Modeling the competition between antenna size mutant and wild type microalgae in outdoor mass culture

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Journal of Biotechnology

jo u r n al h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / j b i o t e c

Modeling the competition between antenna size mutant and wild type microalgae in outdoor mass culture

Tim de Mooij

^a,∗,1

, Kira Schediwy

^a,1

, René H. Wijffels

^a,b

, Marcel Janssen

^a

aBioprocessEngineering,AlgaePARC,WageningenUniversity,PObox16,6700AA,Wageningen,TheNetherlands

bBiosciencesandAquaculture,NordUniversity,Bodø,8049,Norway

a r t i c l e i n f o

Articlehistory:

Received13June2016

Receivedinrevisedform10October2016 Accepted12October2016

Availableonline13October2016

Keywords:

Antennasizemutant Competition Chlorellasorokiniana Arealbiomassproductivity Photosyntheticefficiency

a b s t r a c t

Underhighlightconditions,microalgaeareoversaturatedwithlightwhichsignificantlyreducesthelight useefficiency.Microalgaewithareducedpigmentcontent,antennasizemutants,havebeenproposed asapotentialsolutiontoincreasethelightuseefficiency.Thegoalofthisstudywastoinvestigatethe competitionbetweenantennasizemutantsandwildtypemicroalgaeinmasscultures.Usingakinetic modelandliterature-derivedexperimentaldatafromwildtypeChlorellasorokiniana,theproductivity andcompetitionofwildtypecellsandantennasizemutantsweresimulated.Cultivationwassimulated inanoutdoormicroalgalracewaypondproductionsystemwhichwasassumedtobelimitedbylightonly.

LightconditionswerebasedonaMediterraneanlocation(Tunisia)andamoretemperatelocation(the Netherlands).Severalwildtypecontaminationlevelsweresimulatedineachmutantcultureseparately topredicttheeffectontheproductivityoverthecultivationtimeofahypotheticalsummerseasonof 100days.Thesimulationsdemonstrateagoodpotentialofantennasizereductiontoincreasethebiomass productivityofmicroalgalcultures.However,itwasalsofoundthatafteracontaminationwithwildtype cellsthemutantcultureswillberapidlyovergrownresultinginproductivityloss.

©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Oneofthemostimportantbottlenecksinmicroalgaecultivation is the inefficient utilization of light energy under high irradi- ance.Microalgaeareeasilyoversaturatedwithlightwhichstrongly reducesthelightuseefficiency.Thislimitationcanbealleviatedby geneticallyreducingtheamountoflightenergythatisabsorbedper cell.Thecreationofsuchantennasizemutants,i.e.,microalgaewith areducedpigmentcontent,hasbeenproposedasapotentialsolu- tion(Formighierietal.,2012;Kwonetal.,2013;Mussgnugetal., 2007a;Oeyetal.,2013;Ortetal.,2011;Perrineetal.,2012)tolight saturation.Thelowerpigmentationofthemutantsallowsincreased biomassconcentrationswiththesamelightgradientinthephoto- bioreactor(Melisetal.,1998;Mussgnugetal.,2007b).Thelower biomassspecificlightabsorptionrateleadstoahigherproductiv- ityofmutantculturesthanthatofwildtypeculturesunderhigh lightconditions(Mussgnugetal.,2007b).Inpractice,somemutants wereindeedreportedtodemonstrateimprovedgrowthcharac-

∗Correspondingauthor.

E-mailaddress:[email protected](T.deMooij).

1 Theseauthorscontributedequallytothiswork.

teristicsunderspecificlightconditions(Mussgnugetal.,2007b;

Cazzanigaetal.,2014;MitraandMelis,2008).

Clearly, antenna size mutant generation, especially through directedmutagenesis,isanimmaturetechnology(deMooijetal., 2014).Currentlytherearenosuitableantennasizemutantstrains availablethatcanbeanalyzedfortheirperformanceincompeti- tionexperiments.A betterunderstandingof thephotosynthetic machineryandanadvancedgenetictoolboxarerequiredtocre- atebettermutants.Still,itisinterestingtostudythepotentialof antennasizereductionfor masscultivationofmicroalgaeusing model simulations. Extrapolation of laboratory data utilizing a predictivemodelthatisconstructedonasolidtheoreticalfounda- tionisanattractivealternativetoperformingoutdoorcultivation experiments. Modeling can function as a great tool to investi- gatetheimprovementofmasscultureproductivityusingantenna size mutants. In addition, the impact of competition for light betweenmutantandwildtypestrainscanbepredicted.Compe- titionbetweentheantennasizemutantanditsownwildtypeis expectedtoresultinproductivitylosses.Theoutcomeofsucha modelingapproachresultsinmorerealisticexpectationsandcanbe usedtodeterminegeneticengineeringtargetstooptimizemutant cultivation.

http://dx.doi.org/10.1016/j.jbiotec.2016.10.009

0168-1656/©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).

Theaim of this studywas toestimate antennasize mutant productivityin photobioreactormass cultures and quantifythe competitionbetweentheantennasizemutantanditswildtype.

Knowledge ongrowthproperties of separate cultures (Hobson, 1969;Huismanetal.,1999)isrequiredtoanalyzemixedcultures andtoestimatethecompetitivenessoftheinvolvedspeciesunder lightlimitingconditions.Manymodelsdescribingbiomassproduc- tivityofmicroalgaeareavailabletodate(AciénFernándezetal., 1998;CornetandDussap,2009;Geideretal.,1997;Huesemann etal.,2016; Leeet al.,2014;Quinn etal.,2011; Takacheetal., 2012).Thesemodelsdifferbytheirlevelofcomplexity,modelstrat- egyandneedforparameterization.Inourstudytheproductivity wascalculatedwitha microalgalgrowthmodel whichis based onsumminguplocalratesofphotosynthesiscalculatedforevery positioninthephotobioreactor. Thepresentedmodeltakesinto accountthelightgradientwithinthemicroalgalcultureandalso thewavelengthdependencyoflightabsorption.Themodelisbased onapreviouslyvalidatedgrowthmodelforChlorellasorokiniana undercontinuouslight(Blankenetal.,2016),thatwasobtainedby combiningmodelsofJassbyandPlatt(1976)andPirt(1965)and theLambert-Beerlaw.Themodelhasbeenmodifiedbyaddinga carbonpartitioningmechanismandsimulatedoutdoorlightcon- ditionstodescribegrowthunderday/nightcycles.Byextending themodel,itserveswelltoanswernewresearchquestionsregard- ingthecompetitionofmicroalgaestrainsthathavedifferentlight harvestingcapacities.Thelightmodelwasfurtheradaptedtorepre- sentanoutdoormicroalgalracewaypondproductionsystemtaking intoaccountsolarelevation.Thewildtypepropertiesweredefined basedonexperimentaldataofC.sorokiniana.Antennasizemutants wereconsideredtoonlydifferfromthewildtypeintheirreduced absorptioncrosssectiontoclearlyidentifythepotentialofreduced antennasizes.Productivitiesofthemutantmonocultureswithdif- ferentantennasizereductions(0–90%)wereinvestigated.Several wildtypecontaminationlevelswereseparatelysimulatedineach mutantculturetopredicttheeffectontheproductivityoverthe cultivationtime(100days).

