Circadian Rhythm In SCN And The Dynamical Behavior Of Motif In Biological Network

In history,biology is regarded as an experimental subject with emphasis of description.At the second half of the 20th century,the appearance of molecular biology brought the change of research methods of biology,which made the 21st century be the age of life sciences.The biological revolution aroused by "Plan of Human Genome" brought the new "Post-genome Times".Systmatically understanding the life phenomenon led by the interaction of a great lot of genes and proteins is the task of "Post-genome Times".The change of research mathods indicates the participation of Mathematical methods.Life system is the results of a lot of basic units,such as gene,protein and metabolic products,which arc essentially discrete. The first step of this research method is how to integrate all kinds of biologial databases and give a model as correctly as possible.To solve this problem will meet with many problems of computational mathematics and statistics, for example,how to integrate the data of different databases,how to deal with the model based on a small quantity of data.There are a great deal of work on this aspect.Summarizing the researches,we find that the largescale dynamical network is the most appropriate model.That is to say, life phenomenon must be cognized on the complex system composed by thousands of biological molecules.While the interaction of these thousands of biological molecules show character of network structurally.So life science is faced with a new transitional period that we should cognize life activity of bivalves based on the structure and function of network composed by biological molecules.In this thesis,with the help of dynamical system and complex network, we mainly study the dynamial properties of two kinds of networks about biology.One is the dynamical behavior of motif which is the basic element in gene regulatory network.The other one is the circadian rhythm of mammalian.Firstly,we introduce the phylogeny of molecular biology and give the relative concept and basic theory of complex network and synchronization. Then we introduce the main contents and innovate points of this paper,which can be listed as follows.(1) Dynamics of network motifs in genetic regulatory networks.Network motifs hold a very important status in genetic regulatory networks. We aim to analyze the dynamical property of the network motifs in genetic regulatory networks.The main result we obtained is that the dynamical property of a single motif is very simple with only an asymptotically stable equilibrium point,but the combination of several motifs can make more complicated dynamical properties emerge such as limit cycles.The above-mentioned result shows that network motif is a stable substructure in genetic regulatory networks while their combinations make the genetic regulatory network more complicated.(2) Synchronization between different motifs.Firstly,With the help of opcn-plus-closed-loop(OPCL) method,the synchronization between two networks with different topology structures and different dynamical behaviors is studied.Conditions for two different networks to get synchronization are given.Then based on the theoretical results achieved,the synchronization between different motifs is studied, which verifies the effectiveness and feasibility of the synchronization scheme. The results show that the synchronization of biological network can be gotten by the cluster synchronization among motifs,even different kinds of motifs.(3) Phase synchronization of circadian oscillators induced by a Light-Dark cycle.We mainly analyze the circadian behavior of the population of suprachiasmatic nucleus(SCN) neuron by light-dark cycle.Self-sustained oscillation is generated in individual SCN neuron by a moleculer regulatory network. Cells oscillate with different periods,but the SCN neurons display significant synchronization under the effect of the light-dark(LD) cycle.We present a model for a population of circadian oscillations in the SCN.We show that synchronization can be entrained by a 24-h LD cycle.The results establish not only a theoretical foundation,but also a quantitative basis for understanding the essential cooperative dynamics.(4) The noise effect on circadian oscillators.We study the effect of the Light-Dark cycle and environment noise on the daily rhythms of mammals numerically.The results show that the environment noise makes for phase synchronization but it can not make the oscillators get phase synchronization with period of 24-h.On the contrary, the threshold of the strength of light that makes the oscillators to get the phase synchronization with period of 24-h with environment noise is larger than that in the case without environment noise.(5) Synchronization mechanisms of circadian rhythms in the SCN.In mammals,the suprachiasmatic nucleus(SCN) of the hypothalamus is considered as the master circadian pacemaker.Each cell in the SCN contains an autonomous molecular clock,and the SCN is composed of multiple single-cell circadian oscillators.The fundamental question is how the individual cellular oscillators,expressing a wide range of periods,interact and assemble to create an integrated pacemaker that can govern behavioral and physiological rhythmicity and be reset by environmental light.The key is that the heterogeneous network formed by the cellular clocks within the SCN must synchronize to maintain timekeeping activity.To study the synchronization mechanisms and the circadian rhythm generation,we propose a model based on the structural and functional heterogeneity of the SCN.The model is a heterogeneous network of circadian oscillators in which individual oscillators are self-sustained.By using the proposed model,we show how the special structure of the SCN is exploited in synchronization in an analytical manner,i.e.,why the ventrolateral(VL) part has fewer but compactly connected neurons,while dorsomedial(DM) part has more but sparsely connected neurons.Moreover,we show that the DM part can smooth the periodic but abruptly affect waves of signal.We also study the rhythmic process of the circadian oscillators under the effect of the daily light-dark(LD) cycle,including three courses:information afferent inputs, oscillation,and information efferent outputs.The numerical simulations are also given to demonstrate the theoretical results.At last,a compact summary of this paper is given by combining the advances of the previous researches in this fields and our work.The prospect for furture study is also given.