生物构型对耦合Hindmarsh-Rose神经元系统响应能力的影响

利用Hindmarsh-Rose神经元模型研究了真实的生物细胞连接构型对耦合神经元系统响应能力的影响. 外界刺激信号通过细胞耦合从受刺激的神经元传递到其他神经元,合适的生物构型可以提高系统对刺激信号的响应能力和敏感度;同时,生物构型还会影响神经元系统的同步能力以及选择效应. 模拟的结果可以帮助我们理解面对不同外界刺激,生物体会协调自身结构,选择最佳的构型予以响应.     

随机的长程关联对耦合细胞体系中钙信号传导的作用

利用Euler数值积分的方法,研究了随机的长程关联对耦合细胞体系中钙信号传播的影响,发现当细 胞链中第一个单元受到外界刺激的作用时,由此而引起的钙点火活动会进一步激发其邻近的细胞,在随机连接的 作用下,钙信号就会在整个链中向下传递.结果表明,在该体系中加上少量的随机连接不仅能够极大地增强细胞 之间钙信号的传播能力,而且,适量的这种连接也可以使整个体系的钙离子振荡的有序性得到加强.这些现象表 明,细胞之间的随机扩散联系可能在帮助生物体系进行信息传递的过程中起着十分重要的作用.     

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 .     

耦合生物细胞体系中噪声诱导钙信号的传递和增强

研究了耦合细胞体系中钙振荡的动力学行为,发现体系的一端受到噪声扰动时,能够产生噪声诱导的钙振荡信号,这种信号在沿着耦合体系有效传递的同时,信号本身也能显著增强,并且在体系的另一端能够得到一个规则的信号.分别讨论了耦合强度、噪声强度和耦合方式对信号传递的影响,发现存在合适的耦合强度和噪声强度更有利于钙信号的传递和增强,与以往不同的是,还分别从信号和噪声背景两方面给出了定性的解释;同时发现单向耦合比双向耦合更有利于信号的传递和增强.     

System Size Resonance Associated with Canard Phenomenon in a Biological Cell System

通过研究发现,内噪声对细胞内钙振荡是有影响的,当体系处于由确定性方程所确定的稳定区域时,如果考虑内噪声的作用,就会有随机的钙振荡发生. 并且这种振荡的行为随着体系尺度的变化出现两个最大值,表明了尺度共振现象的发生. 这种行为是与体系的Canard现象密切相关的. 最佳的体系尺度与真实的细胞体积是相吻合的,并且这种吻合基本不随控制参数的改变而改变.     

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.     

双稳动力学系统中耦合效应对逻辑随机共振现象的增强作用

研究了电路耦合作用对逻辑随机共振现象以及逻辑门器件稳定性的影响．相对于单个的逻辑门电路,耦合的逻辑门器件可以在更宽的噪声范围内都保持逻辑运算的准确性,即耦合作用可以增强逻辑随机共振现象．此外,这种增强效应随着耦合体系尺度的增大而增大,但是当体系尺度达到一定程度时,这种增强作用达到一个稳定值．最后还考察了耦合强度的影响,发现随着耦合强度的增加,逻辑门器件可以保持逻辑运算准确性所对应的噪声区间非单调地改变,表现出一种共振的行为.     

二维格子神经元网络的振动共振和非线性振动共振

本文采用数值模拟的方法, 在通过电突触耦合或化学突触耦合的二维格子神经元网络中, 研究了FitzHugh-Nagumo神经元受到双频信号输入时神经元网络对低频信号的响应特性. 结果表明:当固定受到双频输入信号的神经元在体系中所占的比例且FitzHugh-Nagumo神经元参数处于可激发区域时双频信号中的高频部分可诱导出动作电位产生, 而且随着高频输入信号强度的增加, 神经元网络对低频输入信号响应先增大后减小, 出现了极大值, 即发生了振动共振现象. 另外本文还研究了神经元网络对低频输入信号的二次谐波的响应, 同样发现了非线性振动共振现象, 并且体系对低频信号的响应随着其频率ω 的增加也产生共振现象, 即发生了双共振现象. 上述共振现象在以电突触耦合的二维格子神经元网络中和以化学突触耦合的二维格子神经元网络中都可以观察到. 当固定双频输入信号中高频输入信号强度时, 随着受到双频输入信号的神经元在体系中所占比例的变化, 电突触耦合的二维格子神经元网络对低频输入信号的响应与化学突触耦合的二维格子神经元网络对低频输入信号的响应相比有很大的不同.     

