生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声,特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的,但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡;(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳,说明了相干共振现象的发生. 关键词： 生物钟 分子噪声 日夜节律振荡 相干共振     

模型化研究两细胞间基因、蛋白耦合振荡中的噪声效应

本文基于Hill动力学与Michaelis-Menten方程，建立理论模型研究两细胞间基因、蛋白耦合振荡中的噪声效应.研究发现，在Notch信号通路中，两细胞间基因、蛋白耦合振荡呈现了周期振荡特性，表明了细胞间信号传导的同步振荡特性.“内在”噪声和“外在”噪声对两细胞间基因、蛋白耦合振荡有着不同的作用.内噪声有利于细胞间Notch信号通路中各基因、蛋白表达再次提升.外噪声诱导通路中基因、蛋白的表达水平降低，周期振荡变得阻尼.内、外噪声共同作用不仅可使得基因表达适当并呈现出持续振荡模式，而且还可使得细胞间基因转录合成相应的蛋白过程呈现出持续振荡模式.从而表明了基因表达的内、外噪声共同作用有利于控制细胞间基因激活、蛋白合成保持周期节律性.本文理论结果揭示了内外噪声对细胞间Notch信号通路动力学的一种调控机制，确定了内外噪声各自的调控效应，澄清了内外噪声共同作用调控体系持续周期振荡的物理机制，理论结果符合实验，可为设计阻止Notch体系基因、蛋白变异导致的多种疾病和癌症的通路治疗方案提供理论依据.     

自催化三分子模型内噪声随机共振

运用化学Langevin方程 ,数值研究了内噪声对单个和单向耦合自催化三分子模型动力学行为的影响 .研究发现 ,对于单个振子体系 ,内噪声可以诱导持续振荡 ,而且随着系统尺度的增大 ,信噪比经过一个极大值 ,从而证明了内噪声随机共振和最佳尺度效应的存在 ;对于单向耦合系统 ,信噪比还随耦合强度的变化而经过极大值 .此外 ,边界条件对耦合体系的内噪声随机共振行为有很大影响 ,非零流条件下 ,耦合可以增强内噪声随机共振 ,而零流条件下 ,耦合会抑制随机共振 ;当耦合强度适宜时 ,每个振子发生随机共振时的尺度几乎相同 ,表明最佳体系尺度和耦合强度有助于体系达到最佳的化学反应状态 .     

α稳定噪声环境下过阻尼系统中的参数诱导随机共振现象

本文采用随机模拟方法, 研究了过阻尼振子系统在α稳定噪声环境下的参数诱导随机共振现象. 结果表明, 在α噪声环境下, 调节系统参数能够诱导随机共振现象; 而且调节非线性项参数时, 随机共振效果随α稳定噪声的指数的减小而减弱, 但当调节线性项参数时, 随机共振效果则随着α稳定噪声的特征指数的减小而增强. 本文的结论在α稳定噪声环境下, 利用参数诱导随机共振原理进行弱信号检测方面具有重要的理论意义, 并有助于理解不同α稳定噪声对一般随机共振系统的共振效果的影响.     

Coherent Resonance for Rate Oscillations During CO Oxidation on Pt(110) Surfaces: Interplay Between Internal and External Noise

用理论和模拟相结合的方法研究了Pt(110)面上CO催化氧化体系中由化学反应随机性所导致的内涨落和参量扰动带来的外涨落对其速率振荡过程的影响,重点考察了内涨落和外涨落的相互作用．在体系的确定性Hopf分岔点附近区域,噪声可以诱导产生随机振荡,其信噪比随噪声强度的变化会出现极大值,即发生了相干共振．运用随机范式理论,研究发现体系的相干共振行为依赖于一\有效噪声",其强度是内涨落和外涨落的加权和．研究结果表明,在内外噪声强度的参数平面内,随机振荡的信噪比呈现屋脊形,太大的内涨落或外涨落条件下相干共振都不能发生．数值模拟的结果和理论分析符合得很好．     

哺乳动物生理振荡中的最佳内噪声效应

基于哺乳动物生理振子模型，构造了相应的介观随机模型，研究了该系统中内噪声对基因振荡的影响．结果发现通过内噪声随机共振的机制，随机的基因振荡可以在最佳内噪声水平处达到最佳状态．同时，还发现存在一个中间的系统尺度使得随机模型表现出比确定性模型更宽的有效振荡区域，这说明了内噪声增强了体系的鲁帮性．讨论了这些效应可能的生理意义．     

二维映射神经元模型中的相干双共振

在具有稳定次阈值振荡特性的二维映射神经元模型中,研究了在没有外界输入信号时噪声对体系动力学的影响.通过数值计算发现了当体系的确定性动力学处于静息状态时,噪声可以诱导出神经元膜电位的随机振荡,而且随着噪声强度的变化,这种振荡的相干性具有两个极大值.另外我们还研究了当体系的确定性动力学处于稳定次阈值振荡及神经脉冲状态时的噪声效应,结果表明噪声对体系动力学的影响与其确定性动力学的分岔特性密切相关.     

