Application of hybrid cybernetic model in simulating myeloma cell culture co-consuming glucose and glutamine with mixed consumption patterns

Process Biochemistry 48 (2013) 955–964

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Process Biochemistry journal homepage: www.elsevier.com/locate/procbio

Application of hybrid cybernetic model in simulating myeloma cell culture co-consuming glucose and glutamine with mixed consumption patterns J. Geng a , J.X. Bi b , A.P. Zeng c , J.Q. Yuan a,∗ a b c

Department of Automation, Shanghai Jiao Tong University, Key Laboratory of System Control and Information Processing, 800 Dongchuan Road, 200240Shanghai, PR China School of Chemical Engineering, University of Adelaide, SA5005, Australia Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology (TUHH), Denickestrasse 15, D-21073 Hamburg, Germany

a r t i c l e

i n f o

Article history: Received 9 November 2012 Received in revised form 24 February 2013 Accepted 30 March 2013 Available online 6 April 2013 Keywords: Hybrid cybernetic model (HCM) Elementary modes (EMs) Mammalian cell culture Metabolic network Model validation

a b s t r a c t A dynamic model called hybrid cybernetic model (HCM) based on structured metabolic network is established for simulating mammalian cell metabolism featured with partially substitutable and partially complementary consumption patterns of two substrates, glucose and glutamine. Benefiting from the application of elementary mode analysis (EMA), the complicated metabolic network is decomposed into elementary modes (EMs) facilitating the employment of the hybrid cybernetic framework to investigate the external and internal flux distribution and the regulation mechanism among them. According to different substrate combination, two groups of EMs are obtained, i.e., EMs associated with glucose uptake and simultaneous uptake of glucose and glutamine. Uptake fluxes through various EMs are coupled together via cybernetic variables to maximize substrate uptake. External fluxes and internal fluxes could be calculated and estimated respectively, by the combination of the stoichiometrics of metabolic networks and fluxes through regulated EMs. The model performance is well validated via three sets of experimental data. Through parameter identification of limited number of experimental data, other external metabolites are precisely predicted. The obtained kinetic parameters of three experimental cultures have similar values, which indicates the robustness of the model. Furthermore, the prediction performance of the model is successfully validated based on identified parameters. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction Mammalian cell cultures are one of the most popular expression systems to produce glycosylated therapeutic recombinant proteins [1,2], monoclonal antibodies [3], viral vaccines [4,5] and hormones [6], which could find widespread applications in biological science and technology. Unfortunately, two major issues, i.e., low cell viability and low protein production are frequently observed during mammalian cell cultures since the nutrient limitation as well as the accumulation of toxic metabolites [7], are often found to be bottle necks for its applications. In order to solve these problems, understanding the in vivo metabolic regulation of mammalian cell would brighten the way through which industrial production process should be designed and optimized based on the concept of Quality by Design (QbD) [8]. It has been broadly demonstrated that constructing mathematical models of biological process could provide the insight on cell growth process, subsequently control and optimize the growth process. Starting from original unstructured model which did not take care of the intracellular metabolism,

∗ Corresponding author. Tel.: +86 21 34204055; fax: +86 21 34204055. E-mail addresses: [email protected], [email protected] (J.Q. Yuan). 1359-5113/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.procbio.2013.03.019

there have been great progresses achieved during the past decade including flux balance analysis (FBA), metabolic flux analysis (MFA) and other structured modeling approaches. Nevertheless, there are some challenging issues in the existed models where much effort needs to be devoted. For example, simple unstructured model of mammalian cell culture was investigated aiming to unveil the physiology and regulation of the mammalian cell metabolism. The limitation of the unstructured model is that it can only provide a qualitative analysis since this model does not consider the detailed metabolic pathways [9]. Compared with unstructured models, MFA based structured models with different sizes of metabolic networks could embrace all significant pathways present in the mammalian cell metabolism. By making full quantitative use of stoichiometric information, MFA could provide a good insight on the cell metabolism and how they could react with each other in a given environment [5,10]. However, MFA is still relatively dependent on experiments. When external measurements are not sufficient to provide all the information required to obtain a unique solution, MFA would be underdetermined [11]. The determination of intracellular fluxes is then required to solve this problem through the use of isotopic tracer experiments, which is extremely expensive and hardly affordable to many laboratories. Regarding the metabolic behavior of mammalian cell culture, the

