Abstract
In the present paper we propose a method of analysis of the cell kinetic characteristics of in vivo experimental tumours, that uses DNA-BrdUrd flow cytometry data at various times after the bromodeoxyuridine (BrdUrd) injection and mathematical modelling. The model of the cell population takes into account the cell-cell heterogeneity of the progression rate across cell cycle phases within the tumour, and assumes a strict correlation between the durations of S and G2M phases. The model also allows for a nonconstant DNA synthesis rate across S phase. In addition, the measurement process is modelled, considering the possibility of nonimpulsive labelling and providing a representation of the time course of the bivariate DNA-BrdUrd fluorescence distribution. Sequential DNA-BrdUrd distributions were obtained in vivo from a human ovarian carcinoma transplanted in mice and, for comparison, in vitro from a cell line of the same origin. From these data, that included the fractional density and the mean BrdUrd-fluorescence of BrdUrd-positive cells as a function of the DNA-fluorescence, kinetic parameters such as the potential doubling time (T pot) and the mean and variance of the transit times in S and G2M phases, were estimated. This study revealed the presence of a substantial heterogeneity in S and G2M phases within the in vivo cell population and of a lower heterogeneity in the in vitro population. Moreover, our analysis suggests a nonnegligible effect of the BrdUrd pharmacokinetics in the in vivo cell labelling.
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References
Bagwell, C. B. (1993). Theoretical aspects of flow cytometry data analysis, in Clinical Flow Cytometry, K. D. Bauer, R. E. Duque and T. V. Shankey (Eds), Baltimore: Williams and Wilkins, pp. 41–61.
Baisch, H. and U. Otto (1993). Intratumoral heterogeneity of S phase transition in solid tumours determined by bromodeoxyuridine labelling and flow cytometry. Cell Prolif. 26, 439–448.
Baisch, H., U. Otto, U. Hatje and H. Fack (1995). Heterogeneous cell kinetics in tumors analyzed with a simulation model for bromodeoxyuridine single and multiple labeling. Cytometry 21, 52–61.
Begg, A. C., N. J. McNally, D. C. Shrieve and H. Kärcher (1985). A method to measure the duration of DNA synthesis and the potential doubling time from a single sample. Cytometry 6, 620–626.
Bergers, E., P. J. van Diest and J. P. Baak (1996). Tumour heterogeneity of DNA cell cycle variables in breast cancer measured by flow cytometry. J. Clin. Pathol. 49, 931–937.
Bertuzzi, A., N. Del Grosso, A. Gandolfi, C. Sinisgalli and G. Starace (1995a). Cell cycle analysis by the relative movement approach: effect of variability across S-phase of DNA synthesis rate. Cell Prolif. 28, 107–120.
Bertuzzi, A., A. Gandolfi, C. Sinisgalli and G. Starace (1995b). Relationship between DNA synthesis rate and DNA-BrdUrd distribution in pulse labelling experiments, in Mathematical Population Dynamics: Analysis of Heterogeneity, Vol. 2, O. Arino, D. Axelrod and M. Kimmel (Eds), Winnipeg: Wuerz, pp. 71–86.
Bertuzzi, A. and A. Gandolfi (1999). A model for estimating cell kinetic parameters of experimental tumours studied by BrdUrd labelling and flow cytometry. Arch. Control Sci. 9, 41–56.
Bertuzzi, A., A. Gandolfi, C. Sinisgalli and G. Starace (1997). Estimation of cell cycle kinetic parameters by flow cytometry, in Advances in Mathematical Population Dynamics—Molecules, Cells and Man, O. Arino, D. Axelrod and M. Kimmel (Eds), Singapore: World Scientific, pp. 167–180.
Cappella, P., D. Tomasoni, M. Faretta, M. Lupi, F. Montalenti, F. Banzato, M. D’Incalci and P. Ubezio (2001). Cell cycle effects of gemcitabine. Int. J. Cancer 93, 401–408.
Carlton, J. C., N. H. A. Terry and R. A. White (1991). Measuring potential doubling times of murine tumors using flow cytometry. Cytometry 12, 645–650.
Chiorino, G., J. A. J. Metz, D. Tomasoni and P. Ubezio (2001). Desynchronization rate in cell populations: mathematical modeling and experimental data. J. Theor. Biol. 208, 185–199.