α稳定噪声环境下多频微弱信号检测的参数诱导随机共振现象

本文将α稳定噪声与双稳随机共振系统相结合, 研究了不同α稳定噪声环境下高低频(均为多频)微弱信号检测的参数诱导随机共振现象, 探究了α稳定噪声的特征指数α(0 < α ≤ 2)和对称参数β (-1≤ β ≤ 1)及随机共振系统参数a, b对共振输出效应的作用规律. 研究结果表明, 在不同分布的α稳定噪声环境下, 通过调节系统参数a和b均可诱导随机共振来实现多个高、低频微弱信号的检测, 且存在多个a, b参数区间均可诱导随机共振, 这些区间不随α或β的变化而变化; 在高、低频微弱信号检测中, α或β对随机共振输出效应的作用规律相同. 本研究结果将有助于α稳定噪声环境下参数诱导随机共振现象中系统参数的合理选取, 进而可为实现基于随机共振的多频微弱信号检测方法的工程应用奠定基础. 关键词： 随机共振 α稳定噪声')" href="#">α稳定噪声 多频微弱信号检测 平均信噪比增益     

α稳定噪声驱动的非对称双稳随机共振现象

以微弱周期信号激励的非对称双稳系统为模型,以信噪比增益为指标,首先针对加性和乘性α稳定噪声共同作用的随机共振现象展开了研究,然后针对单独加性α稳定噪声激励的随机共振现象进行了研究,探究了α稳定噪声特征指数α和对称参数β分别取不同值时,系统结构参数a,b,刻画双稳系统非对称性的偏度r以及α稳定噪声强度放大系数Q或D对非对称双稳系统共振输出的作用规律.研究结果表明,无论在加性和乘性α稳定噪声共同作用下还是在单独加性α稳定噪声作用下,通过调节a和b或者r均可诱导随机共振,实现微弱信号的检测,且有多个参数区间与之对应,这些区间不随α或β的变化而变化;在研究噪声诱导的随机共振现象时发现,调节噪声强度放大系数也可使系统产生随机共振现象,且达到共振状态时D的区间也不随α或β的变化而变化.这些结论为α稳定噪声环境下参数诱导随机共振中系统参数以及噪声诱导随机共振中噪声强度的合理选取提供了依据.     

乘性和加性α稳定噪声环境下的过阻尼单稳随机共振现象

本文将α稳定噪声与单稳随机共振系统相结合,研究了乘性和加性α稳定噪声环境下的过阻尼单稳随机共振现象,探究了α稳定噪声特征指数α(0α2)、对称参数β(-1β1),单稳系统参数a及乘性α稳定噪声放大系数D对共振输出效应的作用规律.研究结果表明,在不同分布的α稳定噪声环境下,在一定范围内通过调节a或D均可诱导随机共振来实现单个或多个高、低频微弱信号的检测,且a和D分别存在一个最优值可使系统产生最佳的随机共振效应;不同α或β均可对系统共振输出效应产生规律性的影响,且α或β在高、低频微弱信号检测中的作用规律相同;在研究α稳定噪声环境下单、多频单稳随机共振现象时所得结论是相同的.本研究结果可为实现α稳定噪声环境下单稳随机共振系统参数的自适应调节奠定基础.     

Circadian rhythms and molecular noise

Circadian rhythms, characterized by a period of about 24 h, are the most widespread biological rhythms generated autonomously at the molecular level. The core molecular mechanism responsible for circadian oscillations relies on the negative regulation exerted by a protein on the expression of its own gene. Deterministic models account for the occurrence of autonomous circadian oscillations, for their entrainment by light-dark cycles, and for their phase shifting by light pulses. Stochastic versions of these models take into consideration the molecular fluctuations that arise when the number of molecules involved in the regulatory mechanism is low. Numerical simulations of the stochastic models show that robust circadian oscillations can already occur with a limited number of mRNA and protein molecules, in the range of a few tens and hundreds, respectively. Various factors affect the robustness of circadian oscillations with respect to molecular noise. Besides an increase in the number of molecules, entrainment by light-dark cycles, and cooperativity in repression enhance robustness, whereas the proximity of a bifurcation point leads to less robust oscillations. Another parameter that appears to be crucial for the coherence of circadian rhythms is the binding/unbinding rate of the inhibitory protein to the promoter of the clock gene. Intercellular coupling further increases the robustness of circadian 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.     

