电突触耦合神经元的相位同步及放电节律的转化

研究了两个参数失配较大情况下,处于不同放电模式的两个电突触耦合Hindmarsh-rose(HR)神经元的相位同步问题,发现在适当耦合强度下可以实现相同步并呈现出复杂的放电节律.利用峰峰间期(Interspikeinterval,ISI)和平均放电频率证实了相同步的发生,给出并分析了不同放电状态的神经元在电突触耦合下实现相同步后的神经放电节律.从相同步的角度显示,神经元同步后呈现簇放电特征或峰放电特征,除与两耦合神经元独自放电模式有关外,还与电突触耦合强度有一定的内在关系.     

Impulse pattern in bi-directionally coupled model neurons of different dynamics

The effects of bi-directional gap junction coupling of two model neurons with subthreshold oscillations have been examined when the individual neurons are operating at different dynamical states either in the tonic or bursting firing mode. Our simulations indicate that intermediate coupling strengths mostly lead to highly variable, often chaotic impulse patterns whereas transition to completely synchronized activity at high coupling strengths is generally going along with transitions to regular limit cycle activity. The synchronized activity pattern, however, can be completely different from the original pattern of the uncoupled neurons.     

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.     

时滞援助的两抑制性突触耦合的Chay 神经元的同步

一对抑制性突触耦合的混沌Chay神经元的同步模式被研究。结果表明当耦合强度超过临界值时,两抑制耦合的混沌Chay神经元能达到反相的同步。与此同时,两混沌的神经元变为周期而不是原来的混沌运动。然而,如果考虑耦合神经元信息的传导时滞,在有效的时滞下,两个耦合神经元的在相簇同步能增加。在相簇同步窗口的大小随着耦合强度的增加而增加。此结果对于我们理解神经元集群的运动是一个指导。     

Bursting synchronization dynamics of pancreatic β-cells with electrical and chemical coupling

Based on bifurcation analysis, the synchronization behaviors of two identical pancreatic β-cells connected by electrical and chemical coupling are investigated, respectively. Various firing patterns are produced in coupled cells when a single cell exhibits tonic spiking or square-wave bursting individually, irrespectively of what the cells are connected by electrical or chemical coupling. On the one hand, cells can burst synchronously for both weak electrical and chemical coupling when an isolated cell exhibits tonic spiking itself. In particular, for electrically coupled cells, under the variation of the coupling strength there exist complex transition processes of synchronous firing patterns such as “fold/limit cycle” type of bursting, then anti-phase continuous spiking, followed by the “fold/torus” type of bursting, and finally in-phase tonic spiking. On the other hand, it is shown that when the individual cell exhibits square-wave bursting, suitable coupling strength can make the electrically coupled system generate “fold/Hopf” bursting via “fold/fold” hysteresis loop; whereas, the chemically coupled cells generate “fold/subHopf” bursting. Especially, chemically coupled bursters can exhibit inverse period-adding bursting sequence. Fast–slow dynamics analysis is applied to explore the generation mechanism of these bursting oscillations. The above analysis of bursting types and the transition may provide us with better insight into understanding the role of coupling in the dynamic behaviors of pancreatic β-cells.     

Noise-Stabilized Long-Distance Synchronization in Populations of Model Neurons

Rhythmic, synchronous firing of groups of neurons is associated with behaviorally relevant states, and it is thus of interest to understand the mechanisms by which synchronization may be achieved. In hippocampal slice preparations, networks of excitatory and inhibitory neurons have been seen to synchronize when strong stimulation is applied at separated sites between which any coupling must be subject to a significant axonal delay. We extend previous work on synchronization in a model system based on the network architecture of these hippocampal slices. Our new analysis addresses the effects of heterogeneous populations and noisy inputs on the stability of synchronous solutions in the system. We find that, with experimentally motivated constraints on the coupling strength, sufficiently large heterogeneity in the input currents renders synchrony unstable. The addition of noise, however, restores stable near-synchrony. We analytically reduce the high-dimensional biophysical equations for the full population to a simple three-dimensional map, and show that the map's stability properties correctly predict both the loss of stability and the restabilizing effect of the noise.     

