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Inferring average generation via division-linked labeling

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Abstract

For proliferating cells subject to both division and death, how can one estimate the average generation number of the living population without continuous observation or a division-diluting dye? In this paper we provide a method for cell systems such that at each division there is an unlikely, heritable one-way label change that has no impact other than to serve as a distinguishing marker. If the probability of label change per cell generation can be determined and the proportion of labeled cells at a given time point can be measured, we establish that the average generation number of living cells can be estimated. Crucially, the estimator does not depend on knowledge of the statistics of cell cycle, death rates or total cell numbers. We explore the estimator’s features through comparison with physiologically parameterized stochastic simulations and extrapolations from published data, using it to suggest new experimental designs.

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Acknowledgments

The authors thank Søren Asmussen (Aarhus University) for drawing their attention to Asmussen (1998). The work of T.W., L.P. and K.D. was supported by Human Frontier Science Program Grant RGP0060/2012. K.D. was also supported by Science Foundation Ireland Grant 12 IP 1263.

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  1. Leïla Perié

    Present address: Institut Curie, PSL Research University, CNRS UMR168, Paris, France

Authors and Affiliations

  1. Hamilton Institute, Maynooth University, Maynooth, Ireland

    Tom S. Weber & Ken R. Duffy

  2. Division of Immunology, Netherlands Cancer Institute, Amsterdam, The Netherlands

    Leïla Perié

  3. Department of Theoretical Biology and Bioinformatics, Utrecht University, Utrecht, The Netherlands

    Leïla Perié

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  1. Tom S. Weber
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Correspondence to Ken R. Duffy.

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Weber, T.S., Perié, L. & Duffy, K.R. Inferring average generation via division-linked labeling. J. Math. Biol. 73, 491–523 (2016). https://doi.org/10.1007/s00285-015-0963-3

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  • DOI: https://doi.org/10.1007/s00285-015-0963-3

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