Chapter 14, Utilizing Genetically Engineered Organisms Video Solutions, Bioprocess Engineering

Problem 1

Given the following information, calculate the probability of forming a plasmid-free cell due to random segregation for a cell with 50 plasmid monomer equivalents:
a. $40 \%$ of the total plasmid DNA is in dimers and $16 \%$ in tetramers.
b. The distribution of copy numbers per cell is as follows, assuming monomers only:
$$
\begin{array}{cr}
\hline \leq 3 \text { plasmids } & -0 \% \\
4 \text { to } 8 & 4 \% \\
9 \text { to } 13 & 10 \% \\
14 \text { to } 18 & 25 \% \\
19 \text { to } 23 & 25 \% \\
24 \text { to } 28 & 20 \% \\
29 \text { to } 33 & 12 \% \\
34 \text { to } 38 & 4 \% \\
\geq 39 & -0 \% \\
\hline
\end{array}
$$

Pratyush Raitan

Numerade Educator

05:28

Problem 2

Assume that all plasmid-containing cells have eight plasmids; that an antibiotic is present in the medium, and the plasmid-containing cells are totally resistant; and that a newly born, plasmid-free cell has sufficient enzyme to protect a cell and its progeny for three generations. Estimate the fraction of plasmid-containing cells in the population in a batch reactor starting with only plasmid-containing cells after five generations.

Cody Delk

Numerade Educator

01:11

Problem 3

Consider an industrial-scale batch fermentation. A 10,0001 fermenter with $5 \times 10^{10}$ cells $/ \mathrm{ml}$ is the desired scale-up operation. Inoculum for the large tank is brought through a series of seed tanks and flasks, beginning with a single pure colony growing on an agar slant. Assume that a colony $\left(10^{6}\right.$ plasmid-containing cells) is picked and placed in a test tube with $1 \mathrm{ml}$ of medium. Calculate how many generations will be required to achieve the required cell density in the $10,000 \mathrm{l}$ fermenter. What fraction of the total population will be plasmid-free cells if $\mu_{+}=1.0 \mathrm{~h}^{-1}, \mu_{-}=1.2 \mathrm{~h}^{-1}$, and $P=0.0005$ ?

Carson Merrill

Numerade Educator

03:13

Problem 4

Assume that you have been assigned to a team to produce human epidermal growth factor (hEGF). A small peptide, hEGF speeds wound healing and may be useful in treating ulcers. A market size of 50 to $500 \mathrm{~kg} / \mathrm{yr}$ has been estimated. Posttranslational processing is not essential to the value of the product. It is a secreted product in the natural host cell. Discuss what recommendations you would make to the molecular-biology team leader for the choice of host cell and the design of a reactor. Make your recommendations from the perspective of what is desirable to make an effective process. You should point out any potential problems with the solution you have proposed, as well as defend why your approach should be advantageous.

James Kiss

Numerade Educator

01:04

Problem 5

Develop a model to describe the stability of a chemostat culture for a plasmid-containing culture. For some cultures, plasmids make a protein product (e.g., colicin in $E$. coli) that kills plasmid-free cells but does not act on plasmid-containing cells. Assume that the rate of killing by colicin is $k_{T} \mathrm{Cn}_{-}$, where $k_{T}$ is the rate constant for the killing and $\mathrm{C}$ is the colicin concentration. Assume that the colicin production is first order with respect to $n_{+}$.

Carson Merrill

Numerade Educator

02:13

Problem 6

Consider the following data for $E$. coli $\mathrm{B} / \mathrm{r}-\mathrm{pDW} 17$ grown in a minimal medium supplemented with amino acids. Estimate $\Delta \mu$ and $R$. Compare the stability of this system to one with a glucose-minimal medium (Example 14.2).
$$
\begin{array}{lccccc}
\text { Time, h } & \text { Generation } & f_{-} & \text {Time, h } & \text { Generation } & f_{-} \\
\hline 0 & 0 & 0.003 & 0 & 0 & 0.003 \\
4.6 & 2 & 0.010 & 5.2 & 5 & 0.010 \\
11.5 & 5 & 0.04 & 10.3 & 10 & 0.015 \\
16.0 & 7 & 0.08 & 15.5 & 15 & 0.05 \\
23.1 & 10 & 0.30 & 20.6 & 20 & 0.13 \\
27.7 & 12 & 0.43 & 31.0 & 30 & 0.34 \\
34.7 & 15 & 0.55 & 41.4 & 40 & 0.68 \\
46.2 & 20 & 0.96 & 51.7 & 50 & 0.95
\end{array}
$$

Sana Riaz

Numerade Educator

03:12

Problem 7

It has been claimed that gel immobilization stabilizes a plasmid-containing population. A factor suggested to be responsible for the stabilization is compartmentalization of the population into very small pockets. For example, the pocket may start with an individual cell and grow to a level of 200 cells per cavity. Develop a mathematical formula to compare the number of plasmid-free cells in a gel to that in a large, well-mixed tank.

Stanley Enemuo

Numerade Educator

01:24

Problem 8

You must design an operating strategy to allow an $E$. coli fermentation to achieve a high cell density $(>50 \mathrm{~g} / \mathrm{l})$ in a fed-batch system. You have access to an off-gas analyzer that will measure the $p \mathrm{CO}_{2}$ in the exit gas. The glucose concentration must be less than $100 \mathrm{mg} / \mathrm{l}$ to avoid the formation of acetate and other inhibitory products. Develop an approach to control the glucose feed rate so as to maintain the glucose level at $100 \pm 20 \mathrm{mg} / \mathrm{l}$. What equations would you use and what assumptions would you make?

Dominador Tan

Numerade Educator

09:19

Problem 9

Develop a simple model for a population in which plasmids are present at division with copy numbers $2,4,6,8$, or 10 . The model should be developed in analogy to eqs. $14.7$ through 14.9. You can assume that dividing cells either segregate plasmids perfectly or generate a plasmid-free cell.

Rabeya Zahid

Numerade Educator

01:16

Problem 10

Assume you have an inoculum with $95 \%$ plasmid-containing cells and $5 \%$ plasmid-free cells in a 21 reactor with a total cell population of $2 \times 10^{10} \mathrm{cells} / \mathrm{ml}$. You use this inoculum for a 10001 reactor and achieve a final population of $4 \times 10^{10}$ cells $/ \mathrm{ml}$. Assuming $\mu_{+}=0.69 \mathrm{~h}^{-1}$, $\mu_{-}=1.0 \mathrm{~h}^{-1}$, and $P=0.0002$, predict the fraction of plasmid-containing cells.

Josee Pacheco

Numerade Educator

01:17

Problem 11

Assume you scale up from 11 of $1 \times 10^{10}$ cells $/ \mathrm{ml}$ of $100 \%$ plasmid-containing cells to 20,0001 of $5 \times 10^{9}$ cells/ml, at which point overproduction of the target protein is induced. You harvest six hours after induction. The value of $P$ is $0.0005$. Before induction $\mu_{+}=$ $0.95 \mathrm{~h}^{-1}$ and $\mu_{-}=1.0 \mathrm{~h}^{-1}$. After induction $\mu_{+}$is $0.15 \mathrm{~h}^{-1}$. What is the fraction of plasmidcontaining cells at induction? What is the fraction of plasmid-containing cells at harvest?

Lottie Adams

Numerade Educator