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Genetic engineering


plasmid
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Suppose you have a bacterial strain growing in a flask where nutrients are not limiting. The bacteria will grow and divide after replicating their genomes, but cell division isn't perfect so their progeny will be viable and reproductive 99% of the time. You engineer a substrain of the bacteria by adding a gene to its genome that improves its probability of replicating to form viable offspring, but that adds to the size of the bacterial genome so it takes longer to replicate. Will the engineered bacteria outgrow the original strain? How much of an improvement in offspring viability would be needed to do so?

 

Some numbers that might be needed (or might be red herrings):

Let's say you're working with E. coli with a genome size of about 5,000,000 base pairs, and the gene you're introducing is on the small side at 1,000 base pairs. The typical doubling time for E. coli in optimal laboratory culture conditions is about 20 minutes, and let's assume that the doubling time is proportional to the genome size. You're growing them in a flask with 50 ml of media and starting with an inoculum of 1,000 cells of each bacterial strain in the flask, and assume growth will be exponential until they reach a concentration of 5 x 108 cells/ml.

 

Would the answer change if, instead of working with a bacteria, you're working with a virus? Say the virus infects a host cell and utilizes all of the nutrients in the cell to make new virions before killing it and releasing its progeny, and the number of progeny made is inversely proportional to the viral genome size but the time until the cell dies is not affected. If you're working with an adenovirus, its genome size is 36,000 base pairs and let's say it can normally produce 500 virions from one of the host cells you're working with after three days. You start with a petri dish with 107 host cells and infect it with 100 infectious viral particles.

 

Suppose the gene doesn't improve the efficiency of viral replication, but instead reduces its propensity to infect a cell as it floats by? The starting viral strain has a 10% probability of infecting each cell it passes over (note to any biologists out there: that number is completely made up), cells are distributed uniformly on the dish (call it a hexagonal tiling if that will make the math easier), and a virion will travel in a straight line until it infects a cell since it doesn't have to contend with an immune system. Assume that a cell that's infected with one virion will make just as many progeny as a cell that's infected with multiple virions, and the time spent floating is negligible compared to the duration of infection.

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