Excitement and synchronization of small-world neuronal networks with short-term synaptic plasticity

Excitement and synchronization of electrically and chemically coupled Newman-Watts (NW) small-world neuronal networks with a short-term synaptic plasticity described by a modified Oja learning rule are investigated. For each type of neuronal network, the variation properties of synaptic weights are examined first. Then the effects of the learning rate, the coupling strength and the shortcut-adding probability on excitement and synchronization of the neuronal network are studied. It is shown that the synaptic learning suppresses the over-excitement, helps synchronization for the electrically coupled network but impairs synchronization for the chemically coupled one. Both the introduction of shortcuts and the increase of the coupling strength improve synchronization and they are helpful in increasing the excitement for the chemically coupled network, but have little effect on the excitement of the electrically coupled one.     

Selective Modulation of Interhemispheric Functional Connectivity by HD-tACS Shapes Perception

Oscillatory neuronal synchronization between cortical areas has been suggested to constitute a flexible mechanism to coordinate information flow in the human cerebral cortex. However, it remains unclear whether synchronized neuronal activity merely represents an epiphenomenon or whether it is causally involved in the selective gating of information. Here, we combined bilateral high-density transcranial alternating current stimulation (HD-tACS) at 40 Hz with simultaneous electroencephalographic (EEG) recordings to study immediate electrophysiological effects during the selective entrainment of oscillatory gamma-band signatures. We found that interhemispheric functional connectivity was modulated in a predictable, phase-specific way: In-phase stimulation enhanced synchronization, anti-phase stimulation impaired functional coupling. Perceptual correlates of these connectivity changes were found in an ambiguous motion task, which strongly support the functional relevance of long-range neuronal coupling. Additionally, our results revealed a decrease in oscillatory alpha power in response to the entrainment of gamma band signatures. This finding provides causal evidence for the antagonistic role of alpha and gamma oscillations in the parieto-occipital cortex and confirms that the observed gamma band modulations were physiological in nature. Our results demonstrate that synchronized cortical network activity across several spatiotemporal scales is essential for conscious perception and cognition.     

Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology

Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, novel methods of time series analysis have been developed for the examination of task- and performance-related oscillatory activity and its synchronization. Studies employing these advanced techniques revealed that synchronization of oscillatory responses in the beta- and gamma-band is involved in a variety of cognitive functions, such as perceptual grouping, attention-dependent stimulus selection, routing of signals across distributed cortical networks, sensory-motor integration, working memory, and perceptual awareness. Here, we review evidence that certain brain disorders, such as schizophrenia, epilepsy, autism, Alzheimer's disease, and Parkinson's are associated with abnormal neural synchronization. The data suggest close correlations between abnormalities in neuronal synchronization and cognitive dysfunctions, emphasizing the importance of temporal coordination. Thus, focused search for abnormalities in temporal patterning may be of considerable clinical relevance.     

Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction

The properties of equilibria and phase synchronization involving burst synchronization and spike synchronization of two electrically coupled HR neurons are studied in this paper. The findings reveal that in the non-delayed system the existence of equilibria can be turned into intersection of two odd functions, and two types of equilibria with symmetry and non-symmetry can be found. With the stability and bifurcation analysis, the bifurcations of equilibria are investigated. For the delayed system, the equilibria remain unchanged. However, the Hopf bifurcation point is drastically affected by time delay. For the phase synchronization, we focus on the synchronization transition from burst synchronization to spike synchronization in the non-delayed system and the effect of coupling strength and time delay on spike synchronization in delayed system. In addition, corresponding firing rhythms and spike synchronized regions are obtained in the two parameters plane. The results allow us to better understand the properties of equilibria, multi-time-scale properties of synchronization and temporal encoding scheme in neuronal systems.     

Suppressing bursting synchronization in a modular neuronal network with synaptic plasticity

Excessive synchronization of neurons in cerebral cortex is believed to play a crucial role in the emergence of neuropsychological disorders such as Parkinson’s disease, epilepsy and essential tremor. This study, by constructing a modular neuronal network with modified Oja’s learning rule, explores how to eliminate the pathological synchronized rhythm of interacted busting neurons numerically. When all neurons in the modular neuronal network are strongly synchronous within a specific range of coupling strength, the result reveals that synaptic plasticity with large learning rate can suppress bursting synchronization effectively. For the relative small learning rate not capable of suppressing synchronization, the technique of nonlinear delayed feedback control including differential feedback control and direct feedback control is further proposed to reduce the synchronized bursting state of coupled neurons. It is demonstrated that the two kinds of nonlinear feedback control can eliminate bursting synchronization significantly when the control parameters of feedback strength and feedback delay are appropriately tuned. For the former control technique, the control domain of effective synchronization suppression is similar to a semi-elliptical domain in the simulated parameter space of feedback strength and feedback delay, while for the latter one, the effective control domain is similar to a fan-shaped domain in the simulated parameter space.     

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.     

Broadband Criticality of Human Brain Network Synchronization

Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.     

