Model uncertainty-based evaluation of process strategies during scale-up of biopharmaceutical processes

Computers and Chemical Engineering 134 (2020) 106693

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Computers and Chemical Engineering

journalhomepage:www.elsevier.com/locate/compchemeng

Model uncertainty-based evaluation of process strategies during scale-up of biopharmaceutical processes

Johannes Möller

^a,∗

, Tanja Hernández Rodríguez

^c

, Jan Müller

^b

, Lukas Arndt

^a

, Kim B. Kuchemüller

^a

, Björn Frahm

^c

, Regine Eibl

^b

, Dieter Eibl

^b

, Ralf Pörtner

^a

aHamburg University of Technology, Bioprocess and Biosystems Engineering, Hamburg, Germany

bZurich University of Applied Sciences, School of Life Sciences and Facility Management, Chemistry and Biotechnology, Wädenswil, Switzerland

cOstwestfalen-Lippe University of Applied Sciences and Arts, Biotechnology and Bioprocess Engineering, Lemgo, Germany

a rt i c l e i n f o

Article history:

Received 3 August 2019 Revised 29 November 2019 Accepted 21 December 2019 Available online 23 December 2019 Keywords:

Monte Carlo methods Process modeling Parameter distributions Process validation

Model-assisted design of experiments Quality by design

a b s t r a c t

Reliablescale-upofbiopharmaceuticalproductionprocessesiskeyinQualityby Design.Inthisstudy, amodel-basedworkflowisdescribedtoevaluatethebioprocessdynamicsduringprocess transferand scale-upcomputationally. First, a mathematical model describes the bioprocessdynamicsof different statevariables (e.g., cell density, titer).Second, the modelparameter probability distributions arede- terminedatdifferentscalesduetomeasurementuncertainty. Third,thequantifiedparameterdistribu- tionsarestatisticallycomparedtoevaluateiftheprocessdynamicshavebeenchanged.Thisworkflow wastestedforthescale-upofanantibody-producingCHOfed-batchprocess.Significantdifferenceswere identifiedbetweentheprocessdevelopment(30ml)andimplementation(250ml)scale,andthefeeding strategywasvalidatedusingmodel-assistedDesignofExperiments.Then,thevalidatedprocessstrategy wassuccessfully scaledupto2 llaboratory and50 lpilotscale. Insummary,theproposed workflow enablesaknowledge-drivenevaluationtoolforbioprocessdevelopment.

© 2020ElsevierLtd.Allrightsreserved.

1. Introduction

Reliable design and scale-up of biopharmaceutical production processeswithmammaliancellcultureareessentialinQualityby Design (QbD).First, a stableand productive process needs to be identified duringprocess developmentafter clone selection. This includes screening studies of medium components (Torkashvand et al., 2015; Rouiller et al., 2014) and the definition of a sta- ble and effective process strategy (e.g. fed-batch) (Wurm, 2004;

Gmeiner et al., 2015). Mathematical process modeling is an effi- cient tool during this step because it includes the most impor- tant mechanisticsof thebiological system. Moreover, mathemati- cal process modelsdescribe theinteractions betweenprocess pa- rameters andkey performance indicators, which is a substantial partofQbD(Guideline,2009;Herwigetal.,2015;Carrondoetal.,

Abbreviations: Ab, antibody; Amm, ammonium; BR, bioreactor; CI, confidence interval; CFD, computational fluid dynamics; CHO, Chinese hamster ovary; DAPI, 4 ,6-diamidino-2-phenylindole; Glc, glucose; Gln, glutamine; Lac, lactate; MC, Monte Carlo; mDoE, model-assisted Design of Experiments; NRMSD, normalized root mean square deviation; QbD, Quality by Design; RAD, relative average devi- ation; RSM, response surface model; SF, shake flask.

∗ Corresponding author.

E-mail address: johannes.moeller@tuhh.de (J. Möller).

2012). More process knowledge is incorporated duringmodeling ifuncertainty quantificationisperformed,i.e.determiningtheef- fectofinputuncertainties(e.g.experimental variations)onmodel outcomes(Anane etal., 2019;Liu andGunawan,2017; Sin etal., 2009). Uncertainty-based modeling techniques have been widely usedin chemicalsystems orsystemsbiology(Möller etal., 2018, 2019), butnot often inbioprocesssimulation studies (Hernández Rodríguezetal.,2019).

Second, thebioprocess includingits process strategy needs to be scaled up, forwhich mostlydata-driven approaches are used.

Thisisconventionallydonebykeepingahydrodynamicstatecon- stant,e.g.volumetricpowerinput(P/V_L)(Klöckneretal.,2012;Cat- apanoet al., 2009), mixingtime (Varley and Birch, 1999; Rosse- burgetal.,2018),impellertipspeed(JuandChase,1992;Alsayyari etal., 2018) orthe volumetricmass transfercoefficient k_La (Xing etal.,2009;Nienowetal.,1996).Therefore,itisrecommendedto hydrodynamically characterize the bioreactorsat each scale (rec- ommendationseeMeuseletal.,2016).Additionally,computational fluiddynamics(CFD)hasgainedrisingimportancetoobtainanim- provedunderstandingofthebioreactorhydrodynamicsfromsmall tolargescale(Sharmaetal.,2011;Werneretal.,2014;Kaiseretal., 2011;Nienowetal.,2013).However, thecellularbehaviorinclud- ing metabolism and productivity could vary at differentbioreac- torscalesduetoe.g.differencesinthehydrodynamicstress(Sieck https://doi.org/10.1016/j.compchemeng.2019.106693

0098-1354/© 2020 Elsevier Ltd. All rights reserved.

