Delays-based protein switches in a stochastic single-gene network.

In this paper, the protein switch in a single-gene network with time delays is investigated, where the gene expression is assumed to be disturbed by multiplicative and additive noises. The impacts of time delays τ d and τ s in degradation and synthesis processes, time delay τ g in global process and cross-correlation between two noises ( λ i , and i = d , s , g ) 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 ( λ i ) can induce protein switches from ON state to OFF one; (2) for λ i ⩾ 0 , the increase of τ d can induce protein switches from OFF state to ON one, while τ s (or τ g ) can induce protein switches from the ON state to the OFF one, but for λ i < 0 , the τ d (or τ s ) can induce protein switches from the OFF state to the ON one, while τ g 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 τ d can cause the NES phenomenon to disappear; and (4) τ d and τ s play opposing roles in the ST, i.e., the impacts of the time delays τ d and τ s on ST can be canceled each other out. [ABSTRACT FROM AUTHOR]