Abstract.
Most anti-cancer drugs in use today exert their effects by inducing a programmed cell death mechanism. This process, termed apoptosis, is accompanied by degradation of the DNA and produces cells with a range of DNA contents. We have previously developed a phase transition mathematical model to describe the mammalian cell division cycle in terms of cell cycle phases and the transition rates between these phases. We now extend this model here to incorporate a transition to a programmed cell death phase whereby cellular DNA is progressively degraded with time. We have utilised the technique of flow cytometry to analyse the behaviour of a melanoma cell line (NZM13) that was exposed to paclitaxel, a drug used frequently in the treatment of cancer. The flow cytometry profiles included a complex mixture of living cells whose DNA content was increasing with time and dying cells whose DNA content was decreasing with time. Application of the mathematical model enabled estimation of the rate constant for entry of mitotic cells into apoptosis (0.035 per hour) and the duration of the period of DNA degradation (51 hours). These results provide a dynamic model of the action of an anticancer drug that can be extended to improve the clinical outcome in individual cancer patients.
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Baguley, B.C., Marshall, E.S., Finlay, G.J.: Short-term cultures of clinical tumor material: potential contributions to oncology research. Oncol. Res. 11, 115–24 (1999)
Basse, B., Baguley, B.C., Marshall, E., Joseph, W.R., van-Brunt, B., Wake, G.C., 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)
Delves, L.M.: Rayleigh-Ritz-Galerkin Methods chapter~6, pp. 64–79. In Delves and Walsh [4], 1974
Delves, L.M., Walsh, J., ed.: Numerical Solution of Integral equations. Clarendon Press, Oxford, 1974
Gudkov, A.V., Komarova, E.A.: The role of p53 in determining sensitivity to radiotherapy. Nature Reviews Cancer 3, 117–129 (2003)
Hochstadt, H.: Integral Equations. Wiley Interscience, USA, 1973
Jordan, M.A., Wendell, K., Gardiner, S., Derry, W.B., Copp, H., Wilson, L.: Mitotic block induced in HeLa cells by low concentrations of paclitaxel (taxol) results in abnormal mitotic exit and apoptotic cell death. Cancer Res. 56, 816–825 (1996)
Lengauer, C., Kinzler, K.W., Vogelstein, B.: Genetic instability incolorectal cancers. Nature 386, 623–627 (1997)
Mackie, A.G.: Boundary Value Problems. Oliver and Boyd, 1966
Meng, X.W., Fraser, M.J., Feller, J.M., Ziegler, J.B.: Caspase-3 activates endo- exonuclease: further evidence for a role of the nuclease in apoptosis. Apoptosis 5, 243–254 (2000)
Metz, J.A.J., Diekmann, O.: The dynamics of physiologically structured populations. Number 68. Lecture notes in Bio-mathematics, Springer-Verlag, 1986
Morse, P.M., Feshbach, H.: Methods of Theoretical Physics. Volume 1, McGraw-Hill, New York, 1953
Parmar, J., Marshall, E.S., Charters, G.A., Holdaway, K.M., Shelling, A.N., Baguley, B.C.: Radiation-induced cell cycle delays and p53 status of early passage melanoma lines. Oncol. Res. 12, 149–155 (2000)
Peitsch, M.C., Polzar, B., Stephan, H., Crompton, T., MacDonald, H.R., Mannherz, H.G., Tschopp, J.: Characterization of the endogenous deoxyribonuclease involved in nuclear DNA degradation during apoptosis (programmed cell death). EMBO J. 12, 371–377 (1993)
Stakgold, I.: Green’s Functions and Boundary Value Problems. Wiley-InterScience, New~York, 1979
Steel, G.G.: Growth kinetics of tumours Clarendon. Oxford, 1977
Takahashi, M.: Theoretical Basis for cell cycle analysis. II. Further studies on labelled mitosis wave method. J. Theor. Biol. 18, 195–209 (1968)
Telford, W.G., King, L.E., Fraker, P.J.: Comparative evaluation of several DNA binding dyes in the detection of apoptosis-associated chromatin degradation by flow cytometry. Cytometry 13, 137–143 (1992)
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Revised version: 9 October 2003
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Basse, B., Baguley, B., Marshall, E. et al. Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel. J. Math. Biol. 49, 329–357 (2004). https://doi.org/10.1007/s00285-003-0254-2
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DOI: https://doi.org/10.1007/s00285-003-0254-2