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Nomenclature c ej ejmax

cell dry weight per unit volume of culture (g/L) enzyme level associated with EMs maximum enzyme level associated with EMs

ejrel fC,j

relative enzyme level associated with EMs numbers of carbon element contained in the substrates consumed through the jth EM K Michaelis–Menten constant (mM) KAMM, GLN ammonia inhibition constant (mM) kE,j constant for inducible synthesis of enzyme associated with the jth EM (1/h) KLAC, GLC lactate inhibition constant (mM) kjmax maximum uptake rate associated with EMs (mmol/g DW/h) pj return-on-investment associated with the jth EM r vector of regulated fluxes (mmol/g DW/h) vector of uptake rate through EMs (mmol/g DW/h) rM rM,j regulated reaction rate for the jth EM (mmol/g DW/h) kin rM,j kinetic reaction rate for the jth EM (mmol/g DW/h) regulated synthesis rate of enzyme for the jth EM rME,j (mmol/g DW/h) kin rME,j kinetic synthesis rate of enzyme for the jth EM (mmol/g DW/h) Sx stoichiometric coefficient matrix for extracellular metabolites cybernetic variable controlling synthesis of enzyme uj associated with the jth EM vj of cybernetic variable controlling synthesis of enzyme associated with the jth EM vector of concentration of extracellular metabolites x xALA concentration of alanine (mM) concentration of ammonia (mM) xAMM xBIOM concentration of biomass (g/L) concentration of substrate of glucose (mM) xGLC xGLN concentration of substrate of glutamine (mM) xLAC concentration of lactate (mM) EM matrix Z Greek letters ˛j constitutive synthesis rate of enzyme for the jth EM (1/h) ˇj enzyme degradation rate for the jth EM (1/h) specific growth rate (1/h)  Subscripts AMM ammonia GLC glucose glutamine GLN LAC lactate Superscripts kinetic kin max maximum rel relative Metabolites adenosine diphosphate ADP AKG 2-oxoglutarate ALA alanine ATP adenosine triphosphate biomass BIOM

CO2 E4P F6P G6P GAP GLC GLN GLU LAC MAL NAD NADH NADP

carbon dioxide erythrose-4-phosphate fructose-6-phosphate glucose-6-phosphate glyceraldehyde-3-phosphate glucose glutamine glutamate lactate malate nicotinamide adenine dinucleotide, oxidized nicotinamide adenine dinucleotide, reduced nicotinamide adenine dinucleotide phosphate, oxidized NADPH nicotinamide adenine dinucleotide phosphate, reduced ammonia NH3 O2 oxygen pyruvate PYR R5P ribose-5-phosphate S7P sedoheptulose-7-phosphate X5P xylulose-5-phosphate

consideration of both stoichiometrics of the metabolic network and inbuilt cell regulation is essential but still challenging to construct a completely dynamic mathematical model. Therefore, it will be of great importance to develop an effective modeling approach to explore the metabolic behavior of mammalian cell culture independent on the external measurements, which will be undoubtedly beneficial to the industry production process. Hybrid cybernetic modeling (HCM), recently developed by Kim et al. [12], provides an alternative approach and a promising future as it fulfills dynamics by including both stoichiometry and cell regulation on a comprehensive scale, which has been proven to be effective in dealing with large scale metabolic network involving uptake of two substitutable substrates [13] and improving ethanol productivity using mixed culture [14]. The cybernetic postulate indicates that metabolic regulation is controlled response of the organism to its environment toward fulfilling a survival goal, through extended adaption to evolution [15]. The previous works have demonstrated that HCM can be applied in describing both single substrate consumption [12] and substitutable mixed substrates consumptions [12–14]. However, to the best of our knowledge, there is still no report on applying the HCM into mammalian cell culture, in which two substrates featured with partially substitutable and partially complementary patterns are involved. In this work, we applied the hybrid cybernetic framework into the mammalian cell culture for the first time. Through considering both stoichiometrics of the metabolic network and inbuilt cell regulation mechanism, we try to uncover the underlying regulation mechanism between the partially substitutable and partially complementary consumption of glucose and glutamine. With the identified parameters, the model can be used to reasonably predict the concentration variation of alanine and ammonia in different experiments quite well. The model development is based on a metabolic network comprising 19 reactions. The carbon and nitrogen resource, glucose and glutamine are considered as the two major substrates of the cell culture. Lactate, alanine as well as ammonia are the main byproducts during cell growth. External and internal metabolites are linked through Glycolysis Pathway, Pentose Phosphate Pathway, Glutaminolytic Pathway and Tricarboxylic Acid (TCA) Cycle. In combination with metabolic network decomposition