Oscillatory synchronization in large-scale cortical networks predicts perception

Normal brain function requires the dynamic interaction of functionally specialized but widely distributed cortical regions. Long-range synchronization of oscillatory signals has been suggested to mediate these interactions within large-scale cortical networks, but direct evidence is sparse. Here we show that oscillatory synchronization is organized in such large-scale networks. We implemented an analysis approach that allows for imaging synchronized cortical networks and applied this technique to EEG recordings in humans. We identified two networks: beta-band synchronization (~20 Hz) in a fronto-parieto-occipital network and gamma-band synchronization (~80 Hz) in a centro-temporal network. Strong perceptual correlates support their functional relevance: the strength of synchronization within these networks predicted the subjects' perception of an ambiguous audiovisual stimulus as well as the integration of auditory and visual information. Our results provide evidence that oscillatory neuronal synchronization mediates neuronal communication within frequency-specific, large-scale cortical networks.     

Sound Stabilizes Locomotor-Respiratory Coupling and Reduces Energy Cost

A natural synchronization between locomotor and respiratory systems is known to exist for various species and various forms of locomotion. This Locomotor-Respiratory Coupling (LRC) is fundamental for the energy transfer between the two subsystems during long duration exercise and originates from mechanical and neurological interactions. Different methodologies have been used to compute LRC, giving rise to various and often diverging results in terms of synchronization, (de-)stabilization via information, and associated energy cost. In this article, the theory of nonlinear-coupled oscillators was adopted to characterize LRC, through the model of the sine circle map, and tested it in the context of cycling. Our specific focus was the sound-induced stabilization of LRC and its associated change in energy consumption. In our experimental study, participants were instructed during a cycling exercise to synchronize either their respiration or their pedaling rate with an external auditory stimulus whose rhythm corresponded to their individual preferential breathing or cycling frequencies. Results showed a significant reduction in energy expenditure with auditory stimulation, accompanied by a stabilization of LRC. The sound-induced effect was asymmetrical, with a better stabilizing influence of the metronome on the locomotor system than on the respiratory system. A modification of the respiratory frequency was indeed observed when participants cycled in synchrony with the tone, leading to a transition toward more stable frequency ratios as predicted by the sine circle map. In addition to the classical mechanical and neurological origins of LRC, here we demonstrated using the sine circle map model that information plays an important modulatory role of the synchronization, and has global energetic consequences.     

Theta band zero-lag long-range cortical synchronization via hippocampal dynamical relaying

Growing evidence suggests that synchronization among distributed neuronal networks underlie functional integration in the brain. Neural synchronization is typically revealed by a consistent phase delay between neural responses generated in two separated sources. But the influence of a third neuronal assembly in that synchrony pattern remains largely unexplored. We investigate here the potential role of the hippocampus in determining cortico-cortical theta synchronization in different behavioral states during motor quiescent and while animals actively explore the environment. To achieve this goal, the two states were modeled with a recurrent network involving the hippocampus, as a relay element, and two distant neocortical sites. We found that cortico-cortical neural coupling accompanied higher hippocampal theta oscillations in both behavioral states, although the highest level of synchronization between cortical regions emerged during motor exploration. Local field potentials recorded from the same brain regions qualitatively confirm these findings in the two behavioral states. These results suggest that zero-lag long-range cortico-cortical synchronization is likely mediated by hippocampal theta oscillations in lower mammals as a function of cognitive demands and motor acts.     

The role of neuronal synchronization in selective attention

Attention selectively enhances the influence of neuronal responses conveying information about relevant sensory attributes. Accumulating evidence suggests that this selective neuronal modulation relies on rhythmic synchronization at local and long-range spatial scales: attention selectively synchronizes the rhythmic responses of those neurons that are tuned to the spatial and featural attributes of the attended sensory input. The strength of synchronization is thereby functionally related to perceptual accuracy and behavioural efficiency. Complementing this synchronization at a local level, attention has recently been demonstrated to regulate which locally synchronized neuronal groups phase-synchronize their rhythmic activity across long-range connections. These results point to a general computational role for selective synchronization in dynamically controlling which neurons communicate information about sensory inputs effectively.     

Dynamic representation of odours by oscillating neural assemblies

Stimulus evoked oscillatory synchronization of neural assemblies has been most clearly documented in the olfactory and visual systems. Recent results with the olfactory system of locusts show that information about odour identity is contained in spatial and temporal aspects of an oscillatory population response. This suggests that brain oscillations may reflect a common reference for messages encoded in time. Although stimulus-evoked oscillatory phenomena are reliable, their roles in perception, memory and pattern recognition remain to be demonstrated. Using honey bees, we demonstrated that odour encoding involves, as in locusts, the oscillatory synchronization of assemblies of neurons, and that this synchronization is, here also, selectively abolished by the GABA receptor antagonist picrotoxin. In collaboration with Dr Brian Smith's laboratory, we showed, using a behavioural learning paradigm, that picrotoxin-induced desynchronization impairs the discrimination of molecularly similar odourants, but not that of dissimilar odours. It appears, therefore, that oscillatory synchronization of neuronal assemblies is relevant, and essential for fine odour discrimination. Finally, experiments with locust mushroom body neurons, two synapses downstream from the antennal lobe, indicate that their responses to odours become less specific when antennal lobe neurons are desynchronized by picrotoxin injection. These results suggest that oscillatory synchronization and the kind of temporal encoding it affords provide an additional dimension by which the brain can segment spatially overlapping stimulus representations.     

