bioreactor studies of heterologous protein production by ...

Then kf , expressed in generatiod , wül becorne:
k, = pl%, = In 2 x p ( generation-' ) (4-22)
Eq. (4.22) shows that if the probability of piasmid loss @) is constant, kf ( generation" ) is
constant over different dilution rates.
If the difference in specsfic growth rates of plasmid-bea~g and plasmid fke ceils
are negligible. the three-parameter model of plasmid instabiüty kinetics can be simplified to
a one-panmeter model as foiiows:
X' = x,' eq(-pDt) (43)
X- = X,- + X:[I -eq(-pDt)] (4-24)
For the current recombinant yeast, the probabiiïtyp cm be considered independent of the
dilution rate D. In the present case an average value of p couid be caiculated as 0.0499.
Based on p = 0.0499. the kst-order decay rate constants for dinerent dilution rates were
calculated and are listed in Table 4.4. Table 4.4 shows good agreement between predicted
values of kf and measured vaiues of kfi The model can be &O appiied to situations when
probability of plasmid los @) is dependent on the dilution rate. For example, Impoolsup
et ai. (1 W b) found that when expressed in units of generation-', the vaiues of fïrst-onier
decay rate constants (kf) had a tendency to increase with increasing growth rates. It may
be deduced h m Eq. (4.22) that the probability of plasmid 10s @) incnased with
increasing dilution rates. Higher instability at higher dilution rate was also reported for