Gene expression with nonlinear feedback

The dynamic scenarios of gene expression with constant concentrations of active transcription factors have been thoroughly studied both theoretically and experimentally, and is now well understood. However, the stochastic dynamics is more complicated in systems with feedback, in which the gene products either directly or indirectly regulate the transcription of their own genes. Mathematical analysis of models with nonlinear feedback is particularly tricky. In this talk, we consider a class of models, the dynamics of which can be exactly characterized. The theory is applied to the lac system in E. coli and the predictions are compared with results from simulations of more detailed models.