Regulation of oxidative phosphorylation is different in electrically- and cortically-stimulated skeletal muscle

PLOSONE|https://doi.o r g/10.13 7 1/journal.p o ne.0195 6 2 0 Apri l26,2018 1^/28

OPENACCESS

Citation:KorzeniewskiB(2018)Regulationofoxidat ivephosphorylationisdifferentinelectrically- andcortically-

stimulatedskeletalmuscle.PLoSONE13(4):e01956 20.https://doi. o rg/10.1371/ journal.pon e .0195620 Editor:RozalynMAnderson,Universityof WisconsinMadison,UNITEDSTATES Received:November28,2017 Accepted:March26,2018 Published:April26,2018

Copyright:©2018BernardKorzeniewski.Thisisa nopenaccessarticledistributedunderthetermsofth eCreativeCommons Attribut i onLicense ,whichper mitsunrestricteduse,distribution,andreproductioni nanymedium,providedtheoriginalauthorandsourc earecredited.

DataAvailabilityStatement:Allrelevantdataarewit hinthepaper.

Funding:FacultyofBiochemistry,Biophysicsand Biotechnology,JagiellonianUniversityisabenefici aryofKNOWprogram.

Competinginterests:Theauthorhasdeclaredthatno competinginterestsexist.

RESEARCHARTICLE

Regulationofoxidativephosphorylationisdif ferentinelectrically-andcortically-

stimulatedskeletalmuscle

BernardKorzeniewski*

FacultyofBiochemistry,BiophysicsandBiotechnology,JagiellonianUniversity,Krako´w,Poland

*bernard. k orzeniewski @ gmail.com

Abstract

Acomputermodeloftheskeletalmusclebioenergeticsystemwasusedtostudytheregula- tionofoxidativephosphorylation(OXPHOS)inelectrically-stimulatedandcortically-stimu- latedskeletalmuscle.Twotypesofthedependenceoftheintensityofeach-

stepactivation(ESA)ofOXPHOScomplexesonATPusageactivityweretested:power- typedependenceandsaturating-

typedependence.Thedependenceofmuscleoxygenconsumption(V_O₂),

phosphocreatine(PCr),cytosolicADP,ATP,inorganicphosphate(Pi),pHandτp(character- istictransitiontime)oftheprincipalcomponentofthemuscleV_O2on-

kineticsontheATPusageactivitywassimulatedforbothtypesoftheESAintensity- ATPusageactivitydepen-dence.Computersimulationsinvolvingthepower- typedependencepredictsystemproper-

tiesthatagreewellwithexperimentaldataforelectrically-

stimulatedmuscle.Ontheotherhand,modelpredictionsforthesaturating- typedependenceinthepresenceofthe‘addi-

tional’ATPusage(postulatedpreviouslytounderlietheslowcomponentoftheVO2on-

kinetics)reproducewellsystempropertiesencounteredinhumanskeletalmuscleduringvoluntar yexercise.Itispostulatedthatthedifferencebetweentheregulationandkineticpropertiesofthesy steminelectrically-andcortically-

stimulatedmuscleismostlyduetothedifferentmusclefibersrecruitmentpattern.Intheformer,allfi bertypesarerecruitedinparal-

lelalreadyatlowpoweroutput(PO)values,whileinthelattertypeIfibers(withhigherESAintensity) arestimulatedatlowPOvalues,whiletypeIIfibers(especiallytypeIIbandIIxfibers)withlowESAint ensityarerecruitedpredominantlyathighPOvalues.

Introduction

SkeletalmusclecontractionisdrivenbyhydrolysisofATPtoADPandPi.AtrestATPisneededtosustain suchbasicprocesseskeepingthemusclefiberaliveasprotein/RNAsynthe-

sisorion(Na⁺,K⁺,Ca²⁺)circulationacrosscellularmembranes.Duringexercise,ATPismainlyusedby actomyosin-ATPaseandCa²⁺-

PLOSONE|https://doi.o r g/10.13 7 1/journal.p o ne.0195 6 2 0 Apri l26,2018 2^/28 ATPase(SERCA).Thedependenceo

fsystemvariables(V_O2,PCr,cytosoli cPi,ATP,ADP,pH)onATPusageactivi tyisofkeysignificanceforunderstandi ngoftheregulationandbehaviorofthe skeletalmusclebioenergeticsystemd uringrest-to-worktransition.

RegulationofOXPHOSinelectrically-andcortically-stimulatedmuscle

InagivenexercisetypetheATPusageactivityAUT(relativeactivationofATPusage,increaseinitsr ateconstantkUTinrelationtorest)canbeassumedtobelinearlyproportionaltoworkintensity(pow eroutput).The‘additional’ATPusage[1]waspostulatedtobemostlyresponsiblefortheslow- componentoftheV_O_2onkinetics[1–4].Itsinclusioninthecom-

putermodelgivesanexcellentagreementofcomputersimulationswithexperimentaldataconcer ningfluxesandmetaboliteconcentrationsduringrest-work-recoverytransitioninskel-

etalmuscle[1].Itappearsabovethe‘critical’relativeATPusageactivity(relatedtocriticalpower,C P),anditsrelativeactivityisassumedinthepresentstudytobelinearlyproportionaltothedifferenc ebetweenthecurrentandthecriticalrelativeATPusageactivity,andto

increaselinearlywithtime,whichagainagreeswellwithexperimentaldatashowinganincreaseinthein tensityoftheslowcomponentwithworkintensity[5].

Itwaspostulatedthatthemainmechanismresponsiblefortheregulationofthecellbioe- nergeticsystem,especiallyoxidativephosphorylation(OXPHOS),duringworktransitionsinske letalmuscle,heartandothertissuesistheso-calledeach-

stepactivation(ESA)mechanism,aspecialcaseofthebroaderparallel-

activationmechanism.AccordingtoESA,notonlyATPusageandNADHsupply,butalsoallOXP HOScomplexes(complexI,complexIII,complexIV,ATPsynthase,ATP/ADPcarrier,Picarrier)an dglycolysisaredirectlyactivatedbysome

cytosolicmechanismpredominantlyinvolvingcytosolicCa^2+ionsandperhapscalmodulin- likeproteinresponsibleforproteinphosphorylation,duringrest-to-

worktransitioninskeletalandheartmusclecells[1,6–

10].Inskeletalmuscleitislikelythatamixedmechanism(MM)ismanifest,inwhichallOXPHOSco mplexesaredirectlyactivated,buttoasmallerextentthanATPusage,andthereforeamoderatein creasein[ADP]and[Pi]cooperateswithESAtobringaboutOXPHOSactivation[10].Inintactheart invivothereisno(orsmall)changeinmetabo-

liteconcentrationsduringworktransitions[11].Therefore,itwaspostulatedthatESA,directlyactiv atingbothATPusageandOXPHOStothesameextent,isessentiallythesolemechanismoperatin ginintactheartinvivo[12,13].