非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象. 关键词： 尺度随机共振 非对称双稳耦合网络系统 余弦信号 矩形信号     

In- and Anti-transition of Firing Patterns Induced by Random Long-range Connections in Coupled Hindmarsh-Rose Neurons System

研究了在外界刺激电流的作用下,随机的长程关联对耦合的Hindmarsh-Rose神经元放电模式转变的影响．结果表明,当耦合强度较弱时,在神经元网络中加入一定数量的随机的长程关联,神经元的放电模式会从较少的周期态转变到较多的周期态;当耦合强度较强时,在神经元网络中加入一定数量的随机长程关联,神经元的放电模式会产生相反的转变,即从较多的周期态转变到较少的周期态．同时还简单讨论了神经系统的尺度大小和神经元之间的耦合强度,以及不同外界刺激条件下放电模式的强度与临界特性之间的关系．     

系统规模对群体行为的效果

影响细胞群体行为的因素是多种多样的, 除了以前研究的细胞通讯方式和环境因素外, 还与现有文献没有或很少研究的细胞数目(即系统规模)有关. 本文研究了系统规模对一类合成多细胞通讯系统的聚类行为的影响. 在该系统中, 单个系统是由压制振动子和基于延迟的松弛振子整合而成的振子, 而振子之间通过群体感应机制相互耦合. 通过分岔分析和数值模拟发现: 细胞数目的增加不仅可以改变平衡态聚类稳定性区间的大小并诱导新的聚类行为, 而且有利于扩大平衡态聚类的吸引域, 表明细胞分化可能与系统规模有密切关系; 细胞数目的增加还可以极大地丰富平衡态聚类和振动聚类的表现形式和共存方式, 为生物体对环境的适应性提供了良好的基础. 我们的结果不仅扩充了耦合系统的动力学行为, 也为理解多细胞现象奠定了基础. 关键词： 系统规模 群体感应 群体行为 耦合振子     

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.     

Emergence and evolution of multiple clusters of attracting agents

We investigate a multi-agent system with a behavior akin to the cluster formation in systems of coupled oscillators. The saturating attractive interactions between an infinite number of non-identical agents, characterized by a multimodal distribution of their natural velocities, lead to the emergence of clusters. We derive expressions that characterize the clusters, and calculate the asymptotic velocities of the agents and the critical value for the coupling strength under which no clustering can occur. The results are supported by mathematical analysis.For the particular case of a symmetric and unimodal distribution of the natural velocities, the relationship with the Kuramoto model of coupled oscillators is highlighted. While in the generic case the emergence of a cluster corresponds to a second-order phase transition, for a specific choice of the natural velocity distribution a first-order phase transition may occur, a phenomenon recently observed in the Kuramoto model. We also present an example for which the clustering behavior is quantitatively described in terms of the coupling strength.As an illustration of the potential of the model, we discuss how it applies to the dynamic process of opinion formation.     

Clustering Behavior in Globally Coupled Rotator Systems

Spatial clustering behaviors in globally coupled rotator systems are explored, statistical properties of cluster and disordered states are analyzed, scaling relations between the averaged lifetime of the clustering states and the coupling parameter are obtained. It is pointed out that clustering behavior also exists in the weakly antiferromagnetic case. Clustering is also investigated in terms of averaged localization in tangent space, it is shown that localization in tangent space corresponds to broken ergodicity. Influence of local coupling is studied, it is found that there exists a best local coupling which possesses the longest lifetime.     

