They watch the mrna dilution effect while in the

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they watch the mRNA dilution effect while in the experiments of Rosenfeld et al. this is a fluorescently-labeled transcription factor). In the Rosenfeld experiment, at some point while the culture is growing, the production of the protein is stopped by providing a chemical in the medium and then the number of copies per cell is reduced as a result of dilution as the cells divide. (a) For this part of the problem, let’s focus on the protein dilution effect. Work out a differential equation for the change in protein concentration as a function of the time that has elapsed since production of the protein was stopped. Solve the equation and make sure that your result depends upon the cell cycle time. Note that here we are only interested in the dilution 1
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that results from the original N copies of the protein being partitioned into an ever-larger number of daughter cells, not in the dilution that occurs as each individual cell lengthens in preparation for the next round of division. Note also that in this part we’re interested in a continuous model—you’ll look at the discrete version in part (b). HINT: there are two ways to ap- proach this problem. You can consider the change in the concentration as a function of the change in the number of cells into which the original N proteins are partitioned. Or you can note that for a bacterium like E. coli , it is a reasonable assumption to imagine that the cell diameter is unchanged and that the size is controlled by the cell length, such that the change in
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