The development of a fed-batch Corynebacterium glutamicum fermentation model

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The development of a fed-batch The The development development of of a a fed-batch fed-batch Corynebacterium glutamicum fermentation The development of a fed-batch Corynebacterium glutamicum fermentation Corynebacterium glutamicum fermentation model Corynebacterium glutamicum fermentation model model model Pedro A. Lira-Parada, Even Pettersen, Fernando P´ erez-Garc´ıa

Pedro A. Lira-Parada, Even Pettersen, Fernando P´ erez-Garc´ıa Pedro Pettersen, Fernando P´ e Nadav Bar* Pedro A. A. Lira-Parada, Lira-Parada, Even Even Pettersen, erez-Garc´ rez-Garc´ıa ıa Nadav Bar* Fernando P´ Nadav Bar* Pedro A. Lira-Parada, Even Pettersen, Fernando P´ e rez-Garc´ıa Nadav Bar* Nadav Bar* Norwegian University of *Department *Department of of Chemical Chemical Engineering, Engineering, Norwegian University of *Department of Chemical Engineering, Norwegian University Science and Technology, Trondheim, Norway (e-mail:of *Department of Chemical N-7491 Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway (e-mail: Science Technology, N-7491 Trondheim, Norway (e-mail: *Department Chemical Engineering, Norwegian University [email protected]) Science and and of Technology, N-7491 Trondheim, Norway (e-mail:of [email protected]) [email protected]) Science and Technology, N-7491 Trondheim, Norway (e-mail: [email protected]) [email protected]) Abstract: Abstract: Fed-batch Fed-batch bioreactors bioreactors are are multiple multiple input, input, multiple multiple output output non-linear non-linear systems systems with with Abstract: Fed-batch bioreactors are multiple input, multiple output non-linear systems with with a central role in the production of antimicrobials, fine-chemicals and desirable Abstract: Fed-batch bioreactors are multiple input, multiple output non-linear systems a central role in the production of antimicrobials, fine-chemicals and desirable products products aa central role in the production of antimicrobials, fine-chemicals and desirable products Abstract: Fed-batch bioreactors are multiple input, multiple output non-linear systems with of pharmaceutical industry, and as such industrial microbial bio-catalytic processes require role in the production antimicrobials, fine-chemicals and desirable of central pharmaceutical industry, and asofsuch industrial microbial bio-catalytic processesproducts require of pharmaceutical industry, and as such industrial microbial bio-catalytic processes require a central role in the production of antimicrobials, fine-chemicals and desirable products understanding of the microorganism, the bioreactor, and the set of differential equations of pharmaceutical industry, and as such industrial microbial bio-catalytic processes require understanding of the microorganism, the bioreactor, and the set of differential equations that that understanding of microorganism, the bioreactor, and the set set of differential differential equations that of pharmaceutical industry, and as such industrial microbial bio-catalytic require allow the of the In present study, we our preliminary understanding of the the microorganism, thesystem. bioreactor, and the of equations that allow the description description of the fermentation fermentation system. In the the present study, we show showprocesses our preliminary allow the description of the fermentation system. In the present study, we show our preliminary understanding of the microorganism, the bioreactor, and the set of differential equations that modelling results of growth of Corynebacterium glutamicum wild type strain ATCC13032 in allow the description of the fermentation system. glutamicum In the present study, showATCC13032 our preliminary modelling results of growth of Corynebacterium wild typewe strain in aa modelling results of growth of Corynebacterium glutamicum wild type strain ATCC13032 in allow the description of the fermentation system. In the present study, we show our preliminary single sugar system. The differential equations consider an unstructured model of C. glutamicum modelling of The growth of Corynebacterium glutamicum wild type model strain of ATCC13032 in aa single sugarresults system. differential equations consider an unstructured C. glutamicum single sugar system. The differential equations consider an unstructured model of C. glutamicum modelling results of growth of Corynebacterium glutamicum wild type strain ATCC13032 in a to describe the liquid and gas phase, and the results suggest that is possible to model the titers single sugar system. The differential equations consider an unstructured model of C. glutamicum to describe the liquid and gas phase, and the results suggest that is possible to model the titers to describe the liquid and gas phase, and the results suggest that is possible to model the titers single sugar system. The differential equations consider an unstructured model of C. glutamicum in the liquid and concentrations in the gas phase for the simple sugar system. We anticipate to describe the liquid and gas phase, and the results suggest that is possible to model the titers in the liquid and concentrations in the gas phase for the simple sugar system. We anticipate in the liquid and concentrations in the gas phase for the simple sugar system. We with anticipate to the liquid andbasis gas phase, andgas theglutamicum resultsfor suggest that issugar possible to model the other titers that these results are the for further C. fed-batch reactor modelling in describe the liquid and concentrations the phase the simple system. We anticipate that these results are the basis for in further C. glutamicum fed-batch reactor modelling with other that these results are the basis for further C. glutamicum fed-batch reactor modelling with other in the liquid and concentrations in the gas phase for the simple sugar system. We anticipate carbon sources, complex mixtures of them, implementation of novel control and optimization that these resultscomplex are the basis for further C. glutamicum fed-batch reactor modelling with other carbon sources, mixtures of them, implementation of novel control and optimization carbon sources, complex mixtures of them, implementation of control and that these results aredevelopment the basis forof C. glutamicum reactor modelling with other structures, and state estimators from in-situ measurements. carbon sources, complex mixtures of them, implementation of novel novel control and optimization optimization structures, and the the development offurther state estimators fromfed-batch in-situ measurements. structures, and development of state estimators from in-situ measurements. carbon sources, complex mixtures them, implementation of novel control and optimization structures, and the the development of of state estimators from in-situ measurements. © 2019, IFACand (International Federation of Automatic Control) Hosting bymeasurements. Elsevier Ltd. All rights reserved. structures, the development of state estimators from in-situ Keywords: Biotechnology, Biotechnology, fed-batch,Corynebacterium fed-batch,Corynebacterium glutamicum, glutamicum, dynamic dynamic modelling. modelling. Keywords: Keywords: Biotechnology, Biotechnology, fed-batch,Corynebacterium fed-batch,Corynebacterium glutamicum, glutamicum, dynamic dynamic modelling. modelling. Keywords: Keywords: Biotechnology, fed-batch,Corynebacterium glutamicum, dynamic modelling. 