Abstract
Increasing the knowledge of various cell cycle kinetic parameters, such as the length of the cell cycle and its different phases, is of considerable importance for several purposes including tumor diagnostics and treatment in clinical health care and a deepened understanding of tumor growth mechanisms. Of particular interest as a prognostic factor in different cancer forms is the S phase, during which DNA is replicated. In the present paper, we estimate the DNA replication rate and the S phase length from bromodeoxyuridine-DNA flow cytometry data. The mathematical analysis is based on a branching process model, paired with an assumed gamma distribution for the S phase duration, with which the DNA distribution of S phase cells can be expressed in terms of the DNA replication rate. Flow cytometry data typically contains rather large measurement variations, however, and we employ nonparametric deconvolution to estimate the underlying DNA distribution of S phase cells; an estimate of the DNA replication rate is then provided by this distribution and the mathematical model.
Similar content being viewed by others
References
Arino, O., Bertuzzi, A., Gandolfi, A., Sanchez, E., Sinisgalli, C., 2005. The asynchronous exponential growth property in a model for the kinetic heterogeneity of tumour cell populations. J. Math. Anal. Appl. 302, 521–42.
Bagwell, C.B., 1993. Theoretical aspects of flow cytometry data analysis. In: Bauer, K.D., Duque, R.E., Shankey, T.V. (Eds.), Clinical Flow Cytometry: Principles and Application, pp. 41–1. Williams and Wilkins, Baltimore
Bagwell, C.B., Clark, G.M., Spyratos, F., Chassevent, A., Bendahl, P.-O., Stål, O., Killander, D., Jourdan, M.L., Romain, S., Hunsberger, B., Baldetorp, B., 2001. Optimizing flow cytometric DNA ploidy and S-phase fraction as independent prognostic markers for node-negative breast cancer specimens. Cytometry 46, 121–35.
Baisch, H., Otto, U., 1993. Intratumoral heterogeneity of S phase transition in solid tumours determined by bromodeoxyuridine labeling and flow cytometry. Cell Prolif. 26, 439–48.
Basse, B., Baguley, B.C., Marshall, E.S., Wake, G.C., Wall, D.J.N., 2005. Modelling the flow of cytometric data obtained from unperturbed human tumour cell lines: parameter fitting and comparison. Bull. Math. Biol. 67, 815–30.
Begg, A.C., McNally, N.J., Shrieve, D.C., Kärcher, H., 1985. A method to measure the duration of DNA synthesis and the potential doubling time from a single sample. Cytometry 6, 620–26.
Bendahl, P.-O., 1995. Estimation and prognostic value of S-phase fractions in cancer cell populations. Ph.D. thesis, Dept. Math. Stat., Lund University, Lund, Sweden
Bertuzzi, A., Gandolfi, A., Germani, A., Vitelli, R., 1983. Estimation of cell DNA synthesis rate from flow-cytometric histograms. Cell Biophys. 5, 223–36.
Bertuzzi, A., Gandolfi, A., Germani, A., Spanò, M., Starace, G., Vitelli, R., 1984. Analysis of DNA synthesis rate of cultured cells from flow cytometric data. Cytometry 5, 619–28.
Bertuzzi, A., Faretta, M., Gandolfi, A., Sinisgalli, C., Starace, G., Valoti, G., Ubezio, P., 2002. Kinetic heterogeneity of an experimental tumour revealed by BrdUrd incorporation and mathematical modeling. Bull. Math. Biol. 64, 355–84.
Carroll, R.J., Hall, P., 2004. Low order approximations in deconvolution and regression with errors in variables. J. R. Stat. Soc. B 66, 31–6.
Chiorino, G., Metz, J.A.J., Tomasoni, D., Ubezio, P., 2001. Desynchronization rate in cell populations: Mathematical modeling and experimental data. J. Theor. Biol. 208, 185–99.