Hindmarsh-Rose 神经网络的混沌同步

研究了通过特殊构造的非线性函数耦合连接的神经网络的混沌同步问题。在发展基于稳定性准则的混沌同步方法的基础上,给出了计算同步稳定性的误差发展方程,当耦合强度取参考值时,可实现稳定的混沌同步而不需要计算最大条件Lyapunov指数去判定是否稳定。通过对按照完全连接形式构成的Hindmarsh-Rose神经网络的数值模拟,显示可仅从两个耦合神经的耦合强度的稳定性范围预期到许多耦合神经实现同步的稳定性范围。该方法在噪声影响下,对实现神经元的混沌同步仍具有较强的鲁棒性。此外发现随着耦合神经数的增加,满足同步稳定性的耦合强度减小,与耦合神经的数量成反比。     

Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis

Conductance-based models of neurons from the lobster stomatogastric ganglion (STG) have been developed to understand the observed chaotic behavior of individual STG neurons. These models identify an additional slow dynamical process – calcium exchange and storage in the endoplasmic reticulum – as a biologically plausible source for the observed chaos in the oscillations of these cells. In this paper we test these ideas further by exploring the dynamical behavior when two model neurons are coupled by electrical or gap junction connections. We compare in detail the model results to the laboratory measurements of electrically-coupled neurons that we reported earlier. The experiments on the biological neurons varied the strength of the effective coupling by applying a parallel, artificial synapse, which changed both the magnitude and polarity of the conductance between the neurons. We observed a sequence of bifurcations that took the neurons from strongly synchronized in-phase behavior, through uncorrelated chaotic oscillations to strongly synchronized – and now regular – out-of-phase behavior. The model calculations reproduce these observations quantitatively, indicating that slow subcellular processes could account for the mechanisms involved in the synchronization and regularization of the otherwise individual chaotic activities. Received: 28 June 1999 / Accepted in revised form: 30 June 2000     

Real-time decoding of dopamine concentration changes in the caudate-putamen during tonic and phasic firing

The fundamental process that underlies volume transmission in the brain is the extracellular diffusion of neurotransmitters from release sites to distal target cells. Dopaminergic neurons display a range of activity states, from low-frequency tonic firing to bursts of high-frequency action potentials (phasic firing). However, it is not clear how this activity affects volume transmission on a subsecond time scale. To evaluate this, we developed a finite-difference model that predicts the lifetime and diffusion of dopamine in brain tissue. We first used this model to decode in vivo amperometric measurements of electrically evoked dopamine, and obtained rate constants for release and uptake as well as the extent of diffusion. Accurate predictions were made under a variety of conditions including different regions, different stimulation parameters and with uptake inhibited. Second, we used the decoded rate constants to predict how heterogeneity of dopamine release and uptake sites would affect dopamine concentration fluctuations during different activity states in the absence of an electrode. These simulations show that synchronous phasic firing can produce spatially and temporally heterogeneous concentration profiles whereas asynchronous tonic firing elicits uniform, steady-state dopamine concentrations.     

Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time

 We studied the dynamics of precise spike synchronization and rate modulation in a population of neurons recorded in monkey motor cortex during performance of a delayed multidirectional pointing task and determined their relation to behavior. We showed that at the population level neurons coherently synchronized their activity at various moments during the trial in relation to relevant task events. The comparison of the time course of the modulation of synchronous activity with that of the firing rate of the same neurons revealed a considerable difference. Indeed, when synchronous activity was highest, at the end of the preparatory period, firing rate was low, and, conversely, when the firing rate was highest, at movement onset, synchronous activity was almost absent. There was a clear tendency for synchrony to precede firing rate, suggesting that the coherent activation of cell assemblies may trigger the increase in firing rate in large groups of neurons, although it appeared that there was no simple parallel shifting in time of these two activity measures. Interestingly, there was a systematic relationship between the amount of significant synchronous activity within the population of neurons and movement direction at the end of the preparatory period. Furthermore, about 400 ms later, at movement onset, the mean firing rate of the same population was also significantly tuned to movement direction, having roughly the same preferred direction as synchronous activity. Finally, reaction time measurements revealed a directional preference of the monkey with, once again, the same preferred direction as synchronous activity and firing rate. These results lead us to speculate that synchronous activity and firing rate are cooperative neuronal processes and that the directional matching of our three measures – firing rate, synchronicity, and reaction times – might be an effect of behaviorally induced network cooperativity acquired during learning. Received: 16 January 2002 / Accepted in revised form: 26 November 2002 / Published online: 7 April 2003 RID="*" ID="*" Present address: Istituto di Fisiologia Umana, Università di Parma, Via Volturno 39, 43100 Parma, Italy Correspondence to: A. Riehle (e-mail: ariehle@lnf.cnrs-mrs.fr, Tel.: +33-491-164329, Fax: +33-491-774969) Acknowledgements. We wish to thank Sonja Grün, Markus Diesmann, and Bill MacKay for many helpful and exciting discussions and one anonymous referee for her/his helpful comments. Special thanks go to Annette Bastian for her help in data collection, Michèle Coulmance for writing data acquisition and parts of data analysis software, and Marc Martin for animal welfare. This research was supported in part by the CNRS, GIS (Sciences de la Cognition), and ACI Cognitique (Invariants and Variability). FG was supported by the French government (MENRT).     