1. INTRODUCTION Herein, we present a model 1. INTRODUCTION Herein, we present a model for for the the experimental experimental fed-batch fed-batch 1. INTRODUCTION Herein, we present a model for the fed-batch bioreactor with (C. glutamicum), with of 1. INTRODUCTION Herein, we with present model for the experimental experimental bioreactor (C.a glutamicum), with the the use use fed-batch of an an ininbioreactor with (C. glutamicum), with the density, use fed-batch of an an 2inin1. INTRODUCTION Herein, we present a model for the experimental situ NIR probes that correlates with optical bioreactor with (C. glutamicum), with the use of situ NIR probes that correlates with optical density, O O2 in in Industrial microbial microbial biocatalytic biocatalytic processes processes and and system system bioreactor situ NIR probes that correlates with optical density, O in with (C. glutamicum), with the use of an the liquid phase and on-line gas analyzer. The objective of 2insitu NIR probes that correlates with optical density, O in Industrial 2 the liquid phase and on-line gas analyzer. The objective of Industrial engineering microbial biocatalytic biocatalytic processes and system metabolic entail activities related with strain the liquid phase and on-line gas analyzer. The objective of situ NIR probes that correlates with optical density, O this report is to define a basic set of differential equations Industrial microbial processes and system 2 in the liquid phase and on-line gasset analyzer. The objective of metabolic engineering entail activities related with strain this report is to define a basic of differential equations metabolic engineering entail activities related with strain Industrial microbial biocatalytic processes and system development, fermentation, separation and purification this report is to define a basic set of differential equations the liquid phase and on-line gas analyzer. The objective of that aim at describing states in the liquid and gas phase metabolic engineering entail activities related with strain this report isdescribing to define astates basic in setthe of differential equations development, fermentation, separation and purification that aim at liquid and gas phase development, fermentation, separation andFermentation purification metabolic activities related with strain this (Schmid etengineering al.fermentation, (2001);entail Lee et et al. (2015)). (2015)). thatareport aim atisdescribing describing states in the liquid and and gas gas phase to define a basic set of differential equations for C. glutamicum fermentation system. development, separation and purification that aim at states in the liquid phase (Schmid et al. (2001); Lee al. Fermentation for a C. glutamicum fermentation system. (Schmid et et al.fermentation, (2001); aLee Lee et al. (2015)). (2015)). Fermentation development, separation andFermentation purification processes must ensure controlled and stable stable operation, that for C. fermentation system. at describing states in the liquid and gas phase (Schmid al. (2001); et al. for aa aim C. glutamicum glutamicum fermentation system. processes must ensure a controlled and operation, processes must ensure aLee controlled and stable stable operation, (Schmid et al. (2001); et al. (2015)). Fermentation with desired growth and green production of chemicals for a C. glutamicum fermentation system. processes must ensure a controlled and operation, with desired growth and green production of chemicals 2. METHODS with desired growth and green production production of operation, chemicals processes must ensureand a controlled and stable (L¨ ubbert bbert andgrowth Jørgensen (2001)). The literature covers 2. METHODS with desired green of chemicals (L¨ u and Jørgensen (2001)). The literature covers 2. 2. METHODS METHODS (L¨ u bbert and Jørgensen (2001)). The literature covers with desired growth and green production of chemicals modelling efforts of different fermentation systems, work (L¨ ubbert and Jørgensen (2001)). The literature modelling efforts of different fermentation systems,covers work 2.1 Process studied 2. METHODS modelling efforts of different fermentation systems, work (L¨ u bbert and Jørgensen (2001)). The literature covers in the area of baker’s yeast production (Goldrick et al. modelling of different fermentation(Goldrick systems, et work Process studied in the areaefforts of baker’s yeast production al. 2.1 in the the area area of et baker’s yeast Reyman production (Goldrick et al. modelling efforts of fermentation systems, work 2.1 Process Process studied studied (2015); Wang al. different (1977); (1992), analysis in 2.1 in of baker’s yeast production (Goldrick et al. (2015); Wang et al. (1977); Reyman (1992), analysis in 2.1 Process studied (2015); Wang et al. (1977); Reyman (1992), analysis in in the area of baker’s yeast production (Goldrick et al. We conducted mammalian cell cultures (Xing et al. (2009)), Escherichia (2015); Wang et al. (1977); Reyman (1992), analysis in the experiments experiments in in aa system system of of Labfors-5 Labfors-5 mammalian cell cultures (Xing et al. (2009)), Escherichia We conducted the mammalian cell cultures (Xing et al. al. (2009)), Escherichia We conducted the experiments in system of Labfors-5 (2015); Wang al.(1997); (1977); Reyman (1992), analysis in system bioreactor with working V coli (Presser etetcultures al. (1997); Scott and(2009)), Hwa (2011)). (2011)). PreWe conducted the(Infors) experiments in aaL Labfors-5 mammalian cell (Xing et Escherichia system bioreactor (Infors) with 1-2 1-2 Lsystem workingofvolume volume V .. coli (Presser et al. Scott and Hwa Precoli (Presser et al. (1997); Scott and Hwa (2011)). Presystem bioreactor (Infors) with 1-2 L working volume V We conducted the experiments in a system of Labfors-5 mammalian cell cultures (Xing et al. (2009)), Escherichia The variables, units and description are on Table 1, the vious studies with Corynebacterium glutamicum, a mibioreactor (Infors) with 1-2 L are working volume V .. coli (Presser al. (1997); Scott and glutamicum, Hwa (2011)).a PreThe variables, units and description on Table 1, the vious studies etwith Corynebacterium mi- system vious studies with Corynebacterium glutamicum, a PremiThe variables, variables, units andpump description are on Table Table 1, the the system bioreactor (Infors) with 1-2 L working volume coli (Presser et al. (1997); Scott and Hwa (2011)). has autoclavable heads for digital control crobial cell factory, have also considered its kinetics in The units and description are on 1, vious studies with Corynebacterium glutamicum, a miof. crobial cell factory, have also considered its kinetics in system has autoclavable pump heads for digital control Vof crobial cellgrowth factory, have(Khan also considered considered its kinetics kinetics in The system has autoclavable pump heads for digital control of variables, units and description are on Table 1, the vious studies with Corynebacterium glutamicum, a miacid, base, antifoam, and feed. EVE bioprocess platform a Monod form et al. (2005); Sun et al. system has autoclavable pump heads for digital control of crobial cell factory, have also its in a Monod growth form (Khan et al. (2005); Sun et al. acid, base, antifoam, and feed. EVE bioprocess platform a Monod growth form (Khan et al. (2005); Sun et al. acid, base, antifoam, and feed. EVE bioprocess platform system has autoclavable pump heads for digital control of crobial cell factory, have also considered its kinetics in device (Infors) followed and recorded the signals. The fed(2011)) under biotin limitation (Bona and Moser (1997)), antifoam, and EVE the bioprocess a Monod growth form (Khan (Bona et al. and (2005); Sun(1997)), et al. acid, devicebase, (Infors) followed andfeed. recorded signals. platform The fed(2011)) under biotin limitation Moser (2011)) under biotin limitation (Bona and Moser (1997)), devicebase, (Infors) followed andfeed. recorded the signals. The fedacid, antifoam, and EVE bioprocess platform a Monod growth