Nomenclature

Variable ExplanationUnit

c_i Concentrationofcomponenti[mmoll⁻¹]

d_j,max Maximumvalueofadataset[-]

d Differenceinmeans[-]

F Volumefactorforfeedingrate[-]

F_Gln,feed Glutamineconcentrationinfeed[mmoll⁻¹] F_Rate Feedrate[mld⁻¹]

FRate,experimental Implementedfeedrate[mld⁻¹] k_i Growthconstant[-]

K_i Kineticconstant[mmoll⁻¹]

k_La Volumetricmasstransfercoefficient[s⁻¹] P/VL Volumetricpowerinput[Wm⁻³]

q_i Production/consumption rate [mmolcell⁻¹ h⁻¹]

R² Coefficientofdetermination[-]

S Sensitivitycoefficient[-]

t Time[h]

V Reactorworkingvolume[l]

X_d Deadcelldensity[cellsml⁻¹] Xt Totalcelldensity[cellsml⁻¹] Xv Viablecelldensity[cellsml⁻¹] y_j Statevariables[-]

Y_i Yieldcoefficients[-]

y_sim,j Simulationofstatevariables[-]

μ

^{max Maximumspecificgrowthrate[h−1]}

σ

^{2 Variance[-]}

| θ

^(k)

|

^{Meanparameter[-]}

θ

^{(k) Parameter[-]}

etal., 2013;Neunstoecklinetal., 2015) orpH gradients(Ivarsson etal.,2015;Brunneretal.,2017).Sofar,purelydata-basedscale-up proceduresdonotconsiderthedynamicsofthebioprocess.There- fore,itisnotensuredthatthepreviouslydevelopedprocessstrat- egy is scaled up sufficiently and that the process dynamics stay constantduringscale-up.

Inthisstudy,aworkflowisintroducedtocomputationallyeval- uatethe process dynamics,described by a mathematical process model,atdifferentbioreactorscales.Thisconceptisbasedonthe determinationandstatisticalcomparisonoftheprobability distri- butionsofmodelparametersunderconsiderationofexperimental uncertainty.Thus,themodelincorporatesthecurrentprocessun- derstandingandenablesaknowledge-drivendecisionmaking.The workflowistestedforthemodel-basedevaluationofanantibody- producing CHOfed-batch cultivation process during the scale-up fromprocessdevelopmentscale(30mlshakeflask)toprocessim- plementationat250mland2lbioreactorscale.Finally,itisshown howthe mathematicalmodel isused todetermine the operating rangeduringtheprocesstransfertoa50lpilotscalebioreactor.

1.1.Proposedmodeluncertainty-basedworkflow

As can be seen at the beginning of Fig. 1, experimental data sets at two different bioprocess scales are used as input (exem- plary ScaleA andScaleB), e.g. process developmentandprocess implementationscale(typicallyusingdifferentbioreactorsystems).

Pleasenotice that thisstudydoesnotfocus onhow thescale-up needstobeperformedhydrodynamically.Theaimwastodevelop amethodtostatisticallyevaluateiftheprocessdynamicsarecom- parable at both scales and if the targeted process optimum (i.e.

processstrategy)isstillmet.

The basis of the introduced concept is the quantification of model-parametricuncertaintiesunderconsiderationofexperimen-

tal uncertainty due to variability in measurements (box 1). The modelparametersareestimatedmultipletimes(MonteCarlosam- pling) for each investigated scale under the assumption of nor- mally distributedmeasurement errors foreach observable to de- terminetheparameterdistributions.Then,theparameterdistribu- tionsandthepredictionquantilesareusedtovisualizetheprocess variabilitybasedonthemodelparameterdistributions(box 2).In thenextstep(box3),astatisticalcomparisonoftheparameterdis- tributions isperformedto evaluateiftherearestatisticallysignif- icant differences betweenboth scales. The same process dynam- icsand targetedprocess strategy could be ensured ifno changes intheparameterdistributions areidentified.Otherwise,ifthepa- rametersdiffersignificantly,avalidationoftheprocessstrategyis recommended(box4,e.g.adjustingthefeedcomposition).Inthis validation step,a previously introduced model-assisted Designof Experiments(mDoE)conceptisusedtore-adjusttheprocessstrat- egywithareducednumberofexperiments(Mölleretal.,2019b).

Based onthis, it isrecommended to enterfurther process devel- opment/processoptimization studiesor toproceed withscale-up ifthe validation wassuccessful. Thisreflects a knowledge-driven methodologyinQbD andcan berepeatedforeveryscale-up step individually.

2. Materialsandmethods

The process design scaled up in this study was generated at theInstitute of BioprocessandBiosystemsEngineering (Hamburg University of Technology-TUHH) and wasthen transferred to the InstituteofChemistryandBiotechnology(ZurichUniversityofAp- pliedSciences-ZHAW)forscale-up.Therefore,slightlydifferentcul- tivationprotocolsandanalyticalmethodswereappliedduringthis study.

2.1. Mathematicalprocessmodel

Anunstructuredandnon-segregatedmechanisticprocessmodel was used in this studyto compare the dynamics ofthe investi- gated process at different scales. It was previously described in Kern et al. (2016), Möller et al. (2019b) and Kuchemüller et al., 2020.Inbrief,themodeldescribescellgrowth(Xt-totalcellden- sity,X_d -deadcelldensity,Xv-viablecelldensity)andcelldeath basedontheconcentrationsofglucose (c_Glc)andglutamine(c_Gln) andgrowthinhibitionduetoammonium (c_Amm).The progression oftheglucoseandglutamineconcentrationsarecoupledtothefor- mationoflactate(c_Lac)andammonium.Theantibody(c_Ab)ismod- eled tobe expressedconstantly per cell.Themodel alsoincludes the massbalances involvedin the bolusfed-batch processesand themodelequationsaresummarizedinSupplementaryTable1for easierreference.Allcomputationalmethodsinthisstudywereper- formedinMATLAB2018a.