2. Modeldescription 2.1. Structure

Withthekineticmodelthebiomassproductivityofamicroalgae masscultureiscalculatedasafunctionoftheincidentlightinten- sityduringthediurnalcycle.Thechangeofthespectralcomposition withincreasingreactordepthduetothepreferentiallightabsorp- tionofmicroalgaewastakenintoaccount.Themodelallowsfor thecalculationofbiomassproductivityofanantennasizemutant culturebefore,during,andaftercontaminationwithitswildtype.

Inallofthecases,light isassumedtobethelimitingfactor for growthand,consequently,mutantandwildtypearecompetingfor lightenergy.Anextensivedescriptionofthemodelcanbefoundin AppendixA.

Toaccountfortheeffectsofthediurnalcycleandcarbonparti- tioning,functionalbiomassandintracellularcarbohydratereserves wereregardedasseparatecompounds.Thecarbohydratereserves arereferredtoas‘sugar’inthisstudy.Consequently,foreachstrain, twoproductionratesweredistinguished:theproductionoffunc- tionalbiomass(X’)andofsugar(S).

RefertoFig.1foranoverviewofthemodelstructure.Theoverall microalgae production model consists of three modules: Loca- tion,time,andwavelengthdependentlightdistribution(Module 1);specificlightabsorption,andphotosyntheticsugarproduction (Module2);partitioning ofsugar towardsbiomass,anda sugar reservepool(Module3).Thefirstmoduledescribesthelocation- specificlight intensityand the light distributionin theculture

duringtheday.Thesearebasedonsolarelevations,Snell’slaw,Fres- nel’sequations,andLambert-Beer’slaw,whileneglectingtheeffect oflightscattering.Thesecondmoduledescribesthesugarproduc- tionasafunctionofspecificlightabsorptionand,consequently, dependsonthelocallightintensity,biomassconcentration,and strain-specific characteristics. The third module representsthe allocationof photosyntheticallyproduced sugartomaintenance relatedprocesses,totheaccumulationofcarbohydratereserves, andtotheproductionoffunctionalbiomass.Inaddition,theparti- tioningofsugarisdifferentiatedbetweenthedayandnightperiods duringthediurnalcycle.

2.2. Strategyandassumptions

Two ordinary differential equations (Eqs. (A9) and (A10)) describe thechangein production and respiration of thefunc- tionalbiomassandthesugarforeachstrainseparately.TheMatlab built-insolverforstiffdifferentialequations(ode23s)basedonthe 2nd/3rdorderRunge-Kuttamethodwasusedtonumericallyinte- gratethechangeinconcentrationsoverthecultivationtime.This resultsintherespectivefunctionalbiomassandsugarconcentra- tionsasafunctionoftime.

Thesimulatedcultivationtimewas100days.Wesimulatedboth aMediterraneanlocation(Tunisia,Lat.36.867^◦)withahighirradi- anceandclearskyandatemperatelocation(theNetherlands,Lat.

52.117^◦)withconsiderablecloudcover.Onespecificsummerday (July15th,day196oftheyear)wascontinuouslyrepeatedinthe modelforeachlocation.Allsimulationsbeganat8:00amlocalsolar time.Duringtheday,thedilutionratewasmaintainedconstant whiletherewasnoculturedilutionduringthenight.Thedilution ratewasoptimizedforeachstrainandeachlocation(Netherlands andTunisia)tomaximizetheproductivity(SeeAppendixDforopti- mizationprocedure).Theoptimaldilutionratewassubsequently appliedduringthefinalsimulations.

Theoretical antenna size mutants of Chlorella sorokini- ana were simulated. The strain-specific characteristics

␮m,m_S,Y_X/S,q^max_S ,x_S,min

of the mutants were kept identi- caltotheexperimentallydeterminedcharacteristicsofthewild type (Table A3 of Appendix E), i.e., only the biomass specific absorptioncrosssectionforeachwavelength

a_X,

wasaltered by multiplying a_X, with 0.1-0.9, depending on the degree of antennasizereduction(90-10%).Throughouttheentireday/night cycle,a_X,wasassumedtobeconstant.Thewildtypeabsorption crosssectionwasmeasuredundermasscultureconditionswith anincidentlightintensityof1500␮mol_phm⁻²s⁻¹andanoutgoing lightintensityof10␮mol_phm⁻²s⁻¹.Theantennasizemutationis assumedtobestableandnotaffectinganyothercellularproperty, andtheconsideredstrainsareassumedasnotbeingsensitiveto photoinhibition under the simulated light conditions. Different wildtype contamination levelswereconsidered as wellasthe scenarioofareversemutationwhichwasassumedtoresultina contaminationofonecellpercubicmeterattheinitiationofthe 100-dayssimulation.OnecellofC.sorokinianacorrespondstoa massof1.4·10⁻¹¹g,or0.14pg(Rosenbergetal.,2014).Areflective (80%)groundcoverwassimulatedtobesituatedatthebottomof thephotobioreactorpondtoallowafairercomparisonofmutant andwildtypeperformance.

Thearealbiomassproductivity (rCx) wascalculatedbymultiply- ingthetotalbiomassconcentration (X’+S) withthedilutionrate (D) andthereactordepth (d_R):

r_Cx=(X’+S)·D·dR (1)

Fig.1.Calculationschemeforthethreemodules.Module1:location,time,andwavelengthofspecificlightdistribution;Module2:photosyntheticsugarproduction;Module 3:sugarallocationtowardsbiomass,thesugarreservepool,andmaintenanceduringthediurnalcycle.Modelinputsareinovalsandcalculatedvaluesinsolidboxes.

3. Results

Simulationswiththemodelwereperformedformonocultures ofthewildtypeofChlorellasorokinianaandformonoculturesof theantennasizemutantswithavaryingabsorptioncrosssection

a_X,

intherangeofa10–90%reductioncomparedtothewild type.Inaddition,monoculturesoftheantennasizemutantswere

‘contaminated’withwildtypecellsatvariouscontaminationlevels inordertoinvestigatethecompetivenessofthemutantsandthe dynamicsofoutcompetition.Thewildtypeandthemutantswere comparedregardingtheirarealbiomassproductivityattwoloca- tions,theNetherlandsandTunisia,duringahypotheticalsummer seasonof100days.RefertoAppendixCforthelightpatternofone summerdayforbothlocationsthatwasemployedinallsimulated daystoobtainrepetitivelightconditions.Forcontaminatedcul- tures,thelossofproductivityasaresultofthecontaminationwith thewildtypewasalsoinvestigated.

3.1. Simulationoverview

InFig.2A,theday/nightcycleofonecultivationisillustratedfor boththewildtypeandamutantwithan80%antennasizereduction inTunisia.Thenetsugarproductionrate(X·(q_S-m_S))isameasure forthephotosyntheticactivityofthemutantculture.Itisillustrated thatthenetsugarproductionrateofthemutantcultureisconsid- erablyhigherthanthatofthewildtypecultureonlyduringthe brightesthoursoftheday.Inthenightthesugarproductionrateis negativebecausesugarisusedtobuildnewfunctionalbiomassand

sugarispartlyrespiredtosupportboththegrowthprocessesaswell asthemaintenancerelatedprocesses.Themutantcultureexhibits greaterlossesofphotosyntheticallyderivedsugarduringthenight becauseofthehigherbiomassconcentrationand theassociated maintenancerequirementsthatmustbesatisfied.Pleasenotethat thefunctionalbiomassspecificmaintenancerate(ms)isassumed tobethesameforwildtypeandmutant.Therefore,thedifference insugarconsumptionratebetweenwildtypeandmutantiscaused bythedifferenceinbiomassconcentration.

