Mutual and intermittent enhancements of synchronization transitions by autaptic and synaptic delay in scale-free neuron networks

In neural networks, there exist both synaptic delays among different neurons and autaptic self-feedback delays in a neuron itself. In this paper, we study synchronization transitions induced by synaptic and autaptic delays in scale-free neuron networks, mainly exploring how these two time delays affect synchronization transitions induced by each other. It is found that the synchronization transitions induced by synaptic (autaptic) delay are intermittently enhanced when autaptic (synaptic) delay is varied. There are optimal autaptic strength and synaptic coupling strength by which the synchronization transitions induced by autaptic and synaptic delays become strongest. The underlying mechanisms are briefly discussed in terms of the relationships of autaptic delay, synaptic delay, and inter-burst interval. These results show that synaptic and autaptic delays could contribute to each other and enhance synchronization transitions in the neuronal networks. This implies that autaptic and synaptic delays could play a vital role for the information transmission in neural systems.     

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters （e.g., external stimuli）, and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks （LBSW networks） under spike-timing-dependent plasticity （STDP）. By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions （SOPTs）： repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics.     

Delay- and coupling-induced firing patterns in oscillatory neural loops

For a feedforward loop of oscillatory Hodgkin-Huxley neurons interacting via excitatory chemical synapses, we show that a great variety of spatiotemporal periodic firing patterns can be encoded by properly chosen communication delays and synaptic weights, which contributes to the concept of temporal coding by spikes. These patterns can be obtained by a modulation of the multiple coexisting stable in-phase synchronized states or traveling waves propagating along or against the direction of coupling. We derive explicit conditions for the network parameters allowing us to achieve a desired pattern. Interestingly, whereas the delays directly affect the time differences between spikes of interacting neurons, the synaptic weights control the phase differences. Our results show that already such a simple neural circuit may unfold an impressive spike coding capability.     

Transitions to synchrony in coupled bursting neurons

Certain cells in the brain, for example, thalamic neurons during sleep, show spike-burst activity. We study such spike-burst neural activity and the transitions to a synchronized state using a model of coupled bursting neurons. In an electrically coupled network, we show that the increase of coupling strength increases incoherence first and then induces two different transitions to synchronized states, one associated with bursts and the other with spikes. These sequential transitions to synchronized states are determined by the zero crossings of the maximum transverse Lyapunov exponents. These results suggest that synchronization of spike-burst activity is a multi-time-scale phenomenon and burst synchrony is a precursor to spike synchrony.     

How effective delays shape oscillatory dynamics in neuronal networks

Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model through the addition of an explicit, fixed delay (Roxin et al. (2005,2006) [29] and [30]). Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the asynchronous state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. We arrive at two general observations of physiological relevance that could not be explained in previous work. These are: 1 — fast oscillations are always supercritical for realistic transfer functions and 2 — traveling waves are preferred over standing waves given plausible patterns of local connectivity. We finally demonstrate that these results show good agreement with those obtained performing numerical simulations of a network of Hodgkin-Huxley neurons.     

Evidence from human scalp electroencephalograms of global chaotic itinerancy

My objective of this study was to find evidence of chaotic itinerancy in human brains by means of noninvasive recording of the electroencephalogram (EEG) from the scalp of normal subjects. My premise was that chaotic itinerancy occurs in sequences of cortical states marked by state transitions that appear as temporal discontinuities in neural activity patterns. I based my study on unprecedented advances in spatial and temporal resolution of the phase of oscillations in scalp EEG. The spatial resolution was enhanced by use of a high-density curvilinear array of 64 electrodes, 189 mm in length, with 3 mm spacing. The temporal resolution was advanced to the limit provided by the digitizing step, here 5 ms, by use of the Hilbert transform. The numerical derivative of the analytic phase revealed plateaus in phase that lasted on the order of 0.1 s and repeated at rates in the theta (3-7 Hz) or alpha (7-12 Hz) ranges. The plateaus were bracketed by sudden jumps in phase that usually took place within 1 to 2 digitizing steps. The jumps were commonly synchronized in each cerebral hemisphere over distances of up to 189 mm, irrespective of the orientation of the array. The jumps were usually not synchronized across the midline separating the hemisphere or across the sulcus between the frontal and parietal lobes. I believe that the widespread synchrony of the jumps in analytic phase manifest a metastable cortical state in accord with the theory of self-organized criticality. The jumps appear to be subcritical bifurcations. They reflect the aperiodic evolution of brain states through sequences of attractors that on access support the experience of remembering.     

Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks

We study the effect of delays on the dynamics of large networks of neurons. We show that delays give rise to a wealth of bifurcations and to a rich phase diagram, which includes oscillatory bumps, traveling waves, lurching waves, standing waves arising via a period-doubling bifurcation, aperiodic regimes, and regimes of multistability. We study the existence and the stability of the various dynamical patterns analytically and numerically in a simplified rate model as a function of the interaction parameters. The results derived in that framework allow us to understand the origin of the diversity of dynamical states observed in large networks of spiking neurons.     

