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Functional differential equations determining steady size distributions for populations of cells growing exponentially

Published online by Cambridge University Press:  17 February 2009

A. J. Hall  and
G. C. Wake
A. J. Hall
Affiliation:
Plant Physiology Division, DSIR, Palmerston North, New Zealand and Department of Mathematics and Statistics, Massey University, Palmerston North, New Zealand.
G. C. Wake
Affiliation:
Department of Mathematics and Statistics, Massey University, Palmerston North, New Zealand.
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Abstract

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A population of cells growing and dividing often goes through a phase of exponential growth of numbers, during which the size distribution remains steady. In this paper we study the function differential equation governing this steady size distribution in the particular case where the individual cells themselves are growing exponentially in size. A series solution is obtained for the case where the probability of cell division is proportional to any positive power of the cell size, and a method for finding closed-form solutions for a more general class of cell division functions is developed.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 4 , April 1990 , pp. 434 - 453
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Andrews, G. E., “Number Theory”, (W. B. Saunders, Phil. 1971).Google Scholar
[2] Collins, J. F. and Richmond, M. H., “Rate of Growth of Bacillus Cereus Between Divisions”, J. gen. Microbiol. 28 (1962), 15–33.CrossRefGoogle ScholarPubMed
[3] Hall, A. J. and Wake, G. C., “A Functional Differential Equation Arising in the Modelling of Cell Growth”, J. Austral. Math. Soc. Ser. B 30 (1989) 424–435.CrossRefGoogle Scholar
[4] Jolley, L. B. W., “Summation of Series”, (Dover, N.Y. 1961).Google Scholar
[5] Kato, T. and McLeod, J. B., “The Functional Differential Equation y′(x) = ay(λx) + by(x)”, Bull. Amer. Math. Soc. 77 (1971) 891–937.Google Scholar
[6] Koch, A. L. and Schaechter, M., “A Model for Statistics of the Cell Division Process”, J. gen. Microbiol. 29 (1962) 435–454.Google Scholar
[7] Powell, E. O., “A Note on Koch & Schaechter's Hypothesis about Growth and Fission of Bacteria”, J. gen. Microbiol. 37 (1964) 231–249.Google Scholar
[8] Tyson, J. and Diekmann, O., “Sloppy Size Control of the Division Cycle”, J. theor. Biol. 118 (1986) 405–426.Google Scholar