Exemplary,thefirst50daysofthe100dayscultivationperiod areshownforthemutantwithan80%antennasizereductionin Tunisia(Fig.2B–D).Asdemonstratedlater,amonocultureofthis mutantresultsinthehighestarealbiomassproductivity(r_Cx).It canbeobservedingreaterdetailonday50inFig.2BandCthat, duringtheday,biomassisproducedandthebiomassconcentration isincreasing.However,inthemorningandfrom16:00solartime onwards,thebiomassconcentrationisdecreasingastheresultof thelowincidentlightintensityincombinationwithculturedilu- tion.Thecourseofthecultivationisillustratedformonocultures ofthemutantwithandwithoutcontaminationbythewildtype.

The shown contaminationlevel is one wildtype cellper cubic meteratday0.Thecontaminationhassubstantialeffectsonthe courseofthecultivationafterapproximately27days(Fig.2B).The mutantconcentrationthendecreasesrapidlywhilethewildtype concentrationincreases,whichconsiderablyreducesthebiomass productivity.Thewildtypereachesalowerbiomassconcentration andlowerproductivitythanthemutant.Theseeffectsarearesult ofthewildtypeabsorbingmorelightpercellwhichleadstomore

Fig.2. (A)Netsugarproductionrate(X’·(qS-mS)),ameasureforthephotosyntheticactivityminusthemaintenance,presentedforthedurationofoneday/nightcycle.InB, C,andD,anoverviewisprovidedofthefirst50dofa100dsimulationofanantennasizemutantwith80%reductionintheabsorptioncrosssection(aX,)inTunisia.Day50 isplottedonadifferentscaleinBandCtoillustratethevariationoverthecourseofonedayingreaterdetail.Thecultureiscontaminatedatt=0withonewildtypecellper cubicmeter.Thedashedgreylinesdepictthescenarioofanaxenicmutantculturewithoutcontamination.(B)Thebiomassconcentration(CX)ofthemutantandthewild type.(C)Thedailyarealbiomassproductivity(rCx)ofthemixedcultureasthesumoftheproductivityofmutantandwildtypeisdepictedbythesolidblackline.(D)The biomassyieldonincidentlight(YCx/ph)averagedoveronedayisshownbythesolidblacklineandisbasedonthemixedcultureofwildtypeandmutantcells.Thedilution ratewaskeptconstantduringthelightperiod,andnodilutionwasappliedduringthenight.

oversaturationandlightloss.Thisisalsomanifestedasadecrease ofthebiomassyieldonlight(Fig.2D).

3.2. Monoculturesofantennasizemutantsandtheirwildtype Thearealbiomassproductivityofantennasizemutantsinasim- ulatedoutdoorracewaypond photobioreactorwasinvestigated.

Thereductioninabsorptioncrosssectionwasnormalizedtothe wildtype,andareductionof10to90%wassimulated.Theareal biomassproductivityof themutantmonocultureswasfoundto increasewithincreasingantennasizereductionuntilamaximum isreached(Fig.3A).Themaximumproductivitieswerefoundfor cultureswithantennasize reductionsof80%(53.2gm⁻²d⁻¹)in Tunisiaand60%(31.5gm⁻²d⁻¹)intheNetherlands.Afterthemax- imum,thebiomassproductivitydecreaseswhentheantennasize isfurtherreduced.

Comparingthetwolocations,thearealbiomassproductivity washigherinTunisiathanintheNetherlandsforallofthemutants and the wild type. Because of the higher irradiance, both the biomassconcentrationsandtheoptimaldilutionrateswerehigher inTunisiathanintheNetherlands.InTunisia,theincreaseofthe productivitywiththeantennasizereductionissteeperandleading toasharpermaximumthanintheNetherlands.Arelativeproduc- tivityincreaseof39%inTunisiaandof16%intheNetherlandswas observedforthebestperformingmutantstrain.

Thelossinproductivityafterthemaximumhasbeenreachedis primarilycausedbythefactthatlight,afterbeingreflectedatthe bottomduetothegroundcover(i.e.liner),isleavingthephoto- bioreactorpondunusedatthesurfacewhenapplyingaveryhigh antennasizereduction.Itisimportanttonotethatawhitelinerwas simulatedwithan80%reflectivityasdescribedinAppendixB.For anantennareductionof90%inTunisia,upto100␮mol_phm⁻²s⁻¹ is lost in this way at solar noon. In addition, the higher costs formaintenancerequiredforthehighbiomassconcentrationfur- therdecreasetheproductivity.Themaintenance requirementis assumedtobeaconstantandequalforallmutantsandthewild type.Consequently,therelativemaintenancecostsincreaseupto 24%intheNetherlandsfora90%aXreduction(SeeFig.3A).Atmod-

erateantennasizereductionsonly10%ofthetotalproducedsugaris consumedforthepurposeofmaintenance.Thismeansthatathigh antennasizereductionarapidlyincreasingfractionofphotosyn- theticallyproducedsugarisusedformaintenanceinsteadofbeing incorporatedintonewbiomass.Theeffectofmaintenanceishigher forlowerirradianceconditionsaspresentintheNetherlands.

Therelation betweenantenna sizereduction and photosyn- theticefficiencyundersaturatinglightconditionsisalsoreflected inthebiomassyieldonlight(Fig.3B).Becauseofthehigherirra- dianceinTunisia,overallyieldsarelowerthanintheNetherlands.

Onlybeyond80%antennasizereductionthebiomassyieldonlight washigherinTunisiathanintheNetherlands.Forsmallantennae, lightoversaturationinTunisiaisrelativelylowwhilethelightlev- elsduringthemajorityofthedayareabove1000␮mol_phm⁻²s⁻¹ andevenreach1800␮mol_phm⁻²s⁻¹atsolarnoon(SeeAppendix C).

3.3. Culturedynamicsaftermutantmonoculturecontamination bywildtypecells

Antennasizemutant monocultureswitha varyingreduction inabsorptioncrosssection

a_X,

weresimulatedasbeingcon- taminatedwithdifferentlevelsofwildtypecells.Inthiswaythe rateatwhichmutantculturesareovergrownwasinvestigatedas afunctionofthecontaminationlevelandantennasizereduction.

Fig.4Aillustratestheeffectofdifferentcontaminationlevelson thetimeittakesforwildtypecellstobecomethedominantstrain intheculture.OnlytheresultsforTunisiaareshown.Theoptimal antennasizereductionforTunisia,80%,wasselectedinorderto studytheeffectofthecontaminationlevel.Atthehighestcontam- inationlevelof1%,thedecreaseinmutantbiomassconcentrations becomesapparentalreadyafterthreedays.Lowercontamination levelsextendthe duration that theantennasize mutant isthe dominantstrainand duringthis periodlightisusedatahigher efficiencycomparedtothesituationinwhichthewildtypeisthe dominantstrain.However,eveninthebestcasescenariothatwas considered,withacontaminationofonlyonecellpercubicmeter,

Fig.3. (A)Biomassproductivity(rCx)andrelativecostsofmaintenanceprocesses(mS/qS,%),i.ethefractionofproducedsugarusedformaintenanceandnotforgrowth.(B) biomassyieldonincidentlight(YCx/ph)presentedforthewildtype(0%reduction)andantennasizemutantcultures.Forthecalculationofthebiomassyieldonlight,the dailyaveragedproductivityisnormalizedtothedailyamountofincidentlightonthephotobioreactor.

