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Modelling yeast cell growth using stochastic branching processes

Published online by Cambridge University Press:  14 July 2016

P. J. Green
P. J. Green*
Affiliation:
University of Durham
*
∗ Postal address: Department of Mathematics, University of Durham, Science Laboratories, South Road, Durham DH1 3LE, U.K.
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Abstract

This paper aims to demonstrate that the general Crump–Mode–Jagers branching process may be used in a natural way to model the asymmetric growth of budding yeast cells. The models obtained are generalisations of the deterministic model proposed by Hartwell and Unger (1977): all the results that are derived in that paper may be obtained using branching-process methods, but such methods also apply when account is taken of the biologically obvious fact that the various phases of the cell growth are of random rather than fixed duration. In their full generality, branching processes involve more parameters than can be estimated by experiment, but we present below a special case in which this problem is not likely to arise.

A recent paper, Lord and Wheals (1980), discusses more of the biological background than is appropriate here. In the present paper, we show how certain statistical procedures for our model may be developed.

Keywords

GENERAL BRANCHING PROCESSRANDOM CHARACTERISTICBUDDING YEASTASYMMETRIC DIVISIONCELL PHASE COUNTS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981, pp. 799 - 808
Copyright
Copyright © Applied Probability Trust 1981 

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References

Beran, K. (1968) Budding of yeast cells, their scars and ageing. Adv. Microbial Physiol. 2, 143–171.CrossRefGoogle Scholar
Crump, K. S. and Mode, C. J. (1968), (1969) A general age-dependent branching process, I, II. J. Math. Anal. Appl. 24, 494–508; 25, 8–17.Google Scholar
Gani, J. and Saunders, I. W. (1976) On the parity of individuals in a branching process. J. Appl. Prob. 13, 219–230.Google Scholar
Gani, J. and Saunders, I. W. (1977) Fitting a model to the growth of yeast colonies. Biometrics 33, 113–120.Google Scholar
Hartwell, L. H. and Unger, M. W. (1977) Unequal division in Saccharomyces cerevisiae and its implications for the control of cell division. J. Cell Biol. 75, 422–435.Google Scholar
Jagers, P. (1969) A general stochastic model for population development. Skand. Aktuarietidskr. 52, 84–103.Google Scholar
Jagers, P. (1974) Convergence of general branching processes and functionals thereof. J. Appl. Prob. 11, 471–478.Google Scholar
Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
Lord, P. G. and Wheals, A. E. (1980) Asymmetric division of Saccharomyces cerevisiae. J. Bacteriol .Google Scholar
Macdonald, P. D. M. (1978) Age distributions in the general cell kinetic model. In Biomathematics and Cell Kinetics , ed. Valleron, A.-J. and Macdonald, P. D. M. Elsevier/North Holland Biomedical Press.Google Scholar
Smith, J. A. and Martin, L. (1973) Do cells cycle? Proc. Nat. Acad. Sci. U.S.A. 70, 1263–1267.CrossRefGoogle ScholarPubMed