Gene transcription is a stochastic process mostly occurring in bursts. Regulation of transcription arises from the interaction of transcription factors (TFs) with the promoter of the gene. The TFs, such as activators and repressors can interact with the promoter in a competitive or non-competitive way. Some experimental observations suggest that the mean expression and noise strength can be regulated at the transcription level. A Few theories are developed based on these experimental observations. Here we re-establish that experimental results with the help of our exact analytical calculations for a stochastic model with non-competitive transcriptional regulatory architecture and find out some properties of Noise strength (like sub-Poissonian fano factor) and mean expression as we found in a two state model earlier. Along with those aforesaid properties we also observe some anomalous characteristics in noise strength of mRNA and in variance of protein at lower activator concentrations.
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