Computational Modeling of Fed-Batch Cell Culture Bioreactor: Hybrid ...

Preprints of the 9th International Symposium on Advanced Control of Chemical Processes The International Federation of Automatic Control June 7-10, 2015, Whistler, British Columbia, Canada

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Computational Modeling of Fed-Batch Cell Culture Bioreactor: Hybrid Agent-Based Approach Elif Seyma Bayrak1,2, Tony Wang1, Ali Cinar2, Cenk Undey1 

1

Amgen, Inc., Process Development, One Amgen Center Drive, Thousand Oaks, CA 91320 USA (Tel: 805-447-0955; e-mail: cundey@ amgen.com, [email protected]). 2 Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10W 33 rd St,, Chicago, IL, 60616 USA (e-mail:[email protected], [email protected])} Abstract: A hybrid simulation framework was proposed to predict the dynamics in cell culture bioreactors. The model is based on a multi-agent approach where CHO cells are considered as individuals (agents) following a rule base governing their behavior, while a flux balance model is embedded in agents to predict quantitative changes in nutrient and metabolite concentrations. The model takes the measured dissolved oxygen, and sodium data as input along with initial cell culture conditions and predicts the dynamics of viable cell density, viability, concentrations of glucose and lactate. The model showed good agreement with the experimental findings from our laboratory for two sets of cell culture experiments. Keywords: Agent-based simulation, fed-batch, Chinese hamster ovary cell culture, hybrid systems 

1. INTRODUCTION The complexity of therapeutic proteins and their biological production systems represent extraordinary challenges to engineers and optimization of these processes requires good understanding of living cells (Kundu et al., 2010). Chinese hamster ovary (CHO) cell has an extensive use in production of various therapeutic proteins including monoclonal antibodies. While most preferred operating mode has remained as fed-batch process, (Huang et al., 2010) as it combines the advantages of batch and continuous modes, there is still great need for optimization of culture conditions. A mathematical model that offers the ability to perform experiments in silico and accurately predict the interplay between the cells and bioreactor environment can be crucial for optimization, monitoring and process control purposes (Tziampazis and Sambanis, 1994). Many computational modeling approaches have been studied to simulate and optimize cell culture processes. Xing et al. applied Markov chain Monte Carlo Method to model the kinetics of a fed-batch CHO cell culture process in large scale bioreactors. Karra et al. developed a one dimensional population balance model combined with average cell model to account for the heterogeneity to explain the CHO cell cultures media concentration dynamics, and protein production. Nolan et al. studied dynamic flux based approach where cytosolic rate expressions are defined based on extracellular metabolite concentrations and predicted the effects of process variables, including temperature shift, seed density, specific productivity, and nutrient concentrations. Agent-based modeling is an active area with applications in diverse fields ranging from social sciences and economics to traffic control and biology, by providing a novel modeling

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paradigm for dealing with the increasing complexities involved in the real world. Agent-based models (ABM) simulate the actions of individual heterogeneous building blocks, referred as agents, based on rules that originate from knowledge of the system under study (Macal and North, 2010). The rules are often simple and developed to govern mostly local interactions, which results in emergent behavior of whole system as the time evolves. ABMs have advantages over differential/algebraic equation-based mechanistic modeling for its ability to integrate quantitative and qualitative knowledge, deal with multiple levels of actions, hold the history of the individuals, and ease in modeling emergent behavior (Figueredo et al., 2014). ABMs have been used successfully in recent years for modeling biological systems focusing on individual cell behavior such as angiogenesis (Mehdizadeh et al., 2013), osteogenesis of stem cells (Bayrak et al., 2014), brain tumors (Zhang et al., 2009), and arterial adaptation in hypertension (Thorne et al., 2011). Use of ABMs to capture complexity in bioreactors is at an early stage. An ABM coupled with a transport model to simulate the dynamic relationship between cell and its microenvironment was developed for a tissue engineering bioreactor (Kaul et al., 2013). The Euler-Lagrange approach was used with no explicit individual agent definition for addressing the heterogeneity present in both the fluid and cellular phases in fermentation bioreactor (Lapin et al., 2010). In this study, an ABM combined with metabolic flux model has been proposed to predict the dynamics of a cell culture bioreactor. It is hypothesized that this design can capture the influence of initial cell density, glucose feed and dissolved oxygen on cell culture performance parameters such as viable cell density (VCD) and viability over time.

