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Stochastic Transcription with Alterable Synthesis Rates

Background: Gene transcription is a random bursting process that leads to large variability in mRNA numbers in single cells. The main cause is largely attributed to random switching between periods of active and inactive gene transcription. In some experiments, it has been observed that variation in the number of active transcription sites causes the initiation rate to vary during elongation. Results: We established a mathematical model based on the molecular reaction mechanism in single cells and studied a stochastic transcription system consisting of two active states and one inactive state, in which mRNA molecules are produced with two different synthesis rates. Conclusions: By calculation, we obtained the average mRNA expression level, the noise strength, and the skewness of transcripts. We gave a necessary and sufficient condition that causes the average mRNA level to peak at a limited time. The model could help us to distinguish an appropriate mechanism that may be employed by cells to transcribe mRNA molecules. Our simulations were in agreement with some experimental data and showed that the skewness can measure the deviation of the distribution of transcripts from the mean value. Especially for mature mRNAs, their distributions were almost able to be determined by the mean, the noise (or the noise strength), and the skewness.