2.2. MonteCarlo-baseduncertaintyquantification

Thecoreoftheproposedmethodisthequantificationofpara- metric model uncertainties and comparison of these probability distributionsatdifferentbioreactorscalesbasedontheexperimen- tal variability. Therefore, a normally distributed observational er- ror of 5% relative standard deviation wasassumed based on the typicalmeasurementstandard deviationsofanalyticalmethodsin bioprocessevaluation(i.e.expertknowledge)(Wechselbergeretal., 2013).Inordertopropagatethisinputuncertaintyontoparametric uncertainty, Monte Carlo samples were generated (observational error)andthe modelparameters were adaptedusing theNelder- Meadoptimizationalgorithm(NelderandMead,1965;Singerand Singer, 2004). The objective/cost function wasthe weightedsum

J. Möller, T. Hernández Rodríguez and J. Müller et al. / Computers and Chemical Engineering 134 (2020) 106693 3

Fig. 1. Proposed uncertainty-based workflow for the evaluation of scale-up.

ofsquaredresidualsbetweenthesimulations(y_sim,j(t_i))incompar- isontotheexperimentaldata(y_j(t_i))overalltimepointst₁,...,t_N and all variables y₁,...,y_M, normalized on the squared assumed measurement variance

σ

_j^{2, which is defined as 5% of the maxi-}

mum valueofa dataset(y_j,max) forthej-thobservable (i.e.

σ

j= 0.05·d_j,max,maximumvalueofdatasetj).Theexperimentaldata wassampled1000timesandthemodelparameterswereadapted foreachsampling. Theinitial valuesareshowninSupplementary Table2andwerethesameinallcomparedscales.Xvandc_Abwere weighted with 100 and c_Amm with 10. 4 out of 29 experiments were randomly sampled and the parameters were estimated for theexperimentsperformedduringtheidentificationofthefeeding strategy (shake flasks). In the other scales, all experimental data wasused.

2.3. Statisticalcomparisonofprobabilitydistributions

The means of the determined model parameter distributions werestatisticallycomparedfortwodifferentbioreactorscales(see Fig. 1, Scale A and Scale B, respectively) to identify changes in theprocessdynamics.Therefore,therelative95%-confidenceinter- val (CI)forthedifferencein meanswascalculated.Fortwo sam- ples x₁,...,x_n andy₁,...,y_m(representingthedistributionofone model parameterattwo different scales)the meansx andy and thesamplevariances

σ

x²and

σ

y² werecomputed.Accordingtothe centrallimittheorem,thedifferenceinmeansd=x−yofsamples with large sample sizes follows a normal distribution, character- ized byN(^x−y,

σ

x²/n+

σ

y²/m)^.Then,the 95%-confidenceinterval

ofthedifferenceinmeanswerecalculated:

x−y−1.96

σ

x²/n+

σ

y²/m,x−y+1.96

σ

x²/n+

σ

y²/m

. (1)

Inordertotestforastatisticallysignificantdifferenceinmeans ofatleast5%,amodelparameterwasassignedtobesignificantly different,ifthecorrespondingCIcontains5%.

2.4.MonteCarlo-baseduncertaintybands

Quantificationand graphical representation of the propagated uncertainty in the process dynamics was performedwith Monte Carlomethods, thusrepeatedsimulationsoftheprocess withthe 1000previouslydeterminedparametersetswerecarriedout(2.2). Themeanandthe10% and90% quantilesofsimulationwerecal- culatedwith the function ”prctile” (MATLAB 2018a, exact mode) (Langford,2006).

2.5.Validationofprocessstrategy

A validation of the process strategy (box 4 in Fig. 1) is rec- ommendedif themodel parameterdistributions (2.2) are signifi- cantlydifferent.Thisismotivated basedon theidentified change of the bioprocess dynamics and is seen to support knowledge- driven decisionmaking. Commonly, Design ofExperiments (DoE) methods are applied to develop and validate the process strat- egy on different scales (e.g. during late stage process optimiza- tion)(Legmannetal.,2009;Brunneretal., 2017;Abtetal.,2018).

Möller et al., (2019b) proposed a model-assisted DoE method, which combines mathematical process modeling with statistical

Table 1

Summarized performed experiments in this study.

Aim Number of cultivations Working volume (cultivation system)

Process development 29 (2 blocks) 30 ml - 50 ml (shake flask, Corning, Netherlands) Process implementation 3 250 ml (Ambr250, Sartorius Stedim Biotech, Germany) Validation of process strategy 4 250 ml (Ambr 250)

Scale-up 3 2 l (UniVessel, Sartorius Stedim Biotech)

Scale-up 1 50 l (BIOSTAT STR50, Sartorius Stedim Biotech)

toolstosignificantlyreducethenumberofexperiments.Thiscon- ceptwasadapted inthisstudytovalidate theprocessstrategy. In brief, a DoE is planned using suitable software (here: DesignEx- pert11)andtherecommendedexperimentsaresimulatedinstead ofbeing experimentally performed. The responses (e.g. titer) are included into the DoE evaluation witha quadratic response sur- facemodel(allhierarchical,

α

^out<0.1,adjustedR-squaredcriteria).

Pleasesee (Möller etal., 2019b) andKuchemüller etal., 2020for moreinformationaboutthegeneralconceptofmDoE.

2.6.Identifiabilityanalysis

Monte Carlo simulations were used to evaluate whether the parameters can be reliably estimated with acceptable accuracy (Miaoetal.,2011). Therefore,thepropagationofthe inputuncer- taintiesontotheuncertaintyinmodelsimulationswerequantified.

For each model parameter, the whole sample of adapted values (representingtheprobabilitydistributionofthismodelparameter) wasconsidered andthe averagerelativeestimationdeviationwas computed. After adapting the model to each of the N simulated datasetstoobtainparameterestimates

θ

ˆ^{(k)forthek-thparameter,} thesamplemeanofthek-thparameter

θ

^(k)andthecorresponding relativeaveragedeviation(RAD(

θ

^{(k)))wascomputedaccordingto:}

RAD(

θ

^(k))=100%·_N^{1 N}

i=1

| θ

^ˆ_i^(k)−

θ

i^(k)

|

| θ

⁽i^k)

|

^{. (2)}

A low RAD-value reflects a practical identifiabilityof the cor- respondingparametercomponent(Miaoetal.,2011;Ananeetal., 2019). Nevertheless, no general fixed threshold can be applied since the relative average deviation also depends on the mea- surementerror.Therefore,theassessmentreliesontheunderlying problemandexpert.Inourstudy,weconsideredthehistogramsof theobtaineddistributions/samplesinordertodefine anadequate thresholdbelow20%.

