Power-law scaling in protein synthesis of a stochastic regulon

We investigate the protein expression pattern of the lamB gene in Escherichia coli LE392. The gene product LamB is an important membrane protein for maltose transport into cells but it is also exploited by bacteriophage λ for infection. Although our bacterial population is clonal, stochastic gene expression leads to a majority population with a large receptor number and a minority population with a small receptor number. We find that LamB receptor distribution p(n) of the small-n population is scale invariant, p(n) ∼ n−α, where the exponent α depends on growth conditions. A heuristic model is proposed that relates the observed exponent to the protein production rate.