form (Khan et al. (2005); Sun et al. batch experimental set-up (Figure 1) has a volume V with and analysis of the biochemical process hints the need to device (Infors) followed and recorded the signals. The fed(2011)) under biotin limitation (Bona and Moser (1997)), and analysis of the biochemical process hints the need to batch experimental set-up (Figure 1) has a volume V with andtake analysis of the biochemical biochemical process hints the (1997)), need to to device batch experimental set-up (Figure 1) has has volume V with with (Infors) followed and(Figure recorded the aasignals. fed(2011)) under biotin limitation and Moser aa ratio  between the volume occupied by the gas and to into of account CO2 and byproduct concentration batch set-up 1) volume V and analysis the process hints the need ratioexperimental between the volume occupied by the The gas and to take into account CO and (Bona byproduct concentration to take take into of account CO222Paczia aatheratio  between the volume occupied by the gas and and byproduct concentration batch experimental set-up (Figure 1) has a volume V with and analysis the biochemical process hints the need to liquid. The air supply Q contains oxygen in a mole levels (Kiefer et al. (2002); et al. (2012)). C. glutamratio between the volume occupied by the gas and and byproduct concentration to into account CO levels (Kiefer et al. (2002); Paczia et al. (2012)). C. glutam- the liquid. The air supply Q contains oxygen in a mole the liquid. The air supply Q contains oxygen in a mole levels (Kiefer et al. (2002); Paczia et al. (2012)). C. glutama ratio  between the volume occupied by the gas and and byproduct concentration to take into account CO fraction y icum is a gram-positive, rod-shaped bacteria widely used and carbon dioxide y , with an outlet 2 −in and CO2 −in the liquid. air supply Q contains oxygen in a mole levels (Kiefer et al. (2002);rod-shaped Paczia et al.bacteria (2012)).widely C. glutam2 The yO icum is a gram-positive, used fraction carbon dioxide y , with an outlet 2 −in and carbon dioxide yCO2 −in , with an outlet fraction yO icum is a gram-positive, gram-positive, rod-shaped bacteria widely used concentration the liquid. The air supply Q contains oxygen in a mole levels (Kiefer et al. (2002); Paczia et al. (2012)). C. glutamas industrial workhorse in biotechnology for the producof the feed-stream y and carbon dioxide O −in CO −in O 2 2 fraction y icum is a rod-shaped bacteria widely used and carbon dioxide y , with an outlet 2 and O2 −inof the feed-stream yOCO −in carbon dioxide as industrial workhorse in biotechnology for the produc- concentration 2 2 as industrial workhorse in biotechnology for the producof the feed-stream yyyO and carbon fraction yO2 −in icum a gram-positive, rod-shaped bacteria widely used yyconcentration dioxide with andioxide outlet tion of chemicals and heating/cooling element the double jacket CO2 .. The 2of as workhorse in biotechnology for (Kalinowski the producconcentration ofand thecarbon feed-stream and dioxide 2 −in OCO tionindustrial ofis high-value high-value chemicals and aminoacids aminoacids (Kalinowski the,carbon double jacket 2of CO2 The heating/cooling element tion of high-value chemicals and aminoacids (Kalinowski y . The heating/cooling element of the double jacket as industrial workhorse in biotechnology for the producconcentration of the feed-stream y and carbon dioxide et al. (2003)). Such bacteria can grow in different carbon preserves the temperature (T ) of the fermentation system CO2 . The heating/cooling element O tion of high-value chemicals and aminoacids (Kalinowski y of the double jacket 2 CO et al. (2003)). Such bacteria can grow in different carbon preserves the temperature (T ) of the fermentation system 2 et al. Such bacteria can grow in different carbon temperature (T ))pumps of fermentation system tion high-value chemicals and aminoacids (Kalinowski heating/cooling the double jacket sources, giving it its wide of at the acid maintain the pH at et al.of(2003)). (2003)). bacteria in can different carbon ypreserves preserves temperature (Telement of the the of fermentation 2 . The sources, givingSuch it flexibility flexibility in itsgrow wideinrange range of applicaapplicaatCO30°C, 30°C, the acid and and base base pumps maintain the system pH at sources, giving it flexibility flexibility in itsgrow wideinrange range of applicaat 30°C, 30°C, the acid and and base pumps maintain thethe pHpOat at et al. (2003)). Such bacteria can different carbon preserves temperature (T ) of the fermentation system tions and production of chemicals (Becker and Wittmann seven, the stirring element controls and keeps sources, giving it in its wide of applicaat the acid base pumps maintain the pH tions and production of chemicals (Becker and Wittmann seven, the stirring element controls and keeps the pO22 tions and production of chemicals (Becker and Wittmann seven, the stirring element controls and keeps the pO sources, giving it flexibility in its wide range of applicaat 30°C, the acid and base pumps maintain the pH at22 (2015); Blombach and Seibold (2010); Jo et al. (2017)). levels at 30%, and the system has the flexibility to add tions and production of chemicals (Becker and Wittmann seven, the stirring element controls and keeps the pO (2015); Blombach and Seibold (2010); Jo et al. (2017)). levels at 30%, and the system has the flexibility to add (2015); Blombach and (2010); Jo et (2017)). levels at 30%, and the system has the flexibility to add tions and production of Seibold chemicals (Becker and Wittmann the stirring element controls and keeps the pO On of that, glutamicum has been extensively engiliquid inlet of sugar F ,, with aa sugar concentration S 2 in (2015); Blombach Seibold (2010); et al. al. (2017)). at 30%, the system has the flexibility to add On top top of that, C. C. and glutamicum has beenJo extensively engi- alevels aseven, liquid inlet ofand sugar Fin with sugar concentration S in in On of that, C. glutamicum has been extensively engiaa liquid sugar F , with aaflow sugar concentration S (2015); Blombach Seibold (2010); et al. (2017)). atinlet 30%,of and the system has the flexibility to−1 neered the of carbon sources with the feed pump with max rate of 3.5 L hr .. in A −1add On top top for of that, C. and glutamicum has beenJo extensively engi- levels liquid inlet of sugar Fin with sugar concentration S in ,a in neered for the consumption consumption of alternative alternative carbon sources with the feed pump with a max flow rate of 3.5 L hr A −1 −1 with −1 neered for the consumption consumption of alternative alternative carbon sources with theinlet feed pump max flow rate of 3.5 3.5the L hr hr A On top of that, C. glutamicum has been extensively engi- awith liquid of sugar Finflow ,aawith sugar concentration S such as wood-derived compounds (Wendisch et constant 22feed L was applied from bottom −1 ofwith neered the of carbon sources the pump max rate of L .. in A such as for wood-derived compounds (Wendisch et al. al. (2016)). (2016)). constant L min min of air air flow wasaflow applied from the bottom −1 −1 −1 ofwith such as wood-derived compounds (Wendisch et al. (2016)). constant 2 L min air flow was applied from the bottom neered for the consumption of alternative carbon sources with the feed pump a max flow rate of 3.5 L hr .A such as wood-derived compounds (Wendisch et al. (2016)). constant 2 L min−1 of air flow was applied from the bottom such as wood-derived compounds Federation (Wendisch al. (2016)). L min Ltd.ofAll airrights flowreserved. was applied from the bottom 2405-8963 © 2019, IFAC (International of et Automatic Control) constant Hosting by 2Elsevier Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2019.12.263

