Potential dynamic analysis of tumor suppressor p53 regulated by Wip1 protein

The tumor suppressor p53 plays a key role in protecting genetic integrity. Its dynamics have important physiological significance, which may be related to the cell fate. Previous experiments have shown that the wild-type p53-induced phosphatase 1(Wip1) protein could maintain p53 oscillation. Therefore, we add Wip1 to remodel the p53 network. Firstly,we use the binomial τ-leap algorithm to prove our model stable under internal noise. Then, we make a series of bifurcation diagrams, that is, p53 levels as a function of p53 degradation rate at different Wip1 generation rates. The results illustrate that Wip1 is essential for p53 oscillation. Finally, a two-dimensional bifurcation diagram is made and the stability of some p53 dynamics under external noise is analyzed by potential landscape. Our results may have some implications for artificially interfering with p53 dynamics to achieve tumor suppression.

Dynamics analysis in a tumor-immune system with chemotherapy

An ordinary differential equation(ODE)model of tumor growth with the effect of tumor-immune interaction and chemotherapeutic drug is presented and studied.By analyzing the existence and stability of equilibrium points,the dynamic behavior of the system is discussed elaborately.The chaotic dynamics can be obtained in our model by equilibria analysis,which show the existence of chaos by calculating the Lyapunov exponents and the Lyapunov dimension of the system.Moreover,the action of the infusion rate of the chemotherapeutic drug on the resulting dynamics is investigated,which suggests that the application of chemotherapeutic drug can effectively control tumor growth.However,in the case of high-dose chemotherapeutic drug,chemotherapy-induced effector immune cells damage seriously,which may cause treatment failure.

A(2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution

In this paper,we investigate a(2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids.We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasigeostrophic potential vorticity equation with dissipation and topography under the generalized beta effect,and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method.Through the analysis of this model,it is found that the generalized beta effect and basic topography can induce nonlinear waves,and slowly varying topography is an external impact factor for Rossby waves.Additionally,the conservation laws for the mass and energy of solitary waves are analyzed.Eventually,the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method.Based on the solitary wave solutions obtained,we discuss the effects of dissipation and slowly varying topography on Rossby solitary waves.