J. Geng et al. / Process Biochemistry 48 (2013) 955–964

to subsets of elementary modes (EMs), HCM pictures regulation as the optimal distribution of substrate uptake fluxes among EMs such that substrate uptake is maximized. EMs, which are uniquely derived through convex analysis [16], are a minimal set of metabolic pathways by which all feasible metabolic routes can be completely described [17]. Through Elementary mode analysis (EMA), the metabolic network comprising 19 reactions is decomposed into 14 EMs, in which 3 EMs consume glucose and glutamine simultaneously while the rest 11 EMs consume glucose only. Through quasi-steady-state approximation, the model eliminates the necessity to identify kinetic parameters for intracellular reactions. Thus all kinetic parameters are associated with uptake rates of substrates through different EMs. The state variables including substrate (including glucose and glutamine) concentrations, byproduct (including lactate and alanine) concentrations and biomass concentration, which are linked to the regulated uptake distribution rates of EMs through a bioreactor model are then calculated with time evolution after fitting key parameters. Finally, the model performance is validated through parameter identification of three batches of experimental cultures by nonlinear optimization routine. Furthermore, through picturing the profile of cybernetic variables, the relationship among various EMs is explored to illustrate the partially substitutable and partially complementary consumption patterns of mammalian cell culture. The similar values of three sets of kinetic parameters corresponding to three batches of experiments, indicate the robustness of the model efficiency when encountering environment disturbance such as feeding strategy. 2. Materials and methods 2.1. Cell line and culture conditions The myeloma cell line used in this work is X63-Ag-8.653. The basic medium used in flask and spinner cultures is RPMI-1640, which is composed of glucose and glutamine supplemented with extra 2 mM glutamine, 80 ␮g/ml gentamicin and 10% fetal calf serum (FCS) (Invitrogen, UK). FM1 and FM2 are used as the feeding media. FM1 contains 100 mM glucose and 20 mM glutamine with 10×RPMI. FM2 contains 99.4 mM glucose and 22 mM glutamine with 1×RPMI. 2.2. Experiment description Exp. 1: Batch culture for 134 h with initial volume of 120 ml. Exp. 2: Fed-batch culture with pulse feedings at 54.5 h and 113 h. The initial volume is 120 ml. At 54.5 h, 2.5 ml of FCS and 11.5 ml of FM2 were fed into the medium such that glucose concentration reaches 11.4 mM. At 113 h, 10 ml of FCS and 9.4 ml of FM (4.7 ml of FM1 4.7 ml of FM2) was fed after 19.4 ml of supernatant was removed at 113 h. The culture was then continued for another 21 h. Exp. 3: Fed-batch culture with pulse feedings at 54.5 h, 73 h and 113 h. The initial volume is 120 ml. At 54.5 h, 2.5 ml of FCS and 3.5 ml of FM2 were fed into the medium such that glucose concentration reaches 5.6 mM. 8 ml of FCS and 4 ml of FM2 were fed at 73 h. Finally, 10 ml of FCS and 1.3 ml of FM1 was fed after 11.3 ml of supernatant was removed at 113 h. The culture was then continued for another 21 h. 2.3. Analytical methods Viable and dead cell densities were determined by the trypan blue exclusion method using a haemocytometer. Glucose and lactate concentrations were measured with a YSI2700 (Ohio, USA) glucose and l-lactate analyzer. Ammonia concentration was determined using enzyme-based assay kits. Glutamine and other amino acid concentrations were measured by HPLC (KONTRON, Germany) and evaluated with the Software Kroma2000.

3. HCM model of mammalian cell culture

957

where x is the vector of nx concentrations of extracellular components including biomass concentration (c), Sx is the matrix stoichiometrically related flux vector (r) to the exchange fluxes. Division by biomass concentration c of x is needed to represent the specific concentration. Under quasi-steady-state approximation, the flux vector can be represented by a convex combination of EMs [17], which could be described as: r = ZrM

(2)

where Z is the EM matrix, rM is the vector of fluxes through EMs. Substitution of Eq. (1) with the above relationship will result in: dx = Sx ZrM c dt

(3)

The uptake flux of jth EM, represented by rM,j , is controlled by the enzyme concentration and enzyme activity of the jth EM, kin rM,j = vj ejrel rM,j

(4)

where vj is the cybernetic variable corresponding to the enzyme activity of the jth EM, higher value of vj would promote the enzyme synthesis rate. The detailed expression of vj is shown below in Eq. kin is the kinetic expression of the unregulated uptake flux of (8). rM,j jth EM, ejrel is the relative enzyme level of the jth EM, the definition of relative enzyme level is: ejrel =

ej

(5)

ejmax

where ej represents the enzyme concentration of the jth EM. ejmax represents the maximum level of the enzyme concentration, and ejmax could be calculated through following equation [13,18]: ejmax =

˛j + kE,j

(6)

ˇj + YB,j kjmax

where YB,j is the biomass yield values of the jth EM. kjmax is the kinetic parameter of the jth EM. ˛j and ˇj are the constitutive synkin is the enzyme synthesis rate. thesis rate and degradation rate, rME,j The differential equation for enzymes can be written as: dej dt

kin = ˛j + uj rME,j − (ˇj + )ej

(7)

where uj is the cybernetic variable corresponding to the induction of enzyme synthesis rate, higher value of uj indicates the related enzyme synthesis rate would be promoted and vice versa. The expression of uj is shown below in Eq. (8). ˛j and ˇj are the conkin is the enzyme stitutive synthesis rate and degradation rate, rME,j synthesis rate. The four terms of the right-hand side represent constitutive synthesis rates, inducible synthesis rates, degradation rate, as well as dilution rate by growth. The formulations of cybernetic variables uj and vj are determined according to “Matching Law” and “Proportional Law” [19]: uj =

p

j

pk

and vj =

pj max(pk )

(8)

where pj is the return-on-investment associated with the jth EM. In this paper, pj is chosen as the carbon uptake rate indicated as follows:

3.1. Model framework Dynamic mass balance equation for extracellular metabolites is formulated as below:

kin pj = fC,j ejrel rM,j

1 dx = Sx r c dt

where fC,j represents for the carbon number per unit mole of substrate consumed through the jth EM.