2.7.Sensitivityanalysisofmodelstructure

The sensitivity of the model simulations based on the input parameter uncertainties was quantified using the change of the maximumviablecelldensityXv,max.Onemodelparameter

θ

^{(k) at}

a time was varied within its previously derived probability dis- tribution (2.2), meanwhile keeping all other parameters constant and computing the resulting target output values (Loucks and VanBeek,2017).Theresultingprobabilitydistributionofthetarget variablewas compared tothe input probability distribution. This wasrealizedbycomparingtherelativewidthofthe80%-intervals ofbothdistributions,θi andX_v,max,withaquantitativesensitiv- itycoefficientS:

S=

Xv,max

θ^(k) . (3)

AparameterwassignificantlysensitiveifSwasabove5%.

2.8. Engineeringparametersduringscale-up

All investigated bioreactors were hydrodynamically character- ized(Meuseletal.,2016;Kaiser etal., 2015)andengineeringpa- rameterswerecomparedwithrespecttocell growth,metabolism, andproduct titerduringscale-up andinscale-down models(not part of this work). Based on this, a specific power input of 19Wm⁻³wasidentifiedasthescale-upcriterion,whichwaskept constantinthisstudyatallinvestigatedstirredbioreactorscales.

2.9. Cultivations

All cultivations considered in this study were performed in single-use bioreactors and are summarized in Table 1, including theirscaleandcultivationsystem.

2.10. Celllineandpreculture

SuspensiongrowingCHODP-12cells,producinganInterleukin- 8 (IgG-1) antibody (clone #1934, ATCC CRL-12445), were culti- vated in this study (provided by Prof. Dr. T. Noll, Bielefeld Uni- versity, Germany). 1 ml cryo-cultures (1·10⁷ cells ml⁻¹) were thawedandtransferred toa250mlsingle-use Erlenmeyerbaffled flasks (40 ml working volume, Corning, USA). The used medium was TC-42 (chemically defined, animal component-free, Xell AG, Germany), which wassupplementedwith6 mmoll⁻¹ glutamine, 0.1mg·l⁻¹ LONG R3 IGF-1, and 200nmoll⁻¹ Methotrexate (all Sigma-Aldrich).Theincubators(LT-XC,Kuhner,SwitzerlandorMul- titroncell,InforsHT,Switzerland)werecontrolledat37^◦C,5%CO₂ (LT-XC)or 7.5%CO2 (Multitroncell)and85% humiditywithshak- ingspeedsbetween120rpm(25mmshakingdiameter,Multitron cell)-200rpm(12.5mmshakingdiameter,LT-XC).Thecellswere expandedinshakeflasksandnomaintenanceculturewasused.

2.10.1. Identificationoffeedingstrategy

The fed-batch strategy wasdesigned in a previous study (see Möller et al., 2019b) using mDoE to reduce the boundary values of an experimental design. There, the proposed method (mDoE) was tested and compared to the fully implemented experimen- tal design with 29experiments, which were performed inshake flasks (30 ml, 2blocks, 14and 15parallel experiments). In brief, the incubator (LT-XC, Kuhner) was the same as explained above (2.10)withanincreasedshakingspeed(220rpm).Thefeedingde- signwasvaried(feed:Chomacsbasicfeed,XellAG)withregardto thestarttimesofbolusfeeding(48h,72h,96h),thefeedingrate (3mld⁻¹-6mld⁻¹)andconcentrationsofglucose(111mmoll⁻¹ -222mmoll⁻¹)andglutamine(9mmoll⁻¹-38mmoll⁻¹).Inthis study,thisdatawasusedtoestimatethemodelparameterdistri- butionsoftheprocessdevelopmentscale(shakeflasks).Pleasesee (Mölleretal.,2019b)formoreinformation.

2.10.2. Processimplementationandprocessvalidationat250mlscale The formerly identified fed-batch strategy was transferred to the Ambr 250 modular system (Sartorius Stedim Biotech).

0.3·10⁶ cells ml⁻¹ were inoculated andthe startingvolume was 200 ml. Following feeding (feed as above) steps referring to the

J. Möller, T. Hernández Rodríguez and J. Müller et al. / Computers and Chemical Engineering 134 (2020) 106693 5

Fig. 2. Comparison of experimental (Exp:) and mean simulated data (Sim:) summarized for 29 performed fed-batch cultivations in shake flasks (30 ml - 50 ml) (see 2.10.1 ).

R ²reflects goodness of fit against the optimal simulation (x = y); ^∗= R ²for the first 144 h (lactate formation); ^∗∗= R ²for the first 96 h .

starting volume were performed: 48 h: 2.55%; 72h: 5.1%; 96 h, 120h,144h:10.625%.Temperaturewassetto37^◦Candheadspace aeration to 0.1 vvm. Dissolved oxygen wascontrolled at a mini- mum of40%(submerse spargingwithoxygenifneeded).pH was controlled at 7.2with CO₂ submerse sparging. Stirrer speed was adaptedtotheculturevolume,keepingthespecificpowerinputof 19Wm⁻³constant.Duringtheprocessvalidation,thestartingvol- umeofthe bioreactor(previously200 ml)wasalteredto230 ml (F=0.5)and170ml(F=1.5)duetothechangeinfeedingvolumes.

2.10.3. Processscale-up(2lscale)

Cellswere expandedusing125–500 mlsingle-useshakeflasks (Corning) with40–160 mlworking volume. Starting volume was 1440ml(UniVesselSU2Lbioreactor,SartoriusStedimBiotech).The feedingstepswereperformedbasedonthestartingvolumeasde- scribedabove(2.10.2).Allprocessparameterswerethesameasin Ambrexperiments.

