Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 820

D ¼ 64=2 ¼ 32 monomer plasmid equivalents

T ¼ 64=8 ¼ 8 monomer plasmid equivalents

which implies that M ¼ 64 e 32 e 8 ¼ 24 monomer plasmid equivalents. Since a dimer
consists of two monomer equivalents and a tetramer of four monomer equivalents,
the number of copies of replicative units is then

MþD =2þT =4 ¼ total replicative units ¼ 24þ16þ2 ¼ 42 total replicative units

Thus,

P ¼ 2 1 42 ¼ 4:54710 13

(c) When plasmids are not evenly distributed, the probability of forming a plasmid-free cell
changes. In this case,

2 132 þ 2 196
2

4 : 657 10 10 þ 2 : 524 10 29
2

P 32 þ P 96
2 ¼

¼ 2:32810 10 ¼

Note that although this population has the same average copy number as case a), the
probability of forming a plasmid-free cell is 2.147 10 9 greater.

16.5.2. Plasmid Structural Instability
In addition to the problems of segregational instability, some cells retain plasmids but
alter the plasmid so as to reduce its harmful effects on the cell (structural instability). For
example, the plasmid may encode both for antibiotic resistance and for a foreign protein.
The foreign protein drains cellular resources away from growth toward an end product of
no benefit to the cell. However, if the investigator has added antibiotics to the medium,
the cell will benefit from retaining the gene encoding the antibiotic resistance. Normal muta-
tions will result in some altered plasmids that retain the capacity to encode for desirable
functions (for example, antibiotic resistance) while no longer making the foreign protein.
In other cases, cellular recombination systems will integrate the gene for antibiotic resistance
into the chromosome. Cells containing structurally altered plasmids can normally grow
much more quickly than cells with the original plasmids. A culture having undergone
a change in which the population is dominated by cells with an altered plasmid has under-
gone structural instability.

16.5.3. Host Cell Mutations
Mutations in host cells can also occur that make them far less useful as production systems
for a given product. These mutations often alter cellular regulation and result in reduced
target-protein synthesis. For example, if the promoter controlling expression of the foreign
protein utilizes a host cell factor (e.g. a repressor), then modification of the host cell factor
may greatly modulate the level of production of the desired plasmid-encoded protein. The
lac promoter (see our discussion in Chapter 10 of the lac operon) can be induced by adding