Impact of time delay in a stochastic gene regulation network

In this paper, stationary probability distribution (SPD), mean first passage time (MFPT) and stochastic resonance (SR) phenomenon of an abstract model of the Myc/E2F/MiR-17-92 network with time delay and cross-correlation noise sources are investigated. The impacts of time delay tau, additive and multiplicative noise intensities Q and D, and cross-correlation intensity lambda between noises on the SPD, MFPT, and SNR are discussed, respectively. Research results show that: (i) the high protein level (or ON) state is enhanced (or weaken) by the tau (or lambda); (ii) the MFPT as a function of Q. or D exhibits a maximum, which is the signature of the noise enhanced stability (NES) of the ON state. The stability of the ON state can also enhance (or weaken) by the lambda (or tau); (iii) the existence of a maximum and a minimum in the signalto-noise ratio (SNR) is identifying the characteristics of the SR and stochastic reverse-resonance (SRR) phenomenon, tau and lambda enhance the SR and weaken the SRR phenomenon for SNR as a function of Q, while tau (or lambda) weakens (or enhances) the SR phenomenon for SNR as a function of D; and (iv) the time delay weakens the SR, and causes the SR phenomenon to disappear for SNR as a function of lambda. (C) 2017 Elsevier Ltd. All rights reserved.