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of the bioreactor and controlled with a mass flow controller (MFC), anti-foam was added manually when needed. 2.2 Fermentation procedure A C. glutamicum ATCC13032 (or wild-type strain) fresh LB medium plate was used to inoculate a shake flask containing 100 mL of 2TY medium. The flasks was incubated at 30°C and 200 rpm O/N, and the culture was used to inoculate the bioreactor system containing modified CGXII medium (CGXII without MOPS) to an initial OD600 of 1. Initial glucose concentration was 10 g L−1 . Optical densities were measured by using a UV-VIS spectrophotometer (UV-160A; Shimadzu).

Table 1. Model variable, units and description. Variable t V Fin Fout S Sin S0 X X0 y O2 yO2 −in yO2 0 DO2 DO20 yCO2 yCO20 DCO2 DCO20 RX RS µm µ KS Q YXS Y O2 X YCO2 X N α β k L a O2 kL aCO2

Units h m3 L h−1 L h−1 gL g L−1 g L−1 g L−1 g L−1 − − − g L−1 g L−1 − − g L−1 g L−1 kg L−1 h−1 kg L−1 h−1 h−1 h−1 g L−1 L h−1 g g−1 g g−1 g g−1 rpm h−1 rpm−β [-] h−1 h−1

Description Batch time Reactor volume Liquid flow in the bioreactor Liquid flow out the bioreactor Substrate concentration Substrate concentration inlet flow Substrate initial concentration Biomass concentration Biomass initial concentration O2 mol gas phase fraction O2 mol gas inflow fraction O2 initial mol gas fraction Dissolved oxygen concentration Dissolved initial oxygen concentration CO2 mol gas phase fraction CO2 initial mol gas phase fraction Dissolved CO2 concentration Dissolved initial CO2 concentration Rate of biomass formation Rate of substrate consumption Maximum specific growth rate Specific growth rate Monod growth constant Volumetric air flow Biomass from substrate yield O2 from biomass yield CO2 from substrate yield Stirring rate of the bioreactor Mass transfer coefficient constant Mass transfer exponent O2 mass transfer coefficient CO2 mass transfer coefficient

