一类基因调控网络的动力学研究
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摘要
生命现象从动力系统理论来看可以认为是由大量基本单元之间的相互作用产生的行为。这些基本单元本质是离散的,如基因、蛋白质、各种化学小分子。相互作用判定的问题除了实验以外,还涉及到大量的计算数学和统计学的问题。从动力学的角度来看关键就是如何综合各种不同的数据来源以及从小的数据量中尽可能建立正确反映这类作用的模型。目前来看最合适的模型就是以网络为基础的动力学网络。在这个时代,生命现象必须要在成千上万个生物分子所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在整体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。
相对于起步较早的国外,国内在该方面的研究处于起步阶段。即使起步较早的国外,其注意力也往往放在具有特定功能的生物网络构建与实验上,比如利用两个负反馈构建的toggle switch以及三个负反馈构建的re-pressilator。目前国内在合成生物学研究,细胞动力学模拟,具有特定动力学特性的生物网络的设计,构建与网络调控策略的发现技术等方面的研究还比较薄弱。
我们的研究方案着眼点是利用非线性分析与生物信息资源相结合的手段,来建立分析研究一类基因调控网络,讨论生物系统的非线性、多尺度、时滞和随机等因素对基因调控网络行为的影响,清楚了解其生理学基础及调控机制,为人工调控或制药提供科学依据。并可以进一步指导实验设计以及推动系统生物学中合成生物网络的构建等方面研究的发展。
在本文中,我们主要介绍了两方面的研究,在一方面,在实际基因调控网络中,由于不可避免的存在一些随机干扰,以及分子扩散、传输路径的远近等因素,分布型时滞能更为准确的描述基因调控网络中的时滞行为;同时,由于环境的周期变化,以及蛋白、mRNA的生产过程都有可能存在周期行为,应当考虑周期小扰动对基因调控网络的影响。考虑到这两种因素,我们提出并分析了在周期扰动下,分布型时滞基因调控网络的动力学行为。通过研究我们发现外界环境的周期刺激在一定的条件下能诱导出基因调控网络周期行为,它依赖于我们的调控函数的Lipschitiz常数、核函数,以及mRNA和蛋白质的退化速率。
在另一方面,考虑到噪声在基因调控网络中也起着非常重要的作用,它不仅可以影响基因调控网络的整体特性,还可以通过生物体组织产生特有的功能;同时由于目前科学研究手段的局限性,在实验阶段不可避免的出现误差,实验参数不一定能准确测量。同样的,结合两种因素,我们考虑了一类参数在一定区间的基因调控网络在随机干扰时的鲁棒性,并通过数值计算验证了我们理论结果的有效性。
最后,结合目前该领域的研究进展和自己所做的工作,对本文的工作做了总结,并指出了今后该领域进一步工作的展望。
Life system is the results of a lot of basic units, such as gene、protein and metabolic products, which are essentially discrete. The first step of this research method is how to integrate all kinds of biological 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 large-scale dynamical network is the most appropriate model. That is to say, life phenomenon must be cognised on the complex system composed by thousands of biological molecules. While the interaction of these thousands of biological molecules show character of network structurally. Therefore, life science is faced with a new transitional period that we should cognise life activity of bivalves based on the structure and function of network composed by biological molecules.
The previous work of system biology focused on the construction of the special gene network and experiments, such as toggle switch consists of two negative feedback and the repressilator consists of three genes connected in a feedback loop, and there is little result on the synthetic biology, cell dynamics simulation, construction and control strategies of gene networks, discovery of technical.
We studied the various levels of structure present in the biology system by the nonlinear analysis and combining of biological information resources and discussion the nonlinear biological systems with multi-scale, time-delay and noise for theoretical of gene regulatory or pharmaceutical. Moreover, It is can be used for the improvement of the biology experimental design and construction of synthetic biological.
In this thesis,we mainly study two aspects of dynamical of gene network with SUM regulatory logical. One is the periodic oscillation in delayed gene regulatory network with SUM regulatory logical and small perturbations. The other one is robustness of interval gene networks with multiple time-varying delay and noise. Then we introduce the main contents and innovate points of this paper, which can be listed as follows.
(1) A cellular system is generally characterized with significant time delays in gene regulation, in particular, for the transcription, translation, diffusion, and translocation processes. Moreover, periodic perturbations are widespread in the environment. Such time delays and perturbation may affect the dynamics of the entire biological system, both qualitatively and quantitatively.
In the second section, we derive new criteria for evaluating the global stability of periodic oscillation for gene networks with small perturbation and distributed delay, and lager time scales reaction. We results relay on the of Lipschtiz conditions of Hill function, topology of gene regulation networks and delay kernels. In particular, our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the computational complexity but also making analysis of periodic oscillation tractable for even large-scale nonlinear networks.
(2) The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the gene regulatory level. Besides, a cellular system is generally characterized with significant time delays in gene regulation, in particular, for the transcription, translation, diffusion, and translocation processes. Such time delays and stochastic noises may affect the dynamics of the entire biological system, both qualitatively and quantitatively. Moreover, all mathematical models for a biological system involve interval parameters due to the modeling errors, measurements errors, and liberalization approximations. Therefore, it is imperative and of prime importance to consider stochastic effects of the stability property on the interval GNs with time varying delays, to gain deep insight into the essential mechanism of the bimolecular systems.
