepr otonleakactiv-itytozerowillhavetheoppositeeffect.Itisexpectedthatthepresenceofhigheach- stepactiva-

tion(ESA)ofOXPHOS,essentiallyincreasingitscapacityforATPsupplyandallowingtomatchthehighl yelevatedATPusageactivity,leadstoalowcontributionofvLK-

relatedV_O_2tototalV_O₂,muchlowerthanatrest,andthustoahighphenomenologicalATP/O2ratio(ver yclosetothemechanistic,notinvolvingprotonleak,ATP/O2ratio)inintensivelyworkingskeletalmuscle.

Theoreticalmethods

Thepreviously-

developedcomputermodelofthecellbioenergeticsysteminskeletalmuscle[22,23]wasusedfortheoreti calstudies.Thismodelcomprisesexplicitly:oxidativephosphoryla-

tioncomplexes(complexI,complexIII,complexIV,ATPsynthase,ATP/ADPcarrier,Picar-

rier),NADHsupplyblock,ATPusage,protonleak,creatinekinase(CK)system,adenylatekinase(AK),pro tonefflux/influxto/fromblood,

(anaerobic)glycolysis.Thismodelhasbeenwidelyvalidatedthroughcomparisonofcomputersimulation swithexperimentalresults[15–23].

Theintensityofprotonleakinskeletalmuscleisdescribedbythefollowingkineticequa-tion:

v ¼k ·ðe^kLK2·Dp-1Þ ð1Þ wherekLK1=2.5μMmin^-1andkLK2=0.038mV^-

1.ThedependenceofprotonleakintensityonΔpisstronglynon- ohmicaspresentedinFig1.Thisdependencewasextractedfromdiffer- entexperimentaldata(seee.g.,[5–9])inordertorepresentthematleastsemi- quantitatively(anyway,thesedatadiffertosomeextentonefromanother).

InordertoproduceFig1,state4andstate3thatarepresentinisolatedmitochondria,butabsentininta ctskeletalmusclehadtobesimulated.Astatecorrespondingtostate4inisolatedmitochondriacanbein ducedinintactskeletalmusclebyoligomycin(inhibitorofATPsynthase)administration.Ontheotherha

Protonleakatrestandduringexerciseinskeletalmuscle

nd,state3andstate3.5(intheabsenceofESA)inintactskeletalmuscleareinasensehypothetical,becau setheywouldneedturningoffofESAto

Fig1.Dependenceofprotonleakintensity(vLK)onprotonmotiveforce(Δp).State4,state3,rest,moderateworkand heavy/severeworkinskeletalmuscleareindicated.vLKinallstatesisscaledforintactskeletalmuscle.Simulationswerema deusingthemodelversionforintactskeletalmuscle,asdescribedinthetext.

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bereached.Atthepresentstateofknowledgewedonotknowhowtodothisinintactskeletalmuscle,becau seESAispresentinintactskeletalmuscle,butabsentinstate3andstate3.5iniso-

latedmitochondria(atleastintheabsenceofCa^2+ions).Withinthemodelastatecorrespondingtostate4wa sreachedincomputersimulationsbyadecreaseintheactivity(rateconstant)ofATPusagetozero.Astate analogoustostate3inisolatedmitochondriawasreachedbyanincreaseinthisconstanttosaturating(for OXPHOS)valuesintheabsenceoftheeach-stepacti-

vation(ESA)ofOXPHOScomplexes.Inthesesimulations,CKandglycolysiswere‘switchedoff’[18]

(thisconcernsonlythesimulationspresentedinFig1).Theversionofthemodelforintactskeletalmusclera therthantheversionforisolatedmitochondria[18]wasusedinordertoscaletherespirationrateinparticula rstatestointactskeletalmusclerespiration.Themoderateworkstateandheavy/severeworkstateweresi mulatedasdescribedbelow.Generally,thetheoreticalpointsshowninFig1wereobtainedbysimulationo fparticularstatesandrecordingvLKandΔpinthem.ThelinecorrespondingtothegeneralvLK-

ΔpdependencerepresentssimplyEq1.

Thesimulationscarriedoutandpresentedinthisstudyconcernsteady-

statevariablevaluesandnottimecoursesofvariablevalues.Thebasalorinitialsteady-

stateforallsimulationswasreststatewith‘standard’parametervalues.Ineachsimulationoneorafewpa rametervalueswerechanged,asdescribedbelow,andthenthesystemwasallowedtoapproachanew steady-state,inwhichnewvariablevalueswererecorded.

Thesimulationsfordifferentworkintensities(Figs2–

5)weremadebyagradualincreaseinsubsequentsimulationsoftherateconstantofATPusage(hy drolysis)kUT.TherelativeincreaseinkUT(AUT,activationofATPusageinrelationtorest)variedfro mAUT=1timesatrest

2 -1

Fig 2. Dependenceoftotaloxygenconsumption(V_O₂),V_O₂relatedtoprotonleakandV_O₂relatedtoATPsynthesi sonADPconcentration.