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2. METHODS 2.1 Model Structure A hybrid ABM was developed to simulate CHO cell behavior in dynamic cell culture bioreactor conditions (Fig. 1). The model is based on a multi-agent approach where CHO cells are considered as agents perceiving their environment and act based on predefined rules. Their actions and states are influenced by dynamic changes in dissolved oxygen (DO), sodium (Na), glucose (GLC) and lactate (LAC) concentration. Quantitative changes in glucose and lactate concentrations are predicted by modifying the dynamic flux based analysis (dFBA) modeling approach (Nolan and Lee, 2011) where cytosolic rate expressions (vin1, vin2, vin3 in Fig.2) are defined based on extracellular metabolite concentrations (GLC, LAC, CO2), and adopting a simplified metabolic network (Appendix A) for metabolic cell metabolism network (Balcarcel and Clark, 2003) (Fig.2). Model parameters are obtained from fed-batch cell culture experimental data presented in this study (Appendix A).

Fig. 1. Hybrid structure of agent-based model Each CHO agent holds different values of kinetic parameters and updates them over time, and calls the dynamic flux model based on their states during a simulation. The total metabolite and nutrient concentration are calculated at the end of a simulation time step from each agent’s contribution to the environment that will have an impact on the behavior of agents in the following time step. The rule set controlling agent’s states and action is described in detail in Section 2.2. 2.2 CHO Agent Design and Rule Base CHO cell considered as an agent, a software entity that sense the virtual bioreactor environment, processes the information through its internal logic and makes a decision to act. The agent’s environment consists of soluble factors such as DO, GLC, LAC, Na and other cell agents. The agent has a number of variables that determine its internal state, and methods that regulate its behavior (Fig. 3.). The values of the agent’s variables and attributes are instantiated during the run, at each time step. The main states of the CHO agent are the phases in cell cycle such as G1, S, G2M and quiescent phase (G0), additional to phases of programmed cell death such as early apoptosis (EA), late apoptosis (LA) and apoptosis (A). Each CHO agent can sense, migrate, grow through the cell cycle, proliferate and apoptose while consuming the nutrients and producing the metabolites.

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Fig. 2. Simplified network for mammalian cell metabolism (modified from (Balcarcel and Clark, 2003)) Literature and experimental observation based rule set is derived to model the behavior of a CHO cell agent. Environmental conditions are defined based on the relative oxygen, glucose, lactate and sodium concentrations that exist in the bioreactor environment. An environment, where dissolved oxygen and nutrients are higher and toxic byproduct concentration is lower than the defined threshold is considered as highly favorable for the existence of cells. A favorable environment starts with the deficiency of primary carbon source (glucose), sufficient levels of oxygen and relatively low toxic accumulation. This environmental condition causes cells to go through lactate metabolic shift (Mulukutla et al., 2012) where they consume both lactate and glucose. Low oxygen, however, results in reversing this shift and high production of lactate (Zagari et al., 2013). Toxic accumulation is assumed to be caused by either excess lactate or sodium. Sodium is included in the model to account for osmolality influence on cell culture. Principal component analysis (PCA) is performed (results are not reported in this paper) to confirm the high correlation between sodium and osmolality. Higher osmolality can cause a significant reduction in both viable cell density and viability (Zhu et al., 2005). The environmental conditions vary from highly favourable to severe depending on the conditions illustrated in Fig. 4.

Fig. 3. CHO agent’s states, action and its interaction with the environment Each CHO agent senses and decides its environmental conditions at the beginning of each time step during a simulation,. An agent can take different actions and states based on its current environmental state. S phase is the only

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IDE, on a workstation with Mac OS X 10.8.5 operating system, 16 GB of RAM, and an Intel Core i7 processor. The parameter values for flux balance model were estimated from cell culture data using Matlab Simulated Annealing toolbox.