Dolbeare, F. (1995). Bromodeoxyuridine: a diagnostic tool in biology and medicine, Part I: historical perspectives, histochemical methods and cell kinetics. Histochem. J. 27, 339–369.
Dolbeare, F., H. Gratzner, M. G. Pallavicini and J. W. Gray (1983). Flow cytometric measurement of total DNA content and incorporated bromodeoxyuridine. Proc. Natl. Acad. Sci. USA 80, 5573–5577.
Gratzner, H. G. (1982). Monoclonal antibody to 5-bromo-and 5-iododeoxyuridine: a new reagent for detection of DNA replication. Science 218, 474–475.
Kallinowski, F., K. H. Schlenger, S. Runkel, M. Kloes, M. Stohrer, P. Okunieff and P. Vaupel (1989). Blood flow, metabolism, cellular microenvironment, and growth rate of human tumor xenografts. Cancer Res. 49, 3759–3764.
Kriss, J. P. and L. Revesz (1961). Quantitative studies of incorporation of exogenous thymidine and 5-bromodeoxyuridine into deoxyribonucleic acid of mammalian cells in vitro. Cancer Res. 21, 1141–1147.
Massazza, G., A. Tomasoni, A. Lucchini, P. Allavena, E. Erba, N. Colombo, A. Mantovani, M. D’Incalci, C. Mangioni and R. Giavazzi (1989). Intraperitoneal and subcutaneous xenograft of human ovarian carcinoma in nude mice and their potential in experimental therapy. Int. J. Cancer 44, 494–500.
Powell, B. L., B. W. Gregory, T. E. Kute, T. M. Morgan, E. S. Lyerly and R. L. Capizzi (1990). Bromodeoxyuridine incorporation into DNA of human leukemia cells is not concentration dependent. Cytometry 11, 438–441.
Sisken, J. E. and L. Morasca (1965). Intrapopulation kinetics of the mitotic cycle. J. Cell Biol. 25, 179–189.
Steel, G. G. (1977). Growth Kinetics of Tumours: Cell Population Kinetics in Relation to the Growth and Treatment of Cancer, Oxford: Clarendon Press.
Terry, M. H. A., C. G. Milross, N. Patel, K. A. Mason, R. A. White and L. Milas (1997). The effect of paclitaxel on the cell cycle kinetics of a murine mammary adenocarcinoma in vivo. Breast J. 3, 99–105.
Ubezio, P. (1990). Cell cycle simulation for flow cytometry. Comp. Meth. Programs Biomed. 31, 255–266.
Ubezio, P., S. Filippeschi and L. Spinelli (1991). Method for kinetic analysis of drug-induced cell cycle perturbations. Cytometry 12, 119–126.
White, R. A. (1989). Computing multiple cell kinetic properties from a single time point. J. Theor. Biol. 141, 429–446.
White, R. A. (1991). A theory for analysis of cell populations with non-cycling S phase cells. J. Theor. Biol. 150, 201–214.
White, R. A. and M. L. Meistrich (1986). A comment on ‘A method to measure the duration of DNA synthesis and the potential doubling time from a single sample’. Cytometry 7, 486–490.
White, R. A., M. L. Meistrich, A. Pollack and N. H. Terry (2000). Simultaneous estimation of T G2+M, T S, and T pot using single sample dynamic tumor data from bivariate DNA-thymidine analogue cytometry. Cytometry 41, 1–8.
White, R. A., N. H. A. Terry and M. L. Meistrich (1990). New methods for calculating kinetic properties of cells in vitro using pulse labelling with bromodeoxyuridine. Cell Tissue Kinet. 23, 561–573.
Yanagisawa, M., F. Dolbeare, T. Todoroki and J. W. Gray (1985). Cell cycle analysis using numerical simulation of bivariate DNA/Bromodeoxyuridine distributions. Cytometry 6, 550–562.
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Bertuzzi, A., Faretta, M., Gandolfi, A. et al. Kinetic heterogeneity of an experimental tumour revealed by BrdUrd incorporation and mathematical modelling. Bull. Math. Biol. 64, 355–384 (2002). https://doi.org/10.1006/bulm.2001.0280
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DOI: https://doi.org/10.1006/bulm.2001.0280