TheESA,each-

stepactivationintensityAOX(relativedirectactivationofOXPHOSandNADHsupplyinrelationtorest) determineshowmanytimestheactivityofOXPHOSandNADHsupply(therateconstantsofallOXP HOScomplexes:kC1,kC3,kC4,kSN,kEX,kPIandoftheNADHsupplyblock:kDH)is(are)elevatedduringr est-to-worktransition.Insomeprevi-oustheoreticalstudiesapower-typeAOX-

AUTdependencewasassumedasthesimplestpossi-

bility.Accordingtothisdependence,AOXcontinuouslyincreasesasapowerfunctionofAUT(ATPusageact ivity)andneverreachesaplateau.Quantitatively,thepower-

typedependencehasthefollowingform:AOX=AUTpOX,wherethepowercoefficientpOX,equalinmos tsimu-lationsto0.3–

0.5,isthemeasureoftheESAstrength.However,arecenttheoreticalstudy[1]demonstratedthatth eactualAOX-AUTdependenceissaturating-

typeinhumanbilateralkneeextensionexercise.ThismeansthatAOXfirstincreaseswithAUTincrease,bu tafterwardsstabi-

lizesonaconstantlevel.Itwasestimated[1]thatAOX,bydefinitionequalto1atrest,equalsabout5.6in moderateexerciseand5.2inheavy/severeexercise.Atthesametime,theassessedAUT(bydefinitioneq ualto1atrest)wasmuchhigherinheavy/severeexercise:47,thaninmoderateexercise:22.Theref ore,inthiscasetheESA,each-

stepactivationintensityAOXdoesnotincreasebetweenmoderateandheavy/severeworkintensity,w henAUT(PO)islargelyelevated,andtheAOX-AUTdependenceissaturating-type.

Itisofcourseinterestingandimportantforunderstandingofthefunctioningofthesystem howdifferenttypesoftheAOX-

AUTdependenceaffectthedependenceofsystemvariables,suchasmuscleV_O₂,PCr,cytosolicPi,ATP,A DP,pHandthecharacteristictransitiontimeτpoftheprincipalcomponent(phaseII)ofthemuscleV_O2on-

RegulationofOXPHOSinelectrically-andcortically-stimulatedmuscle

kineticsontheATPusageactivity(AUT)

(andthusworkintensity).Itseemsalsointerestinghowthepresenceofthe‘additional’

ATPusageabovethecriticalATPusageactivity(relatedtocriticalpower,CP)affectsthisdependence.

However,themostimportantchallengeistotestwhetherthesaturating-typeversuspower- typeandAOX-

AUTdependenceisabletoaccountforthedifferencesinthekineticpropertiesofthebioenergeticsyste mincortically-stimulated(voluntaryexercise)versuselectrically-stim-

ulatedskeletalmuscle.Inotherwords,itseemsveryinterestingwhethertheregulationofOXPHO Sisdifferentinbothsortsofexerciseand,ifso,whatthisdifferenceconsistsin.

ItwaspostulatedthatESAtendstobemoreintensiveinoxidativeskeletalmuscle(fibers),inmuscl eduringvoluntaryexercise(corticalstimulation)andinintactmusclewithphysiologicalbloodflowth aninglycolyticskeletalmuscle(fibers),inelectrically-stimulatedmuscleandinper-

fusedmuscle[7].Changesinmetabolite(PCr,Cr,ADP)concentrationsandpHduringworktransitio nsaremuchgreateringlycolyticmuscles(composedmostlyoftypeIIfibers)thaninoxidativemuscle s(composedpredominantlyoftypeIfibers)(seee.g.,[14]),anditwaspostu-

latedthatthemainroleofESAistomaintainasgoodmetaboliteandpHhomeostasisaspossible[6–

10].Involuntaryexercise(cortically-

stimulatedmuscle),thereisasequentialpatternofrecruitmentofparticularmusclefibertypeswhen workintensityincreases:oxidativetypeIfiberswithhighOXPHOScapacity(andESAintensity)arer ecruitedmainly(orexclusively)atlowPOvalues,followedbytherecruitmentofalsopredominantlyo xidativetypeIIamusclefibers,andfinallyofpredominantlyglycolytictypeIIxandIIbmusclefiberswh enPOapproachesitsmaxi-

mumvalues.Thisiscontrolledbyneuralstimulationofparticularmotorunits[15,16].Inelectri-cally- stimulatedmuscledifferentmusclefibers(typeIandvarioustypeIIfibers)arestimulatednon- specificallywhenthestimulationfrequencyincreases,evenatloweststimulationfrequencies(ATPusag eactivities),andtheworkperformedisproportionaltothestimulationfrequency.

Thepresentstudyisintendedfirstofalltorevealthedifferencesintheregulationofthebioe- nergeticsystem,especiallyOXPHOS,betweenthecortically-andelectrically-

stimulatedskeletalmuscleduringconstant-

powerexercise.Thedependenceofselectedskeletalmusclebioenergeticsystemvariables(muscleV _O₂,PCr,cytosolicPi,ATP,ADP,pHandτpofthemuscleV_O_2on-

kinetics)onATPusageactivityAUTissimulatedforthreepossibilities:1.Power-typeAOX- AUTdependenceintheabsenceofthe‘additional’ATPusage;2.Saturating-typeAOX-AUTdepen-

denceintheabsenceofthe‘additional’ATPusage;and3.Saturating-typeAOX-

AUTdependenceinthepresenceofthe‘additional’ATPusage.Itishypothesizedthatthepower- typeAOX-

AUTdependenceisabletoaccountforthekineticbehaviorofthesystemencounteredinelectrically- stimulatedmuscle,whilethesaturating-typeAOX-AUTdependenceinthepresenceofthe‘addi- tional’ATPusagecanexplainthesystempropertiesincortically-

stimulatedmuscle(voluntaryexerciseinhumans).Confrontationofcomputersimulationswithvari ousexperimentaldatasupportsthishypothesis.ItispostulatedthatthedifferentregulationofOXPH OSinelectrically-andcortically-

stimulatedskeletalmuscleresultsfromdifferentpatternsofmusclefiberrecruit-

mentwhenAUTincreases.Inelectrically-stimulatedmuscleallfibertypesarerecruitedinparal- lelalreadyatloweststimulationfrequencies.Ontheotherhand,incortically-

stimulatedmuscleduringvoluntaryexercisemostofoxidativetypeIfibers(thatarepostulatedtohav ehighESAintensity)arerecruitedfirst,atlowandmoderateworkintensities,followedbyrecruitmen tofalsopredominantlyoxidativetypeIIafibers,andfinally,athighestworkintensities,ofpredomi- nantlyglycolytictypeIIxandIIbfibers(thatarepostulatedtohavelowESAintensity).