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(V_O₂₌0.27mMmin )toAUT=28timesformoderatework(resultinginV_O2 ofabout 3.5mMmin^-1)andAUT=80timesforheavy/severework(resultinginV_O ofabout8.7 mMmin^-1).Therefore,AUTwasthemeasureordeterminantoftheworkintensity,propor- tionaltoATPusageformechanicalwork.Atthesametimetheactivities(rateconstants)of_0.35

allOXPHOScomplexesandNADHsupplywereelevatedAOX=AUT times.Forinstance, AOX=3.2formoderateexercise(AUT=28)andAOX=4.6forheavy/severeexercise(AUT=80).Thiscorres pondstotheeach-

stepactivation(ESA)mechanismoftheregulationofOXPHOSduringworktransitionspostulatedprevi ously[15–21]

(thepowercoefficientpisthemeasureofESAintensity;p=0.35meansmoderateESA).Or,moreprecis ely,thiscorre-spondstotheso-

calledmixedmechanism,whereallOXPHOScomplexesaredirectlyacti-

vated(ESA),buttoasmallerextentthanATPusage,andthereforetheregulationbythenegativefeedba ckthroughelevatedADPandPico-operateswiththeregulationbyESA

[19,24].Glycolysiswasactivated(itsrateconstantwaselevated)AGL=AUT0.7times[23].In the‘standard’modelversion(Figs2and3)thecontributionofprotonleaktoV_O2atrestequaled63%.

ItwasassumedthatESAconcernsOXPHOScomplexes,butnotprotonleak.ESAissupposedtobe aspecialmechanismthatelevatestheATPproductionrate,andapotentialactivationofprotonleakb yESAwouldbecounter-productive(protonleak

decreasesΔpandthusATPsynthesisrate).Protonleakisnotstimulatedinisolatedmito- chondriabyCa^2+thatcanactivateabouttwiceallOXPHOScomplexes(theCa²⁺-

inducedelevatedstate4respirationwasduetoelevatedprotonmotiveforce,andnottodirectact iva-tionofprotonleak)[25].

Fig3.Dependenceoftotaloxygenconsumption(V_O

2),V_O

2relatedtoprotonleak,V_O

2relatedtoATPsynthesis,Δp,NADH(%oftotalNAD)andphen omenologicalATP/O2ratioonrelativeactivityofATPusage(relativerateconstant,k^UT,oritsactivationinrelationtorest,AUT)inskeletalmusclefor‘stan dard’protonleakactivity.

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TheparametervaluesinthesetofsimulationspresentedinFigs2and3representthe‘stan- dard’or‘reference’conditions.InthesetofsimulationsshowninFig4therateconstant(activ-

ity)ofprotonleakkLK1wasdoubledinrelationtothe‘standard’setofsimulations.Thisresultedinanincreas einthecontributionofprotonleaktoV_O_2atrestto78%.InthesetofsimulationsshowninFig5theratecon stantofprotonleakkLK1wassettozero(noprotonleak).Therefore,thecontributionofprotonleaktoV_O_2at restwasofcourse0%.

Atheavy/severeexerciseinskeletalmusclethe‘additional’ATPusagethatisamajorfactor underlyingtheslowcomponentoftheV_O2on-kinetics[20]wasomittedincomputersimula- tionsinordertoachieveasteady-state.

Generally,withinthemodeltheprotonleak-

relatedV_O_2(orvLKexpressedinV_O_2units)andATPsynthesis-

relatedV_O_2(orvASexpressedinV_O_2units)arerelatedtovLKandvASinsuchawaythat4electrons(e^-)ar eusedforthereductionof1O2molecule,20H^+ionsarepumpedfor4e^-

flowingthroughtherespiratorychainand3.5cytosolicH^+ionsareusedforsynthesisof1cytosolicATPmole cule(2.5H^+ionsforsynthesisof1matrixATPmoleculeand1H^+ionfortransportofATPtocytosolandofAD PandPitomitochondrialmatrix).Thus,vLK-relatedV_O_2equalsvLK/20andvAS-

relatedV_O_2equalsvAS^*3.5/20.

2 2 2

Fig4.Dependenceoftotaloxygenconsumption(V__O),V_Orelatedtoprotonleak,V_OrelatedtoATPsynthesis,Δp,NADH(%oftotalNAD)andphenomeno logicalATP/O2ratioonrelativeactivityofATPusage(relativerateconstant,k^UT,oritsactivationinrelationtorest,AUT)inskeletalmuscleforprotonleakactiv ity(rateconstant)elevatedtwiceinrelationtothe‘standard’value.

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Theoreticalresults

Protonleak-Δpdependence

Thedependenceoftheprotonleakintensity(vLK)onΔpinintactskeletalmuscleusedinthemodel(seeE q1)ispresentedinFig1.Inaccordancewithexperimentaldatathisdependenceisstronglynon- linear(non-ohmic).Particularstatesinskeletalmusclemitochondriaareindi-

catedinthediagram:state4(Δp=195.4mV),state3(Δp=154.1mV),reststate(Δp=191.9mV),moderat eworkstate(Δp=177.5mV)andheavy/severeworkstate(Δp=169.0mV).Thedetailedrelationbetwee nthesestateswasdiscussedinarecentarticle[18].Itshouldbestressedthatstate4andstate3inintactsk eletalmuscleisnotthesameasstate4andstate3inisolatedmitochondria.First,vLKcanbelargerisisola tedmitochondriathaninskeletalmuscle(forthesamemitochondriavolume/amount),astheinnermito chondrialmembranecanbedamagedinsomefractionofmitochondriaduringmitochondriapreparatio n.Second,usuallyahighconstantPiconcentrationisusedintheisolatedmitochondriasystem,whilePilevelch angesbetweendifferentstatesinintactskeletalmuscle[18].