Collective dynamics of multicellular systems

We have studied the collective behaviour of a one-dimensional ring of cells for conditions when the individual uncoupled cells show stable, bistable and oscillatory dynamics. We show that the global dynamics of this model multicellular system depends on the system size, coupling strength and the intrinsic dynamics of the cells. The intrinsic variability in dynamics of the constituent cells are suppressed to stable dynamics, or modified to intermittency under different conditions. This simple model study reveals that cell–cell communication, system size and intrinsic cellular dynamics can lead to evolution of collective dynamics in structured multicellular biological systems that is significantly different from its constituent single-cell behaviour.     

Modulation on the collective response behavior by the system size in two-dimensional coupled cell systems

By the intracellular calcium ionic minimal model proposed by Berridge, we investigated the collective response of two-dimensional (N×N) coupled cell systems to the external stimulation using numerical simulation methods. With a coupled intensity fixed and an appropriate coupled cell number chosen, the kinetic system size resonance was discovered. At the same time, it was found that the system size responding to the external stimulation for different coupled intensities transferred too, especially when the coupled intensity increased, the range of the corresponding system size extended. These phenomena illustrate that the coupled cell number and the coupled intensity can play constructive roles in noisy coupled systems, by which the biology system would probably improve its capability to respond to the external stimulation.     

Optimal intracellular calcium signaling

In many cell types, calcium is released from internal stores through calcium release channels upon external stimulation (e.g., pressure or receptor binding). These channels are clustered with a typical cluster size of about 20 channels, generating stochastic calcium puffs. We find that the clustering of the release channels in small clusters increases the sensitivity of the calcium response, allowing for coherent calcium responses at signals to which homogeneously distributed channels would not respond.     

Multimode dynamics in a network with resource mediated coupling

The purpose of this paper is to study the special forms of multimode dynamics that one can observe in systems with resource-mediated coupling, i.e., systems of self-sustained oscillators in which the coupling takes place via the distribution of primary resources that controls the oscillatory state of the individual unit. With this coupling, a spatially inhomogenous state with mixed high and low-amplitude oscillations in the individual units can arise. To examine generic phenomena associated with this type of interaction we consider a chain of resistively coupled electronic oscillators connected to a common power supply. The two-oscillator system displays antiphase synchronization, and it is interesting to note that two-mode oscillations continue to exist outside of the parameter range in which oscillations occur for the individual unit. At low coupling strengths, the multi-oscillator system shows high dimensional quasiperiodicity with little tendency for synchronization. At higher coupling strengths, one typically observes spatial clustering involving a few oscillating units. We describe three different scenarios according to which the cluster can slide along the chain as the bias voltage changes.     

The effects of coupling and bubble size on the dynamical-systems behaviour of a small cluster of microbubbles

This study endeavours to apply a theoretical model for predicting the dynamics of a bubble cluster of various sizes, within which each bubble may assume different initial conditions from other bubbles in the cluster. The resulting system of coupled Keller-Miksis-Parlitz equations are solved numerically, and the effects of coupling and bubble size on bubble cluster dynamics are examined for a given set of ultrasound parameters. It has been found that the effects of coupling are significant, and a bubble cluster's bifurcation characteristics and route to chaos can be altered by inter-bubble interactions. This gives rise to the possibility of suppressing the chaotic oscillations of microbubbles by varying bubble cluster size. Small equilibrium radii bubbles have little influence on the dynamics of neighbouring bubbles in a cluster via coupling. Furthermore, a bubble system consisting of smaller-sized bubbles transitions from order to chaos at lower driving pressure amplitudes.     

Self-organized transition to coherent activity in disordered media

Synchronized oscillations are of critical functional importance in many biological systems. We show that such oscillations can arise without centralized coordination in a disordered system of electrically coupled excitable and passive cells. Increasing the coupling strength results in waves that lead to coherent periodic activity, exhibiting cluster, local and global synchronization under different conditions. Our results may explain the self-organized transition in a pregnant uterus from transient, localized activity initially to system-wide coherent excitations just before delivery.