时滞与噪声影响 Notch信号通路动力学的模型化研究

本文基于Hill动力学与Michaelis-Menten方程,建立理论模型研究时滞与噪声影响Notch信号通路动力学.研究发现,her1、her7基因转录的时滞性在很大程度上调控着Notch信号通路的动力学行为.由于时滞性的调控,Notch系统动力学经历Hopf分岔,由稳态转变为周期演化特性.通过考察Notch信号通路的噪声效应,我们发现,由于噪声的扰动,Notch系统周期振荡动力学改变.在较小噪声幅值条件下,Notch信号通路中改变的周期节律性可以通过时滞得以平衡恢复,由此表明了her1、her7转录的时滞性促进了Notch信号通路的周期振荡.对于较强噪声环境,时滞效应很难改变Notch信号的巨大突变,其信号通路动力学行为被噪声影响.理论结果符合实验,并揭示了时滞与噪声对Notch信号通路动力学的一种调控机制,可为设计阻止Notch功能异常导致的多种疾病和癌症的通路治疗方案提供理论依据.     

Hes1调控 AKT-MDM2-p53-PTEN通路的一种物理机制

基于Hill动力学与Michaelis-Menten方程，建立理论模型研究发状分裂相关增强子1(hairy and enhancer of split 1,Hes1)调控蛋白激酶B (Protein Kinase B,AKT)-鼠双微体2 (Murine Double Minute2,MDM2)-抗癌基因p53(p53)-第10号染色体缺失的磷酸酶及张力蛋白同源的基因(Phosphatase and tensin homolog deleted on chromosome ten,PTEN)通路的一种物理机制.研究发现，Hes1通过与PTEN结合抑制PTEN表达，并调控AKT信号.表明了Hes1蛋白的合成，以及Hes1与PTEN相互作用调控AKTMDM2-p53-PTEN通路信号，将会有效地控制细胞结果 . Hes1作为AKT-MDM2-p53-PTEN信号通路中上游调节的重要因素，还可以在一定程度上通过影响p53蛋白功能，改变p53对肿瘤的抑制性.理论结果可用于预测Notch通路信号异常诱导的致癌性，并进一步揭示了Notch信号通路影响细胞AKT-MDM2-p53-PTEN通路的激活...     

Mdm2生成速率调控的p53-Mdm2振子的全局动力学和稳定性

肿瘤抑制蛋白p53的动力学在一定程度上可以决定DNA损伤后的细胞命运.p53的动力学行为与p53信号通路中p53-Mdm2振子模块密切相关.然而,p53的负调控子Mdm2的生成速率的增加使其在一些癌细胞中过表达.因此探讨Mdm2生成速率对p53动力学的影响有重要意义.同时,PDCD5作为p53的激活子也调控p53的表达.因此,本文针对PDCD5调控的p53-Mdm2振子模型,通过分岔分析获得了Mdm2生成速率所调控的p53的单稳态、振荡以及单稳态与振荡共存的动力学行为,且稳定性通过能量面进行了分析.此外,噪声强度对p53动力学的稳定性有重要的影响.因此,针对p53的振荡行为,探讨了噪声强度对势垒高度和周期的影响.本文所获得的结果对理解DNA损伤后的p53信号通路调控起到一定的指导作用.     

噪声交叉关联强度的时间周期调制对线性过阻尼系统的随机共振的影响

针对由加性、乘性噪声和周期信号共同作用的线性过阻尼系统, 在噪声交叉关联强度受到时间周期调制的情况下,利用随机平均法推导了系统响应的信噪比的解析表达式. 研究发现这类系统比噪声间互不相关或噪声交叉关联强度为常数的线性系统具有更丰富的动力学特性, 系统响应的信噪比随交叉关联调制频率的变化出现周期振荡型随机共振, 噪声的交叉关联参数导致随机共振现象的多样化.噪声交叉关联强度的时间周期调制的引入有利于提高对微弱周期信号检测的灵敏度和实现对周期信号的频率估计. 关键词： 随机共振 周期振荡型共振 噪声交叉关联强度 信噪比     

癌细胞信号网络动力学研究

癌症不仅是一种基因突变疾病,更是一种涉及诸如增殖、分化、凋亡和侵袭等多条细胞命运抉择的信号转导通路疾病.癌细胞内的信号通路虽然非常复杂但我们可以专注于关键蛋白的信号网络建模,定量研究癌细胞核心信号通路的动力学和功能调控机理.本文结合一些具体网络模型,介绍癌细胞信号网络动力学的研究进展.首先介绍信号网络的基序动力学研究,然后讨论细胞存活、增殖、侵袭、凋亡等单个功能模块的网络建模,以及几个模块耦合的信号网络,和以癌细胞为整体的癌细胞信号网络建模.这些研究表明,基于核心信号通路动力学的研究确实能促进对肿瘤发生发展机理的了解,为肿瘤的治疗和药物靶点的设计提供线索和思路,这些令人振奋的研究将激发未来更多类似的工作.     