(1)

(9)

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Table 1 List of all the 19 reactions in the network. i

Reaction formula

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14

GLC + ATP → G6P + ADP G6P →F6P F6P + ATP → 2 GAP + ADP GAP + 2 ADP + NAD → PYR + NADH + 2 ATP PYR + NADH → LAC + NAD G6P + 2 NADP → R5P + 2 NADPH + CO2 PYR + MAL + 3 NAD → AKG + 3 NADH + 2 CO2 AKG + 2 NAD + ADP → 2 NADH + CO2 + ATP + MAL GLN → GLU + NH3 PYR + GLU → ALA + AKG 2 NADH + 6 ADP + O2 → 2 NAD + 6 ATP MAL + NADP → PYR + CO2 + NADPH ATP → ADP 3.92 GLU + 1.44 NH3 + 0.124 G6P + 0.52 R5P + 1.68 GAP + 4.92 PYR + 0.76 MAL + 29.6 ATP + 7.52 NADPH + 9.2 NAD → BIOM + 2.92 AKG + 9.2 NADH + 4.8 CO2 + 29.6 ADP + 7.52 NADP R5P ↔ X5P R5P + X5P ↔ S7P + GAP S7P + GAP ↔ F6P + E4P X5P + E4P ↔ F6P + GAP GLU + NAD ↔ NADH + NH3 + AKG

R15 R16 R17 R18 R19

3.2. Elementary model analysis of the metabolic network Developed by Schuster and co-workers, EM becomes one of the most useful concepts emerging from the investigation of stoichiometric matrix of the metabolic network [20]. EM is a minimal set of reactions that can be functional at steady state, with the enzymes weighted by the relative flux they need to carry for the mode being functional [17]. A unique set of EMs could be obtained through metabolic network decomposition using convex analysis [16], which are composed of the optimal routines converting the substrate to the final products [21]. All the feasible fluxes at steady state could then be described through the linear combination of these EMs. The central metabolic networks are similar among different mammalian cells, such as hybridoma cells, Chinese hamster ovary cells and Madin Darby canine kidney cells [11]. In this work, the hybridoma cells provided by Zupke and Sinskey [22] is adopted for investigation. Since what we are interested is the relationship between cell growth and byproduct formulation happened during the central metabolism, it is reasonable to assume that the protein synthesis and amino acid metabolism are not involved. The corresponding metabolic network is presented in Fig. 1. Glucose and glutamine are considered as the two substrates which act as the anabolic precursors as well as energy sources. The metabolic network composes glycolytic pathway, pentose phosphate pathway, glutaminolytic pathway and TCA cycle. The full list of reactions involved in the network is shown in Table 1. Among the total 19 reactions, the first 14 reactions are irreversible while the last 5 reactions are reversible. The full names of the abbreviated metabolites in the reaction list are indicated in the Nomenclature part. Eight metabolites, i.e., glucose (GLC), glutamine (GLN), oxygen (O2 ), carbon dioxide (CO2 ), lactate (LAC), ammonia (NH3 ), alanine (ALA) and biomass (BIOM) are considered as extracellular metabolites while the rest are intracellular ones. Using Metatool v5.1[23], a set of EMs which contains 14 EMs is obtained as shown in Table 2, denoted as Zi,1 , . . ., Zi,4 , respectively. Through different combination of the 14 EMs, all the other feasible flux vectors at steady state could be described. Therefore, the obtained 14 EMs are used in our modeling framework. For each EM, there is one enzyme weighted by the relative flux they need to carry for the model being functional. In Table 2, each number in the box represents a relative stoichiometric ratio of the flux through the ith

EM. Each row corresponds to the ith reaction listed in Table 1, and each column corresponds to the involved EM. For example, the first row corresponds to R1, which is related with glucose consumption; the glutamine consumption which is the ninth row, corresponds to R9; and biomass formation in the fourteenth row corresponds to R14. The minus symbol in the last row means the reversible reaction takes the reverse direction. For convenience, we denote EMs listed in Table 1 as EM1 –EM14 . From the values of each EM in Table 2, we could see that EM2 , EM10 and EM11 consume only glucose while the rest 11 EMs consume both glucose and glutamine. 3.3. Model construction With the EMs provided in Table 2, the mammalian cell culture can be modeled using HCM framework. The basic tenet of HCM approach and other cybernetic approach is to maximize certain goal through a regulated way in substrate distribution [12]. Since there are two substrates involved, i.e., glucose and glutamine, EMs consuming different substrates can then be regulated together through the cell culture environment. The concentrations of glucose, glutamine, lactate, ammonia, alanine and biomass are addressed here. Considering the case if there is feeding strategies, the general form of the dynamic equation for external metabolites in Eq. (3) can be rewritten as:

