Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise

Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods.     

Propagation and synchronization of reverberatory bursts in developing cultured networks

Developing networks of neural systems can exhibit spontaneous, synchronous activities called neural bursts, which can be important in the organization of functional neural circuits. Before the network matures, the activity level of a burst can reverberate in repeated rise-and-falls in periods of hundreds of milliseconds following an initial wave-like propagation of spiking activity, while the burst itself lasts for seconds. To investigate the spatiotemporal structure of the reverberatory bursts, we culture dissociated, rat cortical neurons on a high-density multi-electrode array to record the dynamics of neural activity over the growth and maturation of the network. We find the synchrony of the spiking significantly reduced following the initial wave and the activities become broadly distributed spatially. The synchrony recovers as the system reverberates until the end of the burst. Using a propagation model we infer the spreading speed of the spiking activity, which increases as the culture ages. We perform computer simulations of the system using a physiological model of spiking networks in two spatial dimensions and find the parameters that reproduce the observed resynchronization of spiking in the bursts. An analysis of the simulated dynamics suggests that the depletion of synaptic resources causes the resynchronization. The spatial propagation dynamics of the simulations match well with observations over the course of a burst and point to an interplay of the synaptic efficacy and the noisy neural self-activation in producing the morphology of the bursts.     

Exponential synchronization for fuzzy cellular neural networks with time-varying delays and nonlinear impulsive effects

In this paper, the globally exponential synchronization of delayed fuzzy cellular neural networks with nonlinear impulsive effects are concerned. By utilizing inequality techniques and Lyapunov functional method, some sufficient conditions on the exponential synchronization are obtained based on p-norm. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.     

Mechanisms of spontaneous activity in developing spinal networks

Developing networks of the chick spinal cord become spontaneously active early in development and remain so until hatching. Experiments using an isolated preparation of the spinal cord have begun to reveal the mechanisms responsible for this activity. Whole-cell and optical recordings have shown that spinal neurons receive a rhythmic, depolarizing synaptic drive and experience rhythmic elevations of intracellular calcium during spontaneous episodes. Activity is expressed throughout the neuraxis and can be produced by different parts of the cord and by the isolated brain stem, suggesting that it does not depend upon the details of network architecture. Two factors appear to be particularly important for the production of endogenous activity. The first is the predominantly excitatory nature of developing synaptic connections, and the second is the presence of prolonged activity-dependent depression of network excitability. The interaction between high excitability and depression results in an equilibrium in which episodes are expressed periodically by the network. The mechanism of the rhythmic bursting within an episode is not understood, but it may be due to a “fast” form of network depression. Spontaneous embryonic activity has been shown to play a role in neuron and muscle development, but is probably not involved in the initial formation of connections between spinal neurons. It may be important in refining the initial connections, but this possibility remains to be explored. © 1998 John Wiley & Sons, Inc. J Neurobiol 37: 131–145, 1998

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Neural activity and survival in the developing nervous system

Recent evidence suggests that blockade of normal excitation in the immature nervous system may have profound effects on neuronal survival during the period of natural cell death. Cell loss following depression of electrical activity in the central nervous system (CNS) may explain the neuropsychiatric deficits in humans exposed to alcohol or other CNS depressants during development. Thus, understanding the role of electrical activity in the survival of young neurons is an important goal of modern basic and clinical neuroscience. Here we review the evidence from in vivo and in vitro model systems that electrical activity participates in promoting neuronal survival. We discuss the potential role of moderate elevations of intracellular calcium in promoting survival, and we address the possible ways in which activity and conventional trophic factors may interact.     

Robust emergence of small-world structure in networks of spiking neurons

Spontaneous activity in biological neural networks shows patterns of dynamic synchronization. We propose that these patterns support the formation␣of a small-world structure—network connectivity␣optimal for distributed information processing. We␣present numerical simulations with connected Hindmarsh–Rose neurons in which, starting from random connection distributions, small-world networks evolve as a result of applying an adaptive rewiring rule. The rule connects pairs of neurons that tend fire in synchrony, and disconnects ones that fail to synchronize. Repeated application of the rule leads to small-world structures. This mechanism is robustly observed for bursting and irregular firing regimes.     