Fig.4.(A)Effectofthecontaminationlevelontherateatwhichantennasizemutantsareovergrownbywildtypecellsinasimulatedracewaypondphotobioreactorwitha depthof0.2m,situatedinTunisia.Themutantmonocultureshavean80%reductionintheabsorptioncrosssection(a_X).Thedashedlineindicatesthescenarioofamutant monoculturewithnocontamination.Onlyforthelowestcontaminationlevel(4.0·10⁻¹²%,or1cellm⁻³atday0)theassociatedincreaseinwildtypebiomassconcentration isillustratedbythesolidgreyline.(B)Effectofantennasizereductionontherateatwhichthemutantmonoculturesareovergrownbythewildtypecells.Forclarityreasons, thewildtypeconcentrationisnotpresented.Thecontaminationlevelforthesesimulationsequalonewildtypecellpercubicmeteratday0.

themutantswereovergrownbeforehalfofthesimulatedsummer season(100days)hadpassed.

Inadditiontothecontaminationlevel,theeffectoftheantenna sizereductionwasinvestigated(Fig.4B).Again,onecellpercubic meterwaschosen asthecontaminationlevelina monoculture in Tunisia. Clearly, greater reductionsin antennasize result in less competitive mutantsand, therefore, themutants withthe highestpotentialintermsofmasscultureproductivityaremost vulnerableandrapidlyovergrownbywildtypecellswithinone simulatedsummerseason.Forantennasizereductionsbelow40%, themutantsremainthedominantstraininthecultureduringthe simulatedseason.However,asshownbeforeinFig.3,a40%reduced antennasizemutantdoesnotexploitthefullpotentialofantenna sizereduction.

4. Discussion

Inaccordancewithourexpectations,thearealbiomassproduc- tivitywashigherinTunisiathanintheNetherlandsforallmutants andthewildtype.Uptoa39%increaseinproductivitywasesti- matedforan80%antennasizereducedmutantcomparedtothe wildtype.IncontrasttoTunisia,intheNetherlandsunderthemost optimisticconditions,onlya16%increaseinproductivitycouldbe obtainedcomparedtothewildtypecultivation.Thesenumbers emphasize thatboth aconsiderableantennasizereduction and highirradiancearerequiredtoobtainsubstantialgainsinproduc- tivity.Mostantennasizemutantsthathavebeencreateddonot exhibitsuchhighantennasizereductions(deMooijetal.,2014).In Tunisia,saturatinglightconditionsarepresentoveralongerperiod ofthedaythanin theNetherlands.Therefore, anyreductionin

absorptioncrosssectionreducesoversaturationandthusincreases lightuseefficiency(Melisetal.,1998;Mussgnugetal.,2007b;Mitra andMelis,2008;deMooijetal.,2014;Zhuetal.,2010).Theresults showaclearpotentialfortheuseofantennasizemutantsinhigh irradiancelocationssuchasTunisia.

Thetheoreticalmaximumbiomass yieldonlight (Y_Cx/ph)for Chlorellasorokiniana withnitrate asnitrogen sourceis approx- imately 1.57gmol_ph⁻¹ (Kliphuis et al.,2010).Comparedto this value, the simulated yields for wild type cultivation in the Netherlands (0.85gmol_ph⁻¹) and Tunisia (0.68gmol_ph⁻¹)show roomforimprovement.However,inlargescaleproduction,thethe- oreticalmaximumcannotbereachedundersaturatinglight.Using theoptimal80%antennasizereductioninTunisia,thebiomassyield onlightenergywassimulatedtoincreaseto0.95gmol_ph⁻¹,which ishighforlargescalecultivationinanenvironmentofhighirra- diance.Theestimatedproductivitiesandbiomassyieldsonlight areintheexpectedrangesbasedonempiricaldataofC.sorokiniana (Zijffersetal.,2010),whichsupportsthereliabilityofthepresented results.

Smallerantennasizesincreasetheproductivityinenvironments ofhighirradiance.However,thereisanupperlimitbecausethe highertheantennasizereductionis,thehighertheoptimalbiomass concentrationthatisrequiredtoabsorbtheincidentlightintensity.

Athigherantennasizereductions,itbecomespracticallyimpossi- bletoharvestallofthelightthatisavailablearoundsolarnoon.

Consequently,especiallygreenlightisleavingthephotobioreactor unusedafterbeingreflectedatthebottom.Inaddition,20%ofthe lightthatreachesthepondfloorisabsorbedbythepondlinerwhich meansthatamore‘transparent’culturewillalsoresultinmoreloss oflightatthebottom.Theoretically,theproblemcouldbeallevi- atedbyadjustingthebiomassconcentrationoverthecourseofthe entireday,however,inpractice,itisimpossibletomaintainanopti- malbiomassconcentrationthroughouttheentiredayasbiomass growthistooslowtorespondtosunrise,sunsetandthefluctuation lightconditionsduringtheday(Pruvostetal.,2015).

Asthemaintenancerequirementpercellisassumedtobecon- stant,thetotalenergyspentonmaintenanceincreaseslinearlywith thebiomassconcentration.Intherangeof10–80%antennasize reduction,theincreaseinmaintenancecostsisnotabigissuesince theconcomitantincreaseoftheproductivityishigher,andthisout- weighsthemaintenancelosses.However,asdepictedinFig.3A, thefractionofsugarsutilizedformaintenancecanbeashighas 24%fora90%antennasizereductionintheNetherlands.There- fore,anoptimalantennasizereductionwasidentifiedbasedon themodel.Inadditiontothisenergeticallyoptimalantennareduc- tion,inpractice,antennasizereductionmaypossiblybelimitedby structuralconstraintsasthereappearstobeaminimumamount ofchlorophyllmoleculesthatisrequiredfortheassemblyofthe photosystemcorecomplexes(GlickandMelis,1988).

Areflectivegroundcover(i.e.,liner)wassimulatedtobesitu- atedatthebottomofthephotobioreactorpondtoallowafairer comparisonofmutantandwildtypeperformance.Withoutlight reflectionatthebottom,evenahigherfractionoftheincidentlight intensitywouldbelost(absorbedatthepondfloor)inthemutant cultureincomparisontothewildtypeculture.Athighantennasize reductions,thereflectivelinercouldnotpreventconsiderablelight lossesinmutantmonoculturesasunabsorbedlightwasreflected onthepondfloorbutsubsequentlycouldnotbefullyabsorbedin thesuspensionafterwhichitlefttheracewaypondreactoratthe liquidsurface.

Thechoiceforinfinitewidthandlengthofthetheoreticalpho- tobioreactorhastheconsequencethatshadowformationbywalls andreactorequipmentcanbeneglected.Themodelthereforeover- predicts theproductivity compared toreal systems. Thiseffect willdecreasewiththeincreasingreactorsize, asthewalls and equipmentarerelativelysmallinlargereactors.Theassumption

ofconstantdepthmeansthatprecipitationandevaporationare neglected,orsupposedtobalanceeachother.Theeffectofachang- ingdepth,andthereforeachangingbiomassconcentration,could beeasilyimplementedbutsimilartousingrealweatherdata,it wouldblurthefocusontheeffectofantennasizereduction.