电突触耦合Chay神经元同步振荡的研究

从微观解释异常神经元构建组织时癫痫样波形的相互制约关系对神经系统疾病的研究很有意义,而两神经元耦合特性的探索是重要的基础工作。采用Chay提供的Pacemaker神经元模型以电突触耦合来研究不同耦合强度对神经元动态时序的影响,并指出突触作用过程的混沌特征。给出并讨论了不同状态神经元相耦合时非线性振荡的数值计算结果,即：起搏神经元与处于冲动混沌状态神经元、处于冲动混沌和独态冲动状态的异常神经元、异常神经元与处于静息状态神经元的动态时序,还给出了部分相图以及Ca 离子浓度变化的特点。神经元这种负载特性的讨论有助于研究在活组织中癫痫发作的机理、传输和控制。     

Synchronization study in ring-like and grid-like neuronal networks

In this paper, we study the synchronization status of both two gap-junction coupled neurons and neuronal network with two different network connectivity patterns. One of the network connectivity patterns is a ring-like neuronal network, which only considers nearest-neighbor neurons. The other is a grid-like neuronal network, with all nearest neighbor couplings. We show that by varying some key parameters, such as the coupling strength and the external current injection, the neuronal network will exhibit various patterns of firing synchronization. Different types of firing synchronization are diagnosed by means of a mean field potential, a bifurcation diagram, a correlation coefficient and the ISI-distance method. Numerical simulations demonstrate that the synchronization status of multiple neurons is much dependent on the network patters, when the number of neurons is the same. It is also demonstrated that the synchronization status of two coupled neurons is similar with the grid-like neuronal network, but differs radically from that of the ring-like neuronal network. These results may be instructive in understanding synchronization transitions in neuronal systems.     

Dynamics of Time Delay-Induced Multiple Synchronous Behaviors in Inhibitory Coupled Neurons

The inhibitory synapse can induce synchronous behaviors different from the anti-phase synchronous behaviors, which have been reported in recent studies. In the present paper, synchronous behaviors are investigated in the motif model composed of reciprocal inhibitory coupled neurons with endogenous bursting and time delay. When coupling strength is weak, synchronous behavior appears at a single interval of time delay within a bursting period. When coupling strength is strong, multiple synchronous behaviors appear at different intervals of time delay within a bursting period. The different bursting patterns of synchronous behaviors, and time delays and coupling strengths that can induce the synchronous bursting patterns can be well interpreted by the dynamics of the endogenous bursting pattern of isolated neuron, which is acquired by the fast-slow dissection method, combined with the inhibitory coupling current. For an isolated neuron, when a negative impulsive current with suitable strength is applied at different phases of the bursting, multiple different bursting patterns can be induced. For a neuron in the motif, the inhibitory coupling current, of which the application time and strength is modulated by time delay and coupling strength, can cause single or multiple synchronous firing patterns like the negative impulsive current when time delay and coupling strength is suitable. The difference compared to the previously reported multiple synchronous behaviors that appear at time delays wider than a period of the endogenous firing is discussed. The results present novel examples of synchronous behaviors in the neuronal network with inhibitory synapses and provide a reasonable explanation.     

A Simulation Study to Examine the Effect of Common Motoneuron Inputs on Correlated Patterns of Motor Unit Discharge

The influence of common oscillatory inputs to the motoneuron pool on correlated patterns of motor unit discharge was examined using model simulations. Motor unit synchronization, in-phase fluctuations in mean firing rates known as ‘common drive’, and the coefficient of variation of the muscle force were examined as the frequency and amplitude of common oscillatory inputs to the motoneuron pool were varied. The amount of synchronization, the peak correlation between mean firing rates and the coefficient of variation of the force varied with both the frequency and amplitude of the common input signal. Values for ‘common drive’ and the force coefficient of variation were highest for oscillatory inputs at frequencies less than 5 Hz, while synchronization reached a maximum when the frequency of the common input was close to the average motor unit firing rate. The frequency of the common input signal for which the highest levels of synchronization were observed increased as motoneuron firing rates increased in response to higher target force levels. The simulation results suggest that common low-frequency oscillations in motor unit firing rates and short-term synchronization result from oscillatory activity in different bands of the frequency spectrum of shared motoneuron inputs. The results also indicate that the amount of synchronization between motor unit discharges depends not only on the amplitude of the shared input signal, but also on its frequency in relation to the present firing rates of the individual motor units.     