Fig. 4 Environmental definitions based on oxygen, glucose lactate and sodium concentration. High or low conditions are defined based on the thresholds of each variable. state where agent actions are independent of environmental condition, since the committed cells will continue DNA synthesis regardless of nutrient extracellular conditions (Bartek and Lukas, 2001). Cells experiencing highly favorable condition will proceed with cell cycle. Each cell has an embedded clock for time-based actions (i.e. cell cycle). After completing the minimum time required to stay in the current state, an agent will move on to the next state. A favorable condition exists when the primary carbon source (glucose) is deficient and a cell will change its metabolic state to consume the by-products (lactate). Oxygen or nutritional deficiency can cause cells to abort from the cell cycle and become quiescent (G0). A quiescent cell will not go through cell cycle and proliferate, but it will continue its metabolic activities with a reduced metabolic rate. Cells that have gone through metabolic shift are assumed to be less susceptible to environmental change, and have the ability to resume cell cycle activities under severe conditions whereas cells without adaptation go to the hypoxic state (early apoptosis) and may proceed to apoptosis to end their life cycle. The apoptosis probability is introduced to the model with the highest weight allocated to nutrient deficiency followed by oxygen deficiency and toxic by product accumulation (al-Rubeai and Singh, 1998). The rules can be found in Fig. 5. Mean parameter values for the agent population including the thresholds for environmental definitions are listed in Table 1. Most parameter values are estimated from the experimental study and some are adopted from the literature and vary among the individuals and with environmental conditions. 2.3 Model Initiation and Simulation Runs The ABM is implemented in Java using open source agent modeling toolkit Repast (Recursive Porous Agent Simulation Toolkit). Repast includes packages of Java libraries to build 2D and 3D simulation environments, create agents, define relationships among the agents, and build user interfaces and displays. Repast provides a discrete event time scheduler with double precision real numbers for event times, that allows events scheduling for both sequential with priority ranking and concurrent activities (North et al., 2013). The simulations were performed by using Repast Simphony 2.1 with Java jdk version 7, Eclipse Kepler Standard as Java

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Fig. 5. The rule set governing the CHO cell agent behaviour A three-dimensional (3D) model was constructed to simulate a lab-scale 3 L bioreactor and run for 1200 time ticks that corresponds to actual cell culture process duration from inoculation to harvest from experimental data. Each case was run 5 times, mean and standard deviation values were reported. Table 1. CHO cell agent behaviour parameters Behavior Parameter

ABM value

Doubling time (td)

24 hours

G1 phase time

%50 td

S phase time

%30 td

G2M phase time

%20 td

GLC lower limit

0.0014 g/L107 cells

GLC threshold for lactate shift

0.005 g/L107 cells

O2 survival limit

%10

Max. time to spend on EA

21 hr

Max. time to spend on LA

12 hr

Min. lac. required for lac. shift

1 g/L

LAC. upper limit

3 g/L

LAC. lower limit

0.5 g/L

Na upper limit

100 mM

2.4 Experimental Study Cell Lines. The cells used in all experiments were derived from Chinese Hamster Ovary (CHO) cells. It is a proprietary Amgen cell line adapted to serum-free suspension growth

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prior to transfection. Cells were transfected with proprietary DNA vectors encoding recombinant proteins. Medium and Feeds. The basal medium and feeds used were proprietary formulations developed at Amgen. Equipment. Cells were grown in 3L disposable bioreactors connected to Sartorius DCU Quad system. Dissolved oxygen, pH, agitation and temperature were maintained continuously by the Sartorius system based on characterized process conditions. Raman probes were inserted in the bioreactors to collect spectral signals at predefined time intervals. Analytical Methods. Cell counts, glucose, lactate, pH and sodium were performed using Nova Flex instrument at minimum once a day. Raman data were processed and correlated to offline Nova Flex glucose readings. 3. RESULTS A hybrid ABM is developed to capture the dynamics of a fedbatch cell culture bioreactor and predict instant nutrient and metabolite concentration. The model was run to simulate two cases of cell culture condition in which the initial cell concentration, DO and feed time show differences. Case 1 will be referred to as the low VCD case (for low initial viable cell density). After inoculation, glucose level was allowed to drop to a critical level (tc) at which time glucose was fed periodically to an optimized glucose target until harvest. Offline samples at select time points in the process were taken to monitor process trends. Results for glucose (A), lactate (B) concentration, viable cell density (C) and viability (D) are presented in Fig. 6. For glucose, ABM prediction was compared with Raman data in addition to offline Nova Flex measurements. ABM captured the dynamics of glucose change in bioreactor with a good parametric sensitivity. Lactate concentration declined at time point t1 due to the metabolic shift caused by low glucose concentration. At time point t2, zero oxygen was supplied to the culture for 15 min due to maintenance on the oxygen manifold unit. This incident caused high lactate production in

