Theoretical Studies On Several Nonlinear Problems In Gene System

The flurry of genomic research has led to detailed lists of the genes that are at the heart of cellular function. These genes and their protein products form a complex web of interactions, wherein the proteins serve to activate or repress the transcription of the genes. The dissection and analysis of the complex dynamical interactions involved in gene regulation is thus a natural next step in genomic research. Complex gene regulatory networks often show some nonlinear dynamical behavior. Genes may show multi-stable properties including high and low express level, leading to the function of sensitive genetic "switch"; proteins can oscillate with time, serving for the mechanism of some important biological processes such as circadian clock. Moreover, gene expression processes are mesoscopic chemical reactions that are out of equilibrium state, there are large internal noise involved in the processes of transcription and translation. Recently, the study of intrinsic noise in life system, specially, in gene expression processes has drawn ever-growing interests and a variety of important results were reported. As pointed out by McAdams et al., gene expression process is a "noisy business". Currently, most studies in this field focus on where the noise comes from, how to characterize it and what its effect is. However, some recent studies consider how the intrinsic noise systematically facilitates the system properties. Therefore, in this work, we are interested in whether there are any constructive roles of external and internal noise in mesoscopic gene expression processes.In the present work, using some nonlinear approaches, we have studied several dynamic problems in gene system. We found that some complex factors such as environmental noise or internal noise may have constructive roles on the dynamic behavior of gene system. Moreover, we have elementarily studied the noise properties in simple gene networks.First, we have studied the influence of external noise on the dynamics of gene system. It is shown that oscillation can be induced by noise when the system is near the bifurcation point, and stochastic resonance (SR) appeared at a certain noise level. Through the mechanism of SR, the energy transduction of molecular machinery may be enhanced, or the response of gene networks to external feeble signal can be improved, which shed light on some practical functions of SR.Second, we have investigated the effect of internal noise on dynamics of mesoscopic gene expression systems. The systems we have studied include prokaryotic synthetic...