Theoreticalmethods

Computermodel

ThecomputermodelofOXPHOSandtheentirebioenergeticsysteminintactskeletalmuscle[17,18]w asusedinthesimulationscarriedoutinthepresentstudy.Themodelwasrecently

OX

UT

p_G L

modifiedbyreplacingfirst-orderinhibitionofglycolysisbyprotonswiththird-orderinhibi- tion[1].ThismodelcomprisesexplicitlyNADHsupplyblock(TCAcycle,fatty-acidβ-oxida- tion,MASetc.),particularOXPHOScomplexes(complexI,complexIII,complexIV,ATPsynthase ,ATP/ADPcarrier,Picarrier),protonleakthroughtheinnermitochondrialmem-

brane,glycolysis(aerobicandanaerobic),ATPusage,creatinekinase(CK)andprotonefflux/influ xto/fromblood.Thecompletemodeldescriptionofparticularmodelversionsislocatedontheweb site:http://awe.mol.uj.edu. p l/~benio/ .

ESAintensity-ATPusageactivitydependence

TherelativeactivityofATPusage(relativeincreaseinitsrateconstantkUTinrelationtorest)AUTbetween1(r est)and100(maximumAUT)wasusedindifferentsetsofsubsequentcom-

putersimulations.Twotypesofdependenciesoftheintensityofeach- stepactivation(ESA)ofOXPHOS(andNADHsupply)

(relativeincreaseoftherateconstantsofallOXPHOScom-

plexesandNADHsupplyblockinrelationtorest)AOXonAUTweretested:power- typedependenceandsaturating-typedependence.

Thepower-

typedependence,used(assumedasthesimplestpossibility)insomeprevioustheoreticalstudies,wasd escribedbythefollowingequation:

A ¼A^pOX ð1Þ

whereAOX(ESA,each-

stepactivationintensity)istherelativeOXPHOS(+NADHsupply)activity(activationinrelationtore st),AUTistherelativeATPusageactivity(activationinrela-

tiontorest)andthepowercoefficientpOX=0.45isusedinthepresentstudy;pOXisameasureofESAstr ength(pOX=0.45meansarelativelystrongESA).

Thesaturating-

typedependence,introducedforthefirsttimeinthepresentstudyonthebasisofthedataextractedfromex perimentalstudies[1],wasdescribedbythefollowingequa-tion:

A_OX¼ 1þA_OXmax A -1 !

ðAUT-1ÞþK^AUT ð2Þ

whereAOX(ESA,each-

stepactivationintensity)istherelativeOXPHOS(+NADHsupply)activity(activationinrelationtor est),AUTistherelativeATPusageactivity(activationinrela-

tiontorest),AOXmax=5isthemaximumAOX—1(thusmaximumAOX=6)andKAUT=5isthe‘half- saturating’AUTvaluefortheincreaseinAOX.ThevaluesofAOXmaxandKAUTwerechoseninordertorepro ducetheexperimentaldata(seebelow).ThevaluesofAOXandAUTforrest,moderateexerciseandh eavy/severeexercisethatservedtoconstructthisequationweretakenfrom[1].

BothdependenciesarepresentedinFig1.Onecanseethatthesaturating- typedependencefitsbetterthanthepower-

typedependencetotherelationshipbetweentherelativeactivityofOXPHOS(ESA,each-

stepactivationintensity)AOXandtherelativeactivityofATPusageAUTforrest,moderateexerciseandsev ereexerciseextractedfromexperimentaldataconcerningvoluntaryconstant-powerknee-

extensionexerciseinhumans(see[1]).

ThedependencebetweentherelativeglycolysisactivityAGLandAUTwasdescribedinbothcasesbyap ower-typedependence:

A_GL¼A^UT ð3Þ

whereAGListherelativeglycolysisactivation(relativeincreaseintherateconstantofglycoly- siskGLinrelationtorest),AUTisrelativeATPusageactivityandthepowercoefficientpGLisa

Fig1.Power-typevs.saturating-typeAOX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependence.Simulatedpower-typeandsaturating-typeA^OX-

AUTdependences(lines)arecomparedwiththevaluesofA^OXandA^UTextractedfromexperimentaldataforrest,moderateexercisean dsevereexercise(points)[1].Thepower-typedependence,describedbyEq1,ispostulatedtobepresentinelectrically-

stimulatedmuscle,whilethesaturating-

typedependence,describedbyEq2,ispostulatedtobepresentduringvoluntaryexercise(cortically-stimulatedmuscle).

https://doi. o rg/10.1371/ j ournal.pon e .0195620.g001

measureofESAstrengthforglycolysis.pGL=0.8forpower-typeAOX- AUTdependenceandpGL=0.55forsaturating-typeAOX-

AUTdependence.ThesevalueswerefittedinordertoobtainreasonablevaluesofcytosolicpHathighAU T(relativeATPusageactivity)values(about6.75,dropby0.25inrelationtorest,atmaximumAUT=100 usedinthepresentstudy).ThevalueofpGLisdifferentforpower-typeandsaturating-

typeAOX(ESAintensity)-AUTdependence,asAOXathighAUTvaluesisdifferentinthesecases.Thispower- typeAGL(rela-tiveglycolysisactivity)-

AUTdependenceallowsforsignificant(anaerobic)glycolysisstimula-

tionathighworkintensities(AUTvalues)thattakesplaceinrealmusclesundertheseconditions.

‘Additional’ATPusagekinetics

Itwaspostulatedthatthe‘additional’ATPusage[1],underlyingtheslowcomponentofthe V_O2on-

kinetics,appearswhentherelativeATPusageactivityAUTexceedsthecriticalrelativeATPusageactivity (relatedtocriticalpower,seeDiscussion)

[1,4].Theabsolute‘additional’ATPusageactivity(rateinmMmin^-

1)isdescribedinthepresentstudybythefollowingequa-tion:

v_UTadd¼ k_UTadd·v_UT·ðA_UT-A_UTcritÞ·t_exerc ð4Þ

X

wherevUTaddistheabsolute‘additional’ATPusageactivity(inmMmin^-

1),kUTaddisthe‘rateconstant’oftheincreaseintheabsolute‘additional’ATPusageintime(inmin^-

1),AUTistherelativeATPusageactivity(activationinrelationtorest) (unitless),AUTcritisthecriticalrela-

tiveATPusageactivity(unitless)andtexercistime(min)aftertheonsetofexercise.Thisequa- tionmeansthatvUTaddincreasesbothwithAUTaboveAUTcritandwithtimeaftertheonsetofexercise.Thelin earincreaseinthe‘additional’ATPusagevUTaddintimegivesanexcellentagreementofmodelpred ictionswithexperimentaldata[1].TheincreaseofvUTaddintimeisrelatedtotheincreaseintheslowc omponentoftheV_O_2on-

kineticsintime[1,4],whiletheincreaseinthe‘additional’ATPusagevUTaddwithAUTabovethecriticalATP usageAUTcritisduetothefactthattheextentoftheslowcomponentincreaseswithPO[5,19].Inthesi mula-

tionscarriedoutinthepresentstudyitisassumedthatAUTcrit=50(ahalfofthemaximumAUT=100)an dkUTadd=0.0008min^-1.Thefirstassumptionisjustifiedbytheobservation[20]thatthenon-

linearityintheV_O₂-POdependence,beginningatPOvaluewherethe‘addi- tional’ATPusageappears,startedat35–65%ofthemaximumpoweroutput(POmax).