In the third section, we investigated the robustness of the gene networks with noise perturbations and time varying delays, which shows the stochastic interval GN stable in the mean square even with time varying delays if the linear matrix inequality holds. Our theoretical results were derived in the form of LMIs, which is very easy to be verified and also no tuning of parameters is required.
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 future study is also given.
相对于起步较早的国外,国内在该方面的研究处于起步阶段。即使起步较早的国外,其注意力也往往放在具有特定功能的生物网络构建与实验上,比如利用两个负反馈构建的toggle switch以及三个负反馈构建的re-pressilator。目前国内在合成生物学研究,细胞动力学模拟,具有特定动力学特性的生物网络的设计,构建与网络调控策略的发现技术等方面的研究还比较薄弱。
我们的研究方案着眼点是利用非线性分析与生物信息资源相结合的手段,来建立分析研究一类基因调控网络,讨论生物系统的非线性、多尺度、时滞和随机等因素对基因调控网络行为的影响,清楚了解其生理学基础及调控机制,为人工调控或制药提供科学依据。并可以进一步指导实验设计以及推动系统生物学中合成生物网络的构建等方面研究的发展。
在本文中,我们主要介绍了两方面的研究,在一方面,在实际基因调控网络中,由于不可避免的存在一些随机干扰,以及分子扩散、传输路径的远近等因素,分布型时滞能更为准确的描述基因调控网络中的时滞行为;同时,由于环境的周期变化,以及蛋白、mRNA的生产过程都有可能存在周期行为,应当考虑周期小扰动对基因调控网络的影响。考虑到这两种因素,我们提出并分析了在周期扰动下,分布型时滞基因调控网络的动力学行为。通过研究我们发现外界环境的周期刺激在一定的条件下能诱导出基因调控网络周期行为,它依赖于我们的调控函数的Lipschitiz常数、核函数,以及mRNA和蛋白质的退化速率。
在另一方面,考虑到噪声在基因调控网络中也起着非常重要的作用,它不仅可以影响基因调控网络的整体特性,还可以通过生物体组织产生特有的功能;同时由于目前科学研究手段的局限性,在实验阶段不可避免的出现误差,实验参数不一定能准确测量。同样的,结合两种因素,我们考虑了一类参数在一定区间的基因调控网络在随机干扰时的鲁棒性,并通过数值计算验证了我们理论结果的有效性。
最后,结合目前该领域的研究进展和自己所做的工作,对本文的工作做了总结,并指出了今后该领域进一步工作的展望。
Life system is the results of a lot of basic units, such as gene、protein and metabolic products, which are essentially discrete. The first step of this research method is how to integrate all kinds of biological 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 large-scale dynamical network is the most appropriate model. That is to say, life phenomenon must be cognised on the complex system composed by thousands of biological molecules. While the interaction of these thousands of biological molecules show character of network structurally. Therefore, life science is faced with a new transitional period that we should cognise life activity of bivalves based on the structure and function of network composed by biological molecules.
The previous work of system biology focused on the construction of the special gene network and experiments, such as toggle switch consists of two negative feedback and the repressilator consists of three genes connected in a feedback loop, and there is little result on the synthetic biology, cell dynamics simulation, construction and control strategies of gene networks, discovery of technical.
We studied the various levels of structure present in the biology system by the nonlinear analysis and combining of biological information resources and discussion the nonlinear biological systems with multi-scale, time-delay and noise for theoretical of gene regulatory or pharmaceutical. Moreover, It is can be used for the improvement of the biology experimental design and construction of synthetic biological.
In this thesis,we mainly study two aspects of dynamical of gene network with SUM regulatory logical. One is the periodic oscillation in delayed gene regulatory network with SUM regulatory logical and small perturbations. The other one is robustness of interval gene networks with multiple time-varying delay and noise. Then we introduce the main contents and innovate points of this paper, which can be listed as follows.
(1) A cellular system is generally characterized with significant time delays in gene regulation, in particular, for the transcription, translation, diffusion, and translocation processes. Moreover, periodic perturbations are widespread in the environment. Such time delays and perturbation may affect the dynamics of the entire biological system, both qualitatively and quantitatively.
In the second section, we derive new criteria for evaluating the global stability of periodic oscillation for gene networks with small perturbation and distributed delay, and lager time scales reaction. We results relay on the of Lipschtiz conditions of Hill function, topology of gene regulation networks and delay kernels. In particular, our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the computational complexity but also making analysis of periodic oscillation tractable for even large-scale nonlinear networks.
(2) The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the gene regulatory level. Besides, a cellular system is generally characterized with significant time delays in gene regulation, in particular, for the transcription, translation, diffusion, and translocation processes. Such time delays and stochastic noises may affect the dynamics of the entire biological system, both qualitatively and quantitatively. Moreover, all mathematical models for a biological system involve interval parameters due to the modeling errors, measurements errors, and liberalization approximations. Therefore, it is imperative and of prime importance to consider stochastic effects of the stability property on the interval GNs with time varying delays, to gain deep insight into the essential mechanism of the bimolecular systems.
In the third section, we investigated the robustness of the gene networks with noise perturbations and time varying delays, which shows the stochastic interval GN stable in the mean square even with time varying delays if the linear matrix inequality holds. Our theoretical results were derived in the form of LMIs, which is very easy to be verified and also no tuning of parameters is required.
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 future study is also given.
引文
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