Phase-Coherence Transitions and Communication in the Gamma Range between Delay-Coupled Neuronal Populations

Synchronization between neuronal populations plays an important role in information transmission between brain areas. In particular, collective oscillations emerging from the synchronized activity of thousands of neurons can increase the functional connectivity between neural assemblies by coherently coordinating their phases. This synchrony of neuronal activity can take place within a cortical patch or between different cortical regions. While short-range interactions between neurons involve just a few milliseconds, communication through long-range projections between different regions could take up to tens of milliseconds. How these heterogeneous transmission delays affect communication between neuronal populations is not well known. To address this question, we have studied the dynamics of two bidirectionally delayed-coupled neuronal populations using conductance-based spiking models, examining how different synaptic delays give rise to in-phase/anti-phase transitions at particular frequencies within the gamma range, and how this behavior is related to the phase coherence between the two populations at different frequencies. We have used spectral analysis and information theory to quantify the information exchanged between the two networks. For different transmission delays between the two coupled populations, we analyze how the local field potential and multi-unit activity calculated from one population convey information in response to a set of external inputs applied to the other population. The results confirm that zero-lag synchronization maximizes information transmission, although out-of-phase synchronization allows for efficient communication provided the coupling delay, the phase lag between the populations, and the frequency of the oscillations are properly matched.     

Synchronization of chaotic nonlinear continuous neural networks with time-varying delay

In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.     

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks.     

Normal and pathological oscillatory communication in the brain

The huge number of neurons in the human brain are connected to form functionally specialized assemblies. The brain's amazing processing capabilities rest on local communication within and long-range communication between these assemblies. Even simple sensory, motor and cognitive tasks depend on the precise coordination of many brain areas. Recent improvements in the methods of studying long-range communication have allowed us to address several important questions. What are the common mechanisms that govern local and long-range communication and how do they relate to the structure of the brain? How does oscillatory synchronization subserve neural communication? And what are the consequences of abnormal synchronization?     

Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling

In this paper we consider the Hopf bifurcation and synchronization in the two coupled Hindmarsh–Rose excitable systems with chemical coupling and time-delay. We surveyed the conditions for Hopf bifurcations by means of dynamical bifurcation analysis and numerical simulation. The results show that the coupled excitable systems with no delay have supercritical Hopf bifurcation, while the delayed system undergoes Hopf bifurcations at critical time delays when coupling strength lies in a particular region. We also investigated the effect of the delay on the transition of bursting synchronization in the coupled system. The results are helpful for us to better understand the dynamical properties of excitable systems and the biological mechanism of information encoding and cognitive activity.     

Emergence of adaptability to time delay in bipedal locomotion

Based on neurophysiological evidence, theoretical studies have shown that locomotion is generated by mutual entrainment between the oscillatory activities of central pattern generators (CPGs) and body motion. However, it has also been shown that the time delay in the sensorimotor loop can destabilize mutual entrainment and result in the failure to walk. In this study, a new mechanism called flexible-phase locking is proposed to overcome the time delay. It is realized by employing the Bonhoeffer–Van der Pol formalism – well known as a physiologically faithful neuronal model – for neurons in the CPG. The formalism states that neurons modulate their phase according to the delay so that mutual entrainment is stabilized. Flexible-phase locking derives from the phase dynamics related to an asymptotically stable limit cycle of the neuron. The effectiveness of the mechanism is verified by computer simulations of a bipedal locomotion model.     

Intracortical synchronization of the epileptiform field potentials at different stages of ultrastructural reorganizations in neuronally isolates island in rats

A temporal delay (parameter of synchronization) between the incidence of epileptiform discharges in cortical sited located at a distance of 4 mm from each other was studied in rat intact cortex and neuronally isolated cortical slab using the cross-correlation function. Experiments were carried out at different stages of axonal sprouting. By 30 days of isolation, a significant increase in the number of boutons in the V cortical layer coincided with a significant decrease in the delay, whereas a reduction of the number of boutons by 90 days corresponded to its increase. These findings convincingly testify that the newly formed boutons form a basis for increase in synchronization and thus affect the epileptogenesis. The results obtained in this work and literature data suggest that under pathological conditions large pyramids of the V layer form a neuronal network which provides exclusively cortical synchronization of epileptiform field potentials.     

Neuronal model with distributed delay: analysis and simulation study for gamma distribution memory kernel

A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen-Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV(t))((ISI)) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.