The nonlinear dynamics and fluctuations of mRNA levels in cross-talking pathway activated transcription.

Gene transcription is a stochastic process, and is often activated by multiple signal transduction pathways. In this work, we study gene transcription activated randomly by two cross-talking pathways, with the messenger RNA (mRNA) molecules being produced in a simple birth and death process. We derive the analytical formulas for the mean and the second moment of mRNA copy numbers and characterize the nature of transcription noise. We find that the stationary noise strength Φ is close to its baseline limit 1 when the mRNA level is high due to strong activation or stable transcription, or the mRNA level is low due to unstable transcription or ineffective mRNA production. If Φ stays well above 1, then the gene is infrequently active but mRNAs are accumulated rapidly once it is active. In this case, the system generates a transcriptional bursting, and the mean mRNA level peaks at a finite time. By examining the nonlinear dependance of Φ on transcriptional efficiency, we show that the maximum noise strength is attained only when the gene is silent in the majority of cells as observed in recent experiments. By comparing the current findings with our previous results in sequential pathway model, we come up with a profound conclusion that parallel, cross-talking pathways tend to increase transcription noise, whereas sequential pathways tend to reduce transcription noise. A further study on gene transcription activated by entangling pathways may help us reveal the subtle connection between the characteristics of transcription noise and the topology of genetic network.