Study On Stochastic Dynamics Of Nonlinear Gene Regulatory Networks

Gene expression and regulation processes are the core problem of molecular biology and the highlight of biology study.A lot of experiments show the inherently stochastic nature of gene regulatory cascades.Understanding the mechanisms of stochastic has tie gene regulatory networks become a challenging task nowaday.By virtue of the nonlinear stochastic theory and the computer simulation technology, we have investigated the character and function of noise on the nonlinear gene regulatory networks.In this paper,the effects of finite cell size on the gene regulation mechanism are studied when the external or internal noises are considered.The stochastic dynamics of three gene regulation models,including the circadian oscillator system in Drosophila,the cell cycle system in fission yeast,and copy number control system in Escherichia coli,are investigated numerically and theoretically,respectively.Firstly,a circadian oscillator model in Drosophila driven by external noise and internal noise has been studied near a Hopf bifurcation.The light-controlled parameter is suprathreshold.It is found when the system is driven by light noise only,the circadian oscillations can be induced by light fluctuation.There is an optimal light noise intensity at which a remarkable coherent circadian oscillation is observed.When the system is driven by internal noise only,by use of the chemical Langevin equation method,it is found that the coherence resonance phenomenon can be induced by the internal noise.When the system is simultaneously driven by internal and external noise,it is found that external-noise coherence resonance can be suppressed by internal noise,while internal-noise coherence resonance can be enhanced by modulation of the external noise intensity in a certain range of noise intensity.Secondly,the effects of the finite cell size on the cell cycle regulation in the wild type and weel^- cdc25â–³double mutant type are numerically studied.When the system is driven only by the internal noise,our numerical results obtained from the chemical Langevin equations are in qualitative agreement well with some experimental observations and data.The two resettings to the G₂ phase from early stages of mitosis can be induced under the moderate cell size.The quantized cycle times can be observed during such a cell size region.Therefore,a coarse estimation of cell size is obtained from the mesoscopic stochastic cell cycle model.Thirdly,based on a copy number control model of bacterial plasmid,the internal noise near a given steady state is investigated theoretically by using the linear noise approximation.For the noise in the plasmid molecules,a transition occurs with increasing the noise in the signal molecules under certain conditions.A novel noise-reduction mechanism,noise suppression by noise,is found.More importantly, the critical condition for the occurrence of the noise-reduction effect is given in our theoretical treatment.Our study provides a preliminary idea to investigate quantitatively the noise transmit and control in biochemical reaction network.