介观化学体系中涨落的作用机制与规律的研究：非高斯非马尔科夫效应
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摘要
近年来,随着纳米技术和生命科学的发展,介观体系的理论与实验研究已成为科学技术发展的前沿领域。介观尺度上的化学反应可以用离散的随机过程描述,涨落是其内禀属性。按照统计力学的基本原理,介观化学反应体系中的涨落可以达到相当显著的水平,会对体系的统计力学性质产生明显的影响。因而对于介观化学体系中涨落作用机制与规律的研究是目前统计物理领域重要的前沿科学问题之一。
对于真实的介观化学体系而言,由于其本身的复杂性,涨落的作用会随着体系内部机制的差异表现出不同的特性。要想获得对涨落作用的机理上的认识,就必须了解体系的复杂性与涨落之间的内在联系,并深入研究这些复杂因素的特征,机理和调控作用。在本论文中,我们着重介绍了介观化学体系中与涨落作用相关的两类重要机制:
介观化学体系中的非高斯效应
在涨落的作用下,体系的非线性动力学行为会发生显著的改变。以往对涨落效应的理论研究认为涨落的分布满足高斯分布,然而,实际体系的涨落分布通常会对高斯分布有较大偏离。对于非高斯涨落效应的研究近年来吸引了人们的广泛关注,研究的对象涉及非线性动力学的很多领域。但是在一类重要的化学振荡体系——Hopf分岔体系中,非高斯涨落的效应尚未得到系统的研究。在本论文中,我们考察了涨落的非高斯效应在Hopf分岔体系中对噪声诱导振荡行为的调控作用,数值模拟的结果表明非高斯效应会对噪声诱导振荡的规则性产生非平凡的作用,并且涨落的分布和时间相关性在调节噪声诱导振荡的时间行为上存在着密切的联系。利用随机范式理论我们成功的对这一现象的内在机理进行了解释。
介观化学体系中的非马尔科夫效应
近十年来,随着科学技术的发展,人们对介观尺度下生命体系的结构与功能有了越来越多的认识。由于生物体内化学反应过程的随机性与复杂性,其非马尔科夫效应不可避免。一方面,非马尔科夫效应会与体系中的涨落效应相互作用,产生新的有趣的现象;另一方面,非马尔科夫效应本身也会对体系的动力学行为产生显著影响。在本论文中,我们以生理时钟体系为例,利用数值模拟及随机范式分析方法,研究了内涨落与非马尔科夫效应在基因调控过程中的协同效应。我们发现内涨落可以增强体系对非马尔科夫效应的鲁棒性,且随着控制参量的变化,这种鲁棒性会呈现出不同的变化趋势。此外,我们还以基因开关体系为研究对象,考察了非马尔科夫效应对基因网络稳定性的影响。结果表明,非马尔科夫效应不仅可以显著改变基因开关的稳定性,而且会对内涨落作用下稳态之间转变过程的具体动力学性质产生不可忽略的作用。
In recent years, theoretical and experimental studies of mesoscopic systems have become the frontier of science development. In mesoscopic scale, the chemical reactions could be described as discrete stochastic processes and the fluctuation is the intrinsic property. The principal of statistic mechanics indicates that the fluctuation in mesoscopic chemical system is so significant that it will affect the dynamics of the system dramatically. By far, study on the effect of fluctuation in mesoscopic systems has become an important issue for statistic mechanics. It is noted that mesoscopic chemical systems exhibit quite different phenomena under the influence of fluctuation due to the complexity of their intrinsic dynamical features. Therefore, study of the character, mechanism and regulation of these complex factors and the interaction between the complex dynamical behaviors and the fluctuation in the system is crucial for getting an insight to the underlying mechanism of the phenomena induced by fluctuation. In this thesis, we have studied the following two kinds of complex dynamical features in mesoscopic systems which are related with fluctuation:
The non-Gaussian behavior
Fluctuation plays an important role in affecting the non-linear dynamical behaviors of the mesoscopic system. Former works on the effect of fluctuation assume that the fluctuation obeys Gaussian distribution. However, in real physical and chemical systems, the fluctuation constantly exhibits non-Gaussian behavior. The effect of such non-Gaussian fluctuation has drawn great interests in recent years and plenty of interesting features have been uncovered. Nevertheless, the effect of non-Gaussian fluctuation on the oscillation behavior in chemical systems with Hopf bifurcation has not been studied yet. In this thesis, we have investigated the effect of non-Gaussian fluctuation on the noise induced oscillation in the vicinity of Hopf bifurcation. It is found that the non-Gaussian behavior of the fluctuation could induce nontrivial effect on the regularity of the noise induced oscillation. We also found that the correlation time and the distribution of the fluctuation work cooperatively to tune the oscillation behavior. By performing stochastic normal form analysis, we illuminate the underlying mechanism of such phenomenon.
The non-Markovian behavior
In the last decade, with the development of life science, several interesting characters of the structures and functions in living organism have been uncovered. It is demonstrated that the non-Markovian behavior induced by the high degree of complexity during the gene expression process is inevitable in vivo. On one hand, such non-Markovian behavior may interact with the internal fluctuation and trigger many nontrivial dynamical phenomena. On the other hand, the non-Markovian behavior itself could significantly affect the dynamics of mesoscopic chemical systems. In this thesis, we have studied the cooperative effect of internal noise and the non-Markovian behavior in gene regulatory process by using numerical simulation together with stochastic normal form analysis. It is found that internal noise could enhance the robustness of system to non-Markovian behavior and such robustness shows different dependence on the synthetic and degradation rate of the protein. We also study the effect of non-Markovian behavior on the stability of a genetic toggle switch. The results indicate that the non-Markovian behavior could not only affect the stability of the bistable switch, but also the dynamics of the transition process.
