摘要
The time delays in both synthesis and degradation reactions, reflecting the non-Markovian behavior, are intro- duced in the stochastic gene transcriptional dynamics. The effects of the time delays on the stationary proba- bility distribution, mean first passage time and stochastic resonance are discussed in detail based on the delayed stochastic differential equation and the corresponding delay Fokker-Planck equation. The time delays in synthesis reactions and in degradation reactions play a completely opposite role. The time delay in synthesis （degradation） reaction enhances （reduces） the mean first passage time, and tends to reduce （enhance） the signal-to-noise ratio. Finally, the effect of Causs-distributed time delays on the transcriptional system is explored to test whether the previous approximation of employing a certain delay time works well or not.
The time delays in both synthesis and degradation reactions, reflecting the non-Markovian behavior, are intro- duced in the stochastic gene transcriptional dynamics. The effects of the time delays on the stationary proba- bility distribution, mean first passage time and stochastic resonance are discussed in detail based on the delayed stochastic differential equation and the corresponding delay Fokker-Planck equation. The time delays in synthesis reactions and in degradation reactions play a completely opposite role. The time delay in synthesis （degradation） reaction enhances （reduces） the mean first passage time, and tends to reduce （enhance） the signal-to-noise ratio. Finally, the effect of Causs-distributed time delays on the transcriptional system is explored to test whether the previous approximation of employing a certain delay time works well or not.
基金
Supported by the National Natural Science Foundation of China under Grant Nos 11405223 and 81370970
the Youth Innovation Promotion Association of Chinese Academy of Sciences