the cell culture. Same DO profile was provided to challenge the model and ABM captured the increase in lactate production at t2. Viability and VCD showed sharp decrease after t2, following nutrient and oxygen deficiency. In Case 2, the initial cell density was higher and glucose was fed after tc+x (where x is the additional amount of time Case 2 glucose level was allowed to decline before glucose was fed to the culture). Once glucose feeding was initiated, the culture was fed to the same glucose target for the same time interval as Case 1 until the culture was harvested. Results for glucose (A), lactate (B) concentration, viable cell density (C) and viability (D) are presented in Fig. 7. The glucose concentration showed a better agreement than what was observed in low-density case. Lactate concentration decreased and showed steady state behavior in simulations (Experimental fluctuations shown here were smaller than instrumentation lactate error). High-density case resulted in higher VCD and viability, both decreased slightly later due to nutritional deficiency.

Fig. 7. Case 2: Comparison of model prediction with experimental data for high VCD: glucose (A), lactate (B), VCD (C), viability (D) The percentage of cells that underwent metabolic shift and consumed lactate was plotted from simulations (Fig. 8). High density case showed an early metabolic shift due to fast consumption of nutrients. Low density case started metabolic shift later than the high density case and showed variation after time point t2 due to oxygen manifold maintenance work. Root mean squared error (RMSE) values were calculated to evaluate the ABM performance (Table 2). Table 2 RMSE values for model evaluation

Fig. 6. Case 1: Comparison of model prediction with experimental data for low VCD: glucose (A), lactate (B), VCD (C), viability (D)

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Glucose (g/L)

Lactate (g/L)

VCD (106 cells/mL)

Viability (%)

Low VCD

0.84

0.49

2.48

3.99

High VCD

0.93

0.26

4.44

4.24

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Transport equations are not incorporated to account for nonideal mixing in this work due to the small scale of bioreactor of interest (3 L with 2L working volume).

Fig. 8 Percentage of cells under lactate metabolic shift 4. DISCUSSION Computational modeling of cell culture bioreactors used for production of important biopharmaceuticals presents a major challenge due to the complexity of variations in individual cell responses to bioreactor operational conditions. In this study, we introduced a hybrid framework with an agent-based approach to model the interplay between the cells and their living environment. Our motivation was to capture the important dynamics of complex bioreactor system by focusing on natural behavior of cells that was represented as a combination of a rule set and metabolic equations. The rules developed here are generic to mammalian cells. Because the model focuses on CHO cell behavior, rather than specific system level dynamics, it can be easily modified to simulate different operational conditions with minimal change in input parameters. The model has a great flexibility to extend the level of complexity by including more environmental variables and rules owing to the objectoriented nature of agent-based modeling. The hybrid model is currently not capable of predicting dissolved oxygen and sodium, they were assumed to be available and their experimental data were fed to the model at each time point. The way in which the hybrid model is setup offers the ability to plug-and-play more sophisticated mechanistic models that can predict dissolved oxygen, sodium and other cell metabolites. Typically osmolality is used to track bulk osmotic pressure within the cell culture over time. It is a critical parameter to monitor for all cell-based cultures (Ozturk and Palsson, 1991, Takagi et al., 2000), however to the best of our knowledge, there is no mathematical model to account for it. For our process, the sodium level correlated closely with the osmolality trend, which offered an alternative model input to osmolality. ABM models (not shown) were also built with osmolality as model inputs and they showed similar predictability as the ABM models built using sodium. Due to shear sensitivity of mammalian cell culture (Petersen et al., 1988), ideal mixing assumption may not be valid for large scale bioreactors as spatial gradients may be present (Lara et al., 2006). Agent-based modeling is a natural choice to account for the heterogeneity to address this problem.

