Effects of Time Delay on Multistability of Genetic Toggle Switch

The effect of time delay on a genetic toggle switch, whose undelayed dynamics shows low protein expression states (L-states), high expression states (H-states) and coexistence of them different transcription-factor binding rates α, is investigated by using the delayed stochastic simulation method. Interestingly, we find that the delay induces a transition from the coexistence state to L-state or H-state by suppressing the other state. Moreover, the phase diagram on the α-τ plane is obtained by extensive simulations. It is observed that, the coexistence state is remarkably narrowed by increasing delay time, and completely disappearsabove a triple-point-like point where direct transitions between H-state and L-state are possible.