The Study Of Synergy Between Noise And Delay In Switch Of Gene Networks

In this paper, the stochastic and delay effects of different gene expression network systems were investigated. And systems include single-gene network, emergent bistabil-ity model of gene expression system and Myc/E2F/miR-17-92 gene regulation network. Then, in Chapter 2, the related stochastic and delay theory, the methods of analytical approximation and stochastic simulation are also introduced. By virtue of small delay approximation theory and stochastic simulation, in terms of stationary probability densi-ty (SPD), mean first passage time (MFPT) and signal-to-noise ratio (SNR), the dynamic behaviors of different systems are analyzed. The following results show:In Chapter 3, the impacts of time delays Td and Ts in degradation and synthesis processes, time delay Tg in global process and cross-correlation between two noises (Ad, As and λg) on the probability distribution and switch time (ST) from low protein level (OFF state) to high one (ON state) are discussed, respectively. Our results show that (1) the increase of the cross-correlation between two noises (λi) can induce protein switches from ON state to OFF one; (2) for λi> 0, the increase of Td can induce protein switches from OFF state to ON one, while Ts (or Tg) can induce protein switches from the ON state to the OFF one, but for λi< 0, the Td (or Ts) can induce protein switches from the OFF state to the ON one, while Tg can induce protein switches from the ON state to the OFF one; (3) the ST as functions of the noise intensities exhibits a maximum, which is the signature of the noise enhanced stability (NES) of the OFF state, while the increase of Td can cause the NES phenomenon to disappear; and (4) Td and Ts play opposing roles in the ST, i.e., the impacts of the time delays Td and Ts on ST can be canceled each other out.In Chapter 4, the research for the emergent bistability model of gene expression system shows:(1) the multiplicative noise (or additive noise) can induce the switch from high (or low) concentration state to low (or high) one; (2) the mean first passage time (MFPT) of switch from high concentration state to low one as a function of the noise strengths exhibits a maximum, which is the signature of the noise enhanced stability (NES) phenomenon for the high concentration state; (3) as the value of cross-correlation strength λ, time delay r, or strength K of the feedback loop increase, the maximum in the MFPT increases, i.e., A, T, or K can enhance stability of the high concentration state.In Chapter 5, the research for Myc/E2F/miR-17-92 gene regulation network shows: (1) the ON state is enhanced by the time delay or cross-correlation intensity; (2) The MFPT of switch as a function of the noise intensities exhibits a maximum. The cross-correlation intensity between two noises λ, time delay T can enhance stability of the ON state; (3)the existence of a maximum and a minimum in the SNR as a function of intrinsic noise intensity Q is identifying the characteristics of the SR phenomenon and stochastic reverse-resonance phenomenon, however, for the curve of SNR as a function of extrinsic noise intensity D or cross-correlation intensity λ exhibits only a maximum. When the SNR as a function of Q, cross-correlation intensity and time delay enhances the SR phenomenon and weakens the stochastic reverse-resonance phenomenon. However, for the curve of SNR as a function of D, λ enhances the SR phenomenon, and T weakens the SR phenomenon. And for the curve of SNR as a function of λ, T weakens the SR phenomenon, and causes the SR phenomenon to disappear in the gene regulation network.