Cellsinamixedcultureofwildtypeandantennasizemutants arecompetingforlightenergy.Cellswithahigherpigmentation haveacompetitiveadvantageinthissituation,ashasrecentlybeen verifiedincompetitionexperimentswithphycobilisome-deficient cyanobacteriaandthecorrespondingwildtype (Agostoni etal., 2016).However,atthehighlightexposedvolumefractionofthe reactor,themostcompetitivecells,withthehighestabsorption crosssection,aremoreoversaturatedwithlightenergy,resulting inheatdissipation.Stateddifferently,competitivenesscomesata costoflightuseefficiencyandproductivity.Antennasizemutants growslowerthanthewildtypeinthelightlimitingpartofthereac- torwhichmakesthemlesscompetitive.Thelowercompetiveness aswellasthehigherlightuseefficiencyofthemutantswerecon- firmedinoursimulations.Asthephotobioreactorproductivityofa mutantcultureeventuallyreturnstothelevelofthewildtypepro- ductivityafteracontamination,itcanbeconcludedthatthebiggest increaseinproductivityobtainedwithantennasizereductionalso resultsinthemostsignificantlossesuponcontamination.

Thelowertheantennasizereduction,themorecompetitivethe organismbecomesandthelongerittakesbeforeitisoutcompeted bythewildtype.Contaminationcanbecausedbywildtypecells physicallyenteringthephotobioreactororbymutantcellslosing theirphenotypeafterareversemutation,afterwhichthenatural pigmentcontentisrestored.Inregardtothecontaminationlevel, itbecameevidentthat,eveninthemostoptimisticscenariowith aminimalcontaminationofonecellpercubicmeter,theeffects ofcontaminationareconsiderable.Moreover,thecontamination levelisunpredictableandcouldbehigherthantheassumedone cellperm³.Thereforeitcanbestatedthat,unlessnovelmethods arediscoveredtoincreasethecompetitivepowerofantennasize mutants,theconsequences ofwildtype contaminationseverely threatenthepotentialapplicationofantennasizemutantsinlarge- scalelong-termproductionprocesses.

Wehavedemonstratedthatevenacontaminationlevelaslow asone cellper cubic meter atthe beginningof cultivationcan substantiallyreducethepotentialproductivityincreasethatwas aimedforbyusingantennasizemutants.Onceacontamination hasbeendetected,thoroughcleaninganddisinfectionofthepho- tobioreactorpondisrequiredwithnotoleranceforremainingwild typecellsorotherphotosyntheticorganisms.Thisistimeconsum- ingandexpensiveandwillprobablyoutbalancethecostreduction thatcouldhavebeenobtainedbytheapplicationofantennasize reduction.

Would it be possible to increase the competitive power of antennasizemutants?InthestudyofFlynnetal.,themutantswere assumedtohaveadditionalpropertiesthatmadethemmorecom- petitive.Theysimulatedmutantswithanincreasedgrowthrate andnutrient useefficiency,a decreasedminimumphosphorous andnitrogenquota,alowermaintenancerequirementand,under theseconditions,themutantwasexpectedtooutcompetethewild type(Flynnetal.,2013).Itremainsdoubtful,however,whethera mutantwithalloftheaforementionedpropertiescanbedesigned inpracticeandremainstableregardingallmutations.Forexam- ple,inordertoobtainahigherbiomassspecificgrowthrate,many enzymaticstepsmustbeperformedatahigherratewhichdoesnot appeartobefeasible.Anothermethodtoimprovethecompetitive- nessofthemutantratherthanchangingitsgrowthcharacteristics istheapplicationofextremeconditions.Thisconditionshouldide- allyaffecttheviabilityofthewildtypestrainbutnotthatofthe mutant.One couldthinkof a built-inresistanceof themutant, forexample,tolerancetolow/hightemperaturesoratoleranceto

tiveenvironmentthatrewardsinvasivespeciesthatactuallyhave suchacapability(Mooijetal.,2015).Smarttechniquesarerequired toenforcetheeliminationofthewildtypewhilemaintainingthe mutantcells.Perhapsthewildtype’shighersensitivitytolightcan beexploitedasthismakesthemmorepronetophotoinhibition whileantennasizemutantswouldonlyexperiencephotoinhibi- tionatmuchhigherlightintensities.Wildtypecellspossiblyhave tospend more energyonphotosystem IIrepair processes than antennasizemutantsbecausetheirhigherlightabsorbancerate willalsoincreasetheirreversibledamagetothephotosystems.To winthecompetition,thespecificgrowthrateofthemutantshould behigherthanthatofthewildtype.AtsolarnooninTunisia,the biomassspecificgrowthrateofan80%reducedmutantis1.4d⁻¹ versus2.2d⁻¹ forthewildtypeaccordingtoourgrowthmodel.

Consequently,severechronicphotoinhibitionwouldberequired for thewild type toshiftthe equilibrium towards themutant.

ForChlorellasorokinianasuchseverephotoinhibitionhasnotbeen observeduptolightlevelsof2000␮mol_phm⁻²s⁻¹(Cuaresmaetal., 2011;Francoetal.,2012)andforthisreasonphotoinhibitionwas notincludedinthismodel.

AmorecomplexdynamicmodelwaspresentedbyFlynnetal.

(Flynnetal.,2013,2010;Flynn,2001).Inaccordancewithourfind- ings,Flynnandcoworkersestimatedthatundercontinuouslight (1000␮mol_phm⁻²s⁻¹),theuseofantennasizemutantswilllead toanincreasedbiomassproductivity,andthemutantswillbeout- competed bythewildtype after a contamination(Flynnet al., 2010).Thestrengthofourmodelisitssimplicityandthefactthat weonlyconsideredmutantswithareduction oftheabsorption crosssectionwithoutadditionaltraits.Therepetitivelightpattern andthelackofseasonallightandtemperaturevariabilityhasthe advantagethateffectscanbeunequivocallyassignedtotheantenna sizereductionorthecontaminationlevelwhichwasthepurpose ofthisstudy.Theestimationsofourmodelprovidearealisticview ofthepotentialof antennasizemutantsunder largescale out- doorconditions.Theproductivityofourmutantswaslimitedby theinevitablesteeplightgradientinmasscultures,thelowlight absorptioncapacityofmutants,andthefactthatthetotalmain- tenancerequirement canbecomea criticalfactor atsubstantial antennasizereductions.Wealsoincludedtheimpactofday/night cyclesonmicroalgalgrowth.Eventhoughthemodelincludessev- eralsimplificationssuchasthatphotoinhibitionwasnotincluded, itiscapableofpredictingimportanttrendswhichcanbeusedas inputforfutureresearch.