ThetotalabsoluteATPusageactivityAUTtot(inmMmin^-1)isequaltothesumofthenor- maland‘additional’absoluteATPusageactivity:

v_UTtot¼v_UTþv_UTadd ð5Þ

Worktransitions

Duringrest-to-

worktransitioninskeletalmuscletheATPusagewasactivatedAUTtimes(therateconstantofATPu sagekUTwasincreasesAUTtimes).AtthesametimeOXPHOSandNADHsupplywereactivatedAOXti mes(therateconstantsofcomplexI:kC1,complexIII:kC3,complexIV:kC4,ATPsynthase:kSN,ATP/

ADPcarrier:kEX,Picarrier:kPIandNADHsupply:kDHwereincreasedAOXtimes).Glycolysiswasactivated AGLtimes(therateconstantofglycolysiskGLwasincreasedAGLtimes).

Duringtheoppositetransition(work-

toresttransition)therestingATPusageactivity,OXPHOSactivity,NADHsupplyactivityandglyc olysisactivitywererestored.

AninstantaneousincreaseoftheATPusageactivity(increaseinkUT)duringon- transientanddecreaseoftheATPusageactivity(decreaseinkUT)duringoff-

transientwasappliedincomputersimulations.Ontheotherhand,some(althoughrelativelyveryshort, seebelow)delayintheincreaseoftheactivityofOXPHOS(andNADHsupply)andglycolysisduringon- transientandinthedecreaseoftheactivityoftheseprocessesduringoff-

transientwasassumedincomputersimulations.Thetime-

dependentactivationaftertheonsetofelevatedworkwasdescribedbythefollowingequation:

m_X¼A^X- ðA^X- 1Þ·e^-t=tðONÞX ð6Þ whereXisOX(oxidativephosphorylation+NADHsupply)orGL(glycolysis),mXisthecur-

rent(attimet)relativeactivationofX(multiplicityoftherestvalue(s)ofitsrateconstant(s)),t(ON)Xist hecharacteristicactivationtimeofX,andtisthetimeaftertheonsetofelevatedwork(rest-to- worktransition).Thetime-

dependentinactivation(decay)aftertheterminationofmuscleworkwasdescribedbythefollowin gequation:

m¼1þðA-1Þ·e^-t=tðOFFÞX ð7Þ

whereXisOX(oxidativephosphorylation+NADHsupply)orGL(glycolysis),mXisthecur-

rent(attimet)relativeactivationofX(multiplicityoftherestvalue(s)ofitsrateconstant(s)),t(OFF)Xis

thecharacteristicinactivationtimeofXandtisthetimeaftertheterminationofele-vatedwork(work- to-resttransition).

Inthepresentstudythefollowingcharacteristictransitiontimeswereused:t(ON)OX=3s,t(ON)GL=6s ,t(OFF)OX=120s,t(OFF)GL=1s(see[1]).t(ON)OXwasestimatedfor11sinelectrically-

stimulatedmuscle[21].ItwasshownthatV_O_2startstoincreasealmostinstan- taneouslyaftertheonsetofexerciseinelectrically-stimulatedmuscle[22].

InthesimulationspresentedinFigs2–

4the‘additional’ATPusagewasabsent.Therefore,asteady-

statecouldbereached(oratleastapproachedafter6minofexercise—

seeFig4).InthesimulationspresentedinFigs5and6the‘additional’ATPusagepresentaboveAUT crit,under-lyingtheslowcomponentoftheV_O2on-kinetics,waspresent.Asaresult,nosteady- statecouldbereached.Inallsimulations,themuscleworklasted6minaftertheonsetofexercise.Th esimulationsconcerningthedependenceofselectedsystemvariablesontherelativeATPusage activity,presentedinFigs2,3and6,wereterminatedinthe6^thminofexerciseandthevariablevalues wererecorded.InsubsequentsimulationstherelativeATPusageactivityAUTwasincreasedgradu allyfrom1(rest)to100ineachcase(forthepower-typeAOX-AUTdepen-denceandforthesaturating- typeAOX-

AUTdependencewithoutandwiththe‘additional’ATPusage).Timecoursesofsystemvariablesduring rest-to-work-to-recoverytransitionweresim-ulatedformoderateexercise(AUT=35)

(Fig4)andheavy/severeexercise(AUT=80)(Fig5).

Muscleworkwasinitiatedinthe2^ndminofsimulationandterminatedafter6min,inthe8^th minofsimulation.

Thepower-typeAOX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependencewasusedinthesimulationspresentedinFig2,whilethesatur ating-typeAOX-AUTdependencewasusedinthesimulationspresentedinFigs3–

6.The‘additional’ATPusagewaspresentinthesimulationsshowninFigs5and6.

Thethird-orderinhibitionofglycolysisbyH^+ions,introducedrecently[1],wasusedinthe presentstudy.

TheoxygenconcentrationO2=30εMwasassumedinallsimulations.

τpoftheV_O2on-kinetics(seeFig7)wasdeterminedformoderateworkintensity.

TheV_O2on-kineticsisverydifferentinall-outexercisethaninconstant-

powerexercise[23].However,poweroutputdeclinesverysignificantlyduringall- outexercise,whileonlyconstant-powerexerciseisanalyzedinthepresentstudy.

Re-scalingofexperimentaldata

Inordertomakeadirectcomparisonofcomputersimulations,especiallyofrelativechangesinsystemva riablevalues,withexperimentaldata,someoftheexperimentaldatahadtobere-

scaled,asthesystemvariableswereexpressedthereindifferentunitsthanthatappliedinthecomputer modelused.Additionally,whilethecomputermodelusedisdevotedquantitativelytosimulatethevolunt arywhole-bodyexercise(e.g.,cycling)orbipedalknee-

extensionexercise(twoquadricepsesinvolved)inmeanhumans,theexperimentaldata,withwhichco mputersimulationsweredirectlycompared,concernratskeletalmusclestimulatedelectrically[24]orh umancalfmusclesduringvoluntaryexerciseinwell-trainedSherpas[14].

