, Volume 44, Issue 1–2, pp 27–46 | Cite as

Modelling of Mammalian Cells and Cell Culture Processes

  • F.R. Sidoli
  • A. Mantalaris
  • S.P. Asprey


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.

Mammalian cells Model discrimination Model distinguishability Model identifiability Optimal experiment design Parameter precision Population balance model Single cell model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Asprey S.P. and Machietto S. 2000. Statistical tools for optimal dynamic model building. Comput. Chem. Eng. 24: 1261–1267.Google Scholar
  2. 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.Google Scholar
  3. Asprey S.P. and Machietto S. 2002. Designing robust optimal dynamic experiments. J. Process Control 12: 545–556.Google Scholar
  4. Bailey J.E. 1998. Mathematical modeling and analysis in biochemical engineering. Biotech. Progr. 14: 8–20.Google Scholar
  5. Barford J.P., Phillips P.J. and Harbour C. 1992. Simulation of animal cell metabolism. Cytotechnology 10: 63–74.Google Scholar
  6. 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.Google Scholar
  7. 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.Google Scholar
  8. Cain S.J. and Chau C.C. 1998. Transition probability cell cycle model with product formation. Biotech. Bioeng. 58: 387–399.Google Scholar
  9. Cazzador L. and Mariani L. 1993. Growth and production modelling in hybridoma continuous culture. Biotech. Bioeng. 38: 781–787.Google Scholar
  10. 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.Google Scholar
  11. 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.Google Scholar
  12. 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.Google Scholar
  13. Domach M.M. and Shuler M.L. 1984. A finite representation model for an asynchronous culture of E. coli. Biotech. Bioeng. 26: 877–884.Google Scholar
  14. Duncan A. 2002. Antibodies hold the key. Chemistry & Industry.Google Scholar
  15. Eakman J.M., Fredrickson A.G. and Tsuchiya H.M. 1966. Statistics and dynamics of microbial cell populations. Chem. Eng. Progr. 62: 37–49.Google Scholar
  16. 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.Google Scholar
  17. 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.Google Scholar
  18. 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.Google Scholar
  19. Fredrickson A.G., Ramkrishna D. and Tsuchiya H.M. 1967. Statistics and dynamics of procaryotic cell population. Math. Biosci. 1: 327–374.Google Scholar
  20. Gombert A.K. and Nielsen J. 2000. Mathematical modelling of metabolism. Curr. Opin. Biotech. 11: 180–186.Google Scholar
  21. Gray L. and Jasuja R. 2001. B-147 The New Future of Biotechnology: Enabling Technologies and Star Products. Business Communication Company, Inc.Google Scholar
  22. Hatzis C., Srienc F. and Fredrickson A.G. 1995. Multistaged corpuscular models of microbiol growth: Monte carlo simulations. Biosystems 36: 19–35.Google Scholar
  23. 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.Google Scholar
  24. Jacques J.A. 1998. Design of experiments. J. Franklin Inst. 335B: 259–279.Google Scholar
  25. 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.Google Scholar
  26. 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.Google Scholar
  27. 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.Google Scholar
  28. 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.Google Scholar
  29. 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.Google Scholar
  30. 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.Google Scholar
  31. 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.Google Scholar
  32. 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.Google Scholar
  33. 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.Google Scholar
  34. 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.Google Scholar
  35. 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.Google Scholar
  36. 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.Google Scholar
  37. 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.Google Scholar
  38. 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.Google Scholar
  39. 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.Google Scholar
  40. 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.Google Scholar
  41. Morales J.A.A. 2001. Dynamic modelling of mammalian cell culture systems. MSc thesis, University of London.Google Scholar
  42. Nathanson M.H. and Saidel G.M. 1985. Multiple-objective criteria for optimal experimental design: application to ferrokinetics. Am. J. Physiol. 248: R378–R386.Google Scholar
  43. 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.Google Scholar
  44. Phillips P.J. 1996. The interaction of Experimentation and Computer Modelling for Animal Cell Culture, University of Sydney.Google Scholar
  45. Pörtner R. and Schäfer T. 1996. Modelling hybridoma cell growth and metabolism-a comparison of selected models and data. J. Biotech. 49: 119–135.Google Scholar
  46. 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.Google Scholar
  47. Ramkrishna D. 2000. Population balances: Theory and Applications to Particulate Systems in Engineering. Academic Press, New York.Google Scholar
  48. Ramkrishna D. 1979. Statistical Models of Cell Populations. Adv. Biochem. Eng. 11: 1–47.Google Scholar
  49. 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.Google Scholar
  50. Sanderson C.S. 1997. The Development and Application of a Structured Model for Animal Cell Metabolism. Ph.D thesis, University of Sydney.Google Scholar
  51. 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.Google Scholar
  52. 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.Google Scholar
  53. Shuler M. 1999. Single-cell models: promise and limitations. Cytotechnology 71: 225–228.Google Scholar
  54. Srienc F. 1999. Short communication: Cytometric data as the basis for rigorous models of cell population dynamics. J. Biotech. 71: 233–238.Google Scholar
  55. 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.Google Scholar
  56. Tsuchiya H.M., Fredrickson A.G. and Aris R. 1966. Dynamics of microbial cell populations. Adv. Chem. Eng. 6: 125–206.Google Scholar
  57. 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.Google Scholar
  58. Tziampazis E. and Sambanis A. 1994. Modeling of cell culture processes. Cytotechnology 14: 191–204.Google Scholar
  59. 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.Google Scholar
  60. 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.Google Scholar
  61. Villadsen J. 1999. Short communication: On the use of population balances. J. Biotech. 71: 251–253.Google Scholar
  62. Walter E. 1987. Identifiability of Parametric Models. Pergamon Press, Oxford.Google Scholar
  63. 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.Google Scholar
  64. 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.Google Scholar
  65. Zhou W., Rehm J., Europa A. and Hu W.-S. 1997. Alteration of mammalian cell metabolism by dynamic nutrient feeding. Cytotechnology 24: 99–108.Google Scholar
  66. Zullo L.C. 1991. Computer-aided Design of Experiments: An Engineering Approach. Ph.D thesis, University of London.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • F.R. Sidoli
  • A. Mantalaris
  • S.P. Asprey

There are no affiliations available

Personalised recommendations