A model for the statistical fluctuations of protein numbers in a microbial population

A model is presented for the distribution of protein molecules between the cells in a microbial population during steady-state growth. A general expression is derived under the sole assumption that each protein molecule has equal probability of joining either daughter cell at cell division, i.e. a binomial partitioning. With reasonable assumptions about transcription and translation probabilities a specific protein distribution is described. The main result is that this distribution is very broad, especially for small protein numbers; it is definitely not a Poisson distribution. The case of repressor proteins, which have one strong binding site on the chromosome, is treated separately. As a specific example, the distribution of β-galactosidase is described, also in regard to the influence from the statistical fluctuations in the distribution of the lac repressors.