2.10.4. Pilotscale(50l)

Cellswere expandedusing125–500 mlsingle-useshakeflasks (Corning)with40–160mlworkingvolumeandawave-mixedbag with5lworkingvolume(CultibagRM10lbasic,SartoriusStedim

Biotech).Forthepilotscalecultivation,theBIOSTATSTR50(Sarto- riusStedimBiotech)wasusedwith34lstartingvolume. Feeding wasperformedaspreviouslydescribed(2.10.2).

2.11. Analyticalmethods

2.11.1.Identificationoffeedingstrategy

Forthe identification of the feeding strategy (TUHH), thecell concentration was determined with the Z2 particle counter (Z2, Beckman Coulter,USA) andthe viabilitywasmeasured using the DAPI(4,6-diamidino-2-phenylindole,Sigma-Aldrich)method.Glu- cose, glutamine, and lactate concentrations were measured with thebiochemistryanalyzerYSI2900D(YellowSpringsInstruments, USA). The concentration of ammonium wasenzymatically deter- mined withatest kit(AK00091, nzytech,Portugal). The antibody titer was quantified using a high performance liquid chromato- graphicsystem(HPLC,KnauerSmartline,Germany)equippedwith aPoros-Acolumn(ThermoFisherScientific,USA;0.1ml, 4^◦C).Pu- rified water containing 150 mmol l⁻¹ NaCl (Sigma-Aldrich) and 50mmoll⁻¹ Na2HPO4(pH7,Sigma-Aldrich)wasusedasthemo- bile phase (flow rate: 1.5 ml min⁻¹). The samples were filtered (Cellulosefilters,pore size: 0.45μm,Restek,Germany)before in-

Fig. 3. Experimental results (diamonds) of the fed-batch culture at 250 ml bioreactor scale (2.10.2) , solid line is the mean of 10 0 0 simulations based on the MC-based method (see 2.2 ), dashed line represents the 10% and 90% quantiles of the simulations; feeding was performed every 24 h (pointed line) with a start at 48 h.

jection of 50 μl. 100 mmol l⁻¹ glycin (pH 2.5, in purified wa- ter,Sigma-Aldrich)wasappliedtoelutetheantibody,andtheUV signal (280 nm) was measured. The system was calibrated with a standard curve of diluted Rituximab (Roche, Switzerland), and samplesweremeasuredinduplicates.

2.11.2.Processimplementation,re-adjustment,scale-upandpilot scale

For the experiments in stirred bioreactors(ZHAW), living cell densityandviability weremeasured withtheNucleoCounter NC- 200(ChemoMetec,Denmark).Glucose,glutamine,lactate,andam- moniumwereanalyzedwiththeBioProfile100Plus(NovaBiomed- ical, Germany).The antibody was quantified with the Cedex Bio (Roche,Switzerland).

3. Resultsanddiscussion

Thisstudyaimstointroducea modeluncertainty-basedwork- flow (seeFig.1) fortheevaluationofthebioprocessdynamicsat differentscales usingmodelparametricuncertaintyquantification andstatisticaltests.Inthebeginning,thefeedingstrategyandthe mathematicalmodeloftheprocessdevelopmentdata(shakeflask cultures, 30 ml -50 ml) is discussed. Then, the feeding strategy was transferred to 250 ml stirred bioreactors and three cultiva- tionswereperformed.Themodelparameterdistributionswerede- terminedandcompared betweentheprocessdevelopment(shake flask) and 250 ml bioreactor scale. Furthermore, scale-up from 250mlbioprocessesto 2lwasstatisticallyvalidatedandtheob-

J. Möller, T. Hernández Rodríguez and J. Müller et al. / Computers and Chemical Engineering 134 (2020) 106693 7

Fig. 4. Box-plots of the normalized parameters of the process development runs compared to the process validation, box-plots show the intrinsic distribution of 10 0 0 independent parameter estimations per box, normalization of parameters on their individual starting parameter values during parameter estimation (see Supplementary Table 2 ), ^∗= significant, n. sig. = not significant.

tainedparameterdistributions(250mland2l,respectively)were usedtopredictthevariabilityofa50lpilotscalerun.

3.1. Processdevelopment(30ml):Identificationoffed-batchstrategy

As wasdescribed inMöller et al.(2019b), the identified opti- malprocessstrategyinshakeflaskcultivationswas:startofbolus feeding after96h,glucose concentration infeed=222mmoll⁻¹, glutamineconcentration infeed=9mmoll⁻¹ anda feedingrate of10%v/v (^3mld−1)^{.Here,itwasaimedtotransferthisprocess} strategyfromshakeflaskstostirredbioreactorsandscalethepro- cessuptopilotscale.Therefore,itwasevaluatedthattheprocess dynamicsremainconstantduringscale-up.

3.1.1. Estimationofmodelparameters

668datapoints(29fed-batchcultivations,see2.10.1)wereused asdataforthedeterminationofthemodelparameterdistributions (2.2),whicharesummarizedintheSupplementaryFigs.1-16.All cultivationswereadditionallysimulatedwiththemeanoftheindi- vidualparameterdistributionandthecomparisonofthesimulated tothemeasureddataisshowninFig.2.

The viable (Fig. 2, A), dead (Fig. 2, B) and total cell density (Fig.2,C)weresufficientlyreflectedbytheaverageparameterval- ues.Theantibodyconcentration (Fig.2,D)wassimulatedwithan R²=0.56andNRMSD=0.19andreflectsthegeneralrelationships, butthemaximalantibodyconcentrationwaspartlyover-predicted after144h.Themodelingoftheproductformationiswidelydis- cussed inliterature (Zengetal., 1998; PörtnerandSchäfer,1996;

Ben Yahia et al., 2015; Möller et al., 2018) and the here mod- eledconstantcell-specificproductivityisarathersimpleapproach, butsufficientforprocessoptimization.Glucosewassimulatedwith highaccuracyinall cultivations(R²=0.75, NRMSD=0.08),butlac- tate concentration (Fig. 2,F) wasonly simulatedwithhigh accu- racyfortheformationoflactateduringthefirst144h(R²=0.56, indicatedby^∗).After that,nofurtherincreaseinlactatewasmea- sured.ThisisatypicaleffectinpH-uncontrolledshakeflaskculti- vations(Zhouetal.,2011)andnoimpactoflactateoncellgrowth was identified previously for this cell line (Möller et al., 2018;

Table 2

Sensitive model parameters, sensi- tivity analysis as described in 2.7 ,

∗considered significant due to direct linkage to product titer.

