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

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

  •   Massimo Pisu

  •   Alessandro Concas

  •   Giacomo Cao

  •   Antonella Pantaleo

Abstract

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

Aguda B.D., Tang,Y. (1999). The kinetic origins of the restriction point in the mammalian cell cycle. Cell Prolif, 32, 321-335.

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.

Almeida S., Chaves, M., Delaunay, F., Feillet, C. (2017). A comprehensive reduced model of the mammalian cell cycle. IFAC-PapersOnLine. 50, 12617-12622.

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.

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.

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.

Ciliberto, A., Novak, B., Tyson, J.J. (2003). Mathematical model of the morphogenesis checkpoint in budding yeast. J. Cell Biol, 163, 1243-1254.

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.

Davidich, M.I., Bornholdt, S. (2008). Boolean Network Model Predicts Cell Cycle Sequence of Fission Yeast. PloS One, 3(2), e1672.

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.

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.

Florian, J.A., Parker, R.S. (2005). A population balance model of cell cycle-specific tumor growth. IFAC Proceeding Volumes. 38, 72-77.

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.

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.

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.

Gérard, C., Goldbeter, A. (2009). Temporal self-organization of the cyclin/Cdk network. PNAS, 106, 2164-2168.

Gérard, C., Goldbeter, A. (2012). From quiescence to proliferation: Cdk oscillations drive the mammalian cell cycle. Frontiers in physiology, 3, 413-430.

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.

Hanahan, D., Weinberg, R.A. (2011). Hallmarks of cancer: the next generation. Cell. 144, 646-674.

Hatzis, C., Srienc, F., Fredrickson, A.G. (1995). Multistaged corpuscolar models of microbial growth: Monte Carlo simulations. Biosystems. 36, 19-35.

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.

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.

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.

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.

Morgan, D.O. (1995). Principles of Cdk regulation. Nature. 374, 131-134.

Morgan, D.O. (1997). Cyclin-dependent kinases: engines, clocks, and microprocessors. Ann. Rev. Cell Dev. Biol., 13, 261-291.

Morgan, D.O. (2007). The cell cycle: principles of control, New Science Press, London, UK.

Murray, A., Hunt, T. (1993). The Cell Cycle: An Introduction. Oxford University Press, New York, NY, USA.

Nurse, P. (2000). A long twentieth century of cell cycle and beyond. Cell. 100, 71-78.

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.

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.

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.

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.

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.

Pisu, M., Concas, A., Cao, G. (2007). A novel simulation model for stem cells differentiation. J. Biotechnol. 130, 171-182.

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.

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.

Ramkrishna, D. (2000). Population balances. Theory and applications to particulate systems in engineering. Academic Press Inc., San Diego, USA.

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.

Shapiro, G.I., Harper, W. (1999). Anticancer drug targets: cell cycle and checkpoint control. J. Clin. Invest. 104, 645-653.

Sherer, E., Ramkrishna, D. (2008). Stochastic Analysis of Multistate Systems. Ind. Eng. Chem. Res. 47, 3430-3437.

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.

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.

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.

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.

##plugins.themes.bootstrap3.article.details##

How to Cite
Pisu, M., Concas, A., Cao, G., & Pantaleo, A. (2022). Mathematical Modelling and Computational Simulation of Mammalian Cell Cycle Progression in Batch Systems. European Journal of Biology and Biotechnology, 3(1), 1-10. https://doi.org/10.24018/ejbio.2022.3.1.315