Dobrowsky, W., Dobrowsky, E., Wilson, G.D., 2003. In vivo cell kinetic measurements in a randomized trial of continuous hyperfractionated accelerated radiotherapy with or without mitomycin C in head-and-neck cancer. Int. J. Radiat. Oncol. Biol. Phys. 55, 576–82.
Dolbeare, F., Gratzner, H., Pallavicini, M.G., Gray, J.W., 1983. Flow cytometric measurement of total DNA content and incorporated bromodeoxyuridine. Proc. Natl. Acad. Sci. 80, 5573–577.
Dörmer, P., Brinkmann, R., Born, R., Steel, G.G., 1975. Rate and time of DNA synthesis of individual Chinese hamster cells. Cell Tissue Kinet. 8, 399–12.
Haccou, P., Jagers, P., Vatutin, V.A., 2005. Branching Processes: Variation, Growth and Extinction of Populations. Cambridge University Press, Cambridge.
Jagers, P., 1975. Branching Processes with Biological Applications. Wiley, Chichester.
Jagers, P., 1983. Stochastic models for cell kinetics. Bull. Math. Biol. 45, 507–19.
Jagers, P., 1991. The growth and stabilization of populations. Stat. Sci. 6, 269–83.
Johansson, M.C., Baldetorp, B., Bendahl, P.-O., Johansson, R., Oredsson, S.M., 1994. An improved mathematical method to estimate DNA synthesis time of bromodeoxyuridine-labelled cells using FCM-derived data. Cell Prolif. 27, 475–88.
Johansson, M.C., Baldetorp, B., Bendahl, P.-O., Fadeel, I.A., Oredsson, S.M., 1996. Comparison of mathematical formulas used for estimation of DNA synthesis time of bromodeoxyuridine-labelled cell populations with different proliferative characteristics. Cell Prolif. 29, 525–38.
Kimmel, M., Axelrod, D.E., 2000. Branching Processes in Biology. Springer, New York.
Larsson, S., Johansson, M., Oredsson, S., Holst, U., 2005. A Markov model approach shows a large variation in the length of S phase in MCF-7 breast cancer cells. Cytometry A 65, 15–5.
Macdonald, P.D.M., 1970. Statistical inference for the fraction labelled mitoses curve. Biometrika 57, 489–03.
Macdonald, P., 1981. Towards an exact analysis of stathmokinetic and continuous labeling experiments. In: Rotenberg, M. (Ed.), Biomathematics and Cell Kinetics: Proceedings of a Workshop Held at Asilomar California, pp. 125–42. Elsevier, Amsterdam
Puck, T., Steffen, J., 1963. Life cycle analysis of mammalian cells I. A method for localizing metabolic events within the life cycle, and its application to the action of colcemide and sublethal doses of X-irradiation. Biophys. J. 3, 379–97.
Ruppert, D., 1997. Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation. J. Am. Stat. Assoc. 92, 1049–062.
Schutte, B., Reynders, M.M., van Assche, C.L., Hupperets, P.S., Bosman, F.T., Blijham, G.H., 1987. An improved method for the immunocytochemical detection of bromodeoxyuridine labeled nuclei using flow cytometry. Cytometry 8, 372–76.
So, A., Downey, K., 1992. Eukaryotic DNA replication. Crit. Rev. Biochem. Mol. Biol. 27, 129–55.
van Erp, P.E.J., Brons, P.P.T., Boezeman, J.B.M., de Jongh, G.J., Bauer, F.W., 1988. A rapid flow cytometric method for bivariate bromodeoxyuridine/DNA analysis using simultaneous proteolytic enzyme digestion and acid denaturation. Cytometry 9, 627–30.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Larsson, S., Rydén, T., Holst, U. et al. Estimating the Total Rate of DNA Replication Using Branching Processes. Bull. Math. Biol. 70, 2177–2194 (2008). https://doi.org/10.1007/s11538-008-9339-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-008-9339-9