Cerebellar Nuclear Neurons Use Time and Rate Coding to Transmit Purkinje Neuron Pauses

Neurons of the cerebellar nuclei convey the final output of the cerebellum to their targets in various parts of the brain. Within the cerebellum their direct upstream connections originate from inhibitory Purkinje neurons. Purkinje neurons have a complex firing pattern of regular spikes interrupted by intermittent pauses of variable length. How can the cerebellar nucleus process this complex input pattern? In this modeling study, we investigate different forms of Purkinje neuron simple spike pause synchrony and its influence on candidate coding strategies in the cerebellar nuclei. That is, we investigate how different alignments of synchronous pauses in synthetic Purkinje neuron spike trains affect either time-locking or rate-changes in the downstream nuclei. We find that Purkinje neuron synchrony is mainly represented by changes in the firing rate of cerebellar nuclei neurons. Pause beginning synchronization produced a unique effect on nuclei neuron firing, while the effect of pause ending and pause overlapping synchronization could not be distinguished from each other. Pause beginning synchronization produced better time-locking of nuclear neurons for short length pauses. We also characterize the effect of pause length and spike jitter on the nuclear neuron firing. Additionally, we find that the rate of rebound responses in nuclear neurons after a synchronous pause is controlled by the firing rate of Purkinje neurons preceding it.     

New attractor states for synchronous activity in synfire chains with excitatory and inhibitory coupling

 In a feedforward network of integrate-and-fire neurons, where the firing of each layer is synchronous (synfire chain), the final firing state of the network converges to two attractor states: either a full activation or complete fading of the tailing layers. In this article, we analyze various modes of pattern propagation in a synfire chain with random connection weights and delta-type postsynaptic currents. We predict analytically that when the input is fully synchronized and the network is noise free, varying the characteristics of the weights distribution would result in modes of behavior that are different from those described in the literature. These are convergence to fixed points, limit cycles, multiple periodic, and possibly chaotic dynamics. We checked our analytic results by computer simulation of the network, and showed that the above results can be generalized when the input is asynchronous and neurons are spontaneously active at low rates. Received: 27 July 2001 / Accepted in revised form: 23 October 2001     

Neural coding for the retrieval of multiple memory patterns

We investigate the retrieval dynamics in a feature-based semantic memory model, in which the features are coded by neurons of the Hindmarsh–Rose type in the chaotic regime. We consider the retrieval process as consisting of the synchronized firing activity of the neurons coding for the same memory pattern. The retrieval dynamics is investigated for multiple patterns, with particular attention to the case of overlapping memories. In this case, we hypothesize a dynamical nontransitive mechanism based on synchronization, that allows for a shared feature to participate in multiple memory representations. The problem of the choice of a cognitive plausible time-scale for the retrieval analysis is investigated by analyzing the information that can be inferred from finite-time analyses. Different types of indicators are proposed in order to evaluate the temporal dynamics of the neurons engaged in the retrieval process. We interpret the simulation results as suggestive of a role for chaotic dynamics in allowing for flexible composition of elementary meaningful units in memory representations.     

Synchronized dynamics of cortical neurons with time-delay feedback

The dynamics of three mutually coupled cortical neurons with time delays in the coupling are explored numerically and analytically. The neurons are coupled in a line, with the middle neuron sending a somewhat stronger projection to the outer neurons than the feedback it receives, to model for instance the relay of a signal from primary to higher cortical areas. For a given coupling architecture, the delays introduce correlations in the time series at the time-scale of the delay. It was found that the middle neuron leads the outer ones by the delay time, while the outer neurons are synchronized with zero lag times. Synchronization is found to be highly dependent on the synaptic time constant, with faster synapses increasing both the degree of synchronization and the firing rate. Analysis shows that pre-synaptic input during the inter-spike interval stabilizes the synchronous state, even for arbitrarily weak coupling, and independent of the initial phase. The finding may be of significance to synchronization of large groups of cells in the cortex that are spatially distanced from each other.     

Coupling-induced population synchronization in an excitatory population of subthreshold Izhikevich neurons

We consider an excitatory population of subthreshold Izhikevich neurons which exhibit noise-induced firings. By varying the coupling strength J, we investigate population synchronization between the noise-induced firings which may be used for efficient cognitive processing such as sensory perception, multisensory binding, selective attention, and memory formation. As J is increased, rich types of population synchronization (e.g., spike, burst, and fast spike synchronization) are found to occur. Transitions between population synchronization and incoherence are well described in terms of an order parameter $\mathcal{O}$ . As a final step, the coupling induces oscillator death (quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. The oscillator death leads to a transition from firing to non-firing states at the population level, which may be well described in terms of the time-averaged population spike rate $\overline{R}$ . In addition to the statistical-mechanical analysis using $\mathcal{O}$ and $\overline{R}$ , each population and individual state are also characterized by using the techniques of nonlinear dynamics such as the raster plot of neural spikes, the time series of the membrane potential, and the phase portrait. We note that population synchronization of noise-induced firings may lead to emergence of synchronous brain rhythms in a noisy environment, associated with diverse cognitive functions.