Δp,NADH,vLK-relatedV

,contributionofvLK-relatedV

ototal V

O

2

andATP/O

atrest,moderateworkandheavy/severeworkinintact skeletalmuscle

ComputersimulationspredictthatwhenworkintensityincreasesinskeletalmuscleΔp,NADH,protonl eakintensity(vLK-relatedV_O2)anditscontributiontoV_O2decrease,while

Fig5.Dependenceoftotaloxygenconsumption(V_O₂),V_O₂relatedtoprotonleak,V_O₂relatedtoATPsynthesis,ΔpandNADH(%oftotalNAD)andphen omenologicalATP/O2ratioonrelativeactivityofATPusage(relativerateconstant,k^UT,oritsactivationinrelationtorest,AUT)inskeletalmuscleforprotonl eakactivity(rateconstant)settozero(noprotonleak).

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thephenomenologicalATP/O2ratioincreases.Thisdecrease/increaseisgreater,thelargertheworkint ensity.ThiscanbeseeninFigs2and3.Atrest,protonleakaccountsfor63%ofV_O2.Thisisinagreement withtheprotonleakcontributiontoV_O_2estimatedfor60%inratskeletalmuscle[8]

(seeTable1therein).ThecontributionofprotonleaktoV_O2decreasesdramati-

callywithanincreaseinworkintensity,asV_O_2relatedtoATPproductionincreasessignifi- cantlyduetothehugeincreaseintheATPusageactivity.OXPHOScomplexesarestimulated

byESAaswellasbyanincreaseinADPandPi.Atthesametimetheabsoluteprotonleakintensitydecrea sesduetothedecreaseinΔp(compareEq1).Atmoderatework(ATPusageactivationAUT=28times)pro tonleakaccountsforonlyabout3%ofV_O2,whileatheavy/severework(AUT=80times)itaccountsforon lyabout1%ofV_O₂.ThepresenceofprotonleakcausesthatthephenomenologicalATPsynthesis(vA S)-

ADPrelationshipissignificantlysteeper(ofhigherphenomenologicalorder)thanthephenomenologic alV_O₂-ADPrelation-ship,ascanbeseeninFig2.

Withinthemodelthemechanistic(notinvolvingprotonleak)ATP/O2ratioequals5.71(=20/3.5:20 protonspumpedper4electronsor1O2,3.5protonsneededforATPsynthesisandtransport,seeabo ve).Thephenomenological(involvingprotonleak)ATP/O2ratioincreasesfromabout2.1atrest(AUT=

1)toabout5.5duringmoderateexercise(AUT=28)andabout

5.7duringheavy/severeexercise(AUT=80).ThisisdemonstratedinFig3.

FortheparametervaluesusedinthesimulationsshowninFig3NADHdecreaseswithanincrea seinworkintensity.However,NADHcaneitherdecreaseorincreaseduringrest-to-

worktransitiondependingonhowstronglyNADHsupplyisdirectlyactivatedor,morepre- cisely,whatisthebalanceofactivationoftheNADH-producingblockandNADH-

consumingblock(OXPHOS+ATPusage).NADHcanincreasewhentheNADH- producingblockisstimulatedtoagreaterextentthantheNADH-consumingblock[21].

TheestimationofthecontributionofprotonleaktoV_O2equalstoabout60%atrestinratskeletalmu scle[8].However,itismostprobablydifferentindifferentanimals,beinggreater

insmalleranimals.Itcanbepotentiallyaffectedbysomefactors,suchasthyroidhormones,ROSortemp erature.Finally,Marcinekandco-

workers[14]measuredessentiallynoprotonleakinrestingskeletalmuscle.Therefore,intwosubseque ntsimulationstheeffectofdoublingandreducingtozeroofthe‘standard’protonleakactivity(rateconsta nt)waschecked.

Atwo-

foldincreaseinprotonleakactivity(rateconstant)kLK1causesadecreaseinΔpandNADH,especiallyatrest ,whiletheprotonleakintensity(flux)vLK(vLK-

relatedV_O₂)ofcourseincreases.Thecontributionofprotonleak(vLK-

relatedV_O₂)tototalV_O_2atrestincreasesto78%.ThiscanbeseeninFig4.However,theeffectonΔpan dNADHisrather

small,especiallyatwork.ThephenomenologicalATP/O2ratiodecreasessignificantlytoabout

1.3atrest,butonlybyabout3%and1%inrelationtothe‘standard’protonleakactivityduringmoderatean dheavy/severeexercise,respectively.

