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 φ 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, φ *(x). For the special case of the transition probability model, we display φ *(x) explicitly.
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This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).
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Tyson, J.J., Hannsgen, K.B. Global asymptotic stability of the size distribution in probabilistic models of the cell cycle. J. Math. Biology 22, 61–68 (1985). https://doi.org/10.1007/BF00276546
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DOI: https://doi.org/10.1007/BF00276546