Inspired by the statistical companion by Lior Pachter to the paper on "stochastic gene expression in a single cell" from 2002 by Elowitz, Levine, Siggia and Swain, shortened to ELSS, I decided as a part of some reading with the really talented new student Tanvi, to work on a followup for the related (it seems like a follow-up) paper by Rosenfeld, Young, Alon, Swain and Elowitz (RYASE) on "Gene regulation at a single cell level" (2005). The RYASE paper uses a neat gene expression control system which is negatively regulated by anhydrous tetracycline addition, to produce a cI-YFP (that's c-one) fused to the yellow fluorescent protein, which in turn binds to a promoter pR that drives the expression of CFP (cyan fluorescent protein). The most interesting result to my mind was the dose-dependent inheritance of the copy numbers of YFP between equally sized daughter cells. The question is then framed as:
What is the dependence of the difference between protein copies in the two daughter cells [abs(N1-N2)] as a function of the total protein copy number [N1+N2].
The answer found by RYASE paper was that the difference between two daughter cells that has quite a spectacular scatter, nicely to fits a [$ \SQRT{Nt}/2 $] dependence with Nt, where Nt=N1+N2. This is expected from the binomial theorem.
Interestingly enough the data is sort of all over, but the binned average of the data seems to nicely follow a dependence of error (|n1-n2|)/2 with number of total molecules N (x-axis) as \sqrt(N)/2. Could there have been alternative views? How about exactly symmetric segregation- well we'd see the graph linearly increase with N. Fully asymmetric (depending on N1 > N2) would give something parallel to the x-axis.
