Summary
We address the following question: Can one sustain, on the basis of mathematicalmodels, that for cancer cells, the loss of control by circadian rhythm favours a faster populationgrowth? This question, which comes from the observation that tumour growth in mice isenhanced by experimental disruption of the circadian rhythm, may be tackled by mathematicalmodelling of the cell cycle. For this purpose we consider an age-structured population modelwith control of death (apoptosis)rates and phase transitions, and two eigenvalues: one for periodic control coefficients (via a variant of Floquet theory in infinite dimension)and one forconstant coefficients (taken as the time average of the periodic case). We show by a direct proofthat, surprisingly enough considering the above-mentioned observation, the periodic eigenvalue is always greater than the steady state eigenvalue when the sole apoptosis rate is concerned. We also show by numerical simulations when transition rates between the phases of the cell cycle are concerned, that, without further hypotheses, no natural hierarchy between the two eigenvalues exists. This at least shows that, if such models are to take into account the above-mentioned observation, control of death rates inside phases is not sufficient, and that transition rates between phases are a key target in proliferation control.
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References
Arino, O.: A survey of structured cell population dynamics. Acta Biotheor., 43, 3–25 (1995).
Basse, B., Baguley, B.C., Marshall, E.S., Joseph, W.R., van Brunt, B., Wake, G., Wall, D.J.N.: A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. J. Math. Biol., 47, 295 –312 (2003).
Bjarnason, G., Jordan, R.C.K., Sothern, R.B.: Circadian variations in the expression of cell-cycle proteins in human oral epithelium. Am. J. Pathol., 154, 613 –622 (1999).
Chiorino, G., Metz, J.A.J., Tomasoni, D., Ubezio, P. Desynchronization rate in cell populations: mathematical modeling and experimental data. J. Theor. Biol., 208, 185 –199 (2001).
Clairambault, J., Laroche, B., Mischler, S., Perthame, B.: A mathematical model of the cell cycle and its control. INRIA research report # 4892 (2003).
Clairambault, J., Mischler, S., Perthame B.: Circadian rhythm and tumour growth. C. R. Acad. Sci. Paris, Ser. I, 342, 17 –22 (2006).
Cohen, J.E., Friedland, S., Kato, T., Kelly, F.P.: Eigenvalue inequalities for products of matrix exponentials. Lin. Alg. Appl., 45, 55 –95 (1982).
Davis, S., Mirick, D.K., Stevens, R.G.: Night shift work, light at night, and risk of breast cancer. J. Natl Cancer Inst., 93, 1557 –1562 (2001).
Filipski, E., King, V.M., Li, X.M., Granda, T. G., Mormont, M.C., Liu, X.H., Claustrat, B., Hastings, M.H., Lévi, F.: Host circadian clock as a control point in tumor progression. J. Natl. Cancer Inst., 94, 690 –697 (2002).
Filipski, E., Innominato, P.F., Wu, M.W., Li, X.M., Iacobelli, S., Xian, L.J., Lévi, F.: Effect of light and food schedules on liver and tumor molecular clocks in mice. J. Natl. Cancer Inst., 97, 507 –517 (2005).
Fu, L., Pelicano, H., Liu, J., Huang, P., Lee, C.C.: The circadian gene Per2plays an important role in tumor suppression and DNA damage response in vivo. Cell, 111, 41 –50 (2002).
Fu, L., Lee, C.C.: The circadian clock: pacemaker and tumor suppressor. Nature reviews/Cancer, 2003(3): 350–361.
Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms. Cambridge University Press (1996).
Lebowitz, J.L., Rubinow, S.I.: A theory for the age and generation time distribution of a microbial population. J. Math. Biol., 1, 17 –36 (1977).
Léevi, F. (ed.): Cancer chronotherapeutics. Special issue of Chronobiology International Vol. 19 (1) (2002).
Matsuo, T., Yamaguchi, S., Mitsui, S., Emi, A., Shimoda, F., Okamura, H.: Control mechanism of the circadian clock for timing of cell division in vivo. Science, 302, 255 –259 (2003).
Metz, J.A.J., Diekmann, O.: The dynamics of physiologically structured populations. LN in Biomathematics 68, Springer-Verlag (1986).
Michel, P., Mischler, S., Perthame, B.: The entropy structure of models of structured population dynamics. General relative entropy inequality: an illustration on growth models. J. Math. Pures et Appl., 84, 1235 –1260 (2005).
Mischler, S., Perthame, B., Ryzhik L.: Stability in a nonlinear population maturation model. M3AS, 12, 1751 –1772 (2002).
Mormont, M.-C., Lévi, F.: Cancer chronotherapy: principles, applications and perspectives. Cancer, 97, 155 –169 (2003).
Nagoshi, E., Saini, C., Bauer, C., Laroche, T., Naef, F., Schibler, U. Circadian gene expression in individual fibbroblasts: cell-autonomous and self-sustained oscillators pass time to daughter cells. Cell, 119, 693–705 (2004).
Rotenberg, M.: Transport theory for growing cell populations. J. Theor. Biol., 103, 181 –199 (1983).
Schernhammer, E.S., Laden, F., Speizer, F.E., Willett, W.C., Hunter, D.J., Kawachi, I., Fuchs, C.S., Colditz, G.A.: Night-shift work and risk of colorectal cancer in the Nurses’ Health Study. J. Natl. Cancer Inst., 95, 825 –828 (2003).
Schibler, U.: Liver regeneration clocks on. Science, 302, 234 –235 (2003).
Wu M.W., Li X.M., Xian L.J., Lévi F.: Effects of meal timing on tumor progression in mice. Life Sciences, 75, 1181 –1193 (2004).
You, S., Wood, P.A., Xiong, Y., Kobayashi, M., Du-Quiton, J., Hrushesky, W.J.M.: Daily coordination of cancer growth and circadian clock gene expression. Breast Canc. Res. Treat., 91, 47 –60 (2005).
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Clairambault, J., Michel, P., Perthame, B. (2007). A Mathematical Model of the Cell Cycle and Its Circadian Control. In: Deutsch, A., Brusch, L., Byrne, H., Vries, G.d., Herzel, H. (eds) Mathematical Modeling of Biological Systems, Volume I. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4558-8_21
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DOI: https://doi.org/10.1007/978-0-8176-4558-8_21
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