ISSN:
1432-1416
Keywords:
Cell population growth
;
Exponential growth
;
Size/birth-size distributions
;
Fission into unequal parts
;
Fredholm integral equation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract We consider a population of cells growing and dividing steadily without mortality, so that the total cell population is increasing, but the proportion of cells in any size class remains constant. The cell division process is non-deterministic in the sense that both the size at which a cell divides, and the proportions into which it divides, are described by probability density functions. We derive expressions for the steady size/birth-size distribution (and the corresponding size/age distribution) in terms of the cell birth-size distribution, in the particular case of one-dimensional growth in plant organs, where the relative growth rate is the same for all cells but may vary with time. This birth-size distribution is shown to be the principal eigenfunction of a Fredholm integral operator. Some special cases of the cell birth-size distribution are then solved using analytical techniques, and in more realistic examples, the eigen-function is found using a simple, generally applicable numerical iteration.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00160330
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