Mathematical Modelling and Computational Simulation of Mammalian Cell Cycle Progression in Batch Systems



Abstract Views
572

Downloads
450

Citations

Share

##plugins.themes.bootstrap3.article.sidebar##

Submitted Dec 11, 2021
Published Jan 3, 2022
10.24018/ejbio.2022.3.1.315

Abstract viewed = 572 times

Table of Contents

##plugins.themes.bootstrap3.article.main##

Cell cycle and its progression play a crucial role in the life of all living organisms, in tissues and organs of animals and humans, and therefore are the subject of intense study by scientists in various fields of biomedicine, bioengineering and biotechnology. Effective and predictive simulation models can offer new development opportunities in such fields. In the present paper a comprehensive mathematical model for simulating the cell cycle progression in batch systems is proposed. The model includes a structured population balance with two internal variables (i.e., cell volume and age) that properly describes cell cycle evolution through the various stages that a cell of an entire population undergoes as it grows and divides. The rate of transitions between two subsequent phases of the cell cycle are obtained by considering a detailed biochemical model which simulates the series of complex events that take place during cell growth and its division. The model capability for simulating the effect of various seeding conditions and the adding of few substances during in vitro tests, is discussed by considering specific cases of interest in tissue engineering and biomedicine.

Keywords: Cell cycle progression, cyclins and Cdks, mathematical modelling, population balance

