The Analytic Methods Of Bifurcation Of Cell Cycle

So far, the studies on cell cycle have made much progress. Biology experimentsusually studied the relationship of a few genes or proteins. Although this method has madegreat contributions to the studies of cell cycle, it can not offer systematic and globalexplanations to the overall behaviors of this life activity. To understand the biologicalphenomenon of cell cycle more clearly, a set of methods have been set up by integratingthe experimental data of cell cycle, building mathematical models, and then dataprocessing and theoretical analysis. Now this set of analytical methods have been widelyapplied in studying the leading area of medical science and other areas.In the cell cycle experiments, two important issues raise our attention:(1) what causes the oscillation behavior of cyclin in cells(2) what factors affect the oscillation amplitude and frequency of cell cycleTo understand the above two questions, our practices are as follows: firstly, integratethe experimental data of cell cycle by former researchers (mainly refers to Tyson andFerrell) and the mathematical models built by them; secondly, imitate mathematical modelsand gain relevant data, analyze the oscillation intensity and frequency of key proteins incells; thirdly, simplify the mathematical models of cell cycle and imitate, use Hopfbifurcation theory to explore the oscillation behavior of proteins in cell cycle; fourthly,explore the mechanism of bifurcation phenomenon of cell cycle.The thesis draws the following main results:First, according to the intuitive explanation of cell cycle model built by Ferrell, itshould be: the frequency of oscillator and the synthesis rate of cycle protein increasemonotonically. But their model has defects, which causes the synthesis rate and thefrequency of oscillator don’t increase monotonically; we have modified their model, realizing the monotonic relationship between the synthesis rate of cycle protein and thefrequency of oscillator. Our modification is more reasonable.Second, we found that in Ferrell’s modified model, the system has two Hopfbifurcations, and the oscillator cycle exists between the cycles of the two bifurcationpoints.Third, we have simplified Ferrell’s model, making an attempt on four-dimensionalmodel and two-dimensional model. The two simplified models of cell cycle still reserveregulatory network construction of both positive and negative feedback, and show thedynamics of bistability and Hopf bifurcation, which indicates that these simplificationsretain the essence of cell cycle model.Fourth, by using the simplified model with retaining essence, we have made atentative attempt to explore the factors of rate influence. We have obtained that the strengthof two kinds of feedback and degradation rate exerts an obvious effect on the oscillationsof system in bifurcation points.