Abstract
Mammalian cell cultures represent the major source for a number of very high-value biopharmaceutical products, including monoclonal antibodies (MAbs), viral vaccines, and hormones. These products are produced in relatively small quantities due to the highly specialised culture conditions and their susceptibility to either reduced productivity or cell death as a result of slight deviations in the culture conditions. The use of mathematical relationships to characterise distinct parts of the physiological behaviour of mammalian cells and the systematic integration of this information into a coherent, predictive model, which can be used for simulation, optimisation, and control purposes would contribute to efforts to increase productivity and control product quality. Models can also aid in the understanding and elucidation of underlying mechanisms and highlight the lack of accuracy or descriptive ability in parts of the model where experimental and simulated data cannot be reconciled. This paper reviews developments in the modelling of mammalian cell cultures in the last decade and proposes a future direction – the incorporation of genomic, proteomic, and metabolomic data, taking advantage of recent developments in these disciplines and thus improving model fidelity. Furthermore, with mammalian cell technology dependent on experiments for information, model-based experiment design is formally introduced, which when applied can result in the acquisition of more informative data from fewer experiments. This represents only part of a broader framework for model building and validation, which consists of three distinct stages: theoretical model assessment, model discrimination, and model precision, which provides a systematic strategy from assessing the identifiability and distinguishability of a set of competing models to improving the parameter precision of a final validated model.
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References
Asprey S.P. and Machietto S. 2000. Statistical tools for optimal dynamic model building. Comput. Chem. Eng. 24: 1261–1267.
Asprey S.P. and Mantalaris A. 2001. Global parametric identifiability of a dynamic unstructured model of hybridoma cell culture. In: Proceedings of the 8th International Conference on Computer Applications in Biotechnology.
Asprey S.P. and Machietto S. 2002. Designing robust optimal dynamic experiments. J. Process Control 12: 545–556.
Bailey J.E. 1998. Mathematical modeling and analysis in biochemical engineering. Biotech. Progr. 14: 8–20.
Barford J.P., Phillips P.J. and Harbour C. 1992. Simulation of animal cell metabolism. Cytotechnology 10: 63–74.
Batt B.C. and Kompala D.S. 1989. A structured kinetic modeling framework for the dynamics of hybridoma growth and monoclonal antibody production in continuous suspension cultures. Biotech. Bioeng. 34: 515–531.
Bernaerts K., Versyck K.J. and Van Impe J.F. 2000. On the design of optimal dynamic experiments for parameter estimation of a ratkowsky-type growth kinetics at suboptimal temperatures. Int. J. Food Microbiol. 54: 27–38.
Cain S.J. and Chau C.C. 1998. Transition probability cell cycle model with product formation. Biotech. Bioeng. 58: 387–399.
Cazzador L. and Mariani L. 1993. Growth and production modelling in hybridoma continuous culture. Biotech. Bioeng. 38: 781–787.
Cruz H.J., Moreira J.L. and Carrondo M.J.T. 1999. Metabolic shifts by nutrient manipulation in continuous cultures of BHK cells. Biotech. Bioeng. 66: 104–113.
Dalili M., Sayles G.D. and Ollis D.F. 1990. Glutamine-limited batch hybridoma growth and antibody production: experiment and model. Biotech. Bioeng. 36: 74–82.
Diekmann O., Heijmans H.J.A.M. and Thieme H.R. 1984. On the stability of the cell size distribution. J. Math. Biol. 19: 227–248.
Domach M.M. and Shuler M.L. 1984. A finite representation model for an asynchronous culture of E. coli. Biotech. Bioeng. 26: 877–884.
Duncan A. 2002. Antibodies hold the key. Chemistry & Industry.
Eakman J.M., Fredrickson A.G. and Tsuchiya H.M. 1966. Statistics and dynamics of microbial cell populations. Chem. Eng. Progr. 62: 37–49.
Europa A.F., Gambhir A., Fu P.C. and Hu W.S. 2000. Multiple steady states with distinct cellular metabolism in continuous culture of mammalian cells. Biotech. Bioeng. 67: 25–34.
Follstad B.D., Balcarcel R.R., Stephanopoulos G. and Wang D.I.C. 1999. Metabolic flux analysis of hybridoma continuous culture steady state multiplicity. Biotech. Bioeng. 63: 675–683.
Frame K.K. and Hu W.-S. 1991. Kinetic study of hybridoma cell growth in continuous culture. ii. behavior of producers and comparison to nonproducers. Biotech. Bioeng. 38: 1020–1028.