用一类特定的双耦合Duffing振子系统检测强色噪声背景中的周期信号

通过分析耦合参数作用、系统所呈现大尺度周期相态的复杂性以及与系统在无噪声条件下状态的比较，得出耦合振子系统的动力学行为比同类单振子系统的复杂，周期相态更稳定、抗噪能力更强.用构造的一类含特定恢复力项双中强度耦合Duffing振子系统检测色噪声背景中的谐波、方波信号，信噪比分别达到-111.0和-108.45dB. 关键词： 特定双耦合 Duffing振子系统 色噪声 周期信号 信噪比     

太赫兹场和倾斜磁场对超晶格电子动力学特性调控规律研究

微带超晶格在磁场和太赫兹场调控下表现出丰富而复杂的动力学行为, 研究微带电子在外场作用下的输运性质对于太赫兹器件设计与研制具有重要意义. 本文采用准经典的运动方程描述了超晶格微带电子在沿超晶格生长方向(z方向)的THz场和相对于z轴倾斜的磁场共同作用下的非线性动力学特性. 研究表明, 在太赫兹场和倾斜磁场共同作用下, 超晶格微带电子随时间的演化表现出周期和混沌等新奇的运动状态. 采用庞加莱分支图详细研究了微带电子在磁场和太赫兹场调控下的运动规律, 给出了电子运行于周期和混沌运动状态的参数区间. 在电场和磁场作用下, 微带电子将产生布洛赫振荡和回旋振荡, 形成复杂的协同耦合振荡. 太赫兹场与这些协同振荡模式之间的相互作用是导致电子表现出周期态、混沌态以及倍周期分叉等现象的主要原因.     

线状铜电极在磷酸溶液中电流混沌振荡的同步行为

研究了恒电位下两个铜线电极在磷酸溶液中的电流混沌振荡行为 ,通过恒定不同的电位数值 ,改变单个电极的电流振荡混沌行为 ,研究了不同混沌间的相互作用 .调整线电极间的距离 ,研究了电极间距对电流振荡行为的影响 .实验中两电极的振荡间呈现了复杂的耦合作用 ,耦合后的频率与耦合前电极原有的频率不同 .两电极的混沌电流振荡中呈现出同步、准周期同步和反相同步等现象 .电极距离一定时 ,振荡波形差别很大的两电极的电流容易呈现反相同步和准周期同步 ,波形差别不大时容易产生同步 .强的耦合导致电极间电流振荡的同步 ,电极距离的加大 ,电极间电流振荡难以产生同步 .对耦合作用机制也进行了探讨     

驱动场作用下二分量BEC中原子数密度的演化

运用数值模拟研究了二分量玻色-爱因斯坦凝聚体(BEC)原子数密度的动力学行为,讨论了驱动场耦合强度、不同分量间原子作用强度、射频场频率及同分量内原子作用强度对二分量原子数密度演化特性的影响.结果显示:原子数密度随时间近似作周期性振荡,其振荡的周期随驱动耦合场强度、不同分量原子间作用强度的增大而减小,随自耦合强度的增大而增大;射频场频率的变化并不显著改变原子数密度振荡的周期,但它的增大会和自耦合强度的增大一样导致原子密度振荡的振幅减小.     

细胞钙振荡对周期信号的响应和胞间同步

钙离子是细胞中一种很重要的第二信使,通常它以细胞质钙离子浓度振荡的方式转导多种生理学信息,影响细胞分化、成熟和凋亡等各种生理过程.在有些组织如肝脏中,虽然不同的肝细胞个体可以具有非常不同的本征振荡频率,钙振荡却往往以扫过整个肝小叶的周期波的同步形式出现,表明细胞钙振荡在某种耦合因素作用下互相锁相.对一个典型的细胞钙振荡数学模型,通过数值模拟,研究了振荡对外界周期性刺激信号的响应,以及不同细胞之间通过细胞间接头耦合的同步特性.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.     