2.4 Kinetics in the liquid phase We model C. glutamicum growth kinetics with an unstructured Monod growth rate (Ingham et al. (2008); Dey and Pal (2013); Pal et al. (2016)). Fig. 1. Simplified scheme of the experimental fed-batch bioreactor system. The system can measure the reactor temperature, pH, dissolved oxygen pO2 , and can control the temperature with the heating and cooling jacket, the pH set-point (pHsp ) with the acidbase pumps, and the pO2sp with the stirring. The system has an in-situ probe for the turbidity analysis that correlates with biomass formation at low optical density values, and the outlet of the gas phase contains a Blue-In One sensor that monitors O2 and CO2 concentration in the gas phase. 2.3 Fed-batch fermentation model Microbial fermentation systems consists of a vector of x states , u inputs, d disturbances, p parameters, and time of the process t. x˙ = f (x, u, d, t)

(1)

General expression will include different feedings of substrate, acid, base, and will attain to model Where the rates: RX , RDO , RCO2 take into account the reaction kinetics and mass transfer phenomena.

µm S KS + S The biomass rate of formation is: µ=

RX = µX

(2)

(3)

The substrate consumption is proportional to biomass growth rate: RS =

−µX YXS

(4)

We assumed that the oxygen uptake rate of reaction (OU R) is proportional to the growth rate (equation 5), the liquid media only defines the oxygen transfer rate from the gas media to the liquid phase (OT R), and that the driving force is the difference between the equilibrium ∗ and the current concentration CDO concentration CDO (equation 6)(Bird et al. (2007)). Therefore the rate of oxygen in the liquid phase is the difference between OT R and OU R (equation 7). µX OU R = (5) YO2 X (6) OT R = kL aO2 (DO2∗ − DO2 ) RDO2 = (OT R − OU R) (7)



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General hydrodynamic phenomena in stirred tank reactors and derivation of a model that describes the mass transfer rate is in general a laborious task (Garc´ıa-Ochoa and G´ omez-Castro (2001)). The mass transfer coefficient of oxygen kL aO2 is a function of the stirrer speed (N ) or the power per unit of volume ( P ower ), the gas flow velocity V (Vs ), the reactor geometry, the physico-chemical properties of the liquid media, and enhancements factor due to the biological systems (Garc´ıa-Ochoa and G´ omez (2009)). Diverse correlations of the mass transfer coefficient exist including dimensionless proposals, and one of the main objectives is to obtain a general framework that can allow its application from bench scale to pilot scale systems (Kl¨ockner et al. (2013)). Previous studies of the oxygen mass transfer in artificial network and reviews of the topic propose the general correlation as in equation 8, where E is the enhancement factor that takes into account the biological activity, and µa is the effective viscosity of the medium with Ostwald-de Waele model (Garc´ıa-Ochoa and G´ omez-Castro (2004); Garc´ıa-Ochoa and G´ omez (2009)): kL a ∝ (E)(Vs )a (N )b µca

(8)

For the sake of simplicity, we only considered that the mass transfer coefficient of oxygen is a function of the stirrer speed. The previous approach is valid because the reactor and stirrer geometry in our experimental set-up is the same, the mass flow velocity of the gas is constant, and we assumed as a first approach that the physicochemical and biological enhancement factors are relatively constant (Chung et al. (2006)): kL a = α(N )β (9) Where α and β are the constants that correlate the mass transfer coefficient with the stirrer speed. In the liquid media, carbon dioxide is produced or excreted (COE) (10), transported into the gas phase (COT ) (11), and the difference between them defines its kinetics (12): µX COE = (10) YCO2 X COT = kL aCO2 (HyCO2 − DCO2 ) (11) (12) RCO2 = COE − COT R The computation of the carbon dioxide mass transfer coefficient considers: the film theory assumption with the ratio of mass transfer coefficients of different molecules are proportional to their diffusivity ratio, and that the interfacial area for mass transfer is not a function of the molecules (Villadsen et al. (2011); Garc´ıa-Ochoa and G´ omez (2009); Bird et al. (2007)):  DCO2 kL aCO2 = kL aO2 = 0.91kL aO2 (13) D O2 Other power terms (i.e. 23 ) can be used for the diffusivity ratio (Villadsen et al. (2011)), resulting in a difference in the order of hundredths (0.85 the ratio of difussivities instead of 0.91). However, it is noteworthy to mention that the theoretical procedure is consistent with previous literature reports (Xing et al. (2009); Sp´erandio and Paul (1997); Bird et al. (2007)), and a previous discussion of these differences is also available (Royce and Thornhill (1991)). The Henry constants of O2 and the CO2 were

233

obtained from previous reports (Carroll et al. (1991); Sander (2015)), and at 30 ◦ C the values are for HO2 = 0.042 g L−1 atm−1 and HCO2 = 1.53 g L−1 atm−1 . Carbon dioxide in the liquid phase has different equilibrium (Jones and Greenfield (1982)), and we represent them in Figure 2 and in equations (14-17). The mass transfer of CO2 from the liquid phase to the gas phase is in (14), the formation of carbonic acid (H2 CO3 ) is in (15), dissociation of H2 CO3 to + the ion bicarbonate ion (HCO− 3 ) and proton (H ) in (16), and the dissociation of bicarbonate to carbonate (CO2− 3 ) is in (17): CO2 (aq) ⇐⇒ CO2 (g) (14) (15) CO2 (aq) + H2 O ⇐⇒ H2 CO3 H2 CO3 ⇐⇒ HCO3− + H + (16) HCO3− ⇐⇒ CO32− + H +

(17)

