bioreactor studies of heterologous protein production by ...

celi fraction decreases monotonicaiiy with generation number (n) according to the
foilowing equation:
where a = pCc/p+. From Eq. (23) it is obvious that in batch systern with any a > 1.0 and p
> O, H, = O. The Imanaka and Aiaa (1981) model is mtructnred, but elegantly simple.
in principle, any recombinant organisrn satisfying the underlying assmnptions shouid
confonn to the model. Unfortunately, the p and a usuaiiy Vary du~g the culture penod,
and the assumed exponential growth is not exactly followed.
Pioneering deveiopments in stmctured modehg of mDred combinant culture
came h m Bailey's and Shuier's groups working with recombinant E. coli (Lee and
BaiIey, 1984; Seo and Baüey, 1985; Ataai and Shuler, 1986; Kim and Shuler, 1990a; Kim
and Shuler. 1990b). The plasmid stability and the expression of a cloned-gene product has
ken descnbed by a mathematid mode1 based upon the molecular mechanisn of plasmid
replication, partition and transcription. These studies laid the fondation for mer
mathematicai modehg and pointed the way for futm experimental work. Later, at a
singieîeIl level, using population balance models, Hjortso and Bailey mathematicaily
descnbed the plasmid stability in yeast S. cerevisiae with selection pressure (Hjortso and
Bailey, 1984a) and without selection pressure (Hjortso and Bailey, 1984b). Two
assumptions were examined for plasmid partitioning: (i) random and independent
distribution of plasmids between the mother and the daughter tells at partition; and (ii) a
greaar or eqrial probability of a plasmid residing in the mother ceii after division than in