5. Conclusions

Atheoreticalmodelwaspresentedtosimulatecultivationsof antennasizemutantsandthecompetitionwiththeirwildtype undermasscultureconditions.Aswasexpected,thecomparison ofTunisiawiththeNetherlandsdemonstratedthatasubstantial increaseofproductivityisonlypossibleinalocationofhighirra- diance.Inaddition,aconsiderableantennasizereduction(80%)is requiredtoachieve maximalcultureproductivity.Mutantswith suchanantennasizereductionhavenotbeenobtainedyetinprac- tice.Atveryhighantennasizereduction,itbecomesdifficultto efficientlyabsorballincidentlightbecauseofthelowabsorption capacity.Inaddition,highbiomassconcentrationsarerequiredto absorballlight,whichincreasescellularmaintenancescosts.The highertheantennareduction is,themoresensitivethecultiva- tionprocessbecomesforcompetitionwithafullantennastrain.

Accordingtothemodel,antennasizemutantswillalwayslosethe competitionforlightwiththeirwildtypeandtherateofoutcom- petitionwasascertainedtoincreasewithdecreasingantennasize andwithincreasingcontaminationlevels.Basedonthesefindingsit

isanimportantfactorthatdetermineswhetherlong-termstable cultivationcanbeachievedinmasscultures.

Acknowledgements

Thisworkis partoftheresearchprogrammeoftheFounda- tion for Fundamental Research onMatter (FOM) which is part of theNetherlands Organization for Scientific Research (NWO).

Thisproject(10TBSC12-3)wasconductedwithintheresearchpro- grammeof BioSolarCells,co-financedby theDutchMinistryof EconomicAffairs.

AppendixA. :Microalgaegrowthmodel

(A1)Module1:Lightdistributioninaphotobioreactor

Inthisalgaeproductionmodel,ahypotheticalphotobioreactor isstudied(Fig.A1)thatrepresentsapondwithaconstantdepth(dR, 0.20m)andwithinfinitewidthandlength.Theonlyinterfacethat isconsideredforreflectionandrefractionistheair-waterinterface sincethecultureisdirectlyincontactwiththeairattheculturesur- face.Thelightintensityontheculturesurfacemustbedetermined tolaterpredictthelightdistributionwithintheculture.

Thelight intensitygradient inthe microalgaeculture iscal- culated in three consecutive steps. First, the light intensity on a horizontalsurface onearthis calculatedneglectingtheeffect ofatmospheric lightabsorption(Velds etal.,1992).Second,the absorptionoftheatmosphereduetoitsturbidityisincorporated (Veldsetal.,1992).Inthethirdstep,therefractionandreflection oflightpassingtheairwaterinterphase(Cooper,1969;Kastenand Czeplak,1980;Goldstein,2010)isincludedtoobtaintheintensity anddirectionalityofthislightthatentersthemicroalgaeculture (I_ph,0).Foranextensivedescriptionoftheequationsusedtocalcu- latetheincidentlightintensity,refertoAppendixC.

Theincidentlightintensityonahorizontalsurface(I_ph,0)isused asaninputinEq.(A1),whichisbasedonLambert-Beer’slaw.

I_ph,,down(z)=I_ph,0·E_n,·e⁻

a_X

,WT·XWT+a_X,MU·XMU

·z·_cos¹ z (A1) E_n,(nm⁻¹)representstherelativesunlightdistributionforthe rangeofphotosyntheticactiveradiation(seeAppendixEforval- ues).Theabsorptioncrosssectionsofthewildtypestrainandthe mutantaredenotedbya_X,_WTanda_X,_MU,respectively.InEq.(A1), zisthepositioninthepondalongtheverticalpathequalingzeroat thereactorsurfaceand‘dR’atthebottomofthereactor.Thelength ofthelightpathinthecultureisinfluencedbytheanglebetween therefractedsunraysandtheperpendiculartotheculturesurface (anglez,Fig.A1).Inthemodel,thepositionzismultipliedwith theenhancingfactor,theinverseofthecosineof_z,tocorrectfor thelengtheningoftheopticalpathatincreasingz.Anincreasing opticalpathincreasesthechanceoflightabsorptionandresultsin asteeperlightgradientinthez-direction.

To minimize light losses at the bottom of the pond and to obtainafairercomparisonbetweenwildtypeandmutantculture productivity,thepondfloorwassimulatedtobecoveredwitha whitereflectivegroundcover.Thiscoverdiffusivelyreflects80%

(Meinholdetal.,2010)ofthelightatthebottombackintothe culture.Moreover,theapplicationofwhitelinersisalsocommon practiceintheracewaypondconstruction.Theadditionofareflec- tivelinerresultsinasecondlightfluxI_ph,,up(z)fromthepondfloor backtotheculturesurface.Thelightintensityinthecultureonly resultingfromthisfluxisdescribedby:

Iph,,up(z)=Iph,,down(dR)·fR·e

−

aX

,WT·XWT+a_X ,MU·XMU

·(dR−z)·_cos¹

z,dif (A2)

Fig.A1.Schematicoverviewoftheracewaypondphotobioreactor.Thesunlight hitstheculturesurfacewiththelightintensityIph,0,iatthezenithanglez.The lightispartlyreflected

Iph,0,r

andpartlytransmittedintotheculture

Iph,0

.The refractionattheculturesurfaceleadstotherefractedzenithanglez’.Thelight reachingthebottomofthepondis,inpart(80%),diffusivelyreflectedbackintothe culturebyawhitegroundcover.

withd_R beingthereactordepthand f_R beingthefractionof reflectedlight.Theinverseofthecosineof_z,difisthefactorwith whichthereflectedopticallightpathisextended.Thediffusereflec- tioncorrespondstoanaverageangle_z,difof60^◦.

(A3)Module2:Photosyntheticsugarproduction

Tomodelthecompetitionforlightinacultureofanantennasize mutantcontaminatedwithitswildtype,thespecificlightabsorp- tionratesofbothstrainsmustbedistinguished.Thespecificlight absorptionratesthenallowthecalculationofspecificsugarpro- ductionratesforeach strain.Thesugarproduction rate

q_Si

of oneorganism(indicatedbyindexi)inaculturecontainingwild typeandmutantcellscanbedescribedaccordingtothehyperbolic tangentmodelofJassbyandPlatt(JassbyandPlatt,1976):

q_Si=q^max_S ·tanh

q_ph,i·Y_S/ph,m q^max_S

(A3) Thecalculationofthesugar productionrateis basedonthe photonabsorptionrate

q_ph,i

,themaximumyieldofsugaronpho- tons

Y_S/ph,m

,andthemaximumsugarproductionrate

q^max_S

, (seeTableA3ofAppendixEforvalues).Thebiomassspecificlight absorptionrate

q_ph,,i

canbedescribedforwildtype (i=WT) andmutant (i=MU) inone photobioreactorsimultaneouslyby utilizingLambert-Beer’slaw:

dIph,,down

dz =Iph,,down(z)·

a_X

WT,·XWT+a_X MU,·XMU

· 1

cos_z (A4)

dIph,,up

dz =Iph,,up(z)·

a_X

WT,·XWT+a_X MU,·XMU

· 1

cos_z,diff (A5)

qph,,i=

−dIph,,down

dz +dIph,,up

dz

· 1

Xi· aX_i·Xi

aXWT,·XWT+aXMU,·XMU

(A6) withthelightgradients^dIph,,down_dz and^dIph,,up_dz ,theconcentration offunctionalbiomass (X_i),theabsorptioncrosssection

a_Xi,

,the

locallightintensity

I_ph,(z)