⎡

xGLC

⎤

⎡

xGLC,f − xGLC

⎤

⎡ ⎤ ⎢x ⎥ ⎢x ⎥ rM,1 ⎢ GLN ⎥ ⎢ GLN,f − xGLN ⎥ ⎢ ⎥ ⎢ ⎥ ⎢r ⎥ ⎢ ⎥ ⎢ −xBIOM ⎥ ⎢ M,2 ⎥ d ⎢ xBIOM ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ = Sx Z ⎢ ⎥ ⎢ . ⎥c + D⎢ dt ⎢ x ⎥ ⎢ ⎥ −x ALA ⎣ .. ⎦ ⎢ ALA ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ −x ⎣ xAMM ⎦ ⎣ ⎦ AMM rM,14

(10)

−xLAC

xLAC

where D is the dilution rate, xGLC,f and xGLN,f are glucose concentration and glutamine concentration in the feeding medium, respectively. The numerical values of Sx is shown in Eq. (11). Each row corresponds to the six metabolites as shown in the left side in Eq. (10), each column corresponds to the reactions listed in Table 1. Each value indicates the stoichiometric value of metabolite in the corresponding reaction. The minus symbol indicates that the metabolite is consumed while the positive value shows that the metabolite is produced from the corresponding reaction.

⎡ −1 ⎢ ⎢ ⎢ ⎣

Sx = ⎢

0

⎤

0 0

0

0

0 0

0

0

0 0 0

0

0 0 0

0

0

0

0 0

0

0

0 0

0 −1

0

0 0 0

0

0 0 0

0

0

0 0

0

0

0 0

0

0

0

0 0 0

1

0 0 0

0

0⎥

0

0 0

0

0

0 0

0

0

1 0 0 0

0

0 0 0

0

0

0 0

0

0

0 0

0

1

0

0 0 0

−1.44

0 0 0

0 1

0

0 0

0 1 0 0

0

0

0

0 0 0

0

0 0 0

0

0⎥

⎥ ⎦

0⎥ 0

(11) The regulated uptake flux rates rM,j are given in a modified Michaelis–Menten form as follows: ⎧ xGLC xGLN ⎪ j= / 2, 10, 11) ⎨ vj ejrel kjmax K + x K + xGLN GLC GLN GLC,j kin rM,j = (12) xGLC ⎪ vj erel kmax (j = 2, 10, 11) ⎩ j j KGLC,j + xGLC where kjmax denotes the maximum uptake rate associated with the kin are given as follows: jth EM. Similarly, kinetic expressions of rME,j

kin rME,j

⎧ ⎪ ⎨ kE,j K

xGLC xGLN (j = / 2, 10, 11) + xGLC KGLN + xGLN = xGLC ⎪ (j = 2, 10, 11) ⎩ kE,j KGLC,j + xGLC GLC,j

(13)

J. Geng et al. / Process Biochemistry 48 (2013) 955–964

959

Fig. 1. Metabolic network of mammalian cell metabolism.

Table 2 Elementary modes of the metabolic network. i

Zi,1

Zi,2

Zi,3

Zi,4

Zi,5

Zi,6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

3.73 0.5 2.3 4.1 0 3.13 0 0.63 1.47 0 5.62 0 11.8 0.83 1.8 0.9 0.9 0.9 −1.8

0.5 0.5 0.5 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 −1

0.76 0.69 0.5 0 1.40 0 0 4.47 5.01 0 7.69 4.06 33.4 0.54 −0.18 −0.09 −0.09 −0.09 2.89

0.54 0.489 0.36 0 0 0 0 3.19 3.57 1 5.49 2.89 23.8 0.38 −0.13 −0.07 −0.07 −0.06 1.06

0.54 0.489 0.36 0 0 0 1 4.19 3.57 0 8.49 2.89 42.8 0.39 −0.13 −0.07 −0.07 −0.06 2.06

4.16 0.49 1.83 0 0 3.35 0 14.6 17.2 0 30.1 12.7 113 2.58 1.34 0.67 0.67 0.67 7.11

Zi,7 7.13 4.04 4.04 0 0 2.5 0 34.8 39.6 7.5 63.6 31.2 263 4.81 0 0 0 0 13.3

Zi,8 7.13 4.04 4.04 0 0 2.5 7.5 42.3 39.6 0 86.1 31.2 405 4.81 0 0 0 0 20.7

Zi,9 7.13 4.04 4.04 0 7.5 2.5 0 34.8 39.6 0 63.6 31.2 263 4.81 0 0 0 0 20.7

Zi,10

Zi,11

Zi,12

Zi,13

0.5 0.5 0.5 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0

0.5 0.5 0.5 1 0 0 1 1 0 0 3 0 20 0 0 0 0 0 0

1.04 0.80 0.80 1 0 0.19 0 2.62 2.99 1.57 4.79 2.35 20.8 0.36 0 0 0 0 0

1.01 0.96 0.84 1 0 0 0 3 3.36 1.94 5.17 2.72 23.4 0.36 −0.13 −0.06 −0.06 −0.06 0

Zi,14 2.66 0.35 1.54 2.28 0 2.21 0 2.41 3.24 0 7.35 1.78 22.4 0.83 1.19 0.59 0.59 0.59 0

960

J. Geng et al. / Process Biochemistry 48 (2013) 955–964

Fig. 2. Performance of HCM for mammalian cell culture with kinetic parameters fitted to Exp. 1. Solid lines: model simulation results; dashed line: prediction results; hollow circles: experimental data.

