Modulation of gene transcription noise by competing transcription factors

Sequence specific transcription factors (TFs) are critical to ensuring that genes are transcribed in the right cell at the right time. Often, the gene promoter is flanked by multiple binding sites, some of which can be bound by different types of TFs in the cell. To investigate how the transcription noise is modulated by the competition of these TFs at their shared binding sites, we model gene transcription as a renewal process where the time spent in each transcription cycle is assumed to be independently and identically distributed. With the help of the elementary renewal theorem and the central limit theorem, we prove that the stationary noise strength Φ of transcription frequency equals the noise η (2) of the time spent in a single transcription cycle. Subsequent analysis shows that competitive TF binding could produce an unbounded spectrum of Φ, in sharp contrast to the estimate 1/3 ≤ Φ < for single binding pattern activated transcription. We predict several mechanisms by which genes could stay away from abnormally noisy transcription while living with multiple binding patterns. The most efficient one is to maintain a relatively long engaged time by transcription pausing, interrupting, or other means. Alternatively, high noise strength is prevented if all binding patterns activate transcription strongly. When some binding patterns activate transcription weakly, low noise strength is ensured if the binding pattern with the weakest activation strength is utilized frequently.