Parameter S [%]

μmax 103%

k Gln 51%

k Amm 27%

K s,Gln 12%

Y Amm,Gln 45%

q Gln,max 44%

q ^∗_Ab significant

2019b). The concentration ofglutamine is predicted well if con- sideringonly thefirst 96h of cultivation(Fig. 2,G; indicated by

∗∗).However,itdiffersfromthesimulationtowardstheendofthe cultivation,presumablyduetochanging pHandammonium con- centrations(Lüdemannetal.,1994;HaandLee,2014).Cellgrowth is highly dependent on the glutamine availability and the range offedglutamineis ratherhigh(9mmoll⁻¹ -38mmoll⁻¹).This leadsto a negative R²,but an overall acceptable simulation. The concentrationofammoniumwaspredictedwithanR²=0.52.

Overall, theaverage model simulations reflect the culture dy- namics acceptably for the high amount of data and investigated process strategies in shake flask cultures. Furthermore, the pro- cessknowledgeisincreasedthroughoutthe mathematicalmodel- ing(Carrondoetal., 2012).Themodelparameterdistributions re- flecttheparametricuncertaintyandtheprocessvariability,which arefurtherusedtovalidatetheprocessdynamicsduringscale-up.

3.1.2. Identifiabilityanalysis

Practical identifiabilityof each parameter was analyzed based on the obtained parameter distribution, interpreting the corre- spondinghistogramsaswellastheRAD(Miaoetal.,2011).There- fore,the histogramsof all parameters (see Supplementary Figure 17–20) show highfrequencies in the centerand low frequencies on the tails on both sides, for whichpractical identifiabilitywas

Fig. 5. Validation of feeding strategy with mDoE; A: contour plot with recommended experiments (white stars); B: contour plot including performed validation experiments;

∗= experimental data not considered in mDoE.

concluded.This is confirmedby theresulting RAD values,which rangefrom5%-14%.

3.1.3. Sensitivityanalysis

A sensitivityanalysiswasperformedto reduce thenumber of adaptedandcompared parameterstothesensitiveonesonly(see 2.7).TheparametersshowninTable2wereidentifiedtobesensi- tive:

μ

max wasidentified tobethemostsensitiveparameter,which istypical in Monod-type models asthe main parameter describ- ing Xv, which is linked to all differential equations (Supplemen- tary Table1). Moreover, the parameters associated withthe glu- taminemetabolism (q_Gln,max, k_Gln) are sensitive because the glu- tamineconcentration,asamainsubstrate(besidesglucose),isalso directlylinkedto cellgrowth.Theinhibitoryeffectofammonium isalsolinked toXvandtheammonium-relatedmodelparameters Y_Amm,Gln andk_Ammaresensitive.Thesensitivityofglucose-related model parameters is rather low (k_S,Glc). q_Ab describes the cell- specificantibodyproductionandissensitiveregardingtheproduct formationandwasthereforeincluded.Onlytheseparameterswere re-adjustedin thefollowing evaluationofthescale-up procedure andfor the non-sensitive parameters, the previously determined averagevalueswereused(SupplementaryTable3).

3.2.Transferfromprocessdevelopmenttoprocessimplementation

The cell line, the cultivation protocols and the process strat- egy were transferred to a different research institute (TUHH to ZHAW),comparable to a tech transfer from research and devel- opment to process implementation and scale-up. In the begin- ning, the process strategy was scaled up to a stirred bioreactor system(see 2.10.2, working volume: 250 ml) forverification ex- periments.The formerlydetermined feedingstrategy wasslightly adapted due to practical bioreactor handling and to ensure pro- cessrobustness. Therefore, the glucose concentration in the feed waspreviously identified to have only a low impact on the bio- process (Möller et al., 2019b) andwas changed to 111 mmoll⁻¹

to avoid overfeeding. The glutamine concentration in the feed was 9 mmol l⁻¹ and the feeding rate slightly resembled an exponential-likefeeding(see2.10.2).

3.2.1. MC-Baseduncertaintyquantification

Threetestrunswereperformedwiththetransferredandscaled upprocessstrategy(stirredbioreactors,250ml)andthemodelpa- rameters were estimated using the MC-based method (2.2). The experimental dataandthemodel simulationsincludingthe para- metricuncertainty-basedpredictionbandsareshowninFig.3.

Theexponentialgrowthphasewassimulatedwellfortheviable (seeFig.3A)andtotalcelldensity(Fig.3B)startingwithapprox.

0.3·10⁶cellsml⁻¹untilafinalconcentrationof22·10⁶cellsml⁻¹ (168 h). In general, further cell growth in the stationary phase progressed with reduced cell volume, limitations, and inhibitory effects (Zeng et al., 1998). This was only partly included in the model and the maximal cell concentrations (Xv, Xt) were there- foreslightly underestimated in thestationary phase. Theglucose concentration (Fig. 3C) waswell predictedby themodel includ- ingthefeedpulsesandthelateglucoseconsumptionafterthelast feedpulse (t > 138 h). The lactate concentration (Fig.3 D) was predicted with variations during lactate formation but the time and course of lactate uptake waspredicted sufficiently. The lac- tatemetabolismwithmetabolicdysfunctions(knownas”Warburg- effect”)includinghighformationratesatthebeginningofthecul- tivation,followedbyastagnationoflactateaccumulation,andthe switch to lactate uptake is still investigated in research (Hartley et al., 2018; Ulonska et al., 2018; Zalai et al., 2015). As an ex- ample, Hartley et al. (2018) reviewed current theories (e.g., pH, pyruvateavailability,mitochondrialfunction)regardingthelactate metabolism,andhypothesizedthatlactateconsumptionisafunc- tionofthecellular redoxstate (Hartleyetal., 2018). Forthe here aimedcomputationalevaluationofprocessstrategiesduringscale- up, a kinetic description ofcell growth andmetabolism wastar- getedandthepredictionofthelactatedynamicsisthereforeseen sufficient.Glutamine(Fig.3E)andammonium(Fig.3F)weresim- ulated accordingly with the experimental data and the antibody

