SCN中节律行为与生物网络中Motif行为的研究
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摘要
历史上,生物被看成是一门实验性科学,因而更强调描述性。20世纪后半世纪出现的分子生物学引起了生物学研究方法的变革,使21世纪成为生命科学的世纪。“人类基因组计划”引发的生物学革命带来了一个崭新的“后基因组时代”。在系统层面理解大量基因、蛋白质和代谢物相互作用所导致的生命现象是“后基因时代”的任务。这种研究方式的改变标志着数理研究方式的加入。生命系统是大量基本单元之间相互作用产生的现象,这些基本单元本质是离散的,如基因、蛋白质、各种代谢物。这类研究方式的第一步就是如何综合各种生物数据来建立尽可能正确的模型。解决这个问题会碰到许多计算数学和统计学的问题,比如如何综合来自于不同数据库的数据、如何由小数据量来建立模型,现在已经有了大量的这方面的工作。总结现有研究,目前来看最合适的模型就是以网络为基础的大规模的动力学网络。也就是,生命现象必须要在成千上万个生物分子组成的复杂系统的层面上予以认识,而这种成千上万个生物分子的相互作用在结构上都表现出网络的特征,所以可以说今天的生命科学正面临着一个新的转型期;要以生物分子所组成网络的结构和功能来认识生命活动。
在本文,我们主要是用动力系统以及复杂网络的有关知识来研究与生物网络有关的两类动力学性质。一类是基因调控网络的模体(Motif)的动力学行为;另一类是关于人类以及各种哺乳动物生物钟的问题,即24小时昼夜节律问题。在介绍了分子生物学的发展史、复杂网络及同步的相关概念和基本理论后,我们重点介绍了本文的主要工作和创新点。它们可以概括为以下五方面:
(1)基因调控网络模体的的动力学性质。
模体在基因调控网络中占有重要的地位,我们主要分析了基因调控网络中模体的动力学性质。我们得到的主要结论是单个模体的动力学性质非常简单,只有渐近稳定的平衡点;但是多个模体的组合将有非常复杂的动力学性质,比如极限环等。这些结果表明在基因调控网络中模体是一个稳定的结构并且它们的组合使得基因调控网络表现出更加复杂的动力学性质。
(2)不同模体之间的同步。
首先,基于开环闭环(open-plus-closed-loop,OPCL)方法,我们研究了具有不同拓扑结构和不同动力学行为的网络之间的同步,给出了不同网络达到同步的条件;然后利用所得的理论结果,研究了不同模体(Motif)之间的同步,并用数值例子验证了同步机制的有效性和可行性。这个结果表明网络的同步是可以通过模体(Motif)之间的聚类同步来实现,即使对于不同的模体(Motif)也可能通过此条途径实现同步。
(3)日夜光照诱导下的节律振子的相同步。
我们主要分析了视觉交叉上颌(SCN)节律振荡器在日夜光照(LD cycle)影响下的动力学行为。哺乳动物昼夜节律生物钟是自主维持的周期振荡器。在分子水平上,生物钟的振荡由自身调控反馈环路的转录和翻译组成,并接受外界环境因素的影响,通过SCN中枢振荡器的同步整合而产生作用。细胞的振动周期可以各不相同,但是在日夜光照周期的影响下这些振子表现出相同步行为。我们对SCN中的神经元细胞提出一个在光照影响下的模型,并且证明了在一定光照强度下这些神经元细胞在以24小时为周期的光照影响下能达到以24小时为周期的同步,也就是形成昼夜节律。我们的结论为更好地理解细胞在光照作用下的行为提供了理论和量化基础。
(4)外部噪声对节律振子的影响。
我们主要用数值的方法研究了日夜交替的周期光照和环境中的噪声对哺乳动物日常节律的影响。研究结果表明,环境中的噪声有利于细胞的相同步,但是当光照强度不大时,它不能使得细胞同步到以24小时为周期。相反,环境中噪声的存在使得细胞同步到以24小时为周期所需的光照强度的阈值升高。
(5)SCN中昼夜节律的同步机制
在哺乳动物中,SCN被认为是重要的昼夜节律起搏器。SCN内的每个细胞都含有一个自维持分子生物钟,SCN是由大量的节律振子组成的,这些振子的周期分布在20小时到28小时之间。现在的主要问题是,这些具有广泛周期的细胞振子是如何相互作用、组合并在日常光照的影响下整合后成为一个起搏器来调节着生物体的行为和生理的节律性。理论上关键的一点就是由SCN中的细胞生物钟构成的异质网络在周期光照作用下必须达到同步来维持这种时间一致活动。为了研究SCN中的同步机制以及节律的产生过程,我们在SCN的结构和功能异质的基础上提出一个由节律振子构成的异质网络模型,其中每个节点都是自维持振子。根据这个模型,我们从分析的角度说明了SCN的特殊结构产生的原因,也就是说,为什么腹外侧(VL)部分的神经元数目较少且联系紧密,而背内侧(DM)部分的神经元数目较多且联系稀疏?另外,我们证明了DM部分神经元能使变化剧烈的周期光信号的波形图变得更加光滑。我们还研究了在日常光照影响下的生物钟振子产生节律的三个过程:输入通路(input)、中央振荡器(centraloscillator,包括生物钟基因及其自主调节环路)和输出通路(output)。并且用数值模拟验证了理论结果的有效性。
最后,结合目前该领域的研究进展和自己所做的工作,对本文的工作做了全面的总结,并指出了今后该领域进一步工作的展望。
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.
