Dynamical Behaviors of Rb-E2F Pathway Including Negative Feedback Loops Involving miR449

MiRNAs, which are a family of small non-coding RNAs, regulate a broad array of physiological and developmental processes. However, their regulatory roles have remained largely mysterious. E2F is a positive regulator of cell cycle progression and also a potent inducer of apoptosis. Positive feedback loops in the regulation of Rb-E2F pathway are predicted and shown experimentally. Recently, it has been discovered that E2F induce a cluster of miRNAs called miR449. In turn, E2F is inhibited by miR449 through regulating different transcripts, thus forming negative feedback loops in the interaction network. Here, based on the integration of experimental evidence and quantitative data, we studied Rb-E2F pathway coupling the positive feedback loops and negative feedback loops mediated by miR449. Therefore, a mathematical model is constructed based in part on the model proposed in Yao-Lee et al. (2008) and nonlinear dynamical behaviors including the stability and bifurcations of the model are discussed. A comparison is given to reveal the implication of the fundamental differences of Rb-E2F pathway between regulation and deregulation of miR449. Coherent with the experiments it predicts that miR449 plays a critical role in regulating the cell cycle progression and provides a twofold safety mechanism to avoid excessive E2F-induced proliferation by cell cycle arrest and apoptosis. Moreover, numerical simulation and bifurcation analysis shows that the mechanisms of the negative regulation of miR449 to three different transcripts are quite distinctive which needs to be verified experimentally. This study may help us to analyze the whole cell cycle process mediated by other miRNAs more easily. A better knowledge of the dynamical behaviors of miRNAs mediated networks is also of interest for bio-engineering and artificial control.