Gene Expression Changes with Minor Effects on the Population Average Have Major Effects on the Occurrence of Cells with Extreme Protein Concentrations

The cell-to-cell heterogeneity in a bacterial population provides a rich response to environmental changes and robust survival of an isogenic population. Especially, the rare, extreme phenotypes can be important for survival under transient lethal conditions. We analyze the probability of having an extremely high or low protein level in a stochastic model of gene expression. The fraction of rare state cells defined as the cells in the tails of distributions is found to be highly sensitive to small changes of the mean protein level. The result highlights the importance of relatively weak changes to the mean for the occurrence of rare phenotypes.