Intrinsic noise and division cycle effects on an abstract biological oscillator

Oscillatory dynamics are common in biological pathways, emerging from the coupling of positive and negative feedback loops. Due to the small numbers of molecules typically contained in cellular volumes, stochastic effects may play an important role in system behavior. Thus, for moderate noise strengths, stochasticity has been shown to enhance signal-to-noise ratios or even induce oscillations in a class of phenomena referred to as "stochastic resonance" and "coherence resonance," respectively. Furthermore, the biological oscillators are subject to influences from the division cycle of the cell. In this paper we consider a biologically relevant oscillator and investigate the effect of intrinsic noise as well as division cycle which encompasses the processes of growth, DNA duplication, and cell division. We first construct a minimal reaction network which can oscillate in the presence of large or negligible timescale separation. We then derive corresponding deterministic and stochastic models and compare their dynamical behaviors with respect to (i) the extent of the parameter space where each model can exhibit oscillatory behavior and (ii) the oscillation characteristics, namely, the amplitude and the period. We further incorporate division cycle effects on both models and investigate the effect of growth rate on system behavior. Our results show that in the presence but not in the absence of large timescale separation, coherence resonance effects result in extending the oscillatory region and lowering the period for the stochastic model. When the division cycle is taken into account, the oscillatory region of the deterministic model is shown to extend or shrink for moderate or high growth rates, respectively. Further, under the influence of the division cycle, the stochastic model can oscillate for parameter sets for which the deterministic model does not. The division cycle is also found to be able to resonate with the oscillator, thereby enhancing oscillation robustness. The results of this study can give valuable insight into the complex interplay between oscillatory intracellular dynamics and various noise sources, stemming from gene expression, cell growth, and division.     

Cooperative Effects of Noise and Coupling on Stochastic Dynamics of a Membrane-Bulk Coupling Model

Based on a membrane-bulk coupling cell model proposed by Gomez-Marin et al. [ Phys. Rev. Lett. 98 （2007） 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated. For parameters in a certain region, the oscillation can be induced by the cooperative effect of noise and coupling. Whether considering the coupling or not, corresponding coherence resonance phenomena are observed. Furthermore, the effects of two coupling parameters, cell size L and coupling intensity k, on the noise-induced oscillation of membranes are studied. Contrary effects of noise are found in and out of the deterministic oscillatory regions.     

Sustainment and Controlment of Noise-Induced Circadian Oscillations in <Emphasis Type="Italic">Neurospora</Emphasis>: Noise and External Signal Effects

The effect of light noise on a Neurospora circadian clock system in the steady states is investigated. It is found that the circadian oscillations could be induced by light noise, leading to various resonance phenomena including internal signal stochastic resonance (ISSR) and ISSR without tuning in the system. The strength of ISSR could be significantly reinforced with the decrease of the distance of the control parameter to the Hopf bifurcation point of the system. The fundamental frequency of noise-induced circadian oscillations almost does not change with the increment of light noise intensity, which implies that the Neurospora system could sustain intrinsic circadian rhythms. In addition, the ISSR and ISSR without tuning could be both amplified, suppressed or destroyed by tuning the frequency or amplitude of external signal.     

Oscillation regularity in noise-driven excitable systems with multi-time-scale adaptation

We investigate oscillation regularity of a noise-driven system modeled with a slow after-hyperpolarizing adaptation current (AHP) composed of multiple-exponential relaxation time scales. Sufficiently separated slow and fast AHP time scales (biphasic decay) cause a peak in oscillation irregularity for intermediate input currents I, with relatively regular oscillations for small and large currents. An analytic formulation of the system as a stochastic escape problem establishes that the phenomena is distinct from standard forms of coherence resonance. Our results explain data on the oscillation regularity of the pre-B?tzinger complex, a neural oscillator responsible for inspiratory breathing rhythm generation in mammals.     

光子晶体光纤反常色散区抽运产生超连续谱的相干特性分析

使用复互相干度的定义对超连续谱的相干性进行了数值计算,得到了不同功率抽运情况下的脉冲谱展宽以及超连续谱相干性的变化.结果表明孤子自频移以及色散波辐射是抽运波长位于光纤反常色散区情况下超连续谱展宽的主要物理机理,而超连续谱的相干性则主要受到调制不稳定性的影响.调制不稳定性放大抽运脉冲自身携带的随机噪声,使得非线性效应产生的光谱成分具有随机的相位与幅度,引起超连续谱相干性的下降. 抽运功率越高, 调制不稳定性增益越高,噪声对超连续谱产生的作用越强, 超连续谱的相干性越差.要获得高相干的超连续谱, 需采用峰值功率较小的脉冲进行抽运.要获得大谱宽高相干的超连续谱, 则需要合理选择抽运脉冲功率.