2.5 Oxygen and Carbon dioxide in the gas phase The volumetric flow that enters the reactor Q contains oxygen CO2 −in , and it leaves the reactor with a concentration CO2 . The oxygen transfer rate (OT R) takes into account the supply of oxygen into the liquid phase reducing the concentration of oxygen in the gas phase. VG C˙ O2 = Q(CO2 −in − CO2 ) − OT R

(18)

The definition on (18) of operating volume (Vg = VL ), T yi ideal gas assumption (Ci = PRT ), and the Henry law that describes the equilibrium between the liquid and gas phase (DO2∗ = HO2 yO2 ) on equation: yO˙ 2 =

RT kL aO2 Q (yO2 −in − yO2 ) − (HO2 yO2 − DO2 ) (19) VL  PT 

The CO2 mol fraction in the gas phase has a similar expression with the mass transfer from the liquid to the gas phase: Q RT kL aCO2 yCO2 + (HCO2 yCO2 − DCO2 ) yCO ˙ 2 =− VL

PT

(20) We present a simplified scheme of O2 different summary table of the states, mass balances, and kinetics in Table 2. Table 2. Mass balance and kinetic model. Mass balance V˙ = Fin in + µX X˙ = − XF V

(Sin −S)Fin + RS V DOFin ˙ + OU R − OT R DO = − V yO Fin yO˙ 2 = − 2V + PRT OT R T DCO2 Fin ˙ + COE − COT CO2 = − V yCO2 Fin yCO ˙ 2 =− + PRT CT R V T

S˙ =

Kinetics S µ = Kµm+S S

RS = − YµX

XS

OU R =

µX YXO2

OT R = kL aO2 ∆DO2 COE =

µX YCO2 X

CT R = kL aCO2 ∆DCO2

3. PARAMETER ESTIMATION We proceed to estimate parameters with a nonlinear least square optimization technique to minimize the error between the experimental data and the solution of the set of differential equations, in the following manner: e(p) = y ˆ(p) − yexp (21)

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Table 3. Variable, value and units from the parameter estimation routine. Parameter YXO2 YXS YXCO2 α1 β1 µm Ks

Fig. 2. Simplified scheme of the O2 and CO2 states in the fermentation system. A sensor measures O2 and CO2 in the gas phase, the gas-liquid phase tend to physico-chemical equilibrium (equality of fugacities in each phases at temperature and pressure constant) promoting O2 transfer from the gas to the liquid phase via oxygen transfer rate (OTR). In the liquid phase C. glutamicum uses O2 during the oxygen uptake rate (OUR). In terms of carbon dioxide, the cell excretes CO2 (aq) (COE) in the aqueous phase, and CO2 (aq) has different equilibrium in water forming carbonic acid (H2 CO3 ), bicarbonate ion (HCO− 3 ), and 2− carbonate ion (CO3 ), furthermore CO2 (aq) transfers to the gas phase (CTR) giving the signal in the sensor CO2 (g). The main procedure has three main components (Foss and Heirung (2013)) (1) The objective function. (2) Decision variables that correspond to integers, real variables, or other function spaces. (3) Equality and inequality constraints. In a general mathematical formulation refers to the following problem: min f (p) = φ(p, y(y, u, p)) (22a) np p∈R

subject to ci (u, y(y, u, p)) = 0, i ∈ E cj (u, y(y, u, p)) ≥ 0, i ∈ I

(22b) (22c)

A vector of parameters p∗ is the solution of 22 with the constrains ci and cj if: e(p∗ ) ≤ f (p∗ ), ∀p ∈ p − p∗  < 

(23)

The minimization problem was implemented in Matlab, the constraints took into consideration lower and upper bounds within feasible physical ranges, and the results of the parameter estimation method are in Table 3.

Value 0.15 0.043 0.037 11.84 0.15 0.61 20.96

Unit g−1 g−1 g−1 [−] h−1 rpm−β h−1 g L−1

The results of the parameter estimation (table 3) and the simulations (Figure 3) show that we can describe the behaviour of the titers in the liquid and mole fractions in the gas phase. From this approach, we can estimate theoretically the dissolved CO2 in the liquid phase. The values of the oxygen mass transfer coefficient for kL aO2 are in the order of magnitude as previous reports (Garc´ıaOchoa and G´omez (2009)), and the ones of CO2 also since they are estimated from the one of O2 . In these experiments, the in-situ biomass sensor with the near infrared probe (NIR) shows the potential fast tracking use for on-line measurements, that can promote further control applications in the bioreactor. 4. ELASTICITY ANALYSIS The local elasticity analysis is the first step in an identifability analysis (Brun et al. (2002)), and it provides information about function response with parameter modifications (Tortorelli and Michaleris (1994)). The elasticity function is normalized, a feature that is beneficial to set the same basis of different states, models (Benton and Grant (1999)), and it eliminates numerical instability of the states generated with values close to zero. Therefore, dividing the sensitivity function of each state by its respective maximum constant term (i.e. xiref = S0 , Xmax , yO2max , yCO2max ) in eq (24) can remove this numerical issue, we define elasticity as: pj ∂xi pj ∆xi ≈ (24) Eij = xiref ∂pj xiref ∆pj The infinity norm of the elasticity function is a performance descriptor that quantifies the maximum change in an interval of time with a parameter perturbation (Skogestad and Postlethwaite (2007)): Eij (t)∞ = max(|Eij (t)|) i = X, S, P (25) Figure 4 presents the infinity norm of the elasticity of each state as a function of parameters. The sensitivity of substrate and biomass concentration towards the parameters Ks , YXS , µmax are the most relevant, therefore those parameters can be identified from the biomass and substrate concentration if the collinearity index of the subgroup is satisfied (Brun et al. (2002)). The oxygen gas phase composition yO2 is not sensitive to changes in the parameters, this is in agreement with previous reports that consider pseudo-state-conditions for OUR estimation (Royce and Thornhill (1991)). In contrast, the carbon dioxide gas phase composition yCO2 is sensitive to the yields of biomass formation YXS , carbon dioxide production (YCO2 X ) and the parameters of Monod growth, and thus it measurement is relevant to the bacteria growth