Systems analysis of cellular networks under uncertainty

Besides the often-quoted complexity of cellular networks, the prevalence of uncertainties about components, interactions, and their quantitative features provides a largely underestimated hallmark of current systems biology. This uncertainty impedes the development of mechanistic mathematical models to achieve a true systems-level understanding. However, there is increasing evidence that theoretical approaches from diverse scientific domains can extract relevant biological knowledge efficiently, even from poorly characterized biological systems. As a common denominator, the methods focus on structural, rather than more detailed, kinetic network properties. A deeper understanding, better scaling, and the ability to combine the approaches pose formidable challenges for future theory developments.     

Bradykinin-responsive cells of dorsal root ganglia in culture: Cell size,firing, cytosolic calcium,and substance P

Summary 1. We analyze bradykinin-sensitive cells of the mouse dorsal root ganglion in culture from the viewpoints of cell size, electrical responses, and Ca²⁺ concentration change due to bradykinin and immunocytochemistry of substance P.2. Sixteen percent of cells in the cell group 26–30 µm in diameter fired in response to 10 µM bradykinin. None of other cell groups showed a firing response to bradykinin.3. We measured a cytosolic Ca²⁺ change due to bradykinin using a Ca²⁺-sensitive fluorescent dye, Fura 2. The rapid rise (peak time, 20 sec) in the Ca²⁺ concentration was ascribed to Ca²⁺ release from intracellular Ca²⁺ stores. The profound change in the Ca²⁺ concentration was observed again in the cell group 26–30 µm in diameter. Seventeen percent of cells in this group increased the Ca²⁺ concentration by approximately seven times that at resting level.4. Among cells which increase Ca²⁺ concentration responding to bradykinin, 83% of them contain substance P (an immunocytochemical study).5. We conclude that 16–17% of the cell group 26–30 µm in diameter of the dorsal root ganglia in culture are polymodal nociceptors and respond to bradykinin.     

Intercellular calcium signalling in cultured renal epithelia: a theoretical study of synchronization mode and pacemaker activity

We investigate a two-dimensional lattice model representation of intercellular Ca²⁺ signalling in a population of epithelial cells coupled by gap junctions. The model is based on and compared with Ca²⁺ imaging data from globally bradykinin-stimulated MDCK-I (Madin-Darby canine kidney)-I cell layers. We study large-scale synchronization of relevance to our laboratory experiments. The system is found to express a wealth of dynamics, including quasiperiodic, chaotic and multiply-periodic behaviour for intermediate couplings. We take a particular interest in understanding the role of pacemaker cells in the synchronization process. It has been hypothesized that a few highly hormone-sensitive cells control the collective frequency of oscillation, which is close to the natural frequencies (without coupling) of these cells. The model behaviour is consistent with the conjectures of the pacemaker cell hypothesis near the critical coupling where the cells lock onto a single frequency. However, the simulations predict that the frequency in globally connected systems decreases with increasing coupling. It is found that a pacemaker is not defined by its natural frequency alone, but that other intrinsic or local factors must be considered. Inclusion of partly sensitized cells that do not oscillate autonomously in the cell layer increases the coupling necessary for global synchronization. For not excessively high coupling, these cells oscillate irregularly and with distinctive lower frequencies. In summary, the present study shows that the frequency of synchronized oscillations is not dictated by one or few fast-responding cells. The collective frequency is the result of a two-way communication between the phase-advanced pacemaker and its environment.     