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Model predictions were compared with the same cell culture experimental conditions and in each simulated case the model captured the important dynamic changes both qualitatively and quantitatively. The model predicts the glucose with RMSE less than 1g/L and lactate with RMSE less than 0.5 g/L. These are acceptable errors as the cumulative errors from our offline experimental measurement (instrument and random error) are in the same range as the calculated RMSE. The metabolic shift from glucose to lactate is an important consideration in cell culture processes with its impact on nutrient and metabolite profiles as well as the viability of culture (Lao and Toth, 1997). ABM is capable of generating acceptable prediction of cell behavior as cells go through metabolic shift under different process conditions. Another advantage of this model is its adaptive behavior to different conditions of interest and scalability to serve different purposes. Since agent behaviors are analogous to real behaviors of individual cells of the modeled system, agents are a natural choice for the application of adaptive techniques, that makes migration from simulation model to adaptive control model much more straightforward in ABM than in equation-based modeling (Van Dyke Parunak et al., 1998). 5. CONCLUSIONS We have shown the applicability of ABM to cell culture bioreactors in this study. A hybrid simulation framework is proposed to predict the dynamics in cell culture bioreactors using ABM techniques. The ABM applied to fed-batch cell culture has been validated with the experimental findings and has shown good agreement in predicting cell culture behaviour. It has great possibilities in applying adaptive modeling capabilities to further cell culture understanding and control. REFERENCES Al-Rubeai, M. & Singh, R. P. 1998. Apoptosis In Cell Culture. Curr Opin Biotechnol, 9, 152-6. Balcarcel, R. R. & Clark, L. M. 2003. Metabolic Screening Of Mammalian Cell Cultures Using Well-Plates. Biotechnol Prog, 19, 98-108. Bartek, J. & Lukas, J. 2001. Mammalian G1- And S-Phase Checkpoints In Response To Dna Damage. Curr Opin Cell Biol, 13, 738-47. Bayrak, E. S., Mehdizadeh, H., Akar, B., Somo, S. I., Brey, E. M. & Cinar, A. Agent-Based Modeling Of Osteogenic Differentiation Of Mesenchymal Stem Cells In Porous Biomaterials. Engineering In Medicine And Biology Society (EMBC), 2014 36th Annual International Conference Of The Ieee, 2014. IEEE, 2924-2927. Figueredo, G. P., Siebers, P.-O., Owen, M. R., Reps, J. & Aickelin, U. 2014. Comparing Stochastic Differential Equations And Agent-Based Modelling And Simulation For Early-Stage Cancer. Plos One, 9.

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Huang, Y. M., Hu, W., Rustandi, E., Chang, K., YusufMakagiansar, H. & Ryll, T. 2010. Maximizing Productivity Of Cho Cell-Based Fed-Batch Culture Using Chemically Defined Media Conditions And Typical Manufacturing Equipment. Biotechnol Prog, 26, 1400-10. Karra, S., Sager, B. & Karim, M. N. 2010. Multi-Scale Modeling Of Heterogeneities In Mammalian Cell Culture Processes. Industrial & Engineering Chemistry Research, 49, 7990-8006. Kaul, H., Cui, Z. & Ventikos, Y. 2013. A Multi-Paradigm Modeling Framework To Simulate Dynamic Reciprocity In A Bioreactor. Plos One, 8. Kundu, S., Bhatnagar, V., Pathak, N. & Undey, C. 2010. Chemical Engineering Principles In Biologics: Unique Challenges And Applications. Chemical Engineering In The Pharmaceutical Industry. John Wiley & Sons, Inc. Lao, M.-S. & Toth, D. 1997. Effects Of Ammonium And Lactate On Growth And Metabolism Of A Recombinant Chinese Hamster Ovary Cell Culture. Biotechnology Progress, 13, 688-691. Lapin, A., Klann, M. & Reuss, M. 2010. Multi-Scale SpatioTemporal Modeling: Lifelines Of Microorganisms In Bioreactors And Tracking Molecules In Cells. In: Wittmann, C. & Krull, R. (Eds.) Biosystems Engineering Ii. Springer Berlin Heidelberg. Lara, A. R., Galindo, E., Ramirez, O. T. & Palomares, L. A. 2006. Living With Heterogeneities In Bioreactors: Understanding The Effects Of Environmental Gradients On Cells. Mol Biotechnol, 34, 355-81. Macal, C. M. & North, M. J. 2010. Tutorial On Agent-Based Modelling And Simulation. J Of Sim, 4, 151-162. Mehdizadeh, H., Sumo, S., Bayrak, E. S., Brey, E. M. & Cinar, A. 2013. Three-Dimensional Modeling Of Angiogenesis In Porous Biomaterial Scaffolds. Biomaterials, 34, 2875-2887. Mulukutla, B. C., Gramer, M. & Hu, W. S. 2012. On Metabolic Shift To Lactate Consumption In Fed-Batch Culture Of Mammalian Cells. Metab Eng, 14, 138-49. Nolan, R. P. & Lee, K. 2011. Dynamic Model Of Cho Cell Metabolism. Metabolic Engineering, 13, 108-124. North, M. J., Collier, N. T., Ozik, J., Tatara, E., Macal, C., Bragen, M. & Sydelko, P. 2013. Complex Adaptive Systems Modeling With Repast Simphony. Complex Adaptive Systems Modeling, 1. Ozturk, S. S. & Palsson, B. O. 1991. Growth, Metabolic, And Antibody Production Kinetics Of Hybridoma Cell Culture: 2. Effects Of Serum Concentration, Dissolved Oxygen Concentration, And Medium Ph In A Batch Reactor. Biotechnology Progress, 7, 481-494. Petersen, J. F., Mcintire, L. V. & Papoutsakis, E. T. 1988. Shear Sensitivity Of Cultured Hybridoma Cells (Crl8018) Depends On Mode Of Growth, Culture Age And