Aswitchingoffofprotonleak(decreaseofkLK1tozero)elevatesΔpandNADH,especiallyatrest.Thisi sdemonstratedinFig5.Ofcourse,inthiscasethecontributionofprotonleaktoV_O2atrestandworkis0%

andthephenomenologicalATP/O2ratioatallworkintensitiesisidenticalandequaltothemechanisticAT P/O2ratio(5.71).ThephenomenologicalATP/O2ratioincreasesbyonlyabout3%and1%inrelationtothe‘

standard’protonleakactivitydur-ingmoderateandheavyexercise,respectively.

Discussion

Inthepresentstudyacomputermodelofthemusclebioenergeticsystemwasusedtostudythedepend enceofΔp,NADH,protonleakintensity(vLK)(vLK-relatedV_O₂),ATPsynthesisintensity(vAS) (vAS-relatedV_O₂),contributionofvLK-relatedV_O_2andvAS-

relatedV_O_2tototalV_O_2andphenomenologicalATP/O2ratioonworkintensityinskeletalmuscle.

ThesimulatedcontributionofvLKtoV_O_2duringmoderateandheavy/severeexerciseinskeletalmuscl ewasverysmalldespitelargecontributionofvLKtoV_O_2atrestandduringlowexercise.Thiswasmostlyc ausedbythehugeincreaseintheATPusageintensityduringrest-to-

worktransitionandthusinV_O_2relatedtoATPsynthesis.OXPHOScomplexeswerestim-ulatedbyeach- stepactivation(ESA)andbyincreaseinADPandPi.Ontheotherhand,protonleakwasnotdirectlystimul atedanditsintensitydecreasedduetothedropinΔp.

ΔpandvLKindifferentstates

First,itwasshown,whatcouldbeintuitivelyexpectedandwhathasbeenalreadyatleastpartlydemonstr atedintheexperimentalway[8],thatthehighestΔpandvLKwereinstate4,thesmallest–

instate3,whileatrestandduringexercisetheyadoptedintermediatevalues(seeFig2).ΔpandvLKatres twereclosesttostate4,whileduringheavyexercise–tostate3.

V

-ADPdependencevs.vAS-ADPdependence

Theslopes(orders)ofthephenomenological(involvingESA)V_O2- ADPdependenceandthephenomenologicalvAS-

ADPdependencedifferedsignificantly,andthisdifferencewasduetoprotonleak.Thisisdemonstrate dinFig2.V_O2andvAS(expressedinoxygenconsumption

equivalents)divergedsignificantlyatlowADPpresentatrest,wherevLK(vLK-

relatedV_O₂)wasrelativelyverysignificant,whiletheystartedtoconvergeathighADPconcentrationsp res-entduringwork,wherevLKdecreased.

ProtonleakcontributiontoV

dphenomenologicalATP/O

oinskeletal muscle

ProtonleakcontributiontoV_O₂.TheincreaseinthetotalV_O_2andvAS- relatedV_O_2aswellasthedecreaseinvLK-

relatedV_O_2withanincreaseintheATPusageactivity(energydemand),proportionaltomechanicalw orkintensity,for‘standard’protonleakactivityisshowninFig3.Atrestprotonleakwasresponsiblefora bout63%ofV_O₂.Ontheotherhand,

duringheavy/severeexercisetheabsolutevalueofvAS-relatedV_O_2wastens-

foldgreater(duetoESAaswellasADPandPiincreaseinrelationtorest)thantheprotonleak-

relatedV_O_2.Atthesametime,ΔpdecreasedsignificantlywiththeincreaseintheATPusageactivity(energy demand).ThiscausedadecreaseintheabsolutevalueofvLK(vLK-

relatedV_O₂)atheavyworkinrelationtomoderateworkandthemoreinrelationtorest.

ChangesinΔpandNADH.BothΔpandNADHdecreasedwithanincreaseinworkintensi tyinthesimulationsshowninFigs3–

5.InskeletalmuscledifferentelementsoftheATPsupplysystemareactivatedbyESAtoalow erextentthanATPusage.Asaresult,

ADPandPialwaysincrease,whileΔpalwaysdecreasesduringrest-to- worktransition.ΔpisrelatedtothemitochondrialATP/

(ADP^*Pi)ratio(throughATPsynthase)andcytosolicATP/

(ADP^*Pi)ratio(throughATP/ADPcarrierandPicarrier).Therefore,thedecreasein(cytosolicandmitoc hondrial)ATP/(ADP^*Pi)resultingfromtheincreaseinADPandPiimpliesthatΔpalsodecreases.

Ontheotherhand,NADHcaneitherincreaseordecreaseduringrest-to-

worktransitioninskeletalmuscle,dependingonthebalanceoftherelativedirectactivationoftheN ADH-sup-plyblockandNADH-consumingblock(OXPHOS+ATPusage)[21].WhentheNADH- pro-ducingblockisactivatedtoagreaterextentthantheNADH-

consumingblock,NADHincreasesduringrest-to-worktransition[21].

