Theoretical Study On Stochastic Dynamics Of Gene Expression And Regulatory Networks

Gene expression and regulation processes is the core problem of molecular biology and is the highlight of biology study. A lot of experiments show the inherently stochastic nature of gene regulatory cascades. Fluctuations, even very small, will be amplified by the gene networks and finally change the fate of cells which may impact the evolution of lives. Understanding the mechanisms of stochastic gene regulatory networks become a challenging task nowadays.In this paper, we highlight three gene systems: gene regulatory process in single cell, coupled synthetical clock cells and the transmit of immune stimulation in T cell. Our results show the significant role of noise in gene networks.First, we present a theoretical method to study the effect of external noises from the decay rate and synthesize rate of protein acting on a simple gene switch model. In the case of uncorrelated noises, it is shown that only multiplicative noise( fluctuations of degradation reaction rate) can induce a switch process. In the case of correlations between noises, a switch process can also be induced by the cross-correlation intensity between noises. It is found that, under large cross-correlation intensity, a succussive switch process is occurred with the increasing of noise intensities. This work is cited by a review in 'Nature' (Nature443(5),(2006)527-533).Then, we put the complexity of the gene network to correlating system and study the effect of signal fluctuations for the first time. Our result shows both constructive and destructive roles of the noise. We analysis the underlying physical mechanisms and find that (i) when the correlation is weak, the fluctuations act as influx signal which mainly change the frequency of the cells and finally lead the system more regular and (ii) when the system is at synchrony state, the fluctuations act as efflux signal and mainly change the phase difference between the two cells which destroy the synchronization. We also find that some noise intensities can induce the order of the system to be the worst around the frequency-locking state.Finally, the signal transmission from calcium concentration to protein level in T lymphocyte is studied. We construct a mathematical model to simulate this process. The results of our model match well with the observations of experiments. Compared with the constant [Ca²⁺], IL-2 gene is more sensitive to the oscillatory [Ca²⁺] when the signal is weak. Once the period of calcium oscillation is big than 400s, the ability of gene expression will drop to 0 rapidly. When internal noise is introduced to the signal process, an interesting phenomenon, "size resonance", is found whenever the calcium signal is periodic or constant.