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Fig. 4. Infinity norm of the elasticity of the states as a function of the parameters. The states biomass (X) and substrate (S) are only sensitive to changes in µm , KS , and the yield YXS . The results indicate shows that oxygen in the the gas phase, yO2 is not sensitive to parameter perturbation. The dissolved oxygen (DO2 ) and carbon dioxide (DCO2 ) concentrations are highly sensitive to all parameters, and the CO2 gas phase composition yCO2 is sensitive to the yields of biomass formation (YXS ), CO2 production (YCO2 X ) and the parameters of Monod growth (µm , Ks ). and the media conditions. The dissolved oxygen (DO) and dissolved carbon dioxide (DCO2 ) are sensitive to all the parameters, hinting at the importance of O2 and CO2 in the liquid phase. More importantly, it is evident that the dissolved oxygen is a key bacterial descriptor because of its sensitivity to all the parameters, and thus it is affected heavily by the growth and the media conditions. 5. CONCLUSION

Fig. 3. Experimental (blue dots) data and model simulation of the states (dashed lines) of the fed-batch simulation. Initial conditions: V0 = 1L, S0 = 10g L−1 , X0 = 0.045 a.u.(NIR sensor) DO20 = 0.0089g L−1 , DCO20 = 0.0001g L−1 , yO20 = 0.21, yCO20 = 0, and parameters on Table 3. a) Biomass concentration in arbitrary units (a.u) measured with an Optek near infrared probe. b) Oxygen fraction in outlet gas measured with the external galvanic cell of the BlueInOne sensor. c) Substrate concentration simulation d) Dissolved oxygen concentration with insitu Hamilton liquid oxygen probe e) Carbon dioxide fraction in outlet gas measured with the external IRBlueInOne sensor f ) Measurement of stirrer speed g) Simulation of dissolved carbon dioxide concentration h) Simulation of volumetric mass transfer coefficients.

Herein, we showed that is possible to describe the behavior of Corynebacterium glutamicum in the liquid and gas phase in a single sugar system with the use of a nonstructured Monod growth model and a set of differential equations. The fermentation procedures made use of the NIR probes that correlate with optical density measurements. The probes can further develop state estimators that provide relevant information on noisy or immeasurable states. These estimators have the potential to improve control applications of bacterial bio-catalytic processes. ACKNOWLEDGEMENTS The authors would like to acknowledge Haakon E Holck and Christopher Sørmo for his comments, discussions and technical support. REFERENCES Judith Becker and Christoph Wittmann. Advanced biotechnology: Metabolically engineered cells for the bio-based production of chemicals and fuels, materials, and health-care products. Angewandte Chemie International Edition, 54(11):3328–3350, 2015. Tim G. Benton and Alastair Grant. Elasticity analysis as an important tool in evolutionary and population

236

Pedro A. Lira-Parada et al. / IFAC PapersOnLine 52-26 (2019) 231–237

ecology. Trends in Ecology & Evolution, 14(12):467 – 471, 1999. Robert Byron Bird, Warren Earl Stewart, and Edwin N Lightfoot. Transport Phenomena. John Wiley & Sons, 2007. Bastian Blombach and Gerd M Seibold. Carbohydrate metabolism in Corynebacterium glutamicum and applications for the metabolic engineering of l-lysine production strains. Applied microbiology and biotechnology, 86 (5):1313–1322, 2010. R. Bona and A. Moser. Modelling of growth of Corynebacterium glutamicum under biotin limitation. Bioprocess Engineering, 17(2):121–125, Jul 1997. Roland Brun, Martin K¨ uhni, Hansruedi Siegrist, Willi Gujer, and Peter Reichert. Practical identifiability of asm2d parameters—systematic selection and tuning of parameter subsets. Water research, 36(16):4113–4127, 2002. John J Carroll, John D Slupsky, and Alan E Mather. The solubility of carbon dioxide in water at low pressure. Journal of Physical and Chemical Reference Data, 20 (6):1201–1209, 1991. Yu-Cheng Chung, I-Lung Chien, and Der-Ming Chang. Multiple-model control strategy for a fed-batch high cell-density culture processing. Journal of Process Control, 16(1):9–26, 2006. Pinaki Dey and Parimal Pal. Modelling and simulation of continuous l (+) lactic acid production from sugarcane juice in membrane integrated hybrid-reactor system. Biochemical engineering journal, 79:15–24, 2013. Bjarne Foss and Tor Aksel N Heirung. Merging optimization and control. Lecture Notes, 2013. F´elix Garc´ıa-Ochoa and Emilio G´ omez. Bioreactor scaleup and oxygen transfer rate in microbial processes: an overview. Biotechnology advances, 27(2):153–176, 2009. F´elix Garc´ıa-Ochoa and Emilio G´ omez-Castro. Estimation of oxygen mass transfer coefficient in stirred tank reactors using artificial neural networks. Enzyme and microbial technology, 28(6):560–569, 2001. F´elix Garc´ıa-Ochoa and Emilio G´ omez-Castro. Theoretical prediction of gas–liquid mass transfer coefficient, specific area and hold-up in sparged stirred tanks. Chemical engineering science, 59(12):2489–2501, 2004. Stephen Goldrick, Andrei Tefan, David Lovett, Gary Montague, and Barry Lennox. The development of an industrial-scale fed-batch fermentation simulation. Journal of biotechnology, 193:70–82, 2015. John Ingham, Irving J Dunn, Elmar Heinzle, Jir´ı E Prenosil, and Jonathan B Snape. Chemical engineering dynamics: an introduction to modelling and computer simulation. John Wiley & Sons, 2008. Suah Jo, Jinkyung Yoon, Sun-Mi Lee, Youngsoon Um, Sung Ok Han, and Han Min Woo. Modular pathway engineering of Corynebacterium glutamicum to improve xylose utilization and succinate production. Journal of biotechnology, 258:69–78, 2017. Rodney P Jones and Paul F Greenfield. Effect of carbon dioxide on yeast growth and fermentation. Enzyme and Microbial Technology, 4(4):210–223, 1982. J¨ orn Kalinowski, Brigitte Bathe, Daniela Bartels, Nicole Bischoff, Michael Bott, Andreas Burkovski, Nicole Dusch, Lothar Eggeling, Bernhard J Eikmanns, Lars Gaigalat, et al. The complete Corynebacterium glutam-

