Stochastic transcription initiation: Time dependent transcription rates

The noise in the central process such as transcription, replication and translation of the genomic DNA is very important since it can directly affect the phenotypic and behavioral aspects of an organism as well as the entire cellular function. Here we develop a model on the transcription process based on the assumption that the initiation of the transcription is a stochastic event and the transcription rates may be time dependent random quantities. We derive the central measure properties i.e. mean and the variance, of the distribution of the transcription rates. Our results show that the Fano factor which is a measure of deviation from the Poisson distribution associated with the fluctuations in the number of mRNA molecules deviates from unity due to the randomness in the transcription rates. However when the RNA polymerase molecule searches for the promoter sequences on the DNA lattice by random jumps, the Fano factor approaches the Poisson limit as the jump size associated with the RNA polymerase increases. Since the jump size associated with dynamics of RNAP molecule is positively correlated with the degree of super coiling of DNA, we argue that the super coiled or close-packed structure of DNA might have evolved to keep the noises at the transcriptional level in a minimum.