生物系统中的非线性现象

文章通过用非线性科学的基本概念与系统方法分析了芽殖酵母细胞周期网络的动力学行为，说明非线性科学在定量研究生命过程所可能起到的重要作用，同时说明非线性科学现有的分析手段在研究生命系统中的局限性．这样利用非线性动力学研究生物系统的动力学问题，不但可以为系统生物学的研究提供强大的数学工具，同时也可以推动非线性科学本身的发展．这项研究从另一个角度显示了交叉学科的生命力．     

生物系统中的非线性现象

文章通过用非线性科学的基本概念与系统方法分析了芽殖酵母细胞周期网络的动力学行为,说明非线性科学在定量研究生命过程所可能起到的重要作用,同时说明非线性科学现有的分析手段在研究生命系统中的局限性.这样利用非线性动力学研究生物系统的动力学问题,不但可以为系统生物学的研究提供强大的数学工具,同时也可以推动非线性科学本身的发展.这项研究从另一个角度显示了交叉学科的生命力.     

Dynamical Analysis of Protein Regulatory Network in Budding Yeast Nucleus

Recent progresses in the protein regulatory network of budding yeast Saccharomyces cerevisiae have provided a global picture of its protein network for further dynamical research. We simplify and modularize the protein regulatory networks in yeast nucleus, and study the dynamical properties of the core 37-node network by a Boolean network model, especially the evolution steps and final fixed points. Our simulation results show that the number of fixed points N（k） for a given size of the attraction basin k obeys a power-law distribution N（k） χ k^-2.024. The yeast network is more similar to a scale-free network than a random network in the above dynamical properties.     

蛋白质动力学理论研究中的计算机模拟方法

蛋白质是生物体中一种十分重要的高分子物质。蛋白质分子有着自身所特有的化学、物理结构;在溶液中蛋白质分子不仅自身不同部分间存在着相互作用,而且还与溶剂分子间发生着复杂的相互作用,这些都很大程度上影响到分子的结构和演变过程。为了对蛋白质分子进行模拟,很有必要建立适当的描述蛋白质分子结构的模型,引入合理的模型基元间的相互作用,并采用有效的方法进行模拟,本着贴近现实和方便模拟的原则,在本文中我们系统地总结了近年来蛋白质动力学及其物理特性,特别对其模型、势能及模拟方法进行了着重介绍。为了增加一些感性认识,文中还就实验分析、折叠的协作性、搜寻保守残基和动力学过程的熵效应和阻挫效应等几个专题进行了应用介绍。     

蛋白质支链动力学快运动的核磁共振研究

蛋白质的功能不仅取决于其结构,而且受到其构像及其变化的影响. 许多生物化学过程就是由于蛋白质结构的一些动力学变化而完成,如蛋白质-蛋白质,蛋白质-药物配体之间的相互作用. 因此分析蛋白质的动力学变化,就能够对其参与的生化过程进行分析. 作为动力学研究的有力工具之一,核磁共振能够分辨到原子范围内的从千秒到皮秒时间范围的运动过程,因此在动力学研究中有着不可替代的作用. 本文仅就核磁共振在蛋白质支链快运动方法（ps-ns）研究方面的进展进行总结,以期阐明核磁共振的在支链动力学研究中的发展现状.     

无标度网络上的传播动力学

介绍了无标度网络上的传播动力学,在susceptible-infected-susceptible（SIS）模型的基础上考察了一般情况下无标度网络中疾病爆发的临界点问题,得出了关于临界点一般性的表达式.得到的结果在特殊情况下分别退化为已有的一些经典结论.同时分别讨论了这些情况的建模意义和可靠性. 关键词： 无标度网络 传播动力学 susceptible-infected-susceptible模型 临界点     

基于NMR自旋弛豫技术的蛋白质动力学研究

蛋白质的三维结构在很多情况下不能很好地解释其在生理过程中的作用机制. 动力学研究能够获悉蛋白质在不同时间尺度下的内运动信息,建立起动态结构和生物功能的联系. 该文综述了通过NMR自旋弛豫技术研究蛋白质动力学的原理和方法：ps~ns的快运动分析主要采用约化谱密度函数映射和Modelfree方法;μs~ms的慢运动涉及化学/构象交换过程,常借助CPMG和R_1ρ弛豫色散手段. 基于NMR的蛋白质动力学研究,将蛋白质科学从三维空间结构推进到四维时空结构的新层面.     

蛋白质溶液结构及动力学的核磁共振研究

高场液相核磁共振技术作为解析高分辨率蛋白质结构的两大主要手段之一,在近二十几年的时间里得到了迅猛的发展. 一方面,随着谱仪硬件技术、核磁脉冲技术和蛋白质标记技术的不断发展,液相核磁共振技术所能够研究的蛋白质不断突破分子量的限制,可以达到几万,甚至几十万. 另一方面,液相核磁共振技术成功地应用于蛋白质分子动力学的研究中,是目前唯一能够对蛋白质多个位点同时进行动力学研究的实验方法,并且仍在不断地创新、发展和完善中. 本文从蛋白质溶液结构的解析和动力学的研究两个主要方面对液相核磁共振研究的基本方法进行简要的介绍,并结合实例介绍一些最新的研究进展.     

