Properties of the nonlinear and asymmetric time-delay gene transcriptional regulation system

The paper introduces the deterministic model and stochastic model of the nonlinear and asymmetric time-delay gene transcriptional regulation system, and researches the properties of stochastic system with the delay time by computational modeling. With the delay time increasing, it is found that the peak of probability distribution in high steady states is increased, and the peak of probability distribution in low steady states is decreased. The mean of state variable, the normalized variance, and the normalized autocorrelation function are slowly varied with small delay time, On the other hand, the mean of state variable is rapidly increased, and the normalized variance, and the normalized autocorrelation function is rapidly decreased with large delay time.