  Gene expression is a stochastic process governed by the presence of specific
transcription factors. Here we study the dynamics of gene expression in the
presence of feedback, where a gene regulates its own expression. The nonlinear
coupling between input and output of gene expression can generate a dynamics
different from simple scenarios such as the Poisson process. This is
exemplified by our findings for the time intervals over which genes are
transcriptionally active and inactive. We apply our results to the lac system
in E. coli, where parametric inference on experimental data results in a broad
distribution of gene activity intervals.
