Dynamical analysis on gene activity in the presence of repressors and an interfering promoter

Transcription is regulated through interplay among transcription factors, an RNA polymerase (RNAP), and a promoter. Even for a simple repressive transcription factor that disturbs promoter activity at initial binding of RNAP, its repression level is not determined solely by the dissociation constant of transcription factor but is sensitive to timescales of processes in RNAP. We first analyze the promoter activity under strong repression by a slow binding repressor, in which case transcription events occur in bursts, followed by long quiescent periods while a repressor binds to the operator; the number of transcription events, bursting, and quiescent times are estimated by reaction rates. We then examine interference effect from an opposing promoter, using the correlation function of initiation events for a single promoter. The interference is shown to de-repress the promoter because RNAPs from the opposing promoter most likely encounter the repressor and remove it in case of strong repression. This de-repression mechanism should be especially prominent for the promoters that facilitate fast formation of open complex with the repressor whose binding rate is slower than ∼1/s. Finally, we discuss possibility of this mechanism for high activity of promoter PR in the hypmutant of λ-phage.