ProtonleakcontributiontoV_O₂—Standardconditions.Ofcourse,thehugeincreasein vAS-relatedV_O_2anddecreaseinthevLK-relatedV_O_2withtheworkintensityincrease

resultedinadecreaseinthecontributionofvLK-relatedV_O_2tototalV_O₂.Whileitwasas highasabout60%atrest(inagoodagreementwithexperimentaldata[8]),itdroppedto

about3%duringmoderateexerciseandtoabout1%duringheavy/severeexercise.Thiswasassociate dwithanincreaseinthephenomenological(involvingprotonleak)ATP/O2ratio(themechanistic,notinvol vingprotonleak,ATP/O2ratioequals5.71withinthemodel).Itrisedfromabout2.1atresttoabout5.5durin gmoderateexerciseandabout5.7duringheavy/severeexercise(seeFig3).Therefore,themusclecou plingefficiency(theratioofthephenome-

nologicalATP/O2tothemechanisticATP/O2)increasedwiththeworkincrease(andappro- ached1),giventhatallotherfactorsremainedunchanged.AnincreaseintheATP/O2ratio

withanincreaseinV_O_2wasobservedinskeletalmusclemitochondria[26],whereOXPHOS isactivatedbyanincreaseinADPbetweenstate4andstate3,whilevLKdecreasedduetoa

decreaseinΔp.Asimilareffectwasobservedinpermeabilizedskeletalmusclemyofibers:theATP/Orati o(whichisahalfoftheATP/O2ratio)waslessthanoneforlowADPconcentration

(15μM)andthuslowV_O_2,butexceededtwoformoderate(200μM)andmaximal(2000μM) ADPconcentrationandV_O_2[27].

TheverylowcontributionofprotonleaktoV_O2and,consequently,highphenomenologi- calATP/O2ratioinintensivelyworkingskeletalmusclewasmostlycausedbythehuge increaseintheATPusageactivitybetweenrestandmoderateandheavy/severeexerciseand

2

bythefactthatESAconcernedparticularOXPHOScomplexes,butnotprotonleak.ESAincreasedver ysignificantlytheabsolutevalueofthevAS-relatedV_O2,whileitdidnotaffectthevLK-

relatedV_O2.Additionally,thevAS-

relatedV_O2wasstimulatedbyelevatedADPandPi.Ontheotherhand,theabsolutevLK-

relatedV_O2decreasedinworkingskeletalmuscleinrelationtorestduetothedecreaseinΔp.Therefore,th ephenomenological(involvingproton

leak)ATP/O2ratioduringintensivemuscleworkwasveryclosetothemechanistic(notinvolvingprotonl eak)ATP/O2ratio,andthemusclecouplingefficiency(definedastheratioofthephenomenologicalATP/

O2ratiotothemechanisticATP/O2ratio)remainedveryhigh(verycloseto1).

Effectofprotonleakactivity(rateconstant).Elevatedthyroidhormoneslevel[10],mus- cletraining(increaseinUCPssensitivitytofattyacids[28]),increasedtemperature[29]and/orincrease dROSconcentration(activatingUCPs[13])canallelevatetheprotonleakinten-

sity.Therefore,theeffectofdoublingofprotonleakactivity(rateconstant)wassimulated.Thetheoretic alresultsarepresentedinFig4.Onecanseethattheincreaseintheprotonleakactiv-

ity(rateconstantkLK1)elevatedvLK-relatedV_O_2andthetotalV_O₂.Asaresult,thecontribu- tionofprotonleaktoV_O_2atrestrisedto78%.Ontheotherhand,the2-foldactivationof protonleakdiminishedΔpandNADH,especiallyatrest.ThiswascausedbyacceleratedΔp

dissipation.Italsodecreasedmusclecouplingefficiency(relatedtothephenomenologicalATP/O2ratio) duringexercise.However,inthe‘standard’simulationwithoutprotonleakacti-

vation(Fig3)thecontributionofvLK-

relatedV_O_2tototalV_O_2wasverylow:about3%and1%duringmoderateandheavy/severeexercise,re spectively.Atwo-

foldactivationofprotonleakelevatedthesevaluesto6%and2%,respectively.Asaresult,evendoublin gofvLKdecreasedthephenomenologicalATP/O2ratioonlybyabout3%and1%,respectively.

Whenprotonleakwas‘switchedoff’(itsrateconstantkLK1wassettozero),thetotalV_O₂ decreased,asitwasequalthentovAS-

relatedV_O2.ThiswasrelatedtoanincreaseinΔpandNADH,especiallyatrest,ascanbeseeninFig5.Inthi scase,thephenomenological(involvingpro-

tonleak)ATP/O2ratioincreased(inrelationtothecasewith‘standard’protonleakactivity)only byabout3%and1%duringmoderateandheavy/severeexercise,respectively.Thephenomenologi- calATP/O2ratiowasthesameatallworkintensitiesandequaledthemechanisticATP/O2ratio.

