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Population balance equations for cell and microbial cultures revisited
Author(s) -
Fredrickson A. G.
Publication year - 2003
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690490422
Subject(s) - population , population model , determinism , cell cycle , identification (biology) , balance (ability) , domain (mathematical analysis) , state space , mathematics , biological system , computer science , cell , biology , ecology , physics , statistics , mathematical analysis , genetics , neuroscience , demography , quantum mechanics , sociology
The first chemically structured model of growth of a microbial or cell population proposed in 1967 by Fredrickson et al. took account of the particulate nature of the population. This model assumed implicitly that cells passed through the cell cycle continuously without transitions between recognizable cell cycle phases. This article discusses how to generalize or revise the first model so that passages of cells through a series of recognizable cell cycle phases can be accounted for. The 1967 article assumed that cell fission can occur anywhere in state space, although with high probability only in a limited domain of that space. Extension of this concept to cell cycle transitions leads to a model that violates a principle of determinism. Revised models that subdivide state space into nonoverlapping subdomains associated with each phase of the cell cycle are developed to obviate this unacceptable situation. The new models introduce the need for information about cell behavior that does not currently exist and thereby provide motivation for an experimental program aimed at supplying the data necessary for their identification and validation.