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Metabolite Concentration. Journal Of Biotechnology, 7, 229-246. Takagi, M., Hayashi, H. & Yoshida, T. 2000. The Effect Of Osmolarity On Metabolism And Morphology In Adhesion And Suspension Chinese Hamster Ovary Cells Producing Tissue Plasminogen Activator. Cytotechnology, 32, 171-9. Thorne, B. C., Hayenga, H. N., Humphrey, J. D. & Peirce, S. M. 2011. Toward A Multi-Scale Computational Model Of Arterial Adaptation In Hypertension: Verification Of A Multi-Cell Agent Based Model. Front Physiol, 2. Tziampazis, E. & Sambanis, A. 1994. Modeling Of Cell Culture Processes. Cytotechnology, 14, 191-204. Van Dyke Parunak, H., Savit, R. & Riolo, R. L. 1998. AgentBased Modeling Vs. Equation-Based Modeling: A Case Study And Users' Guide. Proceedings Of The First International Workshop On Multi-Agent Systems And Agent-Based Simulation. Springer-Verlag. Xing, Z., Bishop, N., Leister, K. & Li, Z. J. 2010. Modeling Kinetics Of A Large-Scale Fed-Batch Cho Cell Culture By Markov Chain Monte Carlo Method. Biotechnology Progress, 26, 208-219. Zagari, F., Jordan, M., Stettler, M., Broly, H. & Wurm, F. M. 2013. Lactate Metabolism Shift In Cho Cell Culture: The Role Of Mitochondrial Oxidative Activity. New Biotechnology, 30, 238-245. Zhang, L., Chen, L. L. & Deisboeck, T. S. 2009. Multi-Scale, Multi-Resolution Brain Cancer Modeling. Mathematics And Computers In Simulation, 79, 2021-2035. Zhu, M. M., Goyal, A., Rank, D. L., Gupta, S. K., Vanden Boom, T. & Lee, S. S. 2005. Effects Of Elevated Pco2 And Osmolality On Growth Of Cho Cells And Production Of Antibody-Fusion Protein B1: A Case Study. Biotechnol Prog, 21, 70-7. Appendix A. The reactions for the simplified metabolic network in Fig.2: vin1 :GLC + 2NAD+ + 2ADP + Pi  2PYR + 2NADH + 2ATP + 2H2O + 2H+ vin2: PYR + NADH + H+  LAC + NAD+ Rate equations adopted and modified from (Nolan and Lee, 2011):

(A.1) where δ is 1 if lactate shift is on, 0 otherwise; vmax1 = 3.82 e09 g/ L / day / cells; Km1 = 18.73 g/L; Ki1 = 0.68 g/L; exp1 =1.44; vmax2,f = 1.15 e-09 g/ L / day / cells; Km2,f =10.35 g/L; vmax2,r = vmax2,f/8.

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