Transient dynamics in a small ensemble of synaptically coupled Morris-Lecar neurons

We propose a new model of synaptic transmission on the basis of a FitzHugh–Nagumo system with nonlinear recovery. It is shown that the Morrice–Lecar neuron ensemble formed by such couplings shows various structurally stable regimes of transient dynamics in the form of sequential transitions between various metastable oscillatory states of the system.     

Resonant propagation of spike trains in delay-coupled neural subthreshold oscillators

We study the propagation of spike trains through one-dimensional chains of coupled neurons exhibiting subthreshold oscillations. We consider the existence of a synaptic delay that provides a time scale in addition to the ones given by the periods of the input train and of the subthreshold oscillations. These three time scales affect the evolution of the phase of the neural oscillators, preparing the state of the postsynaptic neuron for the presynaptic input, which can trigger a suprathreshold response according to that phase. In the case of pulsed chemical coupling, results from two coupled neurons help infer the success of the propagation through a larger chain. This situation exhibits a resonant behavior with respect to the period of the input spike train, by which successful propagation arises for certain values of the input period, irrespective of the delay. In the presence of additional electrical coupling via gap junctions, the synaptic delay starts to play a relevant role, and a second resonance appears with respect to that time scale.     

Synaptic plasticity modulates autonomous transitions between waking and sleep states: insights from a Morris-Lecar model

The transitions between waking and sleep states are characterized by considerable changes in neuronal firing. During waking, neurons fire tonically at irregular intervals and a desynchronized activity is observed at the electroencephalogram. This activity becomes synchronized with slow wave sleep onset when neurons start to oscillate between periods of firing (up-states) and periods of silence (down-states). Recently, it has been proposed that the connections between neurons undergo potentiation during waking, whereas they weaken during slow wave sleep. Here, we propose a dynamical model to describe basic features of the autonomous transitions between such states. We consider a network of coupled neurons in which the strength of the interactions is modulated by synaptic long term potentiation and depression, according to the spike time-dependent plasticity rule (STDP). The model shows that the enhancement of synaptic strength between neurons occurring in waking increases the propensity of the network to synchronize and, conversely, desynchronization appears when the strength of the connections become weaker. Both transitions appear spontaneously, but the transition from sleep to waking required a slight modification of the STDP rule with the introduction of a mechanism which becomes active during sleep and changes the proportion between potentiation and depression in accordance with biological data. At the neuron level, transitions from desynchronization to synchronization and vice versa can be described as a bifurcation between two different states, whose dynamical regime is modulated by synaptic strengths, thus suggesting that transition from a state to an another can be determined by quantitative differences between potentiation and depression.     

Increased Entropic Brain Dynamics during DeepDream-Induced Altered Perceptual Phenomenology

In recent years, the use of psychedelic drugs to study brain dynamics has flourished due to the unique opportunity they offer to investigate the neural mechanisms of conscious perception. Unfortunately, there are many difficulties to conduct experiments on pharmacologically-induced hallucinations, especially regarding ethical and legal issues. In addition, it is difficult to isolate the neural effects of psychedelic states from other physiological effects elicited by the drug ingestion. Here, we used the DeepDream algorithm to create visual stimuli that mimic the perception of hallucinatory states. Participants were first exposed to a regular video, followed by its modified version, while recording electroencephalography (EEG). Results showed that the frontal region’s activity was characterized by a higher entropy and lower complexity during the modified video, with respect to the regular one, at different time scales. Moreover, we found an increased undirected connectivity and a greater level of entropy in functional connectivity networks elicited by the modified video. These findings suggest that DeepDream and psychedelic drugs induced similar altered brain patterns and demonstrate the potential of adopting this method to study altered perceptual phenomenology in neuroimaging research.     

Oscillatory activity in excitable neural systems

The brain is a complex system and exhibits various subsystems on different spatial and temporal scales. These subsystems are recurrent networks of neurons or populations that interact with each other. The single neurons are microscopic objects and evolve on a different time scale than macroscopic neural populations. To understand the dynamics of the brain, however, it is necessary to understand the dynamics of the brain network both on the microscopic and the macroscopic level and the interaction between the levels. The presented work introduces one to the major properties of single neurons and their interactions. The physical aspects of some standard mathematical models are discussed in some detail. The work shows that both single neurons and neural populations are excitable in the sense that small differences in an initial short stimulation may yield very different dynamical behaviour of the system. To illustrate the power of the neural population model discussed, the work applies the model to explain experimental activity in the delayed feedback system in weakly electric fish and the electroencephalogram (EEG).     

Transition to complete synchronization via near-synchronization in two coupled chaotic neurons

The synchronization transition in two coupled chaotic Morris-Lecar （ML） neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales.     

Role of synaptic filtering on the firing response of simple model neurons

During active states of the brain neurons process their afferent currents with an effective membrane time constant much shorter than its value at rest. This fact, together with the existence of several synaptic time scales, determines to which aspects of the input the neuron responds best. Here we present a solution to the response of a leaky integrate-and-fire neuron with synaptic filters when long synaptic times are present, and predict the firing rate for all values of the synaptic time constant. We also discuss under which conditions this neuron becomes a coincidence detector.     

