Phase synchronization of bursting neural networks with electrical and delayed dynamic chemical couplings

Diffusive electrical connections in neuronal networks are instantaneous, while excitatoryor inhibitory couplings through chemical synapses contain a transmission time-delay.Moreover, chemical synapses are nonlinear dynamical systems whose behavior can bedescribed by nonlinear differential equations. In this work, neuronal networks withdiffusive electrical couplings and time-delayed dynamic chemical couplings are considered.We investigate the effects of distributed time delays on phase synchronization of burstingneurons. We observe that in both excitatory and Inhibitory chemical connections, the phasesynchronization might be enhanced when time-delay is taken into account. This distributedtime delay can induce a variety of phase-coherent dynamical behaviors. We also study thecollective dynamics of network of bursting neurons. The network model presents theso-called Small-World property, encompassing neurons whose dynamics have two time scales(fast and slow time scales). The neuron parameters in such Small-World network, aresupposed to be slightly different such that, there may be synchronization of the bursting(slow) activity if the coupling strengths are large enough. Bounds for the criticalcoupling strengths to obtain burst synchronization in terms of the network structure aregiven. Our studies show that the network synchronizability is improved, as itsheterogeneity is reduced. The roles of synaptic parameters, more precisely those of thecoupling strengths and the network size are also investigated.     

Bistability in pulse propagation in networks of excitatory and inhibitory populations

We study the propagation of traveling solitary pulses in one-dimensional networks of excitatory and inhibitory integrate-and-fire neurons. Slow pulses, during which inhibitory cells fire well before neighboring excitatory cells, can propagate along the network at intermediate inhibition levels. At higher levels, they destabilize via a Hopf bifurcation. There is a bistable parameter regime in which both fast and slow pulses can propagate. Lurching pulses with spatiotemporal periodicity can propagate in regimes for which continuous pulses do not exist.     

Inferring Excitatory and Inhibitory Connections in Neuronal Networks

The comprehension of neuronal network functioning, from most basic mechanisms of signal transmission to complex patterns of memory and decision making, is at the basis of the modern research in experimental and computational neurophysiology. While mechanistic knowledge of neurons and synapses structure increased, the study of functional and effective networks is more complex, involving emergent phenomena, nonlinear responses, collective waves, correlation and causal interactions. Refined data analysis may help in inferring functional/effective interactions and connectivity from neuronal activity. The Transfer Entropy (TE) technique is, among other things, well suited to predict structural interactions between neurons, and to infer both effective and structural connectivity in small- and large-scale networks. To efficiently disentangle the excitatory and inhibitory neural activities, in the article we present a revised version of TE, split in two contributions and characterized by a suited delay time. The method is tested on in silico small neuronal networks, built to simulate the calcium activity as measured via calcium imaging in two-dimensional neuronal cultures. The inhibitory connections are well characterized, still preserving a high accuracy for excitatory connections prediction. The method could be applied to study effective and structural interactions in systems of excitable cells, both in physiological and in pathological conditions.     

兴奋性和抑制性自反馈压制靠近Hopf分岔的神经电活动比较

突触输入刺激神经元产生的电活动,在神经编码中发挥着重要作用.通常认为,兴奋性输入增强电活动,抑制性输入压制电活动.本文选取可调节电流衰减速度的突触模型,研究了兴奋性自突触在亚临界Hopf分岔附近压制神经元电活动的反常作用,与抑制性自突触的压制作用进行了比较,并采用相位响应曲线和相平面分析解释了压制作用的机制.对于单稳的峰放电,快速和中速衰减的兴奋性自突触分别可以诱发频率降低的峰放电和混合振荡(峰放电与阈下振荡的交替),而中速和慢速衰减的抑制性自突触也可以分别诱发频率降低的峰放电和混合振荡.对于与静息共存的峰放电,除上述两种行为外,中速衰减的兴奋性和慢速衰减的抑制性自突触还可以诱发静息.兴奋性和抑制性自突触电流在不同的衰减速度下,分别作用在峰放电的不同相位,才能诱发同类压制行为.结果丰富了兴奋性突触压制电活动反常作用的实例,获得了兴奋性和抑制性自突触压制作用机制的不同,给出了调控神经放电的新手段.     

Oscillatory Dynamics and Oscillation Death in Complex Networks Consisting of Both Excitatory and Inhibitory Nodes

In neural networks, both excitatory and inhibitory cells play important roles in determining the functions of systems. Various dynamical networks have been proposed as artificial neural networks to study the properties of biological systems where the influences of excitatory nodes have been extensively investigated while those of inhibitory nodes have been studied much less. In this paper, we consider a model of oscillatory networks of excitable Boolean maps consisting of both excitatory and inhibitory nodes, focusing on the roles of inhibitory nodes. We find that inhibitory nodes in sparse networks (small average connection degree) play decisive roles in weakening oscillations, and oscillation death occurs after continual weakening of oscillation for sufficiently high inhibitory node density. In the sharp contrast, increasing inhibitory nodes in dense networks may result in the increase of oscillation amplitude and sudden oscillation death at much lower inhibitory node density and the nearly highest excitation activities. Mechanism under these peculiar behaviors of dense networks is explained by the competition of the duplex effects of inhibitory nodes.     

