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The steady-states of a multi-compartment, age–size distribution model of cell-growth

Published online by Cambridge University Press:  01 August 2008

R. E. BEGG ,
D. J. N. WALL  and
G. C. WAKE
R. E. BEGG
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand email: david.wall@canterbury.ac.nz
D. J. N. WALL
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand email: david.wall@canterbury.ac.nz
G. C. WAKE
Affiliation:
Institute of Information and Mathematical Sciences, Massey University, Private Bag 102 904, North Shore Mail Centre, Auckland, New Zealand email: g.c.wake@massey.ac.nz
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Abstract

A model of cell-growth, describing the evolution of the age–size distribution of cells in different phases of cell-growth, is studied. The model is based on that used in several papers by Basse et al. and is composed of a system of partial differential equations, each describing the changes in the age–size distribution of cells in a specific phase of cell-growth. Here, the ‘age’ of a cell is considered to be the time spent in its current phase of cell-growth, while ‘size’ is considered to be the DNA content of the cell. The existence of steady age–size distributions (SASDs), where the age–size distributions retain the same shape but are scaled up or down as time increases, is investigated and it is shown that SASDs exist. A speculative discussion of the stability of these SASDs is also included, but their stability is not conclusively proved.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 4 , August 2008 , pp. 435 - 458
Copyright
Copyright © Cambridge University Press 2008

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