Abstract:
:A mathematical model is formulated for the development of a population of cells in which the individual members may grow and divide or die. A given cell is characterized by its age and volume, and these parameters are assumed to determine the rate of volume growth and the probability per unit time of division or death. The initial value problem is formulated, and it is shown that if cell growth rate is proportional to cell volume, then the volume distribution will not converge to a time-invariant shape without an added dispersive mechanism. Mathematical simplications which are possible for the special case of populations in the exponential phase or in the steady state are considered in some detail. Experimental volume distributions of mammalian cells in exponentially growing suspension cultures are analyzed, and growth rates and division probabilities are deduced. It is concluded that the cell volume growth rate is approximately proportional to cell volume and that the division probability increases with volume above a critical threshold. The effects on volume distribution of division into daughter cells of unequal volumes are examined in computer models.
journal_name
Biophys Jjournal_title
Biophysical journalauthors
Bell GI,Anderson ECdoi
10.1016/S0006-3495(67)86592-5subject
Has Abstractpub_date
1967-07-01 00:00:00pages
329-51issue
4eissn
0006-3495issn
1542-0086pii
S0006-3495(67)86592-5journal_volume
7pub_type
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