Thedatafrom[24]concernthedependenceofPCr,Pi,ATPandADPconcentrationsandpHon muscleelectricalstimulationfrequency(Hz).Metaboliteconcentrationsareexpressedforcellular waterandthemeasuredrestingpHequals7.2.Ontheotherhand,metabolitecon-

centrationswithinthemodelareexpressesforcellvolume,therestingpHequals7.0andmus- cleworkisexpressedastherelativeATPusageactivityAUT(unitless).Therefore,thefollowingre- calculationsweremade:Metsim(mMforcellvolume)=Metexp(mMforcellularwater)/

1.33(assumingthatwateroccupiesabout75%ofthemyocytevolume).Metsimissimulated

metaboliteMetconcentrationandMetexpisexperimentalmetaboliteMetconcentration.Itwasa ssumed,inordertofitbestthesimulationstoexperimentaldata,thatAUT=1

Fig2.Simulated(lines)andexperimental(points)dependenceofsystemvariablesonrelativeATPusageactivityAUTforthepower-typeA^OX(ESA,each- stepactivationintensity)-AUTdependenceintheabsenceofthe‘additional’ATPusage.A,dependenceofV_O2,ADPandpH;B,dependenceofPCr,PⁱandATP.Re- scaled(seesub-section2.5)experimentaldatafrom[24]arepresented(points).Thepower-typeAOX-

AUTdependencewithoutadditionalATPusageispostulatedtobepresentinelectrically-stimulatedmuscle.

https:/ / doi.org/10.13 7 1/journal.pone . 0195620.g002

Fig3.SimulateddependenceofsystemvariablesonrelativeATPusageactivityAUTforthesaturating-typeA^OX(ESA,each-stepactivationintensity)-

AUTdependenceintheabsenceofthe‘additional’ATPusage.A,dependenceofV_O2,ADPandpH;B,dependenceofPCr,PⁱandATP.Thesaturating-typeA^OX- AUTdependencewithoutadditionalATPusageispostulatedtobepresentinvoluntaryexercise(cortically-

stimulatedmuscle)belowcriticalATPusageactivity(criticalpower).

https:// d oi.org/10.137 1 /journal.pone . 0195620.g003

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RegulationofOXPHOSinelectrically-andcortically-stimulatedmuscle

Fig4.Simulatedtimecoursesofsystemvariablesduringtransitionfromresttomoderatemusclework(relativeATPusagea ctivityAUT=35)torecoveryforthesaturating-typeA^OX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependence.A,dependenceofV_O2,ADPandpH;B,dependenceofPCr,PⁱandATP;C,depende nceofATPusage(vUT)aswellasofATPsupplybyOXPHOS(+aerobicglycolysis)

(vOX),creatinekinase(vCK)andanaerobicglycolysis(vGL).Thesaturating-typeAOX-

AUTdependencewithoutadditionalATPusageispostulatedtobepresentinvoluntaryexercisebelowcriticalATPusageactivity(critic alpower).

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correspondstoelectricalstimulationfrequencyfS=0Hz(rest),whileAUT=101correspondstoelectri calstimulationfrequencyfS=2Hz(intensework),andthereforeAUT(unitless)=50^*fS(Hz)+1.Re- scaledexperimentaldatafrom[21]arepresentedinFig2togetherwithcomputersimulations,while originaldata—inFig 8A .

Thedatafrom[14]concernthedependenceofPCr,PiandADPconcentrationsonrelativeATPturnov er(%ofmaximum)indifferentcalfmuscles:soleus,lateralgastrocnemiusandmedialgastrocnemius.P CrandPiconcentrationswereexpressedinarbitraryunits.Again,inordertomakeatleastacomparisonofsim ulatedandexperimental(formedialgastrocnemius)relativechangesinparticularmetaboliteconcentr ationswithworkintensity,someexperimen-taldatare-

scalingwasnecessary.ItwasassumedthatATPturnoverequalto40%ofmaximumcorrespondstoAUT

=80,andthereforeAUT(unitless)=2^*ATPturnover(%ofmaximum).PCrandPiconcentrationswererescaledfro marbitraryunits(a.u.)tomMusingtherecalcula-

tionfactorof32:Metsim(mM)=Metexp(a.u.)^*32.AscalculatedabsoluteADPlevels(theydif-

fersignificantlybetweendifferentexperiments)weregenerallyhigherinthediscussedstudythanthatpr edictedincomputersimulations,inordertodirectlycomparetherelativechangesinADPtheexperiment alvalueswerereducedbyafactoroftwo.Re-

scaledexperimentaldatafrom[14]formedialgastrocnemiusarepresentedinFig6togetherwithcompu tersimulations,whileoriginaldatafordifferentcalfmuscles—inFig 8B .

Theoreticalresults

Intheabsenceofthe‘additional’ATPusagetherelationshipbetweenV_O_2andATPusageactivity(AUT) islinearregardlesstheAOX(ESA,each-stepactivationintensity)-AUTdepen-

dence,asonecanseeinFigs2and3.However,thelatterdependenceaffectssignificantlytherelations hipbetweenmetaboliteconcentrations(andpH)andAUT.Anactive(‘working’)steady-

statewasreachedinthesesimulations–V_O2,metaboliteconcentrationsandpHstabi- lizedduringmuscleworkonconstantlevels–thiscanbeobservedinFig4.

Thepower-typeAOX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependencecausesthatPCr,Pi,ADPandpHchangesignificantlyinrelati ontorest(ADPandPiincrease,PCrandpHdecrease)alreadyatlowAUTvalues.WhenAUTincreasesfurthertowar dshighvalues,thesechanges(excepttheincreaseinADP)slowdown–

therelationshipbetweenPCr,PiandpH,andAUTbecomesmoreflat.Generally,therelationshipbetweenPC randPiconcentrationsandpH,andthe(relative)ATPusageactivityisessentiallynon-

linear,especiallyatlowAUTvalues.Ontheotherhand,ADPincreasesnear- linearlywithAUT.ATPremainsessentiallyconstant.ThisisdemonstratedinFig2.

Inthecaseofthesaturating-typeAOX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependenceintheabsenceofthe‘additional’ATPusagetherelationshipb etweenPCr,PiandpH,andAUTbecomesmorelinear.Thesesystemvariableschangelessinrelationtoresta tlowAUTvalues,butmoreathighAUTvalues,thaninthecaseofthepower-typeAOX-

AUTdependence.Ontheotherhand,ADPincreasessignificantlyathighAUTvalues,andtheADP- AUTrelationshipbecomesessentiallynon-linear.ThisispresentedinFig3.

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RegulationofOXPHOSinelectrically-andcortically-stimulatedmuscle

Fig5.Simulatedtimecoursesofsystemvariablesduringtransitionfromresttoheavy/severemusclework(relativeATPu sageactivityAUT=80)torecoveryforthesaturating-typeA^OX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependenceinthepresenceofthe‘additional’ATPusage.A,dependenceofV_O2,ADPand pH;B,dependenceofPCr,PiandATP;C,dependenceofATPusage(vUT)aswellasofATPsupplybyOXPHOS(+aerobicglycolysi s)(vOX),creatinekinase(vCK)andanaerobicglycolysis(vGL).Thesaturating-typeAOX-

AUTdependencewithadditionalATPusageispostulatedtobepresentinvoluntaryexerciseabovecriticalATPusageactivity(critica lpower).

