Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a variety of settings where the network might operate. These settings are representative of distinct cellular types, abundance of transcription factors and ratio between gene switching and protein synthesis rates. By investigating noise-induced transitions among the different network operative states, our results suggest that gene switching rates are key parameters to shape network response to external perturbations, and that such response depends on the particular biological setting, i.e. the characteristic time scales and protein abundance. These results might have implications on our understanding of irreversible transitions for noise-related phenomena such as cellular differentiation. In addition these evidences suggest to adopt the appropriate mathematical model of the network in order to analyze the system consistently to the reference biological setting.