中子自旋回波：研究蛋白质结构域动力学的利器

蛋白质作为生物系统这种复杂分子机器的重要组成部分之一,理解它们内部的结构及其在不同时间及空间尺度上的运动,对于研究生命的运作机理至关重要。相较于其他实验手段,中子自旋回波技术能探测到更大时空范围的性质,在研究蛋白质内部的结构域动力学方面具有独特的优势。这是一门横跨核物理与核技术、非平衡态统计物理学、分子生物学与蛋白质组学等前沿交叉领域的学科,充满着诸多未知与挑战,也遍布着一探生命奥秘的机遇。文章简述了中子自旋回波实验技术的基本原理和发展历程,阐述其在研究蛋白质结构域动力学方面的方法和技术优势,并介绍了部分实验案例,最后对其应用前景进行探讨与展望。     

小世界网络上的扩散限制的聚集-湮没反应动力学

通过Monte-Carlo模拟,研究了基于NW网络的两种类集团不可逆聚集-湮没过程的动力学行为.在系统中,两个同种类集团相遇,将不可逆地聚集成一个更大的集团;不同种类的两个集团相遇,则发生部分湮没反应.模拟结果表明,1)当捷径量化参数p相对较大或较小时,系统经较长时间演化后,集团密度c(t)和粒子密度g(t)呈现幂律形式,c(t)∝t^－α和g(t)∝t^－β,其中幂指数α和β满足α=2β的关系;2)当p为其他值时,集团密度和粒子密度随时间按非严格的幂 关键词： 聚集-湮没过程 小世界网络 反应动力学 Monte-Carlo模拟')" href="#">Monte-Carlo模拟     

非对称的玻色-爱因斯坦凝聚中的约瑟夫森结的动力学性质

利用半经典量子理论，研究了玻色-爱因斯坦凝聚体处于非对称的约瑟夫森结的动力学行为.结果表明双势阱中不同势阱的基态能量差与其相互作用能量的比率χ=0时，凝聚体表现为约瑟夫森效应；当χ≠0时，凝聚体中既存在量子宏观隧穿效应，又存在量子宏观局域效应. 关键词： 玻色爱因斯坦凝聚 约瑟夫森结 动力学性质     

Synchronization and Bifurcation of General Complex Dynamical Networks

In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.     

Geographical networks: geographical effects on network properties

Complex networks describe a wide range of systems in nature and society. Since most real systems exist in certain physical space and the distance between the nodes has influence on the connections, it is helpful to study geographical complex networks and to investigate how the geographical constrains on the connections affect the network properties. In this paper, we briefly review our recent progress on geographical complex networks with respect of statistics, modelling, robustness, and synchronizability. It has been shown that the geographical constrains tend to make the network less robust and less synchronizable. Synchronization on random networks and clustered networks is also studied.      

Synchronization of networks

We study the synchronization of coupled dynamical systems on networks. The dynamics is governed by a local nonlinear oscillator for each node of the network and interactions connecting different nodes via the links of the network. We consider existence and stability conditions for both single- and multi-cluster synchronization. For networks with time-varying topology we compare the synchronization properties of these networks with the corresponding time-average network. We find that if the different coupling matrices corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand, for non-commuting coupling matrices the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.      

Dynamical robustness analysis of weighted complex networks

Robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high-degree and low-degree nodes. We find that the phenomenon for the low-degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling. For all other parameters, the heterogeneous networks are always highly vulnerable to the failure of high-degree nodes; this point is the same as in the structural robustness analysis. We also find that with random inactivation, heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter. Thus our findings give an integrated picture for the dynamical robustness analysis on complex networks.     

Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method

The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts’ absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation.     

Study of the ‘Raman spectroscopic signature of life’ in mitochondria isolated from budding yeast

The ‘Raman spectroscopic signature of life’ is a Raman band at 1602 cm⁻¹ that sharply reflects the metabolic activity of cell mitochondria. Here we report the study of thissignature in isolated yeast mitochondria. The existence and behaviour of the 1602 cm⁻¹ band in isolated mitochondria have been confirmed to be the same as in living yeast cells: the intensity of the band decreases with timewhen a respiration inhibitor, sodium azide, is added. The present study shows the significance of isolated mitochondria in elucidating the origin of this still unassigned Raman band. Copyright © 2009 John Wiley & Sons, Ltd.     

Long Paths and Cycles in Dynamical Graphs

We study the large-time dynamics of a Markov process whose states are finite directed graphs. The number of the vertices is described by a supercritical branching process, and the edges follow a certain mean-field dynamics determined by the rates of appending and deleting. We find sufficient conditions under which asymptotically a.s. the order of the largest component is proportional to the order of the graph. A lower bound for the length of the longest directed path in the graph is provided as well. We derive an explicit formula for the limit as time goes to infinity, of the expected number of cycles of a given finite length. Finally, we study the phase diagram.     

Dynamical evolution processes of traffic flow and travel cost in urban transportation networks

Considering such a fact that travellers dynamically adjust their routes and the resultant link traffic flows in a network evolve over time, this paper proposes a dynamical evolutionary model of the traffic assignment problem with endogenous origin-destination （OD） demands. The model＇s stability is analysed and the resultant user equilibrium （UE） state is shown to be stable under certain conditions. Numerical results in a grid network indicate that the model can generate convergent flow patterns and finally terminates at the UE state. Impacts by the parameters associated with OD demand function and link cost function are also investigated.