,andthefactor

1 cos_z

thatcorrects thelightpathforitsdeviationfromthezdirection.Apparently,the lightregimeinthereactor(Eqs.(A4)and(A5))isdictatedbythe totallightabsorptioncapacityofboththewildtypeandmutant strain.Thebiomassspecificlightabsorptionrates(q_ph,,i)(Eq.(A6)) dependontheabsorbedfractionofthistotallightenergywhichis basedonthelightabsorptioncapacityandbiomassconcentration ofeachstrain.Eqs.(A4)–(A6)arecombinedtogive:

qph,i,(z)=a_X,_i·

Iph,,down(z)· 1

cos_z+Iph,,up(z)· 1 cosz,diff

(A7) BycombiningEqs.(A3)and(A7)andaddingthewavelength dependencyofY_S/ph,m,thespecificsugarproductionratesofthe mutantandwildtypewereobtained:

q_Si(z)=q^max_S ·tanh

=700

=400(q_ph,i,(z)·Y_S/ph,m,)· q^max_S

(A8)

Thespecificsugarproductionrates(Eq.(A8))wereconcurrently simulatedin onephotobioreactorforboth strainstomodelthe competitionforlight.Theproducedsugarispartlyusedformain- tenancerelatedprocesses,partlystoredinthesugarreservepool, andpartlyusedforproductionofnewfunctionalbiomass.

(A9)Module3:Partitioningofproducedsugarduringthediurnal cycle

Thecarbohydratestarchisanimportantenergyreserveforthe growthofmicroalgaeinday/nightcycles(Sharkey,2015;Ogbonna andTanaka,1996).Synthetizedstarchisstoredassemi-crystalline granules(Sonnewald andKossmann,2013)and canbeoxidized bythecelltogainenergyandreducecarbonupondemand(Lacour etal.,2012).Theaccumulationofstarchoccursduringthedaywhen itservesasanenergysinkwhilethedegradationprimarilyoccurs duringthenighttoprovideenergyandcarbon(Lacouretal.,2012;

SukenikandCarmeli,1990;Postetal.,1985;Fábregasetal.,2002).

Amechanismofcarbonpartitioningduringthediurnalcycle wasdeveloped.Thismechanismincludespartitioningofthepho- tosyntheticallyproducedsugartothefunctionalbiomassandthe sugarreservepool.Thelongerthenightperiodandthelowerthe currentsugarreserves,themoresugarisstoredinthesugarpool duringthedaytoaccumulatesufficientreservesfortheentirenight period.Additionally,sugarfromthesugarpoolisconvertedinto functionalbiomassataratethatdependsonthesugaravailabil- ity.Theconversionratewillautomaticallybere-adjustedinsucha waythatitwouldbestableuntiltheendofthenightifnoadditional sugarisgenerated.Thisleadstoaminimumsugarfractioninthe totalbiomassattheendofthenight.

The production rates of functional biomass and sugar are describedintwodifferentialequations(Eqs.(A9)and(A10))which areappliedonbothstrainssimultaneously:

(A9)

(A10)

mX=0forx_S,i>x_S,min,i m_S=0forx_S,i=x_S,min,i

The biomass accumulation rate (Eq. (A9)) and the sugar accumulation rate (Eq. (A10)) depend, among others, on the totalbiomassconcentration (Cx_i) andtheconcentrationoffunc- tional biomass (X_i) and sugar (S_i). m_X is the maintenance requirement

molX·molX−1

·s⁻¹

coveredbydegradationoffunc- tionalbiomass.Themolarfractionofsugarinbiomassisgivenas x_S,i=S_i/(X_i+S_i).Theindexiindicatesthattheequationsneedto beseparatelyappliedonthetwostrains,wildtype (i=WT) and mutant (i=MU).Thecultivationtime,t(0–24h),isthelocalsolar time.

Thedifferentialequationsdescribingtheaccumulationoffunc- tionalbiomassandsugarsinthephotobioreactor(Eqs.(A9)and (A10))both include fourterms. The first term depends onthe sugar productionrate(Eqs. (A8))and,therefore, theamountof absorbedlight.Carbonfixatedandreducedbyphotosynthesispar- titionsbetweenthesynthesisoffunctionalbiomassandthesugar pool.Thepartitioningdependsonthesugar fractionofbiomass

x_S,i

attheinvestigatedtimepointandtheduration(hours)of thelightperiod

P_light

inoneday/nightcycleof24h.Theshorter thelightperiod,themoresugarreservesareneededduringthe nighttocoverthemaintenancerequirementandsupportthegen- erationoffunctionalbiomassinthedark(Lacouretal.,2012).To restorethesugarreservesfortheconsumptionduringthenight, lowsugarfractionsinthebiomassleadtoahighallocationrateof photosyntheticallyproducedsugartothesugarpool.Thisbehavior issimulatedbyaDroopbasedequation(Gibsonetal.,2008).

ThesecondtermoftheequationsEqs.(A9)and(A10)describes thespecificmaintenancerequirementofthefunctionalbiomass.

Themaintenancerequirement (m_S) isprimarilycoveredbytheres- pirationofsugar.Sufficientsugarreservestofulfillmaintenance requirementsareensuredbythesugaraccumulationmechanism.

However,intheexceptionalcasethatthesugarreservesaretoolow (x_S,i≤x_S,min,i),theonlywaytofulfillmaintenancerequirements (mX) isbythedegradationoffunctionalbiomass,asshownbythe secondtermofEq.(A9).

Independentfromlightconditions,thethirdtermensuresthe conversionofsugartofunctionalbiomass.Thisrateislinearduring thenightandresultsintheminimumsugarfractionx_S,min,iatthe endofthenight.Basedonstarchturnover(Klein,1987),aminimum productionrateoffunctionalbiomassisensuredovertheentire courseofthedayassoonassugarhasbeenaccumulated.First,the releasedsugarisusedformaintenancerelatedprocesses,andthe remainingsugarsubsequentlyentersthefunctionalbiomasspro- duction.Thisway,functionalbiomassisproducedduringthenight attheexpenseofthesugarpool.Sugarisemployedforthepro- ductionoffunctionalbiomassaccordingtothefunctionalbiomass yieldonsugarY_X/S.Thisyieldhasavaluelessthan1,reflecting thefactthatasignificantportionofthesugarneedstoberespired toretrievesufficientenergyintheformofATPtoincorporatethe remainingsugarintofunctionalbiomass.

Thelasttermofthedifferentialequationsdescribestheremoval offunctionalbiomassandthesugarreservesbytheappliedsystem dilution,astheracewaypondreactorisoperatedasachemostat.

Dilutionisonlyappliedduringdaylighthours.

AppendixB. :Equationstocalculatelocationand wavelength-specificlightdistribution

(A11)Solarpowerandsunlightangleonahorizontalsurface Inthiscalculation,theeffectoftheturbidityoftheatmosphere isfirstneglected,however,thepredictedsolarpowerislatercor-

poweronahorizontalsurface (Ee) dependsontheintensityofsun- light reachingtheearth andthezenith angle

z,Eq.A12

.The latteristheanglebetweenthesunraysandtheperpendicularto theearth’ssurface(Fig.3).

