We present an analytical treatment of a genetic switch model consisting of two mutually inhibiting genes
operating without cooperative binding of the corresponding transcription factors. Previous studies have
numerically shown that these systems can exhibit bimodal dynamics without possessing two stable fixed
points at the deterministic level. We analytically show that bimodality is induced by the noise and find the
critical repression strength that controls a transition between the bimodal and nonbimodal regimes. We also
identify characteristic polynomial scaling laws of the mean switching time between bimodal states. These
results, independent of the model under study, reveal essential differences between these systems and
systems with cooperative binding, where there is no critical threshold for bimodality and the mean
switching time scales exponentially with the system size.

T. Biancalani and M. Assaf, Phys. Rev. Lett. 115, 208101 (2015)