Bistability and noise-induced transient behaviour of steady states in a cancer network with the regulation of microRNA

MicroRNAs (miRs) regulatory network models are highly non-linear due to the negative regulation of gene expression at the post-transcriptional level by miRs and can produce interesting dynamics of the system such as bistability for miR-transcriptional factors interactions. In this article, we focus on the miR-17-92 cluster and its interaction with transcriptional factors (proteins) E2F and Myc. Environmental fluctuations (noise) and randomness in the bio-chemical reactions can be very important and change the dynamical role of miR-17-92 in the regulatory network. We have formulated a stochastically forced miR-17-92 and E2F-Myc interaction model and study the phenomena of intrinsic and extrinsic noise which can induce random switching between steady states or the destruction of the bistability. Using a method that employs stochastic sensitivity functions we have constructed confidence ellipses to determine the configurational arrangements of equilibrium and spatial arrangements of random states near stable equilibria. Simulations are carried out to numerically show the flow of the solution trajectories under noise. Finally, we summarize the simulation results and the impact of noise on the dual non-linear role of miR-17-92 cluster to act as an oncogene or as a tumour suppressor gene.