bioreactor studies of heterologous protein production by ...

43.3. Plasmid hstabiiity Kinetics in Conb'nuous Culture
4.3.3.1. Mathematid Analysis
Assummg that the ceils are m balanced growth, according to Imanaka and Aiba (1981).
the change in plasmid-bearing ce& in the continuous culture system can be descnbed by:
The anaiyticai solution of Eq. (4.1) is as follows:
..Y+ = x,' exp(p+ - pp* - D)t = x0+ exp(-kft) (43)
where k = -( p' - pp* - D) . a m-order decay rate constant, which is aiways positive
because p* S D. Eq. (4.2) shows that the decay of phmici-bearing c& foiiows fmt-
order kinetics and the concentration of plamid-bearing cells decreases with culture time
during continuous culture. Since the total cefl concentration X, is observed constant
during the culture process (See Figwe 4.17). the fiaction of plasmid-besring cells
( F = X+ / X, ) &O foîiows an exponential decay pattern:
F = F, exp(-k!t) (4.3)
Similarly. the change in plasruid-ke œUs in the culture system can be descnbed as
follows:
Eq. (4.2) and (4.4) can be solved analytically to give:
X- = X,- expC(p- - D )~J + [pp+~o' G][exp[((p- - Dut - eq(-k,t)] (43