Fredrickson A.G., Ramkrishna D. and Tsuchiya H.M. 1967. Statistics and dynamics of procaryotic cell population. Math. Biosci. 1: 327–374.
Gombert A.K. and Nielsen J. 2000. Mathematical modelling of metabolism. Curr. Opin. Biotech. 11: 180–186.
Gray L. and Jasuja R. 2001. B-147 The New Future of Biotechnology: Enabling Technologies and Star Products. Business Communication Company, Inc.
Hatzis C., Srienc F. and Fredrickson A.G. 1995. Multistaged corpuscular models of microbiol growth: Monte carlo simulations. Biosystems 36: 19–35.
Hiller G.W., Aeschlimann A.D., Clark D.S. and Blanch H.W. 1991. A kinetic analysis of hybridoma growth and metabolism in continuous suspension culture on serum-free medium. Biotech. Bioeng. 38: 733–741.
Jacques J.A. 1998. Design of experiments. J. Franklin Inst. 335B: 259–279.
Jang J.D. and Barford J.P. 2000. An unstructured kinetic model of macromolecular metabolism in batch and fed-batch cultures of hybridoma cells producing monoclonal antibody. Biochem. Eng. J. 4: 153–168.
Kim B.-G. and Shuler M.L. 1990. A structured, segregated model for genetically modified E. coli cells and its use for prediction of plasmid stability. Biotech. Bioeng. 36: 581–592.
Körkel S., Bauer I., Bock H.G. and Schloder J.P. 1999. A sequential approach for nonlinear optimum experimental design in dae systems. In: Proceedings of the International Workshop on Scientific Computation in Chemical Engineering.
Kromenaker S. and Srienc F. 1991. Cell-cycle-dependent protein accumulation by producer and nonproducer murine hybridoma cell lines: a population analysis. Biotech. Bioeng. 38: 665–677.
Kurokawa H., Park Y.S., Iijima S. and Kobayashi T. 1994. Growth characteristics in fed-batch culture of hybridoma cells with control of glucose and glutamine concentration. Biotech. Bioeng. 44: 95–103.
Lee Y.-K., Yap P.-K. and Teoh A.-P. 1995. Correlation between steady-state cell concentration and cell death of hybridoma cultures in chemostat. Biotech. Bioeng. 45: 18–26.
Linardos T.I., Kalogerakis N. and Behie L.A. 1991. The effect of specific growth rate and death rate on monoclonal antibody production in hybridoma chemostat culture. Can. J. Chem. Engin. 69: 429–438.
Linz M., Zeng A.-P., Wagner R. and Deckwer W.-D. 1997. Stoichiometry, kinetics, and regulation of glucose and amino acid metabolism of a recombinant BHK cell line in batch and continuous cultures. Biotech. Progr. 13: 453–463.
Liou J.J., Srienc F. and Fredrickson A.G. 1997. Solutions of population balance models based on a successive generations approach. Chemical Eng. Sci. 52: 1529–1540.
Lüdemann I., Pörtner R., Schaefer C., Schick K., Sramkova K., Reher K., Neumaier M., Franek F. and Markl H. 1996. Improvement of culture stability of non-anchorage-dependent cells grown in serum-free media through immobilization. Cytotechnology 19(2): 111–124.
Mantzaris N.V., Liou J.J., Daoutidis P. and Srienc F. 1999. Numerical solution of a mass structured cell population balance model in an environment of changing substrate concentration. J. Biotech. 71: 157–174.
Mantzaris N.V., Daoutidis P. and Srienc F. 2001a. Numerical solution of multi-variable cell population balance models. I. Finite difference methods. Comput. Chem. Eng. 25: 1411–1440.
Mantzaris N.V., Daoutidis P. and Srienc F. 2001b. Numerical solution of multi-variable cell population balance models. II. Spectral methods. Comput. Chem. Eng. 25: 1441–1462.
Mantzaris N.V., Daoutidis P. and Srienc F. 2001c. Numerical solution of multi-variable cell population balance models. III. Finite element methods. Comput. Chem. Eng. 25: 1463–1481.
Martens D.E., Sipkema E.M., de Gooijer C.D., Beuvery E.C. and Tramper J. 1995. A combined cell-cycle and metabolic model for the growth of hybridoma cells in steady-state continuous culture. Biotech. Bioeng. 48: 49–65.
Mason R.L., Gunst R.F. and Hess J.L. 2003. Statistical Design and Analysis of Experiments: With Applications to Engineering and Science, John Wiley & Sons, New York, USA.
Morales J.A.A. 2001. Dynamic modelling of mammalian cell culture systems. MSc thesis, University of London.