对于真实的介观化学体系而言,由于其本身的复杂性,涨落的作用会随着体系内部机制的差异表现出不同的特性。要想获得对涨落作用的机理上的认识,就必须了解体系的复杂性与涨落之间的内在联系,并深入研究这些复杂因素的特征,机理和调控作用。在本论文中,我们着重介绍了介观化学体系中与涨落作用相关的两类重要机制:
介观化学体系中的非高斯效应
在涨落的作用下,体系的非线性动力学行为会发生显著的改变。以往对涨落效应的理论研究认为涨落的分布满足高斯分布,然而,实际体系的涨落分布通常会对高斯分布有较大偏离。对于非高斯涨落效应的研究近年来吸引了人们的广泛关注,研究的对象涉及非线性动力学的很多领域。但是在一类重要的化学振荡体系——Hopf分岔体系中,非高斯涨落的效应尚未得到系统的研究。在本论文中,我们考察了涨落的非高斯效应在Hopf分岔体系中对噪声诱导振荡行为的调控作用,数值模拟的结果表明非高斯效应会对噪声诱导振荡的规则性产生非平凡的作用,并且涨落的分布和时间相关性在调节噪声诱导振荡的时间行为上存在着密切的联系。利用随机范式理论我们成功的对这一现象的内在机理进行了解释。
介观化学体系中的非马尔科夫效应
近十年来,随着科学技术的发展,人们对介观尺度下生命体系的结构与功能有了越来越多的认识。由于生物体内化学反应过程的随机性与复杂性,其非马尔科夫效应不可避免。一方面,非马尔科夫效应会与体系中的涨落效应相互作用,产生新的有趣的现象;另一方面,非马尔科夫效应本身也会对体系的动力学行为产生显著影响。在本论文中,我们以生理时钟体系为例,利用数值模拟及随机范式分析方法,研究了内涨落与非马尔科夫效应在基因调控过程中的协同效应。我们发现内涨落可以增强体系对非马尔科夫效应的鲁棒性,且随着控制参量的变化,这种鲁棒性会呈现出不同的变化趋势。此外,我们还以基因开关体系为研究对象,考察了非马尔科夫效应对基因网络稳定性的影响。结果表明,非马尔科夫效应不仅可以显著改变基因开关的稳定性,而且会对内涨落作用下稳态之间转变过程的具体动力学性质产生不可忽略的作用。
In recent years, theoretical and experimental studies of mesoscopic systems have become the frontier of science development. In mesoscopic scale, the chemical reactions could be described as discrete stochastic processes and the fluctuation is the intrinsic property. The principal of statistic mechanics indicates that the fluctuation in mesoscopic chemical system is so significant that it will affect the dynamics of the system dramatically. By far, study on the effect of fluctuation in mesoscopic systems has become an important issue for statistic mechanics. It is noted that mesoscopic chemical systems exhibit quite different phenomena under the influence of fluctuation due to the complexity of their intrinsic dynamical features. Therefore, study of the character, mechanism and regulation of these complex factors and the interaction between the complex dynamical behaviors and the fluctuation in the system is crucial for getting an insight to the underlying mechanism of the phenomena induced by fluctuation. In this thesis, we have studied the following two kinds of complex dynamical features in mesoscopic systems which are related with fluctuation:
The non-Gaussian behavior
Fluctuation plays an important role in affecting the non-linear dynamical behaviors of the mesoscopic system. Former works on the effect of fluctuation assume that the fluctuation obeys Gaussian distribution. However, in real physical and chemical systems, the fluctuation constantly exhibits non-Gaussian behavior. The effect of such non-Gaussian fluctuation has drawn great interests in recent years and plenty of interesting features have been uncovered. Nevertheless, the effect of non-Gaussian fluctuation on the oscillation behavior in chemical systems with Hopf bifurcation has not been studied yet. In this thesis, we have investigated the effect of non-Gaussian fluctuation on the noise induced oscillation in the vicinity of Hopf bifurcation. It is found that the non-Gaussian behavior of the fluctuation could induce nontrivial effect on the regularity of the noise induced oscillation. We also found that the correlation time and the distribution of the fluctuation work cooperatively to tune the oscillation behavior. By performing stochastic normal form analysis, we illuminate the underlying mechanism of such phenomenon.
The non-Markovian behavior
In the last decade, with the development of life science, several interesting characters of the structures and functions in living organism have been uncovered. It is demonstrated that the non-Markovian behavior induced by the high degree of complexity during the gene expression process is inevitable in vivo. On one hand, such non-Markovian behavior may interact with the internal fluctuation and trigger many nontrivial dynamical phenomena. On the other hand, the non-Markovian behavior itself could significantly affect the dynamics of mesoscopic chemical systems. In this thesis, we have studied the cooperative effect of internal noise and the non-Markovian behavior in gene regulatory process by using numerical simulation together with stochastic normal form analysis. It is found that internal noise could enhance the robustness of system to non-Markovian behavior and such robustness shows different dependence on the synthetic and degradation rate of the protein. We also study the effect of non-Markovian behavior on the stability of a genetic toggle switch. The results indicate that the non-Markovian behavior could not only affect the stability of the bistable switch, but also the dynamics of the transition process.
引文
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