References

  1. Aguda B.D., Tang,Y. (1999). The kinetic origins of the restriction point in the mammalian cell cycle. Cell Prolif, 32, 321-335.
     Google Scholar
  2. Ahmadian, M., Tyson, J.J., Peccoud, J., Cao, Y. (2020). A hybrid stochastic model of the budding yeast cell cycle. npj Syst Biol Appl, 6, 1-10.
     Google Scholar
  3. Almeida S., Chaves, M., Delaunay, F., Feillet, C. (2017). A comprehensive reduced model of the mammalian cell cycle. IFAC-PapersOnLine. 50, 12617-12622.
     Google Scholar
  4. Banfalvi, G. (2017) Cell Cycle Synchronization: Methods and Protocols, Methods in Molecular Biology, vol. 1524, 2nd ed., Springer Science+Business Media, Humana Press, New York, USA.
     Google Scholar
  5. Chen, K.C., Csikasz-Nagy, A., Gyorffy, B., Val, J., Novak, B., Tyson, J.J. (2000). Kinetic analysis of a molecular model of the budding yeast cell cycle. Mol. Biol. Cell, 1, 369-391.
     Google Scholar
  6. Chen, K.C., Calzone, L., Csikasz-Nagy, A., Cross, F.R., Novak, B., Tyson, J.J. (2004). Integrative analysis of cell cycle control in budding yeast. Mol. Biol. Cell, 15, 3841-3862.
     Google Scholar
  7. Ciliberto, A., Novak, B., Tyson, J.J. (2003). Mathematical model of the morphogenesis checkpoint in budding yeast. J. Cell Biol, 163, 1243-1254.
     Google Scholar
  8. Csikasz-Nagy, A., Battogtokh, D., Chen, K.C., Novak, B., Tyson J.J. (2006). Analysis of a generic model of eukaryotic cell-cycle regulation. Biophys J, 90, 4361-4379.
     Google Scholar
  9. Davidich, M.I., Bornholdt, S. (2008). Boolean Network Model Predicts Cell Cycle Sequence of Fission Yeast. PloS One, 3(2), e1672.
     Google Scholar
  10. Fadda, S., Cincotti, A., Cao G. (2012a). Novel Population Balance Model to Investigate the Kinetics of In Vitro Cell Proliferation: Part I. Model development. Biotechnol. Bioeng.109, 772-781.
     Google Scholar
  11. Fadda, S., Cincotti, A., Cao G. (2012b). A Novel Population Balance Model to Investigate Kinetics of In Vitro Cell Proliferation: Part II. Numerical Solution, Parameters’ Determination and Model Outcomes. Biotechnol. Bioeng. 109, 782-796.
     Google Scholar
  12. Florian, J.A., Parker, R.S. (2005). A population balance model of cell cycle-specific tumor growth. IFAC Proceeding Volumes. 38, 72-77.
     Google Scholar
  13. Fredrickson, A.G., Mantzaris, N.V. (2002). A new set of population balance equations for microbial and cell cultures. Chem. Eng. Sci. 57, 2265-2278.
     Google Scholar
  14. Fuentes-Garí, M., Misener, R., García-Munzer, D., Velliou, E., Georgiadis, M.C., Kostoglou, M., Panoskaltsis, E.N., Mantalaris, A. (2015a). A Mathematical Model of Subpopulation Kinetics for the Deconvolution of Leukaemia Heterogeneity. J. R. Soc., Interface, 12, 20150276.
     Google Scholar
  15. Fuentes-Garí, M., Misener, R., Georgiadis, M.C., Kostoglou, M., Panoskaltsis, E.N., Mantalaris, A., Pistikopoulos, E.N. (2015b). Selecting a Differential Equation Cell Cycle Model for Simulating Leukemia Treatment. Ind. Eng. Chem. Res. 54, 8847-8859.
     Google Scholar
  16. Gérard, C., Goldbeter, A. (2009). Temporal self-organization of the cyclin/Cdk network. PNAS, 106, 2164-2168.
     Google Scholar
  17. Gérard, C., Goldbeter, A. (2012). From quiescence to proliferation: Cdk oscillations drive the mammalian cell cycle. Frontiers in physiology, 3, 413-430.
     Google Scholar
  18. Gérard, C., Goldbeter, A. (2014). The balance between cell cycle arrest and cell proliferation: control by the extracellular matrix and by contact inhibition, Interface Focus, 4, 1-13.
     Google Scholar
  19. Hanahan, D., Weinberg, R.A. (2011). Hallmarks of cancer: the next generation. Cell. 144, 646-674.
     Google Scholar
  20. Hatzis, C., Srienc, F., Fredrickson, A.G. (1995). Multistaged corpuscolar models of microbial growth: Monte Carlo simulations. Biosystems. 36, 19-35.
     Google Scholar
  21. Karra, S., Sager, B., Karim, M.M. (2010). Multi-scale modeling of heterogeneities in mammalian cell culture processes. Ind. Eng. Chem. Res. 49, 7990–8006.
     Google Scholar
  22. Liu, Y.H., Bi, J.X., Zeng, A.P., Yuan, J.Q. (2007). A population balance model describing the cell cycle dynamics of myeloma cell cultivation. Biotechnol. Prog. 23, 1198-1209.
     Google Scholar