Generally,largechangesintheprotonleakactivity(rateconstantkLK1)seemedtohaveonly

aminorimpactonthephenomenologicalATP/O2ratioandmusclecouplingefficiencyduringintenseexe rcise.ThiswasvalidforsuchabroadrangeoftheprotonleakcontributiontoV_O_2atrestasabout0–

80%.Therefore,theexactdeterminationofthiscontribution[8]isnotveryimportantinthiscontext,altho ughitisofcauseveryimportantinthecontextofthermogene-sisatrestandbasalmetabolicrate.

vLK-

relatedV

ntototalV

dATP/O

nisolatedmitochondri avs.intactworkingmuscle

Isolatedmitochondria,atleastintheabsenceofCa²⁺,lackESA.Therefore,V_O cannotbeele- vatedhereasmuchasinintactskeletalmuscle.Additionally,theinnermitochondrialmem-

branecanbedamagedinsomefractionofmitochondriaduringtheisolationprocedure.Thiswouldelev atestate4respirationrelatedtoprotonleak.Forthesereasonsitcanbeexpectedthatthecontributionof vLK-

relatedV_O_2tototalV_O_2ismuchsmallerinintensivelyworkingmusclethaninisolatedmitochondriaa ndtheATP/O2ratioissomewhathigher.Forthisrea-

son,theexperimentalmeasurementsoftherelativeprotonleakintensity(e.g.,oftherespira-

torycontrolratio,RCR)andATP/O2inisolatedmitochondria,althoughveryvaluableformanypurpose s,cannotbedirectlyextrapolatedtointactworkingmuscle.

PhenomenologicalATP/O

ratioandATPsupplybyanaerobicglycolysis

phenomenologicalATP/O2ratio’usedthroughoutthepresentarticlemeans‘involv- ingprotonleak’,asopposedto‘mechanisticATP/O2ratio’,notinvolvingprotonleak.How- ever,itshouldbestressedthattheterm‘phenomenologicalATP/O2ratio’meansinfact

‘oxidativephenomenologicalATP/O2ratio’.As,inintactmuscle,especiallyduringheavy/severeexercis e,whereATPsupplybybothaerobicandanaerobicglycolysisispresent,the‘overall’or‘observed’‘phen omenologicalATP/O2ratio’ishigherthanthe‘oxidativephenom-

enologicalATP/O2ratio’,relatedonlytoATPproductionbyOXPHOS.Theoverallphenome-

nologicalATP/O2ratiocanbeevenhigherthanthemechanisticATP/O2ratioforOXPHOS.Thisfactshoul dbealwayskeptinmindwhenspeakingabouttheATP/O2ratioanditshouldbealwaysspecifiedwhichAT P/O2ratioismeantinagivencase.Ontheotherhand,anynon-

mitochondrialoxygenconsumption(forinstancebytheantioxidantsystem)

(seeref.8)decreasestheoverallphenomenologicalATP/O2ratio.Itispostulatedheretodistinguishthree sortsoftheATP/O2ratio:1.mechanisticATP/O2ratioforOXPHOSwithoutprotonleak;2.oxidativepheno menologicalATP/O2ratioforoxidativeATPsupplyinvolvingofprotonleak;

3.overallphenomenologicalATP/O2ratioforoxidative(inthepresenceofprotonleak)and glycolytic(byaerobicandanaerobicglycolysis)ATPsupply,takingintoaccountthenon-mito- chondrialoxygenconsumption.

Studylimitations

Itmustbestressedthatevenawell-

testedcomputermodelcanbeonlyanapproximationofthecomplexreality.

ItislikelythattherelativecontributionofvLK-

relatedV_O_2tototalV_O_2atrestinbiggermammals(includinghumans)islowerthaninrats.Thisis becausetheprotonleakintensityis

inverselyproportionaltothemammalbodymass[11]andbiggermammalsneedlessthermo- genesisperbodymassinordertomaintainhighconstantbodytemperature.Protonleakintensitycanb eaffectedbyexercise-

inducedmuscletemperatureand/orcytosolicROSincrease.Therefore,thestrictlyquantitativetheore ticalpredictionsobtainedinthepresentstudyshouldbetreatedwithsomecaution.Nevertheless,these limitationsdonotaffectthegeneralconclusiondrawninthepresentstudy.

Conclusions

Computersimulationsdemonstratedthatwhilethecontributionoftheprotonleakthroughtheinner mitochondrialmembranetoVO2waslargeatrestandatlowwork,itdecreasedpro-

gressivelywithworkintensityandbecameverysmallatmoderateandheavy/severework.Theabs olutevalueoftheprotonleakflux(vLK)andvLK-

relatedVO2decreasedtogetherwithanincreaseinworkintensityinskeletalmuscle,whichwascause dbyadecreaseinΔp,giventhatsuchfactorsasROSorelevatedtemperaturedonotstimulateitsign ificantly.Ontheotherhand,theATPsynthesisrate(vAS)andvAS-

relatedVO2increasedlinearlywithworkintensity(ATPdemandactivity).Whileinrestingskeletalmus cleat‘standard’protonleakactivity

thecontributionofvLK-

relatedV_O_2tototalV_O_2amountedabout60%,thiscontributiondroppedtoabout3%duringmoderateexe rciseand1%duringheavy/severeexercise.Thiswas