As it is well known that cell growth would be inhibited by the over producing of lactate and ammonia [24], the inhibition term should be incorporated in the reaction rate and enzyme synthesis rate expression: kin rM,j = rM,j

1 1 1 + xGLC /KLAC,GLC 1 + xGLN /KAMM,GLN

kin rME,j = rME,j

1 1 1 + xGLC /KLAC,GLC 1 + xGLN /KAMM,GLN

(14) (15)

In the above equations, the initial relative enzyme concentration (ejrel,0 ) is set as 0.2 according to previous literatures [18], and a single set of Michaelis and inhibition constants (i.e., KLAC, GLC and KAMM, GLN ) is assigned for each experiment. Parameters related with enzyme balance equations (kE,j , ˛j , ˇj ) are set to be the same among all EMs, with values taken from previous report [25]. Kinetic parameters of the maximum flux uptake rate (kjmax ) are determined through parameter identification. Since there are 14 EMs in total, to avoid the over parameterization problem, global optimization method is firstly applied to obtain a relatively reasonable initial guess of the kinetic parameters, and local optimization method is then proceeded for getting further close fitting with experimental data. 4. Results and discussion The model performance is validated based on three different batches of experimental data, including one batch experiment (Exp. 1) and two fed-batch experiments (Exp. 2 and Exp. 3), respectively. The corresponding simulation results are indicated in Figs. 2–4,

Fig. 3. Performance of HCM for mammalian cell with kinetic parameters fitted to Exp. 2. Solid lines: model simulation results; dashed lines: prediction results; hollow circles: experimental data.

respectively. The constructed model applied in each experiment contains totally 24 parameters, 14 of which are kinetic parameters while others are batch independent constants including Michaelis–Menten constants associated with glucose-consuming and glutamine-consuming, two inhibition constants associated with glucose and glutamine and parameters related with enzyme balance equation, respectively. As mentioned, the kinetic parameters kjmax are determined through parameter identification for each experiment. The Michaelis–Menten constants are determined from data fitting process with data of batch experiment and then fixed and applied to the other two experiments, fed-batch Exp. 2 and fedbatch Exp. 3. The initial guesses for the Michaelis–Menten constants of glucose and glutamine is set as 0.1 mM and 0.5 mM respectively. The inhibition constants are determined with their typical values suggested from the literature [24]. The values for initial relative enzyme concentration (ejrel,0 ) and parameters related with enzyme balance equations (kE,j , ˛j , ˇj ) are set to be the same among all EMs. The values of all batch independent parameters are given in Table 3. The kinetic parameters of three cultures are shown in Table 4. Fig. 2 shows the profile of model fitting results based on data points from Exp. 1 batch culture. The experimental data of time dependent concentration variation for glucose, glutamine, cell mass and lactate are selected to identify the kinetic parameters. As can be seen from the data points shown in Fig. 2, although the initial concentrations of both glucose and glutamine are very high, the low initial enzyme concentration and its poor activity still lead to low initial cell growth rate and lactate production rate. When the concentration of enzymes increases to an appreciable level, glucose and glutamine start to be consumed with high consumption

J. Geng et al. / Process Biochemistry 48 (2013) 955–964

961

Table 4 Batch dependent parameter values.

Fig. 4. Performance of HCM for fed batch Exp. 3 with kinetic parameters fitted to Exp. 1. Solid lines: model simulation results; dashed lines: prediction results; hollow circles: experimental data.

rates. When glucose and glutamine are almost depleted, there is no enough nutrients to activate enzyme synthesis, as a result, cell growth, lactate production, ammonia production and alanine production are inhibited. Accordingly, the simulation results (lines shown in Fig. 2) exhibit the similar trend on concentration variation along with reaction time and the values match well with the experimental data, which clearly indicates the high model performance when applied in simple batch culture of Exp. 1. Based on the identified parameters from the simulation results, we predicted the time dependent concentrations of both alanine and ammonia, and compared them with the corresponding experimental data at each time point, as shown in Fig. 2a and b, respectively. Notably, the predicted results exhibit good agreement with experimental data, which further confirm the availability of the model performance. Herein, glucose and glutamine provide resources not only for lactate production and alanine production, respectively, but also for