icum ATCC 13032 genome sequence and its impact on the production of l-aspartate-derived amino acids and vitamins. Journal of biotechnology, 104(1-3):5–25, 2003. Noor Salam Khan, Indra Mani Mishra, RP Singh, and Basheshwer Prasad. Modeling the growth of Corynebacterium glutamicum under product inhibition in lglutamic acid fermentation. Biochemical Engineering Journal, 25(2):173–178, 2005. P Kiefer, E Heinzle, and C Wittmann. Influence of glucose, fructose and sucrose as carbon sources on kinetics and stoichiometry of lysine production by Corynebacterium glutamicum. Journal of Industrial Microbiology and Biotechnology, 28(6):338–343, 2002. Wolf Kl¨ockner, Riad Gacem, Tibor Anderlei, Nicole Raven, Stefan Schillberg, Clemens Lattermann, and Jochen B¨ uchs. Correlation between mass transfer coefficient k l a and relevant operating parameters in cylindrical disposable shaken bioreactors on a benchto-pilot scale. Journal of biological engineering, 7(1):28, 2013. Sau L Lee, Thomas F O’Connor, Xiaochuan Yang, Celia N Cruz, Sharmista Chatterjee, Rapti D Madurawe, Christine MV Moore, X Yu Lawrence, and Janet Woodcock. Modernizing pharmaceutical manufacturing: from batch to continuous production. Journal of Pharmaceutical Innovation, 10(3):191–199, 2015. Andreas L¨ ubbert and Sten Bay Jørgensen. Bioreactor performance: a more scientific approach for practice. Journal of Biotechnology, 85(2):187–212, 2001. Nicole Paczia, Anke Nilgen, Tobias Lehmann, Jochem G¨atgens, Wolfgang Wiechert, and Stephan Noack. Extensive exometabolome analysis reveals extended overflow metabolism in various microorganisms. Microbial cell factories, 11(1):122, 2012. Parimal Pal, Ramesh Kumar, D VikramaChakravarthi, and Sankha Chakrabortty. Modeling and simulation of continuous production of l (+) glutamic acid in a membrane-integrated bioreactor. Biochemical Engineering Journal, 106:68–86, 2016. KA Presser, DA Ratkowsky, and T Ross. Modelling the growth rate of Escherichia coli as a function of ph and lactic acid concentration. Appl. Environ. Microbiol., 63 (6):2355–2360, 1997. G Reyman. Modelling and control of fed-batch fermentation of bakers’ yeast. Food Control, 3(1):33–44, 1992. Patrick NC Royce and Nina F Thornhill. Estimation of dissolved carbon dioxide concentrations in aerobic fermentations. AIChE journal, 37(11):1680–1686, 1991. Rolf Sander. Compilation of henry’s law constants (version 4.0) for water as solvent. Atmospheric Chemistry & Physics, 15(8), 2015. A Schmid, JS Dordick, B Hauer, Al Kiener, M Wubbolts, and B Witholt. Industrial biocatalysis today and tomorrow. Nature, 409(6817):258, 2001. Matthew Scott and Terence Hwa. Bacterial growth laws and their applications. Current opinion in biotechnology, 22(4):559–565, 2011. Sigurd Skogestad and Ian Postlethwaite. Multivariable feedback control: analysis and design, volume 2. Wiley New York, 2007. Mathieu Sp´erandio and Etienne Paul. Determination of carbon dioxide evolution rate using on-line gas analysis during dynamic biodegradation experiments. Biotech-



Pedro A. Lira-Parada et al. / IFAC PapersOnLine 52-26 (2019) 231–237

nology and bioengineering, 53(3):243–252, 1997. Kaibiao Sun, Andrzej Kasperski, Yuan Tian, and Lansun Chen. Modelling of the Corynebacterium glutamicum biosynthesis under aerobic fermentation conditions. Chemical engineering science, 66(18):4101–4110, 2011. D. A. Tortorelli and P. Michaleris. Design sensitivity analysis: Overview and review. Inverse Problems in Engineering, 1(1):71–105, 1994. John Villadsen, Jens Nielsen, and Eli Keshavarz-Moore. Bioreaction Engineering Principles. Springer, 2011. Henry Y Wang, Charles L Cooney, and Daniel IC Wang. Computer-aided baker’s yeast fermentations. Biotechnology and bioengineering, 19(1):69–86, 1977. Volker F Wendisch, Luciana Fernandes Brito, Marina Gil Lopez, Guido Hennig, Johannes Pfeifenschneider, Elvira Sgobba, and Kareen H Veldmann. The flexible feedstock concept in industrial biotechnology: metabolic engineering of Escherichia coli, Corynebacterium glutamicum, Pseudomonas, Bacillus and yeast strains for access to alternative carbon sources. Journal of biotechnology, 234:139–157, 2016. Zizhuo Xing, Brian M Kenty, Zheng Jian Li, and Steven S Lee. Scale-up analysis for a cho cell culture process in large-scale bioreactors. Biotechnology and bioengineering, 103(4):733–746, 2009.

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