Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 856

16.19. Assume you have an inoculum with 98% plasmid-containing cells and 2% plasmid-
free cells in a 2-L reactor with a total cell population of 2 10 13 cells/L. You use this
inoculum for a 1000-L reactor and achieve a final population of 4 10 10 cells/mL.
Assuming

m G ¼ 0.8 h 1 , and P / þ ¼ 0.000002, predict the fraction of
plasmid-containing cells.
16.20. Assume you scale up from 1 L of 1 10 13 cells/L of 100% plasmid-containing cells to
27,000 L of 5 10 12 cells/L, at which point overproduction of the target protein is
induced. You harvest 6 h after induction. The value of P is 0.00004. Before induction
m G þ ¼ 0.8 h 1 and

m G þ ¼ 0.5/h,

m G þ is 0.1 h 1 . What is the fraction of
plasmid-containing cells at induction? What is the fraction of plasmid-containing cells
at harvest?
16.21. A batch fermenter receives 1 L of medium with 5 g/L of glucose, which is the growth-
rate-limiting nutrient for a mixed population of two bacteria (a strain of E. coli and
Azotobacter vinelandii). Azotobacter vinelandii is five times larger than E. coli. The
replication rate constants for the two organisms are:

m G ¼ 0.9 h 1 . After induction

m ECmax ¼ 1.0 h 1 , k dEC ¼ 0.05 h 1 ,

m AVmax ¼ 1.5 h 1 , k dAV ¼ 0.10 h 1 , K SAV ¼ 0.02 g/L. The yield
coefficients are YF EC/S ¼ 0.5 g-dw/g-glucose and YF AV/S ¼ 0.35 g-dw/g-g1ucose. The
inoculum for the fermenter is 0.03 g-dw/L of E. coli (1 10 11 cells/L) and 0.15 g-dw/L
of A. vinelandii (1 10 11 cells/L).
What will be the ratio of A. vinelandii to E. coli at the time when all of the glucose is
consumed?
16.22. Mixed cultures (more than one distinct microbial species) are common in nature.
Using two otherwise noninterfering species of different growth kinetics for feeding on
the same substrate as an example, discuss the continuous culturing (chemostat)
outcome. The two species are A and B. The kinetic relationships are:
m Amax ¼ 1.25

K SEC ¼ 0.01 gL 1 ;

m Bmax and K SA ¼ 2.5 K SB . The death rates are negligible to both species.
(a) Is it possible to maintain both species A and B in the chemostat? Determine the
corresponding dilution rate.
(b) For a given high substrate feed rate or dilution rate (see D > m Bmax ), which

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species would survive?
(c) For a given lowsubstrate feed rate (seeD < 0.8 m Bmax ), which specieswould survive?

(d) Is the solution in a) sustainable?
16.23. We know that two bacteria competing for a single nutrient in a chemostat (well-mixed)
could not coexist. Consider the situation where B can adhere to a surface but A cannot.
Assume a is the surface area available per unit reactor volume and the rate of
attachment is first order in X B with a rate constant k aB . The total sites available for
attachment are X BmaxAt aV. The attached cells can detach with a first-order
dependence on the attached cell concentration X BAt with a rate constant of k dB .
Attached cells grow with the same kinetics as suspended cells.
(a) Without mathematical proofs, do you think coexistence may be possible? Why or
why not?
(b) Consider the specific case below and solve the appropriate balance equations
for D ¼ 0.4 h 1 : m Bmax ¼ 0.5/h, K SA ¼ K SB ¼ 0.01 kg/m 3 ,YF A/S ¼

YF B/S ¼ 0.5 kg/kg, S 0 ¼ 5 kg/m 3 , a ¼ 0.1 m 2 /m 3 , X BmaxAt ¼ 1 10 2 kg/m 2 ,
k aB ¼ 1 10 5 kg 1

m Amax ¼ 1.0 h 1 ;

$ m 3 $ h 1 , k dB ¼ 20 h 1