在本文,我们主要是用动力系统以及复杂网络的有关知识来研究与生物网络有关的两类动力学性质。一类是基因调控网络的模体(Motif)的动力学行为;另一类是关于人类以及各种哺乳动物生物钟的问题,即24小时昼夜节律问题。在介绍了分子生物学的发展史、复杂网络及同步的相关概念和基本理论后,我们重点介绍了本文的主要工作和创新点。它们可以概括为以下五方面:
(1)基因调控网络模体的的动力学性质。
模体在基因调控网络中占有重要的地位,我们主要分析了基因调控网络中模体的动力学性质。我们得到的主要结论是单个模体的动力学性质非常简单,只有渐近稳定的平衡点;但是多个模体的组合将有非常复杂的动力学性质,比如极限环等。这些结果表明在基因调控网络中模体是一个稳定的结构并且它们的组合使得基因调控网络表现出更加复杂的动力学性质。
(2)不同模体之间的同步。
首先,基于开环闭环(open-plus-closed-loop,OPCL)方法,我们研究了具有不同拓扑结构和不同动力学行为的网络之间的同步,给出了不同网络达到同步的条件;然后利用所得的理论结果,研究了不同模体(Motif)之间的同步,并用数值例子验证了同步机制的有效性和可行性。这个结果表明网络的同步是可以通过模体(Motif)之间的聚类同步来实现,即使对于不同的模体(Motif)也可能通过此条途径实现同步。
(3)日夜光照诱导下的节律振子的相同步。
我们主要分析了视觉交叉上颌(SCN)节律振荡器在日夜光照(LD cycle)影响下的动力学行为。哺乳动物昼夜节律生物钟是自主维持的周期振荡器。在分子水平上,生物钟的振荡由自身调控反馈环路的转录和翻译组成,并接受外界环境因素的影响,通过SCN中枢振荡器的同步整合而产生作用。细胞的振动周期可以各不相同,但是在日夜光照周期的影响下这些振子表现出相同步行为。我们对SCN中的神经元细胞提出一个在光照影响下的模型,并且证明了在一定光照强度下这些神经元细胞在以24小时为周期的光照影响下能达到以24小时为周期的同步,也就是形成昼夜节律。我们的结论为更好地理解细胞在光照作用下的行为提供了理论和量化基础。
(4)外部噪声对节律振子的影响。
我们主要用数值的方法研究了日夜交替的周期光照和环境中的噪声对哺乳动物日常节律的影响。研究结果表明,环境中的噪声有利于细胞的相同步,但是当光照强度不大时,它不能使得细胞同步到以24小时为周期。相反,环境中噪声的存在使得细胞同步到以24小时为周期所需的光照强度的阈值升高。
(5)SCN中昼夜节律的同步机制
在哺乳动物中,SCN被认为是重要的昼夜节律起搏器。SCN内的每个细胞都含有一个自维持分子生物钟,SCN是由大量的节律振子组成的,这些振子的周期分布在20小时到28小时之间。现在的主要问题是,这些具有广泛周期的细胞振子是如何相互作用、组合并在日常光照的影响下整合后成为一个起搏器来调节着生物体的行为和生理的节律性。理论上关键的一点就是由SCN中的细胞生物钟构成的异质网络在周期光照作用下必须达到同步来维持这种时间一致活动。为了研究SCN中的同步机制以及节律的产生过程,我们在SCN的结构和功能异质的基础上提出一个由节律振子构成的异质网络模型,其中每个节点都是自维持振子。根据这个模型,我们从分析的角度说明了SCN的特殊结构产生的原因,也就是说,为什么腹外侧(VL)部分的神经元数目较少且联系紧密,而背内侧(DM)部分的神经元数目较多且联系稀疏?另外,我们证明了DM部分神经元能使变化剧烈的周期光信号的波形图变得更加光滑。我们还研究了在日常光照影响下的生物钟振子产生节律的三个过程:输入通路(input)、中央振荡器(centraloscillator,包括生物钟基因及其自主调节环路)和输出通路(output)。并且用数值模拟验证了理论结果的有效性。
最后,结合目前该领域的研究进展和自己所做的工作,对本文的工作做了全面的总结,并指出了今后该领域进一步工作的展望。
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.
引文
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