duetoahugeincreaseintheATPusageactivityandthusintheATPsynthesis-

relatedV_O₂.ThegreatincreaseinV_O_2duringrest-to-worktransitionwasdirectlyrelatedtoeach- stepacti-

vation,ESA,ofOXPHOScomplexesandtoactivationofOXPHOSbyADPandPiincrease.Protonleakwas

notactivateddirectlyanditsabsolutevaluedecreasedduetothedecreaseinΔp.Asaresult,thecontribut ionofLK-relatedVO2tototalV_O_2decreasedverysignificantly

duringrest-to-

intensiveworktransition.Thiswasassociatedwithasignificantincreaseinthephenomenological(inv olvingprotonleak)ATP/O2ratio.Atwo-

foldincreaseintheactivity(rateconstant)ofprotonleakincreasedthecontributionofvLK-

relatedV_O2tototalV_O2toabout80%atrest,about6%atmoderateexerciseandabout2%atheavy/se vereexercise.Aremovalofprotonleak(reductionofitsactivitytozero)wasassociatedwithanincreasei nthephenomenologicalATP/O2ratiobyabout3%duringmoderateexerciseand1%duringheavy/seve reexerciseinrelationto‘standard’protonleakactivity.Therefore,evenlargevariationsintheprotonlea kactivityhaveonlyasmallimpactonthesystempropertiesduringmoderateandheavy/severeexercis e(althoughtheyhaveabigeffectatrestandduringlowexercise).Inotherwords,whateverthe(realistic) contributionofprotonleaktoV_O_2atrest,itissmalldur-ingintensework.

Acknowledgments

ThisstudywasfundedbytheKNOWprogram,whichsupportstheFacultyofBiochemistry,Biophysicsa ndBiotechnologyofJagiellonianUniversity.Thefundershadnoroleinstudydesign,datacollectionand analysis,decisiontopublish,orpreparationofthemanuscript.

AuthorContributions

BernardKorzeniewski.Datacuration:BernardK orzeniewski.

Formalanalysis:BernardKorzeniewski.Funding acquisition:BernardKorzeniewski.Investigation :BernardKorzeniewski.Methodology:BernardK orzeniewski.

Projectadministration:BernardKorzeniewski.

Resources:BernardKorzeniewski.Software :BernardKorzeniewski.Supervision:Bernar dKorzeniewski.Validation:BernardKorzenie wski.Visualization:BernardKorzeniewski.

Writing–originaldraft:BernardKorzeniewski.

Writing–review&editing:BernardKorzeniewski.

References

1. BrandMD,ChienL-

F,AinscowEK,RolfeDFS,PorterRK.Thecausesandfunctionsofmitochondrialprotonleak.BiochimBiop hysActa.1994;1187:132–139.PMID:8075107

2. BrookesPS.MitochondrialH⁺lea

kandROSgeneration:anoddcouple.FreeRadicBiolMed.2005;38:12 –23.https://doi.o r g/10.1016/j . freeradbi o med.2004 . 10.01 6 PMID :15589367

3. DivakaruniAS,BrandMD.Theregulationandphysiologyofmitochondrialprotonleak.Physiology.

2011;26:192–205.https://doi.o r g/10.11 5 2/physiol.0 0 046.201 0 PMID :21670 1 65

4. GarlidKD,BeavisAD,RatkjeSK.Onthenatureofionleaksinenergy-transducingmembranes.Bio- chimBiophysActa.1989;976:109–120.PMID:26759 8 0

5. BrownGC,Lakin-ThomasPL,BrandMD.Controlofrespirationandoxidativephosphorylationiniso- latedratlivercells.EurJBiochem.1990;192:355–362.PMID:2209591

6. KrishnamoorthyG,HinklePC.Non-ohmicprotonconductanceofmitochondriaandliposomes.Bio- chemistry.1984;23:1640–1645.PMID:6722116

7. NichollsDG.InfluenceofrespirationandATPhydrolysisonprotonelectrochemicalgradientacrossinnerm embraneofrat-livermitochondriaasdeterminedbyiondistribution.EurJBiochem.1974;50:305–

315.PMID:4452361

8. RolfeDFS,BrandMD.Protonleakandcontrolofoxidativephosphorylationinperfused,restingratskel- etalmuscle.BiochimBiophysActa.1996;1276:45–50.PMID:8764890

9. RolfeDFS,NewmanJMB,BuckinghamJA,ClarkMG,BrandMD.Contributionofmitochondrialprotonleakt orespirationrateinworkingskeletalmuscleandlivertoSMR.AmJPhysiolCellPhysiol.1999;276:C692–

C699.