Ee=S0·R¯²

R²·cosz≈S0·

1+0.033·cos

360 365·(d−1)

·cosz (A11) InEq.(A11),alllightisassumedtopassfromthecenterofthe suntotheearthneglectingeffectsoftheatmosphere.Theyearly averagedsolarpoweronearthisdescribedbythesolarconstant(S0, 1367W·m⁻²(FröhlichandBrusa,2016)).Thesolarpowervaries withthefactor ^R_R^¯2₂ overtheyearduetotheellipsoidalshapeof theearth’sorbit(DuffieandBeckman,2016).Thedaytimeandthe locationdependencyoftheinsolationarebothdescribedbythe zenithangle:

z=cos⁻¹

sin·sinı+cos·cosı·cosω

(A12) The latitude () is directly named in Eq. (A12) while the longitude is indirectly included through the hour angle (ω=15·(t_solar−12)[^◦]). The position of the sun is highest at 0^◦ or t_solar=12h. The tilt of the earth relative to the sun throughout the year is described by the solar declination

ı=23.45·sin

360·(284+d) 365

[^◦]

.

Thesolarpowerneglectingtheatmosphere (Ee) cannowbecor- rectedfor atmospheric absorption.Asa simplification,thetotal global irradiation is considered as direct light even though it includesadiffusepart.Thus,thesolarpowerreachingtheearth ataspecificlocation (G_clear) andwithaclearskyisdescribedas:

G_clear=0.84·Ee·e

−^0.027_cosz^TL

(A13) TheturbidityfactoroftheatmospherebyLinke (TL) hasbeen determined experimentally. Under a clear sky, the factor only depends onthetime duringtheyearandthelocationonearth (Veldsetal.,1992;Chaâbaneetal.,2004).Thecalculatedsurface- specificsolarpowerusingtheturbidityfactorisconvertedintothe lightintensity.Thelightintensityintherangeofthephotosynthetic activeradiation(PAR,400to700nm)iscalculatedusingaconver- sionfactoraccordingtoASTMG173-03ReferenceSpectraderived fromSMARTSv.2.9.2:

I_ph,0,i=G_clear·1.982·10⁻⁶mol_ph,PAR

J_solar (A14)

(A15)Lightgradientresultingfromrefractionandreflectionon theculturesurface

ThesunlightwiththeintensityI_ph,0,i hitstheculturesurface which is assumed tohave thesameproperties asa water sur- face.Twoeffectsoccurtheresimultaneously;lightisrefractedand reflected.Duetorefraction,thezenithangle

z

changesaccord- ingtoSnell’slawtoz’.Thus,thefactor

1 cos(z’)

describingthe lightpathdependentontheculturedepthreadsas:

1 cos

z’

= 1

cos

sin⁻¹

_nair

nwater·sinz

^(A15)

The enhancing factor (Eq. (A15)) is based onthe refractive indexes ofair (n_air)and water(nwater)and trigonometric equa- tions. Thisexpressionis usedtorelatetheculturedepthtothe lightpath.ByapplyingLambert-Beer’s,thisaffordscalculationof thelightdistributioninsidetheculture.Theincidentlightinten- sityisreducedcomparedtothedescriptioninEq.(A14)sincelight ispartly reflectedbytheculturesurfaceandpartly transmitted intotheculture.Thereflectedlight intensityis subtractedfrom

Fig.A2. GlobalincidentlightintensityinthePARrangeonahorizontalsurfacein TunisiaandtheNetherlandsinthecourseofoneday/nightcycle.Thelightintensityis derivedfromthelightmodelasdescribedinAppendixB.Nocloudcoverisassumed inTunisiawhilethelightintensityisevenlyreducedby40%intheNetherlandsto simulatethecloudcover.

thelightintensityhittingtheculturesurfaceaccordingtoFresnel’s equations:

I_ph,0=I_ph,0,i−1 2·

Rs+Rp

·I_ph,0,i (A16)

withthereflectivityoflightpolarizedintheplaneofincidence Rs=

n_air·cosz’−nwater·cosz n_air·cosz’+nwater·cosz

2

and perpendicular totheplaneof incidenceRp=

nwater·cosz’−nair·cosz nwater·cosz’+nair·cosz

2

.

AppendixC. :Lightpatterns

Theirradianceandthelightangleweresimulatedforasunny location (Sidi Bou Said, Tunisia) and a location with a higher cloudage(DeBilt,theNetherlands).Measurementsshowedaglobal insolation of 16.67MJm⁻²d⁻¹ in mid-July (1971–1986) in the Netherlands(Veldsetal.,1992).Thisinsolationcorrespondsto62%

ofthepredictedinsolationunderaclearsky.Comparedtothat, inTunisia,theaverageinsolationinJuly(>10years)issignificantly higher(26.64MJm⁻²d⁻¹over>10years)(Alnaseretal.,2004).This valueis5%lowerthanthepredictedinsolationinTunisia.Whilethe lowcloudageinTunisiawasneglectedinthesimulations,aconstant cloudageof40%wasassumedintheNetherlands.Alllightincluding thediffusepartwasassumedtobedirecttosimplifythesimula- tions.Theresultinglightpatternsforthechosensummerdayin JulythatwasusedinallsimulationsarepresentedinFig.A2.

AppendixD. :Dilutionoptimizationprocedure

Thedilutionratewasseparatelyoptimizedforthearealbiomass productivityofeachstrain.Theoptimizationoftheconstantdilu- tionrateduringthedaywasperformedemployingacontrolled randomsearchalgorithm.Theboundariesforthedilutionratewere settozeroandthemaximumgrowthrateto(0.27h⁻¹).Within

Fig.A3.Arealproductivityversusdilutionrateofamutantthatis80%reducedin aXsimulatedforcultivationinTunisia.Dilutiononlyoccurredduringlighthoursat aconstantrate.Duringthenight,therewasnodilution.Thedailylightintensitywas 55.8molphm⁻²d⁻¹.

theseboundaries, 50 random values for the dilution ratewere drawn. A cultivation period of 15days wassimulated for each dilutionrate.Theaverageproductivitywascalculatedforthelast 24h.Alldilutionratesandthecorrespondingproductivitieswere recordedonalistwith50datapairs.Stepwise,thedilutionrates andproductivitiesinthelistwerereplacedwithdatapairscon- taininghigherproductivities.First,fourdilutionrates(D_r,1toD_r,4) wererandomlydrawnandcombinedwiththelastdilutionratein thelist (D_end) toreturnanewvalue(D_new,Eq.(A17)).

Dnew=2·

i=4 i=1D_r,i

4

−D_end (A17)

Second,thesamesimulation asdescribedabovefollowedfor thenewdilutionrateiftheboundaryconditionswerestill met.

Otherwise,anewvaluewasgeneratedandthesimulationwasper- formedwiththefirstvaluewithintheboundaryconditions.Third, theproductivityresultingfromthissimulationwascomparedto thelowestproductivityinthelist.Thedatapairwiththelowest productivitywasreplacedifitthenewproductivitywashigher.The newdatapairwasdiscardedifthenewproductivitywaslower.By repeatingthispattern,adensedatasetaroundtheoptimaldilution ratewasgenerated(SeeFig.A3foranexample).Thedilutionrate correspondingtothemaximumarealbiomass productivitywas usedforallsimulationswiththerespectivestrain.

AppendixE. :Modelvariablesandparameters

SeeTableA1andTableA2. AppendixF. Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound,in theonlineversion,athttp://dx.doi.org/10.1016/j.jbiotec.2016.10.

009.