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

Plasmids are extra-chromosomal 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: the fluctuation of gene expression as in the simple model, but also the growth and division of bacteria, the non-uniform distribution of their ages, the random partition of proteins at divisions and the replication and partition of plasmids and chromosome. We show how using the chromosome as a reference helps extracting the plasmid copy number noise in a self-consistent manner.