Modeling And Dynamics Analysis Of Biological Regulatory Networks

In biological bodies, periodic and circadian rhythms are common phenomena. Investigating the dynamics of circadian rhythms at molecular and cellular levels can help understand the mechanisms of the system. It has been found that the dysregulation of cell cycle may lead to tumor, where the tumor suppressor p53 plays important roles. Investigating the post-translational networks of p53 is important to learn the functions of the gene. At the same time, the dynamics behavior of complex biological networks, such as adaptivity, sensitivity, and entrainment of periodic solution, is the key to understanding the biological systems. In this thesis, we construct biological regulatory networks, and investigate the dynamics of circadian systems and p53 gene regulatory networks. The thesis mainly focuses on the following three sections:(1) Dynamics of circadian rhythm and jet-lag in mammalsCircadian rhythm in mammals is mainly governed by suprachiasmatic nucleus(SCN) located in hypothalamus. VL(ventral-lateral) and DM(dorsalmedial) in SCN are respectively dense and sparse, light-sensitive and not light-sensitive. According to the characteristics of sub-regions in structure and function, we build a SCN network and propose a modified Kuramoto model, and find that circadian rhythm is regulated by all neurons in SCN from perspective of phase synchronization. The simulation results demonstrate that the order parameter is positively correlated with connection probability, coupling strength and the light density, but is negatively correlated with the mean degree in sub-region. We also investigate the jet-lag phenomenon with the above model and find that jet-lag adjustment depends mainly on the degree of jet-lag and SCN structure instead of light density.(2) Dynamics of post-translation modifications of p53The expression of p53 is usually low in normal conditions, but is up-regulated when cells are damaged, which will leads to cell repair or cell apoptosis. It has been found that the functions of P53 are closely related to the post-translation modifications of p53, such as phosphorylation, acetylation and ubiquitination. We build two p53 regulatory networks and the corresponding ODE models in response to two type of DNA damage. The simulation results show that P53 will be phosphorylated and oscillates when the cells are damaged slightly, and cell repair will be induced. When the cells are severely damaged, P53 will be acetylated and accumulates, and cell apoptosis will be initiated.(3) Dynamics at equilibrium point and periodic orbit of biological regulatory systemsTo investigate the dynamics behavior of biological regulatory networks, we present mathematical definitions of adaptability and sensitivity of general attractors. We analyze the adaptability and sensitivity of the networks at stable equilibrium points. With classic repressilator model of Escherichia coli, we notice that the adaptability can be improved by changing input. We further propose a new control approach that can improve both adaptability and sensitivity. In addition, the output of some biological regulatory networks are found to has the same characteristics as input even their adaptabilities are not good. With a simplified p53 model, we find that the output can entrain to input regardless of constant input or periodic input in an infinitesimally contracting system.