  It is well-known that gene activation/deactivation dynamics may be a major
source of randomness in genetic networks, also in the case of large
concentrations of the transcription factors. In this work, we investigate the
effect of realistic extrinsic noises acting on gene deactivation in a common
network motif - the positive feedback of a transcription factor on its own
synthesis - under a variety of settings, i.e., distinct cellular types,
distribution of proteins and properties of the external perturbations. At
variance with standard models where the perturbations are Gaussian unbounded,
we focus here on bounded extrinsic noises to better mimic biological reality.
Our results suggest that the gene switching velocity is a key parameter to
modulate the response of the network. Simulations suggest that, if the gene
switching is fast and many proteins are present, an irreversible noise-induced
first order transition is observed as a function of the noise intensity. If
noise intensity is further increased a second order transition is also
observed. When gene switching is fast, a similar scenario is observed even when
few proteins are present, provided that larger cells are considered, which is
mainly influenced by noise autocorrelation. On the contrary, if the gene
switching is slow, no fist order transitions are observed. In the concluding
remarks possible implications of the irreversible transitions for cellular
differentiation are briefly discussed.
