Sister cells carrying a fluorescently tagged protein are imaged just after division

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Biophysics & Medical Physics · Data analysis and model fitting in the laboratory

Forces, Machines and Signals, Ch Numbers and noise in a small system

Problem

Sister cells carrying a fluorescently tagged protein are imaged just after division, and the pairs are binned by total intensity I1+I2I_1+I_2. The bin means, as (total intensity, mean of (I1−I2)2(I_1-I_2)^2) in arbitrary units, are (400,1050)(400,1050), (800,1930)(800,1930), (1200,3080)(1200,3080), (1600,3950)(1600,3950), (2000,5100)(2000,5100), (2400,5920)(2400,5920). ((a)) Fit a line through the origin to find the fluorescence per molecule ν\nu. ((b)) A second laboratory images the same strain some minutes after division, so that each daughter has made new copies. Take a parent with NN copies and consider two idealised cases: (i) each daughter independently makes a Poisson number of new copies with mean μ\mu; (ii) each daughter makes exactly mm new copies. For each case find ⟨(I1−I2)2⟩\langle(I_1-I_2)^2\rangle in terms of the mean total intensity, and say what a line forced through the origin would report for ν\nu. ((c)) In case (ii), with the true ν\nu from (a) and m=100m = 100, a bin sits at total intensity 12001200. What fraction of ν\nu is the ratio ⟨(I1−I2)2⟩/(I1+I2)\langle(I_1-I_2)^2\rangle/(I_1+I_2) in that bin, and what feature of the plot would warn the second laboratory?

Browse the problem library