Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-29T02:58:52.135Z Has data issue: false hasContentIssue false
  • English
  • Français

The Distribution of DNA in Exponentially-Growing Cell Populations

Published online by Cambridge University Press:  05 September 2017

P. D. M. MaCdonald
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper illustrates a simple method of deriving distributions for samples from cell populations in exponential growth. The distribution of the elapsed proportion of the DNA-synthetic phase of the cell cycle is derived and used to find the distribution of DNA content in a random sample of cells. Allowing for a normally-distributed measurement error, the resulting distribution agrees well with DNA distributions observed empirically. The statistical analysis of DNA distributions, and the interpretation of the distributional parameters in terms of cell population kinetics, are discussed and illustrated with an example.

Type
Part IX — Biomathematics and Epidemiology
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 387 - 401
Copyright
Copyright © 1975 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, P. W. and Macdonald, P. D. M. (1973) An analysis of the mitotic cell cycle in the root meristem of Zea mays. Proc. R. Soc. Lond. B 183, 385–398.Google Scholar
Bartlett, M. S. (1963) Statistical estimation of density functions. Sankhya A 25, 245–254.Google Scholar
Bartlett, M. S. (1969) Distributions associated with cell populations. Biometrika 56, 391–400.Google Scholar
Bartlett, N. S. (1970) Age distributions, Biometrics 26, 377–385.Google Scholar
Bartlett, M. S. and Macdonald, P. D. M. (1968) ‘Least-squares’ estimation of distribution mixtures. Nature, Lond. 217, 195–196.CrossRefGoogle Scholar
Bartlett, M. S. and Macdonald, P. D. M. (1971) Statistical estimation of the derivatives of density functions. Nature Physical Science, Lond. 229, 125–126.CrossRefGoogle Scholar
Brockwell, P. J. and Kuo, W. H. (1973) Labelling experiments and phase-age distributions for multiphase branching processes. J. Appl. Prob. 10, 739–747.Google Scholar
Cleaver, J. E. (1967) Thymidine Metabolism and Cell Kinetics. North-Holland Publishing Co., Amsterdam.Google Scholar
Clowes, F. A. L. (1971) The proportion of cells that divide in root meristems of Zea mays L. Ann. Bot. 35, 249–261.Google Scholar
Dean, P. N. and Jett, J. H. (1974) Mathematical analysis of DNA distributions derived from flow microfluorometry. J. Cell Biol. 60, 523–527.Google Scholar
Gregor, J. (1969) An algorithm for the decomposition of a distribution into Gaussian components. Biometrics 25, 79–93.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Howard, A. and Pelc, S. R. (1953) Synthesis of desoxyribonucleic acid in normal and irradiated cells and its relation to chromosome breakage. Heredity 6, Suppl. Symposium on chromosome breakage. 261–273.Google Scholar
Kiefer, J. and Wolfowitz, J. (1956) Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Statist. 27, 887–906.CrossRefGoogle Scholar
Macdonald, P. D. M. (1970) Statistical inference from the fraction labelled mitoses curve. Biometrika 57, 489–503.CrossRefGoogle Scholar
Macdonald, P. D. M. (1973) On the statistics of cell proliferation. The Mathematical Theory of the Dynamics of Biological Populations, eds. Bartlett, M. S. and Hiorns, R. W. Academic Press, London. 303–314.Google Scholar
Macdonald, P. D. M. (1974) Stochastic models for cell proliferation. Mathematical Problems in Biology, Victoria Conference, ed. van den Driessche, P. Springer-Verlag, Berlin. 155–163.Google Scholar
Reddy, S. B., Erbe, W., Linden, W. A., Landen, H. and Baigent, C. (1973) Die Dauer der Phasen im Zellzyklus von L–929–Zellen. Biophysik 10, 45–50.CrossRefGoogle Scholar
Steel, G. G. (1968) Cell loss from experimental tumours. Cell Tissue Kinet. 1, 193–207.Google Scholar