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Finally,the‘additional’ATPusage,appearingabovethecriticalATPusageactivity,wastakenintoac countinsimulationsforthesaturating-typeAOX(ESA,each-stepactivationinten-sity)-

AUT(relativeATPusageactivity)dependence.Ofcourse,inthiskindofsimulations,anactive(‘working’)ste ady-

statecannotbeachievedabovethecriticalATPusageactivity(relatedtocriticalpower,seeDiscussion), althoughitisstillreachedbelowit.Forthisreason,inthe6^thminofmuscleworkthevaluesofsystemvariabl eswererecorded,theworkwasterminatedandmusclepassedtotherecoveryphase.

Thesimulatedtimecoursesofselectedsystemvariablesduringrest-to-work-to-

recoverytransitionformoderateworkintensity/relativeATPusageactivityAUT=35(belowthecriti- calATPusageactivityAUTcrit=50)andforhighworkintensity/relativeATPusageactivityAUT=80(ab ovethecriticalATPusageactivityAUTcrit=50)aredemonstratedinFig4andFig5,respectively.

ItcanbeseenthatatmoderaterelativeATPusageactivityAUTthechangesinV_O_2andmetabolitelevel sintimeduringrest-to-

worktransitionarealsomoderate.V_O_2increasesabout16timesinrelationtorest,ADPincreases3.5time s,Piincreases3.5times,PCr

decreasesto66%oftherestingvalueandpHdropsslightlyby0.05pHunits(Fig 4A and4B ).Asteady -stateisreached(oratleastapproachedduringthe6minofexercise),asV_O₂,metab-

oliteconcentrationsandpHstabilizeonconstantlevels.Duringrecoveryvariablevaluesreturntore stingvalues.ApHon-overshootandoff-undershoot,relatedtoH+consumption/pro-

ductionbycreatinekinase,canbeobserved.ThetotalATPusageactivityisconstantduringmuscle work.Whileduringthefirst<0.5minofmuscleworkasignificantfractionofATPissuppliedbycreatin e-

kinasecatalyzedreaction,duringtherestofmuscleworkmostATPisproducedbyOXPHOS,withav erysmallcontributionofanaerobicglycolysis(Fig4C).Duringmusclerecovery,ATPforPCrre- synthesisissuppliedexclusivelybyOXPHOS.

AthighrelativeATPusageactivityAUTandinthepresenceofthe‘additional’ATPusage,changesintim einV_O_2andmetabolitelevelsduringrest-to-

worktransitionaremuchgreaterthanatmoderateAUTandtheycontinuetoproceedduringwork.After6m inutesofmuscleworkV_O_2increases41timesinrelationtorest,ADPincreases11.6times,Piincreases6.4tim es,PCrdecreasesto24%oftherestingvalueandpHdropsby0.17pHunits(Fig5Aand5B).Asteady- stateisnotreached,asV_O_2increases(theslowcomponentoftheV_O_2on-kinet-

icsappears)andmetaboliteconcentrationsandpHchangecontinuouslyduringwork.During recoverythevariablevaluesreturntorestingvalues.ApHon-overshootandoff-

undershootcanbeobservedrelatedtoH+consumption/productionbycreatinekinase.ThetotalATP usageactivity(normal+‘additional’ATPusageactivity)increasesgraduallyduringmusclework(

duetoanincreaseinthe‘additional’ATPusageactivity).CreatinekinaseisthemainATPproduce rattheonsetofmusclework,butATPsupplyisquicklytakenoverbyOXPHOSand,toamuchsmall erextent,byanaerobicglycolysis(Fig5C).ATPsynthesisbyOXPHOSduringexercise(and,conse quently,V_O2)increasescontinuously(stimulatedbytheincreaseinADPandPi)inordertomatchth eelevatedtotalATPusage(the‘additional’ATPusage

Fig6.Simulated(lines)andexperimental(points)dependenceofsystemvariablesonrelativeATPusageactivityAUTforthesaturating-typeA^OX(ESA,each- stepactivationintensity)-

AUTdependenceinthepresenceofthe‘additional’ATPusageabovethecriticalATPusageactivity.A,dependenceofV_O2,ADPandpH;B,dependenceofPCr,Pⁱand ATP.Re-scaled(seesub-section2.5)experimentaldataformedialgastrocnemiusfrom[14]arepresented.Thesaturating-typeAOX-

AUTdependencewithadditionalATPusageispostulatedtobepresentinvoluntaryexerciseabovecriticalATPusageactivity(criticalpower).

https:/ / doi.org/10.137 1 /journal.pone . 0195620.g006

th

increasingintime).Duringmusclerecovery,ATPforPCrre- synthesisissuppliedexclusivelybyOXPHOS.

Thepresenceofthe‘additional’ATPusageaffectssignificantlythedependenceofsystem variablesontherelativeATPusageactivityAUTforthesaturating-typeAOX(ESA,each-

stepactivationintensity)-AUT(relativeATPusageactivity)dependence.Thisisdemonstratedin Fig6.Firstofall,therelationshipbetweenV_O2(determinedinthe6 minofexercise)and AUTbecomesnon-linear.TheincreaseofV_O_2withAUTacceleratesabovethe‘critical’ATP

usageactivity–theV_O2-AUTrelationshipbecomessteeperandacharacteristic‘changepoint’

[20,25]appears.ThisisrelatedtothepresenceoftheslowcomponentoftheV_O_2on-

kineticsresultingfromtheappearanceofthe‘additional’ATPusage(thecausalrelationbetweenthe slowcomponentandtheV_O₂-poweroutputnonlinearityinstep-

incrementalexercisewasfirstpostulatedexplicitlybyZoladzandco-

workers[20]).PCrandPiconcentrationschangemoreinrelationtorestathighATPusageactivities,whenco mparedwiththesimulationsforthesaturating-typeAOX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependencewithoutthe‘additional’ATPusage(Fig3).Thisresultsineve nmorelinearPCr-AUTandPi-

AUTdependencies.Ontheotherhand,ADPincreasesverysignificantlyathighAUTvaluesandtheADP- AUTrelationshipbecomesstronglynon-

linear.The‘additional’ATPusagealsoacceleratesthedecreaseinpHwithAUTabovethe‘critical’ATPusa geactivity–thepH-AUTrelationshipbecomesprogressivelysteeperathighAUTvalues.

ThesimulatedrelationshipbetweensystemvariablesandtherelativeATPusageactivity AUTforthepower-typeAOX(ESAintensity)-AUTdependenceinthepresenceofthe‘addi-

tional’ATPusagewasofcourseidenticalasthatintheabsenceofthe‘additional’ATPusageforAUT (relativeATPusageactivity)<AUTcrit(criticalATPusageactivity)(notshown)(com-

pareFig2).ForAUT>AUTcritagreaterdecreaseinPCrandincreaseinPiandADPinthefor- merthaninthelattercasewaspredicted.Thenon-linearityintheV_O₂-

AUTrelationshipappeared.Generally,thePCr-andPi-AUTdependencesremainedstronglynon- linear,theADP-

AUTrelationshipbecomemoderately‘bentupward’,whilepHdecreaseslightlyacceler- atedathigherAUTvalues(notshown).