J. Möller, T. Hernández Rodríguez and J. Müller et al. / Computers and Chemical Engineering 134 (2020) 106693 9

Fig. 6. Experimental results (diamonds) of the fed-batch culture at 2 l bioreactor scale, solid line is the median of 10 0 0 simulations based on the MC-based method (see 2.2 ), dashed line represents the 10% and 90% quantiles of the simulations; feeding was performed every 24 h (pointed line) with a start at 48 h.

concentration(Fig.3G)increasedconstantlyupto387±16mgl⁻¹ (average of216hand240h),whichwasalsosimulated.The vol- ume (Fig. 3 H) was simulated as measured. R² and NRMSD are shown in Supplementary Table 4. Overall, the simulations are in goodagreementwiththeexperimentaldataandthemodelreflects the bioprocessdynamicssufficiently. Adescription ofthe mecha- nisticlinksusingamathematicalprocessmodelisthebasisofthe proposedconceptandanappropriatedescriptionofthebioprocess needs tobe ensured ifthe workflowis appliedto adifferentcell lineorprocess.

3.2.2. Statisticalcomparisonofparameterdistributions

As proposed in the parametric uncertainty-based workflow (Fig.1, box3), themeans of theparameter distributions are sta-

tisticallycompared to evaluate ifthe dynamics ofthe bioprocess changed(Fig.4).ThemeanparametervaluesarelistedinSupple- mentaryTable3.

Anincrease of23% wasdeterminedinthe meanof

μ

^max,norm, whichshowsahighercellgrowthinpHandpO₂ controlledbiore- actors.Moreover,theglutamine-dependent modelparameters dif- fer significantly between both scales thus indicating an average lower maximal uptakerate (qGln,max,norm) and a differentaffinity totheglutamineavailability (k_Gln,norm,K_s,Gln,norm).Thesametrend wasidentified forYAmm,Gln,norm witha higher ammonium forma- tion in the bioreactor experiments compared to the shake flask cultivations.ThedissociationofNH₃ toNH₄ isaffectedbythepH, thus explaining different ammonium concentrations in the con- trolled bioreactor experiments compared to the shake flask cul-

Fig. 7. Box-plots of the normalized parameters of the process implementation runs (250 ml) compared to the process scale-up (2 l), box-plots show the intrinsic distribution of 10 0 0 independent parameter estimations per box, normalization of parameters on their individual starting parameter values during parameter estimation (Supplementary Table 2 ), ^∗= significant, n. sig. = not significant.

tures(Lüdemann et al., 1994). q_Ab,norm waswidely distributed in the shakeflask cultivation,which indicates its correlation to the differentinvestigatedfeedingstrategies.Thewidthofthewhiskers wasnarrowerinthebioreactorrunsandthemeanq_Ab,normwasre- ducedinthetransferredprocess.However,theoverallprocesstiter wascomparableinbothscales duetoa higherviablecelldensity in the bioreactor cultivations. The means of K_Amm,norm were not significantlydifferentbetweenbothscales.

In summary, differences in the dynamics of the growth and metabolism could be statisticallyidentified for the transfer from processdevelopment(shakeflask)toprocessimplementationscale (stirredbioreactor).Moreover,thesedifferencescouldbequantified andactions couldberecommendedbasedontheproposed work- flow. Therefore, a re-validation of the formerly determined pro- cessstrategywasrecommendedtoensurethatthetargeteddesign space(i.e.processstrategy)isstillmet(Fig.1,box4).

3.3.Validationofprocessstrategy

The validation of the formerly determined process strat- egy during process implementation was performed using mDoE (Möller et al., 2019b). Therefore, the glutamine concentration in the feed (F_Gln,feed) and the relative feeding rate (F_Rate·F= F_Rate,experimental) were defined as experimental factors. As an ex- ample, if F is defined as two, it means that all feed pulses (FRate,experimental, see 2.10.2) were doubled. Validation cultivations were planned using an I-optimal DoE design mode (16 rec- ommended experiments). The planned cultivations were simu- latedusing the model (mean model parameters asin 3.2.2) and the maximal antibody concentration wasdefined as response. A quadraticresponsesurfacemodel(RSM)wasestimated(DesignEx- pert11)andthecontourplotisseeninFig.5A.

The current process settings (Fig. 5 A) were at the maximal achievable antibody concentrations within a flat area, which re- flectsa stablepoint ofoperation.Tovalidate the processstrategy andto ensureprocess stability,four validationexperiments were planned(whitestars Fig.5A). Itwasaimed toensurethe stabil-

ityoftheprocessandtoidentifytheshapeofthemaximum.The validationcultivationswereexperimentallyperformedandtheex- perimentalsettingswereincludedwiththeirrespectivemaximum antibody concentrations as design points in the DoE (Fig. 5 B).

Theshapeofthemaximalantibodyconcentrationslightlychanged with an optimal area between the performed validation cultiva- tions,withoutharshboundaries,andaflatarea.Theprocessstabil- itycould, therefore,beensured andtheformerly definedprocess (Fig.5A/B)wasnotchanged.The mainadvantageofusingmDoE hereisthatthestabilityoftheprocess couldbe validatedforthe quantifiedchangesintheprocessdynamicsthroughoutthemodel parameteruncertaintydetermination.

3.4. Scale-upfrom250mlto2l

The implemented and validated process strategy was scaled up to 2 l scale, with the same hydrodynamicsas at the 250ml scale(see2.10.3).Threetestrunswereperformedandthescale-up wasevaluatedasproposed intheworkflow(Fig.1).Therefore,the model parameter distributions of the 2 lbioreactor experiments wereestimatedusingtheMC-basedmethod(2.2) andstatistically comparedtothe250mlscale.