Existence and stability of persistent states in large neuronal networks

We study the existence and stability of persistent states in large networks of quadratic integrate-and-fire neurons. The networks consist of two populations, one excitatory and one inhibitory. The stability of the asynchronous state is studied analytically. Our study demonstrates the role of recurrent inhibition and inhibitory-inhibitory interactions in stable persistent activity in large neuronal networks.     

Phase locking in networks of synaptically coupled McKean relaxation oscillators

We use geometric dynamical systems methods to derive phase equations for networks of weakly connected McKean relaxation oscillators. We derive an explicit formula for the connection function when the oscillators are coupled with chemical synapses modeled as the convolution of some input spike train with an appropriate synaptic kernel. The theory allows the systematic investigation of the way in which a slow recovery variable can interact with synaptic time scales to produce phase-locked solutions in networks of pulse coupled neural relaxation oscillators. The theory is exact in the singular limit that the fast and slow time scales of the neural oscillator become effectively independent. By focusing on a pair of mutually coupled McKean oscillators with alpha function synaptic kernels, we clarify the role that fast and slow synapses of excitatory and inhibitory type can play in producing stable phase-locked rhythms. In particular we show that for fast excitatory synapses there is coexistence of a stable synchronous, a stable anti-synchronous, and one stable asynchronous solution. For slower synapses the anti-synchronous solution can lose stability, whilst for even slower synapses it can regain stability. The case of inhibitory synapses is similar up to a reversal of the stability of solution branches. Using a return-map analysis the case of strong pulsatile coupling is also considered. In this case it is shown that the synchronous solution can co-exist with a continuum of asynchronous states.     

Bifurcation in neuronal networks with hub structure

We investigate bifurcations in neuronal networks with a hub structure. It is known that hubs play a leading role in characterizing the network dynamical behavior. However, the dynamics of hubs or star-coupled systems is not well understood. Here, we study rather subnetworks with a star-like configuration. This coupled system is an important motif in complex networks. Thus, our study is a basic step for understanding structure formation in large networks. We use the Morris-Lecar neuron with class I and class II excitabilities as a node. Homogeneous (coupling the same class neurons) and heterogeneous (coupling different class neurons) cases are considered for both excitatory and inhibitory coupling. For the homogeneous system class II neurons are suitable for achieving both complete and cluster synchronization in excitatory and inhibitory coupling, respectively. For the heterogeneous system with inhibitory coupling, the class I hub neuron has a wider parameter region of synchronous firings than the class II hub. Moreover, the class I hub neuron with the excitatory synapse gives rise to bifurcations of synchronized states and multi-stability (coexistence of a few different states) is observed.     

Stochastic phase dynamics and noise-induced mixed-mode oscillations in coupled oscillators

Synaptically coupled neurons show in-phase or antiphase synchrony depending on the chemical and dynamical nature of the synapse. Deterministic theory helps predict the phase differences between two phase-locked oscillators when the coupling is weak. In the presence of noise, however, deterministic theory faces difficulty when the coexistence of multiple stable oscillatory solutions occurs. We analyze the solution structure of two coupled neuronal oscillators for parameter values between a subcritical Hopf bifurcation point and a saddle node point of the periodic branch that bifurcates from the Hopf point, where a rich variety of coexisting solutions including asymmetric localized oscillations occurs. We construct these solutions via a multiscale analysis and explore the general bifurcation scenario using the lambda-omega model. We show for both excitatory and inhibitory synapses that noise causes important changes in the phase and amplitude dynamics of such coupled neuronal oscillators when multiple oscillatory solutions coexist. Mixed-mode oscillations occur when distinct bistable solutions are randomly visited. The phase difference between the coupled oscillators in the localized solution, coexisting with in-phase or antiphase solutions, is clearly represented in the stochastic phase dynamics.     

Detrended Fluctuation Analysis on Correlations of Complex Networks Under Attack and Repair Strategy

We analyze the correlation properties of the Erdos-Rényi random graph (RG) and the Barabási-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability pre. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of pre.     

Intermittent synchronization in a network of bursting neurons

Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical network of the basal ganglia, formed by excitatory and inhibitory bursters of the subthalamic nucleus and globus pallidus, involved in motor control and affected in Parkinson's disease. Recent experiments have demonstrated the intermittent nature of the phase-locking of neural activity in this network. Here, we explore one potential mechanism to explain the intermittent phase-locking in a network. We simplify the network to obtain a model of two inhibitory coupled elements and explore its dynamics. We used geometric analysis and singular perturbation methods for dynamical systems to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently, synchronous oscillations are generated by overlapped spiking which crucially depends on the geometry of the slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of activity patterns with overlapped spiking, and the other slower variable enhances the robustness of an irregular and intermittent activity pattern. While the analyzed network and the explored mechanism of intermittent synchrony appear to be quite generic, the results of this analysis can be used to trace particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson's disease.     

