Inference of plasmid-copy-number mean and noise from single-cell gene expression data

Plasmids are extrachromosomal DNA molecules which code for their own replication. We previously reported a setup using genes coding for fluorescent proteins of two colors that allowed us, using a simple model, to extract the plasmid-copy-number noise in a monoclonal population of bacteria [J. Wong Ng et al., Phys. Rev. E 81, 011909 (2010)]. Here we present a detailed calculation relating this noise to the measured levels of fluorescence, taking into account all sources of fluorescence fluctuations: not only the fluctuation of gene expression as in the simple model but also the growth and division of bacteria, the nonuniform distribution of their ages, the random partition of proteins at divisions, and the replication and partition of plasmids and chromosome. We show how to use the chromosome as a reference, which helps extracting the plasmid-copy-number noise in a self-consistent manner.