10. HarperM-

E,BrandMD.ThequantitativecontributionofmitochondrialprotonleakandATPturnoverreactionstothe changedrespirationratesfromhepatocytesofdifferentthyroidstatus.JBiolChem.1993;268:14850–

14860.PMID:83920 6 0

11. PorterRK,BrandMD.BodymassdependenceofH⁺lea

kinmitochondriaanditsrelevancetometabolicrate.N ature.1993;362:628–630.https://doi.o r g/10.10 3 8/362628a 0 PMID :83852 7 4

12. BrandMD,CoutureP,ElsaPL,WithersKW,HulbertAJ.Evolutionofenergymetabolism.Protonper- meabilityoftheinnermembraneoflivermitochondriaisgreaterinamammalthaninareptile.BiochemJ.1991;

275:81–86.PMID:1850242 13. EchtayKS,RousselD,St-

PlerreJ,JekabsonsMB,CadenasS,StuartJA,etal.Superoxideactivatesmitochondrialuncouplingprotei ns.Nature.2002;415:96–99.https://doi.o r g/10.1038 / 415096 a PMID:

11780125

14. MarcinekDJ,SchenkmanKA,CiesielskiWA,ConleyKE.Mitochondrialcouplinginvivoinmouseskele- talmitochondria.AmJPhysiolCellPhysiol.2004;286:C457–

C463.https://doi.o r g/10.11 5 2/ajpcell. 00237.200 3 PMID :14522819

15. KorzeniewskiB.RegulationofATPsupplyduringmusclecontraction:theoreticalstudies.BiochemJ.

1998;330:1189–1195.PMID:94940 8 4

16. KorzeniewskiB.Regulationofoxidativephosphorylationindifferentmusclesandvariousexperimentalcon ditions.BiochemJ.2003;375:799–804.https:// d oi.org/10.10 4 2/BJ200 3 088 2 PMID :12901719 17. KorzeniewskiB.Regulationofoxidativephosphorylationthroughparallelactivation.BiophysChem.

2007;129:93–110.https://doi.o r g/10.10 1 6/j.bpc.20 0 7.05.01 3 PMID :17566 6 29

18. KorzeniewskiB.Regulationofoxidativephosphorylationduringworktransitionsresultsfromitskineticprop erties.JApplPhysiol.2014;116:83–94.https://d o i.org/10.115 2 /japplph y siol.00759. 2 01 3 PMID:

24157529

19. KorzeniewskiB.‘Idealized’state4andstate3inmitochondriavs.restandworkinskeletalmuscle.

PLoSOne.2015;10(2):e0117145.https://doi.o r g/10.1371/jo u rnal.pone.0 1 1714 5 PMID :25647 7 47 20. KorzeniewskiB,RossiterHB.Each-

stepactivationofoxidativephosphorylationisnecessarytoexplainmusclemetabolitekineticresponsestoe xerciseandrecoveryinhumans.JPhysiol.2015;593:5255–

5268.https:// d oi.org/10.11 1 3/JP271 2 9 9 PMID :26503399

21. KorzeniewskiB.Regulationofoxidativephosphorylationthrougheach-stepactivation(ESA):Evi- dencesfromcomputermodeling,ProgBiophysMolBio.2016;125:1–23.

22. KorzeniewskiB,ZoladzJA.Amodelofoxidativephosphorylationinmammalianskeletalmuscle.Bio- physChem.2001;92:17–34.PMID:11527576

23. KorzeniewskiB,LiguzinskiP.Theoreticalstudiesontheregulationofanaerobicglycolysisanditsinflu- enceonoxidativephosphorylationinskeletalmuscle.BiophysChem.2004;110:147–

169.https:/ / doi. org/10.1016 / j.bpc.2004 . 01.01 1 PMID :152231 5 1

24. LiguzinskiP,KorzeniewskiB.Metaboliccontrolovertheoxygenconsumptionfluxinintactskeletalmus- cle:insilicostudies.AmJPhysiolCellPhysiology.2006;291:C1213–C1224.

25. GlancyB,WillisWT,ChessDJ,BalabanRS.Effectofcalciumontheoxidativephosphorylationcas- cadeinskeletalmusclemitochondria.Biochemistry.2013;52:2793–

2809.https://doi.o r g/10.10 2 1/ bi3015983PMID:23547908

26. MogensenM,SahlinK.Mitochondrialefficiencyinratskeletalmuscle:influenceofrespirationrate,sub- strateandmuscletype.ActaPhysiolScand.2005;185:229–236.https://doi.o r g/10.11 1 1/j.1365- 20

1 X. 2005.0148 8 . x PMID :16218 9 28

27. LarkDS,TorresMJ,RyanTE,AndersonEJ,NeuferPD.Directreal-

timequantificationofmitochondrialoxidativephosphorylationefficiencyinpermeabilizedskeletalmusclemy ofibers.AmJPhysiolCellPhy-siol.2016;311:C239–

C245.https: / /doi.org/10.1 1 52/ajpce l l.00124.201 6 PMID :27335172

28. TonkonogiM,KrookA,WalshB,SahlinK.Endurancetrainingincreasesstimulationofuncouplingofskeleta lmusclemitochondriainhumansbynon-esterifiedfattyacids:anuncoupling-protein-mediatedeffect?

BiochemJ.2000;351:805–810.PMID:11042 1 37

29. JarmuszkiewiczW,Woyda-PloszczycaA,KozielA,MajerczakJ,ZoladzJA.Temperaturecontrolsoxi- dativephosphorylationandreactiveoxygenspeciesproductionthroughuncouplingInratskeletalmus- clemitochondria.FreeRadicalBiolMed.2015;83:12–20.