Delay-induced intermittent transition of synchronization in neuronal networks with hybrid synapses

We study the dependence of synchronization transitions in scale-free networks of bursting neurons with hybrid synapses on the information transmission delay and the probability of inhibitory synapses. It is shown that, irrespective of the probability of inhibitory synapses, the delay always plays a subtle role during synchronization transition of the scale-free neuronal networks. In particular, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. In addition, it is found that, for smaller and larger probability of inhibitory synapses, intermittent synchronization transition is relatively profound, while for the moderate probability of inhibitory synapses, synchronization transition seems less profound. More interestingly, it is found that as the probability of inhibitory synapses is large, regions of synchronization are upscattering.     

小世界神经元网络随机共振现象:混合突触和部分时滞的影响

实际神经元网络中,信息传递时电突触和化学突触同时存在,并且有些神经元间的时滞很小可以忽略.本文构建了带有不同类型突触耦合的小世界网络,研究部分时滞、混合突触及噪声对随机共振的影响.结果表明:兴奋性和抑制性突触的比例影响共振的产生;在抑制性突触为主的网络里,几乎不产生随机共振.系统最佳噪声强度和化学突触比例大致呈线性递增关系;特别是在以化学耦合为主的混合突触网络里,仅当兴奋性突触与抑制性突触比例约为4:1时,噪声才可诱导网络产生共振行为.在此比例下,引入部分时滞发现时滞可诱导网络产生随机多共振,且随网络中时滞边比例的增加,系统响应强度达到最优水平的时滞取值区间逐渐变窄;同时发现,网络中含有的化学突触越多,部分时滞诱导产生的多共振行为越强.此外,当时滞为系统固有周期的整数倍时,时滞越大共振所对应的噪声区域越广;并且网络中时滞边越多,越容易促使噪声和时滞诱导其产生明显的共振行为.     

Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For initial networks with considerably larger inhibitory strengths, we observe the emergence of a complex evolved topology, where neurons sparsely connected to other neurons, also a typical topology of the brain. The presence of noise enhances the strength of both types of synapses, but if the initial network has synapses of both natures with similar strengths. Finally, we show how the synchronous behaviour of the evolved network will reflect its evolved topology.     

Effects of Inhibitory Signal on Criticality in Excitatory-Inhibitory Networks

We study the criticality in excitatory-inhibitory networks consisting of excitable elements. We investigate the effects of the inhibitory strength using both numerical simulations and theoretical analysis. We show that the inhibitory strength cannot affect the critical point. The dynamic range is decreased as the inhibitory strength increases.To simulate of decreasing the efficacy of excitation and inhibition which was studied in experiments, we remove excitatory or inhibitory nodes, delete excitatory or inhibitory links, and weaken excitatory or inhibitory coupling strength in critical excitatory-inhibitory network. Decreasing the excitation, the change of the dynamic range is most dramatic as the same as previous experimental results. However, decreasing inhibition has no effect on the criticality in excitatory-inhibitory network.     

Maximum-entropy closures for kinetic theories of neuronal network dynamics

We analyze (1 + 1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we show how to systematically extend this kinetic theory to obtain higher-order, kinetic equations and to include coupled networks of both excitatory and inhibitory neurons.     

Neuronal growth: a bistable stochastic process

The fundamentally stochastic nature of neuronal growth has hardly been addressed in neuroscience. We report on the stochastic fluctuations of a neuronal growth cone's leading edge movement, the basic step in neuronal growth. Describing the edge movement as a stochastic bistable process leads to an isotropic noise parameter that is successfully used to test the model. An analysis of growth cone motility confirms the model, and predicts that linear changes of the bistable potential, as known from stochastic filtering, result in directed growth cone translocation.     

Burst synchronization of electrically and chemically coupled map-based neurons

Burst synchronization and burst dynamics of a system consisting of two map-based neurons coupled through electrical or chemical synapses are discussed. Some basic characteristic quantities are introduced to describe burst synchronization and burst dynamics of neurons. It is observed that excitatory coupling leads to in-phase burst synchronization but inhibitory coupling results in anti-phase one. By using the basic characteristics of burst dynamics, the effects of the intrinsic bursting properties and the coupling schemes on complex bursting behaviors are also presented for both inhibitory and excitatory couplings. The results are instructive to identify bursting behaviors through experimental data.     

Neural signal transduction aided by noise in multisynaptic excitatory and inhibitory pathways with saturation

We study the stochastic resonance phenomenon in saturating dynamical models of neural signal transduction, at the synaptic stage, wherein the noise in multipathways enhances the processing of neuronal information integrated by excitatory and inhibitory synaptic currents. For an excitatory synaptic pathway, the additive intervention of an inhibitory pathway reduces the stochastic resonance effect. However, as the number of synaptic pathways increases, the signal transduction is greatly improved for parallel multipathways that feature both excitation and inhibition. The obtained results lead us to the realization that the collective property of inhibitory synapses assists neural signal transmission, and a parallel array of neurons can enhance their responses to multiple synaptic currents by adjusting the contributions of excitatory and inhibitory currents.