Thesimulateddependenceofthecharacteristictransitiontimeoftheprincipalphaseofthemus cleV_O2on-kineticsτpontherelativeATPusageactivityAUTforthepower-typeandsatu-rating- typeAOX(ESAintensity)-

AUTdependenceisdemonstratedinFig7.OnecanseethatinthefirstcaseτpdecreaseswithAUT,whileinthe secondcaseitremainsessentiallyconstant,apartfromthelowestAUTvalues,whereitmoderatelyincr easeswithAUT.Generally,thesimu-

latedτpvaluesareratherlow(butstillwellwithinthevaluesreportedforhumansubjects),becausearel ativelyhighESAintensitywasusedinthesesimulationsandτpdependssignifi-

cantlyonESAintensity[26].WhenalowerESAintensitywasusedincomputersimulations(e.g.,AO Xmax=3–4.5),longerτpswereobtained(28–

40s).Inextremecases,thesimulatedτpcanbelowerthan10s(forAOXmax>~12)orhigherthan50s(for AOXmax=2)(seealso[7,26,27]).Therefore,theESA-

dependentrangeofτpcoverstheentirerangeofτpencounteredinhumans,fromverywell- trainedathletestoelderlypeopleandpatientswithnumerousdiseases(seee.g.,

[28]).However,τpdependsalsoontheresting(withoutESA)OXPHOSactivity/mitochondriacontent[

26].

Discussion

Thepresenttheoreticalstudydemonstratesthatthepower-typeAOX(ESA,each-stepactiva- tionintensity)-

AUT(relativeATPusageactivity)intheabsenceofthe‘additional’ATPusagepredictssignificantlydifferen

tkineticbehaviorofthebioenergeticsysteminskeletalmusclethanthesaturating-typeAOX- AUTdependenceinthepresenceofthe‘additional’ATPusage.

Fig7.SimulatedrelationshipofthecharacteristictransitiontimeτpoftheprincipalphaseofthemuscleV_O2on- kineticsonrelativeATPusageactivity(A^UT)forthepower-typeandsaturating-typeAOX(ESA,each- stepactivationintensity)-AUTdependencies.TherelativeactivationofOXPHOSduringrest-to-

worktransitionAOXwasincreasedasafunctionofA^UTaccordingtoEq1forpower-typedependenceandtoEq2forsaturating- typedependence.Thepower-typeAOX-AUTdependencewithout‘additional’ATPusageispostulatedtobepresentinelectrically- stimulatedmuscle,whilethesaturating-typeAOX-

AUTdependencewith‘additional’ATPusageispostulatedtobepresentinvoluntaryexercise(cortically-stimulatedmuscle).

https:// d oi.org/10.1371/ j ournal.po n e.0195620.g 0 07

Intheformercase,V_O_2increaseslinearlywithAUT,thedependenceofPCr,cytosolicPiandpHonAUTis stronglynon-

linear(largechangesatlowAUTvalues,smallerchangesathigherAUTvalues),whileADPincreasesnea r-linearlywithAUT.Ontheotherhand,inthelattercase,theV_O₂-AUTdependsissignificantlynon- linear(itbendsupwardabovethecriticalATPusageactivity),PCrdecreasesandPiincreasesnear- linearlywithAUT,theADP-AUTand

pH-AUTdependenceisstronglynon-

linear(theincreaseinADPanddecreaseinpHwithAUTacceleratesathigherAUTvalues).Asitisdiscussedbelo w,computersimulationsusingthepower-typeAOX-

AUTdependencereproducewellexperimentaldataforelectrically-

stimulatedskeletalmuscle,whilesimulationsusingthesaturating-typeAOX-AUTdependenceinthepres- enceoftheadditionalATPusage(underlyingtheslowcomponentoftheV_O2on-

kinetics)areabletoaccountsatisfactorilyforthekineticbehaviorofthebioenergeticsystemincortically- stimulatedskeletalmuscle(voluntaryexerciseinhumans).Itisarguedthatthedifferencebetweentheel ectrically-andcorticallystimulatedmuscleresultsfromdifferentpatternsofvar-

iousmusclefibersrecruitment.Generally,itisconcludedthattheregulationofOXPHOSisdifferentinel ectrically-andcortically-stimulatedskeletalmuscle.

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RegulationofOXPHOSinelectrically-andcortically-stimulatedmuscle

Fig8.Experimentaldependenceofskeletalmusclebioenergeticsystemvariablesonparameters/variablesrelatedtoA TPusageactivity.A.Original(notre-scaled)dependenceofPCr,Pi,ADP,ATP,pHafter8–

12minofstimulationonelectricalstimulationfrequencyinratskeletalmuscle(TableIandIIin[24]).B.Original(notre- scaled)dependenceofPCr,PiandADPafter4minofexerciseonATPturnoverrate(%ofmaximal)inhumancalfmuscleduri ngvoluntaryconstant-powerexercise(pedalpressing)

(extractedfromFig6in[14]).C.DependenceofthedecreaseinPCrandpH(inrelationtorest)after6minofexerciseonworkin tensityinhumanquadricepsmusclesduringvoluntaryconstant-powerexercise(bilateralkneeextension)

(closedsymbols,[2];opensymbols,[35]).

https:// d oi.org/10.1371/ j ournal.po n e.0195620.g 0 08

Power-typevs.saturating-typeA

OX

-A

UT

dependence

Ithasbeenshownpreviously[10,29]thatintheabsenceofESAhugechangesinmetabolite(ADP,PCr, Pi,ATP)levelsalreadyatlowandmoderateworkintensitiestakeplace.WhentherelativeATPusageact ivityAUTreachesthevalueofabout30,OXPHOScapacitybecomessat-

urated,asanincreaseinADPandPicannotfurtheractivateit,muscleV_O2reachesitsmaxi- mumatlessthan4mMmin^-1andthesystemcollapses(PCrandATPfalltozero).

ComputersimulationscarriedoutinthepresentstudyshowthatinthepresenceofESA(each- stepactivationofOXPHOScomplexesandNADHsupply),butintheabsenceofthe‘additional’ATPusa ge,theV_O₂-

AUTrelationshipislinearevenathighAUT(relativeATPusageactivity)values,asitcanbeseeninFigs2and3.Th epower-typeAOX(ESAintensity)-AUTdependencegeneratesPCr-AUT,Pi-AUTandpH-

AUTrelationshipsthatarestronglynon-

linear:PCr,PiandpHchangequicklywiththeAUTincreaseatlowAUTvalues,butthesechangesslowdownsigni ficantlyathigherAUTvalues.Ontheotherhand,theADP-AUTrela-tionshipisnear-

linear.ThisisdemonstratedinFig2.ThesesimulatedsystempropertiesresultfromrelativelylowOXPH OSstimulationbyESAatlowAUTvalues,butrelativelystrongOXPHOSstimulationbyESAathighAUTvalues inthecaseofthepower-typeAOX-AUTdependence(compareFig1).