3.4.1. MC-baseduncertaintyquantification

The model-based simulations, with 10% and 90% quantiles of simulationandtheexperimentaldata,areshowninFig.6.

Overall,themodelpredictionsoftheprocessatthe2l(Fig.6) scale were comparable tothe process implementation at 250ml scale(Fig.3).DifferencesinR²andNRMSD(seeSupplementaryTa- ble5)werelow.

3.4.2. Statisticalcomparisonofparameterdistributions

Thedynamicsoftheprocesswerequantifiedwiththestatistical comparisonof the parameterdistributions (Fig. 7).The means of theparameterdistributionsareshowninSupplementaryTable2.

μ

^max,norm, k_Gln,norm, K_s,Gln,norm, YAmm,Gln,norm, qGln,max,norm, and q_Ab,norm were identified to be not significantly different on a 5%

J. Möller, T. Hernández Rodríguez and J. Müller et al. / Computers and Chemical Engineering 134 (2020) 106693 11

Fig. 8. Experimental results (diamonds) of the fed-batch culture at 50 l pilot scale, solid line is the mean of 20 0 0 simulations with the parameters previously estimated based on the proposed MC method (see 2.2 ) for the process implementation (250 ml bioreactor) and scale-up (I) (2 l bioreactor) experiments, dashed line represents the 10% and 90% quantiles of the simulations; feeding was performed every 24 h (pointed line) with a start at 48 h.

significance level. K_Amm,norm wasslightly higherin the scaled up processthanduringtheprocessimplementationruns(250ml),but no differences were present in the maximal ammonium concen- tration andthischangewasthereforeneglected.Insummary,the process dynamicsremainstableduringthescale-up fromprocess implementationtoprocessscale-up.

In conventional scale-up studies, the pure cultivation data of both scales (250mland2 l,respectively) wouldhavebeen com- paredandaheuristic decisionofthegoodness ofscale-upwould havebeendrawn(e.g.samemaximaltiter,trends)(Rameezetal., 2014;Lietal.,2013). Intheproposed workflow,themodeluncer- tainty isquantified based on theavailable experimental variabil-

ityandmeasurementerror.Therefore,theprocessvariabilityisde- termined ona timely axis(10% and 90% quantilesof simulation, Fig.6) andin theparameter distributions (Fig.7). Thisenables a knowledge-driven decision-making routine based on the process dynamicswiththe incorporationoftheavailable datainthepro- cessmodel.In accordancewiththe proposedworkflow (Fig.1,3) scale-uphasproceededwiththeconfirmedprocessstrategy.

3.5.Scale-upto50lpilotscale

The process strategy wasfurther scaled up to 50lpilot scale and one verification cultivation was performed. In general, the

quantificationofthemodelparameter distributionsrequires mul- tiplecultivationruns(i.e.3),whichwerenotavailableforthepilot scale.Therefore,the formerlydetermined parameter distributions (250ml and2l, respectively) were used topredict the expected processvariabilityofthepilotscalerunapriori,asshowninFig.8. Thesimulatedmeanandthe10%and90%quantilesareingood alignmentwiththeexperimentaldata.Theantibodyconcentration (Fig. 8 G) increasedconstantly up to 367 mg l⁻¹ and is compa- rableto the formerly performed processes in smaller scales and otherstudieswiththesamecellline(Mölleretal.,2019a,2019b).

Themainadvantageofpredictingthe10%and90%quantilesofthe pilotscalebasedonthepreviouslydeterminedparameterdistribu- tions is that the experimental variability is incorporated, even if the process knowledge was gained at smaller scales (Hernández Rodríguez etal., 2019; Xing etal., 2010). Furthermore,the a pri- orisimulation of the scaled up process and its comparison with newlyavailable dataatthe respectivescalecan be usedtoprove the currentprocess understanding. Differences betweenthe data andsimulationscouldassistintheidentificationofvariationsinso farnottargetedscale-up parameters,even iftheywere not mod- eled(Brunneretal.,2017;Narayananetal.,2019).Insummary,the processstrategywassuccessfullyscaledupto50lpilotscaleand theformerlyobtainedknowledgewasconsideredwiththepredic- tionofthe10%and90%quantiles.

4. Conclusion

Aworkflowforaknowledge-drivencomputationalevaluationof theprocessstrategyduringscale-upwasintroduced.Therefore,the processdynamicsaredescribedbyamathematicalprocess model andthemodelparametersarerepresentedasprobabilityfunctions, whichare determined based on theexperimental variability. The probability functions derived at differentscales are then statisti- callycomparedtoidentifychangesinthebioprocessdynamicsand validationofthe process strategy isrecommended ifthedynam- icsaresignificantlydifferent.Otherwise,scale-upcanproceed,and theprocess strategy isto be considered sufficient. Thisworkflow wasdiscussed onthescale-up ofaCHODP-12fed-batchprocess, whichwassuccessfullyscaledupto50lpilotscale.Theintroduced approachprovidesanovel,knowledge-drivendecision-makingtool forbioprocess development and implementation. Further studies willfocus on the automated re-design of process strategies with the consideration of the process model during scale-up and the combination of computational fluid dynamics with the process model.

AuthorContributionStatement Allauthorscontributedtothepaper.

DeclarationofCompetingInterests

Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

The authors declare the following financial interests/personal relationshipswhichmaybeconsidered aspotentialcompetingin- terests:

Acknowledgment

Funding: This study was partially funded by the German FederalMinistryofEducationandResearch(BMBF,Grant031B0305 and031B0577A). Connflictofinterests:The authors declarethat therearenoconflictsofinterest.Specialthanks:Wekindlythank KrathikaBhatforEnglishproofreading.

Supplementarymaterial

Supplementary material associated with this article can be found, in the online version, at 10.1016/j.compchemeng.2019.

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