Are the number of proteins that end up in daughter

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are the number of proteins that end up in daughter cells 1 and 2 respectively. Show that q < ( N 1 - N 2 ) 2 > = N (hint: you’ll need to use the binomial theorem.) Next, look at the Rosenfeld paper and explain how measuring fluores- 2
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cence variations can be used to calibrate the exact number of copies of the fluorescent protein in a cell. Assume that the fluorescence intensity in each cell can be written as I = αN , where α is some calibration factor and N the number of proteins. Make a plot of q < ( I 1 - I 2 ) 2 > versus I tot and explain how to get the calibration factor α from this plot. (d) Now we are going to repeat the Rosenfeld experiment numerically in order to fit the calibration factor. Consider a fluorescent protein such that the calibration factor between the intensity and the number of fluorophores is 50. Generate intensity data by choosing N 1 + N 2 = 10 , 50 , 100 , 1000 and 5000 and for each case, “partition” the proteins from the mother cell to the two daughters 100 times (i.e. as if you are looking at 100 mother cells divide for each choice of the protein copy number). Then, make a plot of the resulting q < ( I 1 - I 2 ) 2 > vs I tot just as we did analytically in the previous problem. What I mean is that you need to make a plot of all of your simulation results. Then, do a fit to your “data” and see how well you recover the calibration factor that you actually put in by hand. Plot the fit on the same graph as all of the “data”. 3
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