Table 3 Batch independent parameter values. Parameter

Unit

Value

kE,j ˛j ˇj KLAC, GLC KAMM, GLN KGLC KGLN

1/h 1/h 1/h mM mM mM mM

0.5 0.005 0.98 30 15 0.5 2

Parameter

Unit

Exp. 1

Exp. 2

Exp. 3

k1max k2max k3max k4max k5max k6max k7max k8max k9max max k10 max k11 max k12 max k13 max k14

mM/h mM/h mM/h mM/h mM/h mM/h mM/h mM/h mM/h mM/h mM/h mM/h mM/h mM/h

6.68 0.09 0.13 0.022 0.54 0.14 0.79 0.77 0.24 4.57 0.15 11.08 1.65 0.21

7.49 0.08 0.10 0.020 0.52 0.10 0.72 0.65 0.22 3.96 0.15 12.69 1.63 0.20

7.94 0.09 0.11 0.019 0.49 0.15 0.85 0.81 0.24 3.38 0.16 12.83 1.56 0.20

cell growth and ammonia production, which are indicated as partially complementary and partially substitutable [26]. In addition, with the cybernetic regulation variables, HCM could describe the initial enzyme adaptation process well. Besides the simple batch experiment, the model performance is further verified by fitting with experimental data from more complicated fed-batch experiments, as shown in Fig. 3 for Exp. 2 and Fig. 4 for Exp. 3, respectively. In Exp. 2, glucose and glutamine are fed twice at 54.5 h and 113 h, respectively while it is fed for three times at 54.5 h, 73 h and 113 h in Exp. 3. Similarly, the parameter identification is firstly accomplished through data fitting with experimental data related with glucose, glutamine, lactate, and cell mass. Compared with that of simple batch culture in Exp. 1, the reaction process turns to be a bit complicated for fed-batch experiment. As shown in Fig. 3, one can see that glucose and glutamine are consumed as batch culture for catabolism and cell growth at the stage of before feeding. At the time of 54.5 h, glucose and glutamine concentrations have decreased to less than one third of their original concentrations, which results in the fact that enzymes which is responsible for lactate production rate and cell growth are inhibited due to lack of nutrients. After the pulse feeding, although the concentrations of glucose and glutamine go back to a high level immediately, the lactate and cell mass concentrations still slightly decrease first because of the dilution effect and then gradually increase after the inhibited enzymes recover to an appreciable level to adapt the higher level of glucose and glutamine after feeding. This is the so-called cell inbuilt regulation mechanism which could be described well by cybernetic models. The same phenomenon happens for the second feeding. As described above, the concentration variation along with the reaction time exhibits more complicated compared to that of Exp. 1 due to the feeding effect of glucose and glutamine. It is notable that it will be convincing if the model performance can still be effective in such a complicated experiment, which undoubtedly further demonstrate the availability of the constructed model. The simulation results shown in Fig. 3 clearly indicate the perfect match with the trend of experimental data. As can be seen, the simulated cell growth rate also slightly decreases at the time points of feeding and then gradually increases along with the reaction time, which is due to the inhibition effects of ammonia and lactate as long as their accumulation increase. With the identified parameters, the model is applied to predict the concentration variation of ammonia and alanine, as shown in Fig. 3a and b, respectively. The predicted results also match well with the experimental data. For the experiment having three times of feeding in Exp. 3, the model performance can still be validated well, as shown in Fig. 4, which means

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Fig. 5. Performance of HCM prediction for batch Exp. 1 with kinetic parameters of fed-batch Exp. 2. Dashed lines: prediction results; hollow circles: experimental data.

Fig. 6. Performance of HCM prediction for fed-batch Exp. 3 with kinetic parameters of fed-batch Exp. 2. Dashed lines: prediction results; hollow circles: experimental data.

that our constructed model is truly effective in the simulation of mammalian cell metabolism. As listed in Table 4, three sets of kinetic parameters obtained from fitting process based on experimental data from Exp. 1, Exp. 2 and Exp. 3 exhibit quite a small variation although the complexity of the different experiments are quite different, which provide direct evidence for the efficiency of the model. In order to further prove the prediction efficiency of our model, we apply one single set of parameter which is the kinetic parameters of Exp. 2 (as listed in Table 4), to predict the other two experimental data, i.e., Exp. 1 and Exp. 3 and the prediction results are shown in Figs. 5 and 6, respectively. The batch experimental data is firstly predicted (Fig. 5) and there is a satisfied match between the prediction results (dashed line) and the experimental data points (hollow circles) although not each data point is exactly fitted. It will be more important and meaningful to make the reasonable prediction when the situation becomes complicated, for example, reactions under variable conditions or perturbation. Herein, in order to further validate the efficiency of the developed model, the prediction of Exp. 3 having three times of pulse feeding process is proceeded and the results are shown in Fig. 6. As can be clearly seen, the prediction results (dashed lines) of glucose, glutamine, lactate and biomass are still well fitted with experimental data (hollow circles) with an acceptable mismatch. It is clearly demonstrated that applying the kinetic parameters of fed batch experiment with one pulse feeding, both batch experiment without feeding strategy and fed batch experimental with three times of feeding could be predicted quite reasonably which verifies the robustness of the developed model.

