The Research On The Dynamic Behaviours Of The Rb-E2F Pathway Including MiR449

Experiments have shown that microRNAs(miRNAs) play an important role in reg-ulating gene networks, they can orchestrate whole cellular programs by simultaneously regulating expression of a group of genes. Restoring miRNAs to normal levels in cancer cells can reverse the aberrant cell growth. So understanding how to control the normal levels of miRNAs in the cancer cells is a critical step in controlling cancer. In this paper, we presented a method to control microRNA levels and investigated the gene regulative network involving the Rb-E2F pathway and miRNA(miR449). On one hand, we studied the influence of noise on the dynamical behaviors of the Rb-E2F pathway by using a math-ematical model, we discovered a relationship between noise density and system response, found and defined the phenomenon of stochastic resonance, discovered that we can control the stochastic resonance through the optimal noises intensity, and determined that microR-NA levels can be controlled. These findings are propitious in providing a novel way to heal the cancer. On the other hand, we studied the influence of time-delay on the dynamical behaviors of the R.b-E2F pathway by using another mathematical model. It is shown that under certain assumptions the steady state of the delay model is asymptotically stable for all delay values, there is a critical value under another set of conditions, the steady state is stable when the time delay is less than the critical value, while the steady state is changed unstable when the time delay is greater than the critical value. Thus, Hopf bifurcation appears at the steady state when the delay passes through the critical value. Numerrical simulations were presented to illustrate the theoretical results.