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Modelling the flow of cytometric data obtained from unperturbed human tumour cell lines: Parameter fitting and comparison

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An Erratum to this article was published on 01 September 2005

Abstract

In this paper we firstly present three alternative formulations of a mathematical model for human tumour cell lines unperturbed by cancer therapy. The model counts the number density of cells in each phase of the cell cycle over time where cells are differentiated by their DNA content. Data are available from the Auckland Cancer Society Research Centre, Auckland, New Zealand, in the form of DNA histograms or profiles from 11 different human tumour cell lines (i.e. in vitro) unperturbed by cancer therapy. We then apply one (computationally fast) formulation of the model and discover that although in general different combinations of parameter values give rise to very different DNA profiles it is possible that different combinations of parameter values give rise to virtually identical profiles. Experimental estimates of the rate of transition from the G 1-phase (growth) to the S-phase (DNA synthesis) enable us to uniquely determine other model parameters of interest that give the least square error between the model and data. We finally apply our model to each of the 11 different cell lines and compare cell cycle phase transit times. Although the DNA histograms of each of the cell lines have similar shapes these cell lines have different combinations of transit times to each other, which could explain why they often react very differently when exposed to anti-cancer therapies during laboratory experiments. An understanding of the in vitro situation may give an insight into why some human cancer patients do not respond to cancer therapy.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103, Leipzig, Germany

    Britta Basse

  2. Auckland Cancer Society Research Centre, Faculty of Medical and Health Sciences, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Bruce C. Baguley & Elaine S. Marshall

  3. Centre for Mathematics in Industry, Massey University at Albany, Private Bag 102 904, North Shore MC, Auckland, New Zealand

    Graeme C. Wake

  4. Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    David J. N. Wall

Authors
  1. Britta Basse
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  2. Bruce C. Baguley
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  3. Elaine S. Marshall
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  4. Graeme C. Wake
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  5. David J. N. Wall
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Corresponding author

Correspondence to Britta Basse.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1016/j.bulm.2005.06.001.

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Basse, B., Baguley, B.C., Marshall, E.S. et al. Modelling the flow of cytometric data obtained from unperturbed human tumour cell lines: Parameter fitting and comparison. Bull. Math. Biol. 67, 815–830 (2005). https://doi.org/10.1016/j.bulm.2004.10.003

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  • DOI: https://doi.org/10.1016/j.bulm.2004.10.003

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