Fig. 7 shows the cybernetic values of batch culture of Exp. 1 with the time evolution. As the feature involved in mammalian cell metabolism, the partially complementary and partially substitutable relationship between glucose consumption and glutamine consumption could be reasonably illustrated. According to the expression for the definition of cybernetic values, it is indicated that high cybernetic value represents high activity of the associated EMs. From the comparison results of cybernetic values for different 14 EMs involved in Exp. 1, as shown in Fig. 7, one can see that three EMs, i.e., EM1 , EM10 , EM12 exhibit higher cybernetic value of enzyme synthesis and enzyme activity among all EMs. This is consistent with the results shown in Table 4 that the max and kmax ) associated with EM , three kinetic parameters (k1max , k10 1 12 EM10 , and EM12 play the most significant roles in the cell culture process among all kinetic parameters, which also means that these three elementary modes play the most important roles during the fermentation process. Among these 3 EMs, EM10 represents the elementary mode which involves glucose uptake only while EM1 and EM12 involve elementary modes with both glucose and glutamine uptake. As EM1 and EM12 involve flux uptake of two substrates, the relationship between the glucose and glutamine could be considered as complementary consumption pattern. And the high value of cybernetic variables related with EM10 indicate that glucose itself could also be individually functional to produce some products, i.e., lactate. As a result, glucose and glutamine could be considered to be consumed in a substitutable pattern. Therefore, partially complementary and partially substitutable consumption pattern could be concluded as the relationship between the two substrate involved in mammalian cell culture, which is consistent with previous literature [26].

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Fig. 7. Cybernetic values of 14 EMs with time evolution in Exp. 1. Dashed lines: cybernetic values of v; solid lines: cybernetic values of u.

5. Conclusions A hybrid cybernetic model (HCM) is developed for mammalian cell culture based on the structured metabolic network, which takes account of both stoichiometric information of metabolic networks and cell inbuilt regulation mechanism involving two different types of substrates, i.e., glucose and glutamine. Three batched of experiments involving different feeding strategies are used to validate the model efficiency by data fitting process. The subsequently reasonable prediction results without extra experimental support further demonstrate the model’s efficiency. In addition, the partially complementary and partially substitutable feature involved in the glucose and glutamine consumptions is clearly illustrated according to the results of time dependent cybernetic values for all 14 EMs. Applying HCM in mammalian cell culture could stimulate the continuous interests in extending its possible applications to more complicated interactions between cell regulation and metabolic flux exchanges. Acknowledgments Ms. J. Geng sincerely thanks Prof. D. Ramkrishna and Dr. H. S. Song in Purdue University for the helpful guidance on HCM operation during two-year exchange programme supported by Chinese Scholarship Council (CSC). We sincerely thank Mrs. Angela Walter/GBF and Mr. Joachim Hammer/GBF for the analytical assistances. This study is supported by the Doctoral Program of Higher Education of China (Grant No. 20110073110018)

and the National Science Foundation of China (Grant No. 61025016). GBF (Gesellschaft für Biotechnologische Forschung GmbH, now called Helmholtz Zentrum für Infektionsforschung, Braunschweig/Germany) is acknowledged for providing all experimental and analysis facilities. References [1] Dietmair S, Hodson MP, Quek LE, Timmins NE, Chrysanthopoulos P, Jacob SS, et al. Metabolite profiling of CHO cells with different growth characteristics. Biotechnol Bioeng 2012;109:1404–14. [2] Altamirano C, Illanes A, Becerra S, Cairo JJ, Godia F. Considerations on the lactate consumption by CHO cells in the presence of galactose. J Biotechnol 2006;125:547–56. [3] Dhir S, Morrow KJ, Rhinehart RR, Wiesner T. Dynamic optimization of hybridoma growth in a fed-batch bioreactor. Biotechnol Bioeng 2000;67:197–205. [4] Vesikari T, Block SL, Guerra F, Lattanzi M, Holmes S, Izu A, et al. Immunogenicity, safety and reactogenicity of a mammalian cell-culture-derived influenza vaccine in healthy children and adolescents three to seventeen years of age. Pediat Infect Dis J 2012;31:494–500. [5] Bonarius HPJ, Hatzimanikatis V, Meesters KPH, deGooijer CD, Schmid G, Tramper J. Metabolic flux analysis of hybridoma cells in different culture media using mass balances. Biotechnol Bioeng 1996;50:299–318. [6] Sidoli FR, Mantalaris A, Asprey SP. Modelling of mammalian cells and cell culture processes. Cytotechnology 2004;44:27–46. [7] Morgan JA, Sengupta N, Rose ST. Metabolic flux analysis of CHO cell metabolism in the late non-growth phase. Biotechnol Bioeng 2011;108:82–92. [8] Juran JM. Quality control handbook. New York, New York: McGraw-Hill; 1951. [9] Palsson B. The challenges of in silico biology. Nat Biotechnol 2000;18: 1147–50. [10] Bonarius HPJ, Houtman JHM, Schmid G, de Gooijer CD, Tramper J. Metabolicflux analysis of hybridoma cells under oxidative and reductive stress using mass balances. Cytotechnology 2000;32:97–107.

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