Thekineticbehaviorofthesystemissignificantlydifferentforthesaturating-typeAOX(ESA,each- stepactivationintensity)-

AUT(relativeATPusageactivity)dependenceintheabsenceofthe‘additional’ATPsupply(Fig3).Namely ,relativelylittlechangesinPCr,Pi,pHandADPwiththeAUTincreaseatlowAUTvaluescanbeobserved.Chan gesinPCrandPionlyslightlyslowdownathighAUTvaluesandthePCr-AUTandPi-

AUTrelationshipsbecomemuchmorelinearthanforthepower-typeAOX-

AUTdependence.ThisiscausedbyrelativelyhighOXPHOSstimulationbyESAalreadyatlowAUTvaluesandb ythefactthatthisstimula-tiondoesnotincreasefurtherathigherAUTvaluesinthecaseofthesaturating- typeAOX-

AUTdependence(compareFig1).Ontheotherhand,thedecreaseinpHwithAUTisslightlyfasterathigherAU Tvalues(Fig3),unlikeforthepower-typeAOX-AUTdependence.Thisisdemon-stratedinFig3.

Impactof‘additional’ATPusage

Theinclusionofthe‘additional’ATPusage[1]abovethecriticalATPusageactivity(AUTcrit)intheca seofthesaturating-typeAOX-AUTdependencecausesthatthesystemcannotreachasteady-

stateforAUT(relativeATPusageactivity)>AUTcrit(criticalATPusageactivity).Thiscanbeseenwhenon ecomparessimulationsofrest-to-work-to-recoverytransitionformoder-

atework(AUT=35<AUTcrit=50)(Fig4)andheavy/severework(AUT=80>AUTcrit=50)(Fig5).

ThecriticalrelativeATPusageactivityAUTcritisstrictlyrelatedtocriticalpower,thatisthepowerout putabovewhichitisnotpossibletoreachasteady-

state[30,31].Asaresult,abovecriticalpowerexercisecannotbecontinuedforalong(potentiallyunli mited)time[30,31].

Inheavy/severeexercisesystemvariables(muscleV_O₂,PCr,Pi,ADP,pH)changesignifi- cantlyimmediatelyaftertheonsetofexerciseandthen,unlikeinmoderateexercise,continuetochang econtinuouslywithslowerpace,neverreachingasteadystate.ThisisdemonstratedinFig5vs.Fig4.T hetotalATPusageactivityincreasesgraduallyduringexercise,reflecting

theincreaseinthe‘additional’ATPusageactivity.Thisleads,throughanincreaseinADPandPi,to aslowcontinuousincreaseinATPsupplybyOXPHOSinordertomatchtheelevatedATPconsum ption,andconsequentlyacontinuousincreaseinmuscleV_O2.Thelastphenom-

enonhasbeennamedthe‘slowcomponent’oftheV_O2on-kinetics[32].ThepulmonaryV_O₂ slowcomponentisgeneratedprincipallywithintheexercisingskeletalmuscles[32,33].

Thepresenceofthe‘additional’ATPusageinthesystemwiththesaturating-typeAOX(ESA,each- stepactivationintensity)-AUT(relativeATPusageactivity)dependenceaffectssig-

nificantlythesystemvariables-AUTrelationships.PCr-AUTandPi-AUTrelationshipsbecomenear- linear,whiletheADP-AUTrelationshipbecomesstronglynon-

linear.ThedecreaseofpHwithAUTacceleratessignificantlyabovethecriticalATPusageactivity(relatedto criticalpower).ThisisdemonstratedinFig6.Finally,theV_O₂-AUTrelationshipbecomesessentiallynon- linear:abovethecriticalATPusageactivitytheincreaseofV_O2withAUTacceleratesandtheV_O2-

AUTrelationshiphasanincreasinglysteeperslope.Acharacteristic‘changepoint’[20,25]appears.Thissys tempropertyisrelatedtothepresenceoftheslowcomponentofthe

V_O2on-kineticsresultingfromtheappearanceofthe‘additional’ATPusage.Thecausalrela-

tionbetweentheslowcomponentandtheV_O2-POnonlinearitywasfirstpostulatedexplicitlyforstep- incrementalexercise(increaseby30Waftereach3min)byZoladzandco-workers

[20].

Comparisonofcomputersimulationswithexperimentaldata

Selectedexperimentaldataconcerningthedependenceofsystemvariables(PCr,Pi,ATP,ADP,pH)o nsomeparameter/variablerelatedtotheATPusageactivityindifferentexperi-

mentalsystemsarepresentedinFig8.Someofthesedata,afterre-

scaling,arealsoshowninFig2andFig6inordertomakedirectcomparisonofthesedata(especiall yofrelativechangesinmetabolitesandpH)withcomputersimulations.Preferencewasgiventom easurementsofmetaboliteconcentrations/pHusing³¹PMRSoverchemicaldeterminationinmu sclebiop-

siesandtosufficientlywiderangeofelectricalstimulationfrequencyorworkintensityvalues(assu medtobeproportionalinagiventypeofexercisetotheATPusageactivity).

Inratskeletalmusclestimulatedelectrically[24]thefallinPCrandriseinPiwiththestim- ulationfrequency(after8–

12minofexercise)isrelativelyquickatlowstimulationfrequencies,butslowsdownathigherstimul ationfrequencies.ThisisdemonstratedinFig 8A .Suchakineticbehaviorisdecidedlysimilartothe pronouncednon-linearityofthePCr-AUTandPi-AUTrelationshipsimulatedforthepower-

typeAOX(ESA,each-stepactivationintensity)-

AUT(relativeATPusageactivity)dependenceintheabsenceofthe‘additional’ATPusage.Thisisdire ctlydemonstratedinFig2,wherecomputersimulationsarecomparedwithre-

scaledexperimentaldata(seesub-

section2.5)presentedinFig 8A .TheexperimentalandtheoreticalPCr-AUTandPi- AUTdependenciesaredecidedlysimilar.Alsotheexperimentalandtheoreti-calATP-

AUTdependenciesaresimilar,althoughexperimentalATPsomewhatdecreasesathigheststimulationfre quencies,mostprobablyduetoAMPdeamination.Thisprocesswasnotinvolvedinthepresentst udy,butitsimpactonthesystemwasanalyzedpreviously[34]

(seebelowfordiscussion).ThesimulatedpH-

AUTdependenceagreeswellwiththemeasuredpHdecreasewithstimulationfrequency,apartfromon

eexperimentalpointforthehigheststimulationfrequency,inwhichthemeasuredpHfallsinrelatio ntorestsignificantlymore