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?

Cell growth rate is essential for understanding how various factors affect the expansion of cell cultures. In bioprocessing, this is often quantified as the specific growth rate, denoted \( \mu \). It describes the rate at which cells divide and grow over time. Here, two rates are given:

\( \mu_+ = 0.95 h^{-1} \) before induction and \( \mu_{-} = 1.0 h^{-1} \) for non-plasmid containing cells. After induction, plasmid-containing cells grow at a slower rate: \( \mu_+ = 0.15 h^{-1} \). These changes highlight how plasmid presence and induction processes can affect the vitality and reproductivity of the cells.

Monitoring the growth rate after the induction step is crucial. It helps predict the productivity and stability of the bioprocess, and how long to continue cultivation before harvesting to maximize the yield of desired products.

Plasmid-containing cells are central to many bioprocesses because they can be programmed to produce target proteins. Before induction, all cells in this scenario are plasmid-containing at 100%. After scaling up to 20,000 ml, the concentration changes but it's important to monitor the fraction of cells that still retain the plasmid.

Let's break it down:

• Before induction, we have a concentration of \(1 \times 10^{10} \) cells/ml in 11 ml, almost entirely plasmid-containing.
• At induction, the fraction of plasmid-containing cells drops due to dilution – calculated as \( \frac{11}{20000} \times 100 \%\rightarrow 0.055 \% \).

After induction, the challenge is to sustain a high fraction of plasmid-containing cells since they grow slower than non-plasmid-containing cells. Decreases in fractions during fermentation can result in reduced productivity of the desired protein, hence monitoring and maintenance of plasmid stability is imperative.

Scaling up bioprocesses from a small volume to industrial scales deals with complex challenges. In this example, you scale from 11 ml to 20,000 ml. The goal is to maintain similar conditions to ensure the same product yield and quality.

Key considerations include:

• Mixing and oxygen transfer rates, which may change with volume.
• Nutrient availability and waste product accumulation.
• Proportional dilution, which impacts the fraction of plasmid-containing cells.

Also, calculating the fraction of plasmid-containing cells at different stages is essential to ensure the bioprocess remains efficient. After scaling, using the growth rates given, you can predict how the proportion of plasmid-containing cells changes, ensuring optimal harvesting time. In short, effective scaling up in bioprocess engineering ensures that small-scale successes can be translated into large-scale industrial successes.