Nathanson M.H. and Saidel G.M. 1985. Multiple-objective criteria for optimal experimental design: application to ferrokinetics. Am. J. Physiol. 248: R378–R386.
Paredes C., Prats E., Cairo J.J., Azorin F., Cornudella L. and Godia F. 1999. Modification of glucose and glutamine metabolism in hybridoma cells through metabolic engineering. Cytotechnology 30: 85–93.
Phillips P.J. 1996. The interaction of Experimentation and Computer Modelling for Animal Cell Culture, University of Sydney.
Pörtner R. and Schäfer T. 1996. Modelling hybridoma cell growth and metabolism-a comparison of selected models and data. J. Biotech. 49: 119–135.
Pörtner R., Schilling A., Lüdemann I. and Märkl H. 1996. High density fed-batch cultures for hybridoma cells performed with the aid of a kinetic model. Bioprocess Eng. 00: 000–000.
Ramkrishna D. 2000. Population balances: Theory and Applications to Particulate Systems in Engineering. Academic Press, New York.
Ramkrishna D. 1979. Statistical Models of Cell Populations. Adv. Biochem. Eng. 11: 1–47.
Ramkrishna D., Fredrickson A.G. and Tsuchiya H.M. 1968. On the relationships between various distribution functions in balanced unicellular growth. Bull. Math. Biophys. 30: 319–323.
Sanderson C.S. 1997. The Development and Application of a Structured Model for Animal Cell Metabolism. Ph.D thesis, University of Sydney.
Sanderson C.S., Barton G.W. and Barford J.P. 1995. Optimisation of animal cell culture media using dynamic simulation. Comput. Chem. Eng. 19: S681–S686.
Schilling C.H., Edwards J.S. and Palsson B.O. 1999. Toward metabolic phenomics: analysis of genomic data using flux balances. Biotech. Progr. 15: 288–295.
Shuler M. 1999. Single-cell models: promise and limitations. Cytotechnology 71: 225–228.
Srienc F. 1999. Short communication: Cytometric data as the basis for rigorous models of cell population dynamics. J. Biotech. 71: 233–238.
Tomita M., Hashimoto K., Takahashi K., Shimizu T.S., Matsuzaki Y., Miyoshi F., Saito K., Tanida S., Yugi K., Venter J.G. and Hutchison C.A.III 1999. E-cell: Software environment for whole-cell simulation. Bioinformatics 15: 72–84.
Tsuchiya H.M., Fredrickson A.G. and Aris R. 1966. Dynamics of microbial cell populations. Adv. Chem. Eng. 6: 125–206.
Tyson J.J. and Novak B. 2001. Regulation of the eukaryotic cell cycle: molecular anatagonism, hysteresis, and irreversible transitions. J. Theor. Biol. 210: 249–263.
Tziampazis E. and Sambanis A. 1994. Modeling of cell culture processes. Cytotechnology 14: 191–204.
Versyck K.J., Claes J.E. and Van Impe J.F. 1997. Practical identification of unstructured growth kinetics by application of optimal experimental design. Biotech. Progr. 13: 524–531.
Versyck K.J., Bernaerts K., Geeraerd A.H. and Van Impe J.F. 1999. Introducing optimal experimental design in predictive modeling: A motivating example. Int. J. Food Microbiol. 51: 39–51.
Villadsen J. 1999. Short communication: On the use of population balances. J. Biotech. 71: 251–253.
Walter E. 1987. Identifiability of Parametric Models. Pergamon Press, Oxford.
Wu P., Ray N.G. and Shuler M.L. 1992. A single cell model of Chinese hamster ovary cells. Ann NY Aca Sci 665: 152–187.
Zeng A.-P., Deckwer W.-D. and Hu W.-S. 1998. Determinants and rate laws of growth and death of hybridoma cells in continuous culture. Biotech. Bioeng. 57: 642–654.
Zhou W., Rehm J., Europa A. and Hu W.-S. 1997. Alteration of mammalian cell metabolism by dynamic nutrient feeding. Cytotechnology 24: 99–108.
Zullo L.C. 1991. Computer-aided Design of Experiments: An Engineering Approach. Ph.D thesis, University of London.
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Sidoli, F., Mantalaris, A. & Asprey, S. Modelling of Mammalian Cells and Cell Culture Processes. Cytotechnology 44, 27–46 (2004). https://doi.org/10.1023/B:CYTO.0000043397.94527.84
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DOI: https://doi.org/10.1023/B:CYTO.0000043397.94527.84