Stochasticity In Gene Transcriptional Regulation System: Fluctuations Induce Gene Switch

Based on the kinetic model of genetic regulation system proposed by Smolen et al. [Am. J. Physiol. 274, c531(1998)], the effects of fluctuations in the degradation reaction rate and the synthesis reaction rate of transcription factor have been investigated through the numerical computation and the analysis theory. Since the state of gene should not be observed obviously, it is often to study the state of gene through the level of the protein expressed by the gene in cells. If the level of the protein is high, the gene is thought to be open. If the level is low, the gene is thought to be close.In the case of uncorrelated noises, it is shown that only the fluctuation of degradation reaction rate can induce a switch process, and the mean first passage time (MFPT) between the high concentration state and low concentration one is decreased when the noise intensity of degradation reaction rate is increased.In the case of correlations between noises, a switch process can also be induced by the cross-correlation intensity between noises and by the fluctuation of synthesis reaction rate in the genetic regulatory system. It is found that, under large cross-correlation intensity, a succussive switch process (i.e. "on" "off" "on", which we call reentrance transition or twice switch) is occurred with the increasing of noise intensities, and there exists a critical noise intensity at which the MFPT of the switch process is the largest. When the system is initially at high concentration state, with the increasing of the cross-correlation, although the stationary probability distribution (SPD) of the TF-A monomer concentration at low concentration state is increased, yet the MFPT is decreased due to the decreasing of the SPD of the transient states between the two steady stable states which acts just like a "channel".Noise inducing the switch of gene between "open" and "close" is one of the most intuitionistic and important roles of noises to the original regulatory system. Those parameters such as D, a and A may provide targets for pharmacological intervention. And some special purposes of gene therapy may be reached by the control of such parameters.