A detailed analysis of the stability and flipping dynamics of a delayed exclusive toggle switch is performed. We use forward flux sampling method combined with delayed stochastic simulation algorithm to get the stationary distribution function, the switching rate, and pathways, as well as the transition state ensemble. Interestingly, under the influence of time delay, the stationary distribution corresponding to the stable states become narrower and the population in the transition region is significantly enhanced. In addition, the flipping rate increases monotonically with delay. Such findings demonstrate that time delay could reduce the stability of the bistable genetic switch dramatically. Furthermore, the transition pathways, characterized by the difference in the protein numbers and the state of operator, show larger discrepancy between the forward and backward switching process with increasing delay, indicating that transcriptional and translational delay can remarkably affect the flipping dynamics. Specifically, for the transition state, the difference in the probability of finding the operator site bound by the two different protein dimers is enlarged by delay, which further illustrates the crucial role of time delay on the stability and switching dynamics of genetic toggle switches.

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