Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 828

Based on Eqns (16.48) and (16.49) , we can determine the ratio of plasmid-free cells as

X
X þ þX

y ¼

y 0 exp½ðm G m G þ þP

y þ0 ðm G m G þ þP

=þ m G þ ÞþP =þ m G þ =þ m G þ ÞtP =þ m G þ

y 0
y þ0 ðm G m G þ þP =þ m G þ ÞþP =þ m G þ

exp½ðm G m G þ þP =þ m G þ Þt

¼

m G m G þ þ

(16.50)

If we let

m =þ ¼ P =þ m G þ (16.51a)

Dm ¼ m G m G þ þP =þ m G þ (16.51b)

The Eqn (16.50) can be simplified to yield

y 0
1y 0 Dmþm =þ m =þ expðtDmÞ
y 0
1y 0 Dmþm =þ þðDmm =þ ÞexpðtDmÞ

y ¼ (16.52)

Eqn (16.52) can be applied directly to determine the specific rates and probability of loosing
plasmid if a series of experimental data are available. Fig. 16.17 illustrates the instability
profile for three limiting cases:

(1) m G m G þ >> P / þ m G þ growth-rate-dependent instability dominant

(2) m G m G þ P / þ m G þ segregational instability dominant

(3) m G þ >>m G þ P / þ m G þ effective selective pressure

The difference in specific growth rates can be altered by medium and host e vector design.

(a) (b) (c)

1

1 1

0.75 0.75 0.75

y -

y - y -

0.5 0.5 0.5

y*

0.25 0.25 0.25

0 0 0

0

0 0

time

time time

µ G- - µ G+ >> P -/+ µ G+ µ G- - µ G+ ≤ P -/+ µ G+ µ G+ >> µ G- + P -/+ µ G+

FIGURE 16.17 The shape of plasmid-free cell fraction versus time for three limiting cases of specific growth
rates.