The Research Of Nonlinear Time-Delay Effects In Gene Transcriptional Regulation System

Smolen et al. have proposed a time-delay gene transcriptional regulation system [Am. J. Physiol. 277, C777 (1999)]. Two fluctuations of the protein degradation rate and the protein synthesis rate are introduced in this deterministic positive-feedback model, and the two noises have effects on the system by the numerical modeling computation. When the delay time is a constant, it is found that either of the uncorrelated two noises can induce gene switch transition, and also found that the two noises and the correlated noise can induce gene switch. In addition, system instability is increasing with the time delay increasing, and the system occurs easily new properties by comparing a no-time-delay model with a time-delay model of the deterministic model or the stochastic model.In the further, it is found that difference delay times have some effects on the gene transcriptional regulation system. Here, all these delay times are small, for time delay affects system properties with the delay time increasing. The effects of nonlinear time-delay on the stochastic system have been numerically investigated. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.In addition, cells have the capabilities of auto regulation. Based on the no-time-delay and time-delay gene transcriptional regulation systems of positive and negative feedback proposed by Smolen et al. [Am. J. Physiol. 274, C531 (1998), Am. J. Physiol. 277, C777 (1999)], it is found that the two systems can occur oscillations, and found that oscillation region and range of the time-delay system are larger than the no-time-delay system. These changes induce more easily system oscillations, thus the time delay can increase system instability.In the conclusion, it is found that time delays can increase system instability by studying nonlinear time-delay gene transcriptional regulation system, also found that these parameters such as time delays, transcriptional rate, and noises can take as the control parameters of gene switch in the time-delay gene regulation systems. These parameters may be used in gene medication research and gene therapy.