  23. Mancuso, L., Liuzzo, M.I., Fadda, S., Pisu, M., Cincotti, A., Arras, M., Desogus, E., Piras, F., Piga, G., La Nasa, G., Concas, A., Cao, G. (2009). Experimental analysis and modeling of in vitro mesenchymal stem cells proliferation. Cell proliferat. 42, 602-616.
     Google Scholar
  24. Mancuso, L., Liuzzo, M.I., Fadda, S., Pisu, M., Cincotti, A., Arras, M., La Nasa, G., Concas, A., Cao, G. (2010). In vitro ovine articular chondrocyte proliferation: Experiments and modeling. Cell Proliferat. 43, 310-320.
     Google Scholar
  25. Morgan, D.O. (1995). Principles of Cdk regulation. Nature. 374, 131-134.
     Google Scholar
  26. Morgan, D.O. (1997). Cyclin-dependent kinases: engines, clocks, and microprocessors. Ann. Rev. Cell Dev. Biol., 13, 261-291.
     Google Scholar
  27. Morgan, D.O. (2007). The cell cycle: principles of control, New Science Press, London, UK.
     Google Scholar
  28. Murray, A., Hunt, T. (1993). The Cell Cycle: An Introduction. Oxford University Press, New York, NY, USA.
     Google Scholar
  29. Nurse, P. (2000). A long twentieth century of cell cycle and beyond. Cell. 100, 71-78.
     Google Scholar
  30. Pantaleo, A., Kesely, K.R., Pau, M.C., Tsamesidis, I., Schwarzer, E., Skorokhod, O.A., Chien, H.D., Ponzi, M., Bertuccini, L., Low, P.S., Turrini, F.M. (2017). Syk inhibitors interfere with erythrocyte membrane modification during P falciparum growth and suppress parasite egress. Blood. 130, 1031-1040.
     Google Scholar
  31. Pisu, M., Concas, A., Cao, G. (2015). A novel quantitative model of cell cycle progression based on cyclin-dependent kinases activity and population balances. Comp. Biol. and Chem, 55,1-13.
     Google Scholar
  32. Pisu, M., Lai, N., Cincotti, A., Delogu, F., Cao, G. (2003). A simulation model for the growth of engineered cartilage on polymeric scaffolds. Int. J. Chem. React. Eng. http://www.bepress.com/ijcre/vol1/A38.
     Google Scholar
  33. Pisu, M., Lai, N., Cincotti, A., Concas, A., Cao, G. (2004). Model of engineered cartilage growth in rotating bioreactors. Chem. Eng. Sci. 59, 5035-5040.
     Google Scholar
  34. Pisu, M., Concas, A., Lai, N., Cao, G. (2006). A novel simulation model for engineered cartilage growth in static systems. Tissue Eng., 12, 2311-2320.
     Google Scholar
  35. Pisu, M., Concas, A., Cao, G. (2007). A novel simulation model for stem cells differentiation. J. Biotechnol. 130, 171-182.
     Google Scholar
  36. Pisu, M., Concas, A., Fadda, S., Cincotti, A., Cao, G. (2008). A simulation model for stem cells differentiation into specialized cells of non-connective tissues. Computational Biology and Chemistry. 32, 338-344.
     Google Scholar
  37. Qu Z., Weiss, J.N., MacLellan, W.R. (2003). Regulation of the mammalian cell cycle: A model of the G1-to-S transition. Am J Physiol, 284, C349-364.
     Google Scholar
  38. Ramkrishna, D. (2000). Population balances. Theory and applications to particulate systems in engineering. Academic Press Inc., San Diego, USA.
     Google Scholar
  39. Secchi, C., Orecchioni, M., Carta, M., Galimi, F., Turrini, F., Pantaleo, A. (2020). Signaling Response to Transient Redox Stress in Human Isolated T Cells: Molecular Sensor Role of Syk Kinase and Functional Involvement of IL2 Receptor and L-Selectine. Sensors. 20, 466-482.
     Google Scholar
  40. Shapiro, G.I., Harper, W. (1999). Anticancer drug targets: cell cycle and checkpoint control. J. Clin. Invest. 104, 645-653.
     Google Scholar
  41. Sherer, E., Ramkrishna, D. (2008). Stochastic Analysis of Multistate Systems. Ind. Eng. Chem. Res. 47, 3430-3437.
     Google Scholar
  42. Trobridge, G., Russell, D.W. (2004). Cell Cycle Requirements for Transduction by Foamy Virus Vectors Compared to Those of Oncovirus and Lentivirus Vectors. Journal of virology. 78, 2327-2335.
     Google Scholar
  43. Tyson, J.J. (1991). Modeling the Cell-Division Cycle - Cdc2 and Cyclin Interactions, Proceedings of the National Academy of Sciences of the United States of America. 88, 7328-7332.
     Google Scholar
  44. van Vugt, M.A., Bras, A., Medema, R.H. (2004). Polo-like kinase-1 controls recovery from a G2 DNA damage-induced arrest in mammalian cells. Mol Cell. 15, 799-811.
     Google Scholar
  45. Weis, M.C., Avva, J., Jacobberger, J.W., Sreenath, S.N. (2014). A Data-Driven, Mathematical Model of Mammalian Cell Cycle Regulation. PloS One, 9, e97130.
     Google Scholar