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.     

Analysis of a phase synchronized functional network based on the rhythm of brain activities

Rhythm of brain activities represents oscillations of postsynaptic potentials in neocortex, therefore it can serve as an indicator of the brain activity state. In order to check the connectivity of brain rhythm, this paper develops a new method of constructing functional network based on phase synchronization. Electroencephalogram (EEG) data were collected while subjects looking at a green cross in two states, performing an attention task and relaxing with eyes-open. The EEG from these two states was filtered by three band-pass filters to obtain signals of theta (4--7 Hz), alpha (8--13 Hz) and beta (14--30 Hz) bands. Mean resultant length was used to estimate strength of phase synchronization in three bands to construct networks of both states, and mean degree K and cluster coefficient C of networks were calculated as a function of threshold. The result shows higher cluster coefficient in the attention state than in the eyes-open state in all three bands, suggesting that cluster coefficient reflects brain state. In addition, an obvious fronto-parietal network is found in the attention state, which is a well-known attention network. These results indicate that attention modulates the fronto-parietal connectivity in different modes as compared with the eyes-open state. Taken together this method is an objective and important tool to study the properties of neural networks of brain rhythm.     

Large Deviations, Dynamics and Phase Transitions in Large Stochastic and Disordered Neural Networks

Neuronal networks are characterized by highly heterogeneous connectivity, and this disorder was recently related experimentally to qualitative properties of the network. The motivation of this paper is to mathematically analyze the role of these disordered connectivities on the large-scale properties of neuronal networks. To this end, we analyze here large-scale limit behaviors of neural networks including, for biological relevance, multiple populations, random connectivities and interaction delays. Due to the randomness of the connectivity, usual mean-field methods (e.g. coupling) cannot be applied, but, similarly to studies developed for spin glasses, we will show that the sequences of empirical measures satisfy a large deviation principle, and converge towards a self-consistent non-Markovian process. From a mathematical viewpoint, the proof differs from previous works in that we are working in infinite-dimensional spaces (interaction delays) and consider multiple cell types. The limit obtained formally characterizes the macroscopic behavior of the network. We propose a dynamical systems approach in order to address the qualitative nature of the solutions of these very complex equations, and apply this methodology to three instances in order to show how non-centered coefficients, interaction delays and multiple populations networks are affected by disorder levels. We identify a number of phase transitions in such systems upon changes in delays, connectivity patterns and dispersion, and particularly focus on the emergence of non-equilibrium states involving synchronized oscillations.     

Simultaneous EEG and fMRI in the macaque monkey at 4.7 Tesla

Simultaneous electroencephalography (EEG)/functional magnetic resonance imaging (fMRI) acquisition can identify the brain networks involved in generating specific EEG patterns. Yet, the combination of these methodologies is hampered by strong artifacts that arise due to electromagnetic interference during magnetic resonance (MR) image acquisition. Here, we report corrections of the gradient-induced artifact in phantom measurements and in experiments with an awake behaving macaque monkey during fMRI acquisition at a magnetic field strength of 4.7 T. Ninety-one percent of the amplitude of a 10 microV, 10 Hz phantom signal could successfully be recovered without phase distortions. Using this method, we were able to extract the monkey EEG from scalp recordings obtained during MR image acquisition. Visual evoked potentials could also be reliably identified. In conclusion, simultaneous EEG/fMRI acquisition is feasible in the macaque monkey preparation at 4.7 T and holds promise for investigating the neural processes that give rise to particular EEG patterns.     

Frequency Switches at Transition Temperature in Voltage-Gated Ion Channel Dynamics of Neural Oscillators

Understanding of the mechanisms of neural phase transitions is crucial for clarifying cognitive processes in the brain. We investigate a neural oscillator that undergoes different bifurcation transitions from the big saddle homoclinic orbit type to the saddle node on an invariant circle type, and the saddle node on an invariant circle type to the small saddle homoclinic orbit type. The bifurcation transitions are accompanied by an increase in thermodynamic temperature that affects the voltage-gated ion channel in the neural oscillator. We show that nonlinear and thermodynamical mechanisms are responsible for different switches of the frequency in the neural oscillator. We report a dynamical role of the phase response curve in switches of the frequency, in terms of slopes of frequency-temperature curve at each bifurcation transition. Adopting the transition state theory of voltagegated ion channel dynamics, we confirm that switches of the frequency occur in the first-order phase transition temperature states and exhibit different features of their potential energy derivatives in the ion channel. Each bifurcation transition also creates a discontinuity in the Arrhenius plot used to compute the time constant of the ion channel.     

Synaptic multistability and network synchronization induced by the neuron–glial interaction in the brain

The dynamics of a synaptic contact between neurons that forms a feedback loop through the interaction with glial cells of the brain surrounding the neurons is studied. It is shown that, depending on the character of the neuron–glial interaction, the dynamics of the signal transmission frequency in the synaptic contact can be bistable with two stable steady states or spiking with the regular generation of spikes with various amplitudes and durations. It is found that such a synaptic contact at the network level is responsible for the appearance of quasisynchronous network bursts.