Automatic synchronization and distribution of biological databases and software over low-bandwidth networks among developing countries

Bioinformatics involves the collection, organization and analysis of large amounts of biological data, using networks of computers and databases. Developing countries in the Asia-Pacific region are just moving into this new field of information-based biotechnology. However, the computational infrastructure and network bandwidths available in these countries are still at a basic level compared to that in developed countries. In this study, we assessed the utility of a BitTorrent-based Peer-to-Peer (btP2P) file distribution model for automatic synchronization and distribution of large amounts of biological data among developing countries. The initial country-level nodes in the Asia-Pacific region comprised Thailand, Korea and Singapore. The results showed a significant improvement in download performance using btP2P--three times faster overall download performance than conventional File Transfer Protocol (FTP). This study demonstrated the reliability of btP2P in the dissemination of continuously growing multi-gigabyte biological databases across the three Asia-Pacific countries. The download performance for btP2P can be further improved by including more nodes from other countries into the network. This suggests that the btP2P technology is appropriate for automatic synchronization and distribution of biological databases and software over low-bandwidth networks among developing countries in the Asia-Pacific region. AVAILABILITY: http://everest.bic.nus.edu.sg/p2p/     

Computation by ensemble synchronization in recurrent networks with synaptic depression

While computation by ensemble synchronization is considered to be a robust and efficient way for information processing in the cortex (C. Von der Malsburg and W. Schneider (1986) Biol. Cybern. 54: 29–40; W. Singer (1994) Inter. Rev. Neuro. 37: 153–183; J.J. Hopfield (1995) Nature 376: 33–36; E. Vaadia et al. (1995) Nature 373: 515–518), the neuronal mechanisms that might be used to achieve it are yet to be uncovered. Here we analyze a neural network model in which the computations are performed by near coincident firing of neurons in response to external inputs. This near coincident firing is enabled by activity dependent depression of inter-neuron connections. We analyze the network behavior by using a mean-field approximation, which allows predicting the network response to various inputs. We demonstrate that the network is very sensitive to temporal aspects of the inputs. In particular, periodically applied inputs of increasing frequency result in different response profiles. Moreover, applying combinations of different stimuli lead to a complex response, which cannot be easily predicted from responses to individual components. These results demonstrate that networks with synaptic depression can perform complex computations on time-dependent inputs utilizing the ability to generate temporally synchronous firing of single neurons.     

基因组尺度集成细胞网络模型研究进展

细胞网络研究是系统生物学的一个研究热点,通过结合计算机模型和实验技术,从系统角度分析复杂的生物系统,可以为生物实验提供指导和预测。近十年来,国内外许多研究团队致力于基因组规模代谢网络、基因调控网络和信号转导网络模型的构建和分析,并取得了一定成果。而不同类型网络的集成和分析是当前生物网络研究中一个新的方向,并带来了诸多新的挑战。在本文中,主要对基因组尺度集成细胞网络模型的研究进展,特别是对代谢网络和转录网络的集成进行了详细论述,着重于集成网络的构建和分析方法,最后对该领域研究前景进行了展望。     

Induction and propagation of transient synchronous activity in neural networks endowed with short-term plasticity

Transient, task related synchronous activity within neural populations has been recognized as the substrate of temporal coding in the brain. The mechanisms underlying inducing and propagation of transient synchronous activity are still unknown, and we propose that short-term plasticity (STP) of neural circuits may serve as a supplemental mechanism therein. By computational modeling, we showed that short-term facilitation greatly increases the reactivation rate of population spikes and decreases the latency of response to reactivation stimuli in local recurrent neural networks. Meanwhile, the timing of population spike reactivation is controlled by the memory effect of STP, and it is mediated primarily by the facilitation time constant. Furthermore, we demonstrated that synaptic facilitation dramatically enhances synchrony propagation in feedforward neural networks and that response timing mediated by synaptic facilitation offers a scheme for information routing. In addition, we verified that synaptic strengthening of intralayer or interlayer coupling enhances synchrony propagation, and we verified that other factors such as the delay of synaptic transmission and the mode of synaptic connectivity are also involved in regulating synchronous activity propagation. Overall, our results highlight the functional role of STP in regulating the inducing and propagation of transient synchronous activity, and they may inspire testable hypotheses for future experimental studies.