Deterministic and stochastic dynamics in a gene regulatory network mediated by miRNA

MicroRNAs are able to modulate gene expression at the posttranscriptional level and play an essential role in various biological processes. In this paper, we establish a general model of an miRNA-mediated gene regulatory network motif with extracellular stimulus. Dynamical properties of the regulatory motif without stimulus focus on diverse codimension-1 and codimension-2 bifurcation analyses of two important feedback strengths as the parameters. Under varying levels of stimulus, we further consider stochastic dynamics controlled by crucial behaviors of monostability, bistability, excitability and oscillation in four typical regions on different two-parameter bifurcation diagrams. Furthermore, we apply potential landscapes to characterize global dynamics and stability behind physical properties of the stochastic behaviors. More essentially, our model can qualitatively simulate experimental findings of long-term memory formation in Aplysia .