Abstract
Growth-rate functions in analytic form have been obtained for cell cultures in which the doubling times follow the Gaussian and Poisson distributions. The growth-rate functions are calculated by using Laplace transforms to solve an integral equation previously presented. Oscillatory solutions result if a substantial fraction of the cells in a culture are synchronized to divide at some particular time. The synchrony and, hence, the oscillatory character of the growth-rate function eventually disappear because of the non-zero variance of the doubling-time distribution. If their variances are sufficiently small, the Gaussian and Poisson doubling-time distributions lead to growth-rate functions that become identical in the limit of large time.
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Literature
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This investigation was aided by a research grant from the National Cancer Institute, Public Health Service, NIH-CA-06835-02.
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Hirsch, H.R., Engelberg, J. Decay of cell synchronization: Solutions of the cell-growth equation. Bulletin of Mathematical Biophysics 28, 391–409 (1966). https://doi.org/10.1007/BF02476821
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DOI: https://doi.org/10.1007/BF02476821