Mechanical oscillations at the cellular scale

Active phenomena which involve force generation and motion play a key role in a number of phenomena in living cells such as cell motility, muscle contraction and the active transport of material and organelles. Here we discuss mechanical oscillations generated by active systems in cells. Examples are oscillatory regimes in muscles, the periodic beating of axonemal cilia and flagella and spontaneous oscillations of auditory hair cells which play a role in active amplification of weak sounds in hearing. As a prototype system for oscillation generation by proteins, we discuss a general mechanism by which many coupled active elements such as motor molecules can generate oscillations.     

外光注入半导体激光器实现时钟分频

从理论和实验上研究了利用光注入半导体激光器对高重复速率光脉冲产生的周期振荡和时钟分频现象.结果表明，光注入半导体激光器引起的二倍周期振荡是使注入脉冲重复频率分频的直接原因.通过耦合速率方程，数值模拟了半导体激光器在外光注入时输出光的时间序列和功率谱，并且分析了激光腔内各种周期振荡的特征.研究表明，当注入光使半导体激光器出现稳定的二倍周期振荡，且注入光的重复频率为此振荡频率的二倍时，时钟分频即可产生实验中，采用重复频率为6.32GHz的光脉冲注入Fabry-Perot激光器，实现了3.16GHz时钟分频信号 关键词： 周期振荡 时钟分频 光谱侧带 光注入     

Stability of two-mode internal resonance in a nonlinear oscillator

We analyze the stability of synchronized periodic motion for two coupled oscillators, representing two interacting oscillation modes in a nonlinear vibrating beam. The main oscillation mode is governed by the forced Duffing equation, while the other mode is linear. By means of the multiple-scale approach, the system is studied in two situations: an open-loop configuration, where the excitation is an external force, and a closed-loop configuration, where the system is fed back with an excitation obtained from the oscillation itself. The latter is relevant to the functioning of time-keeping micromechanical devices. While the accessible amplitudes and frequencies of stationary oscillations are identical in the two situations, their stability properties are substantially different. Emphasis is put on resonant oscillations, where energy transfer between the two coupled modes is maximized and, consequently, the strong interdependence between frequency and amplitude caused by nonlinearity is largely suppressed.     

Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling

In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the damping terms. Hopf bifurcations and amplitude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.     

Control coherence resonance by noise recycling

We study the effect of recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay, in a parameter region below the threshold of supercritical Hopf bifurcation, by focussing on the performance of noise induced oscillations and coherence resonance. For fixed noise intensity, the amplitude and signal-to-noise ratio of the oscillation show periodic dependences on the delay time. The optimal noise intensity for the occurrence of coherence resonance also shows a periodic dependence on the delay. A theoretical analysis based on the stochastic normal form theory is presented, which qualitatively reproduces the simulation results with good agreement. This work presents a possible strategy for controlling noise induced oscillations and coherence resonance by deliberately adjusting the parameters of the recycled noise.     

Selective effects of noise by stochastic multi-resonance in coupled cells system

By investigating a stochastic model for intracellular calcium oscillations proposed by Höfer, we have analyzed the transmission behavior of calcium signaling in a one-dimensional two-way coupled hepatocytes system. It is shown that when the first cell is subjected to the external noise, the output signal-to-noise ratio (SNR) in the cell exhibits two maxima as a function of external noise intensity, indicating the occurrence of stochastic bi-resonance (SBR). It is more important that when cells are coupled together, the resonant behavior in the 1st cell propagates along the chain with different features through the coupling effect. The cells whose locations are comparatively close to or far from the 1st cell can show SBR, while the cells located in the middle position can display stochastic multi-resonance (SMR). Furthermore, the number of cells that can show SMR increases with coupling strength enhancing. These results indicate that the cells system may make an effective choice in response to external signaling induced by noise, through the mechanism of SMR by adjusting coupling strength.     

Oscillatory expression and variability in p53 regulatory network

The effect of delay, nonlinearity and noise on oscillatory motion is of permanent interest for theoretical and experimental research. Here we explore a negative feedback loop between p53 and Mdm2 with a time delay, which is a key circuit in the response of cells to damage. This circuit shows noisy sustained oscillations in individual human cells following DNA damage, and damped oscillations at the cell population level. We demonstrate the effect of delay on the oscillation, and the correlation in time course. In a multi-species system, the events at different time points which span a time delay are coupled even when the delay is large compared with the other characteristic times of the system. We also clarify that the dynamics at the single-cell level appears to be coherent resonance, and the origin of the damped oscillation at the macroscopic level out of the sustained ones at the single-cell level can be ascribed to the dephasing process which is induced by the interplay between nonlinearity and noise. The findings are consistent with experimental observations and advance our understanding of the dynamics of the p53 network.