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J Math Biol. 1985;22(1):61-8.

Global asymptotic stability of the size distribution in probabilistic models of the cell cycle.

Abstract

Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for psi n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, psi*(x). For the special case of the transition probability model, we display psi*(x) explicitly.

PMID:
4020305
DOI:
10.1007/bf00276546
[Indexed for MEDLINE]

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