Gamma rhythms and beta rhythms have different synchronization properties

Experimental and modeling efforts suggest that rhythms in the CA1 region of the hippocampus that are in the beta range (12-29 Hz) have a different dynamical structure than that of gamma (30-70 Hz). We use a simplified model to show that the different rhythms employ different dynamical mechanisms to synchronize, based on different ionic currents. The beta frequency is able to synchronize over long conduction delays (corresponding to signals traveling a significant distance in the brain) that apparently cannot be tolerated by gamma rhythms. The synchronization properties are consistent with data suggesting that gamma rhythms are used for relatively local computations whereas beta rhythms are used for higher level interactions involving more distant structures

Contrasting roles of axonal (pyramidal cell) and dendritic (interneuron) electrical coupling in the generation of neuronal network oscillations

Electrical coupling between pyramidal cell axons, and between interneuron dendrites, have both been described in the hippocampus. What are the functional roles of the two types of coupling? Interneuron gap junctions enhance synchrony of γ oscillations (25-70 Hz) in isolated interneuron networks and also in networks containing both interneurons and principal cells, as shown in mice with a knockout of the neuronal (primarily interneuronal) connexin36. We have recently shown that pharmacological gap junction blockade abolishes kainate-induced γ oscillations in connexin36 knockout mice; without such gap junction blockade, γ oscillations do occur in the knockout mice, albeit at reduced power compared with wild-type mice. As interneuronal dendritic electrical coupling is almost absent in the knockout mice, these pharmacological data indicate a role of axonal electrical coupling in generating the γ oscillations. We construct a network model of an experimental γ oscillation, known to be regulated by both types of electrical coupling. In our model, axonal electrical coupling is required for the γ oscillation to occur at all; interneuron dendritic gap junctions exert a modulatory effect

Physics of Psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media

Sensory arrays made of coupled excitable elements can improve both their input sensitivity and dynamic range due to collective non-linear wave properties. This mechanism is studied in a neural network of electrically coupled (e.g. via gap junctions) elements subject to a Poisson signal process. The network response interpolates between a Weber-Fechner logarithmic law and a Stevens power law depending on the relative refractory period of the cell. Therefore, these non-linear transformations of the input level could be performed in the sensory periphery simply due to a basic property: the transfer function of excitable media.Comment: 4 pages, 5 figure

Axonal gap junctions between principal neurons: a novel source of network oscillations, and perhaps epileptogenesis

We hypothesized in 1998 that gap junctions might be located between the axons of principal hippocampal neurons, based on the shape of spikelets (fast prepotentials), occurring during gap junction-mediated very fast (to approximately 200 Hz) network oscillations in vitro. More recent electrophysiological, pharmacological and dye-coupling data indicate that axonal gap junctions exist; so far, they appear to be located about 100 microm from the soma, in CA1 pyramidal neurons. Computer modeling and theory predict that axonal gap junctions can lead to very fast network oscillations under three conditions: a) there are spontaneous axonal action potentials; b) the number of gap junctions in the network is neither too low (not less than to approximately 1.5 per cell on average), nor too high (not more than to approximately 3 per cell on average); c) action potentials can cross from axon to axon via gap junctions. Simulated oscillations resemble biological ones, but condition (c) remains to be demonstrated directly. Axonal network oscillations can, in turn, induce oscillatory activity in larger neuronal networks, by a variety of mechanisms. Axonal networks appear to underlie in vivo ripples (to approximately 200 Hz field potential oscillations superimposed on physiological sharp waves), to drive gamma (30-70 Hz) oscillations that appear in the presence of carbachol, and to initiate certain types of ictal discharge. If axonal gap junctions are important for seizure initiation in humans, there could be practical consequences for antiepileptic therapy: at least one gap junction-blocking compound, carbenoxolone, is already in clinical use (for treatment of ulcer disease), and it crosses the blood-brain barrier

Synchronization in a System of Globally Coupled Oscillators with Time Delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results

Synchronisation in networks of delay-coupled type-I excitable systems

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.Comment: 10 pages, 9 figure

Synchronization and resonance in a driven system of coupled oscillators

We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective synchronization of the system, is derived; it is found that the total order parameter decreases monotonically with noise, indicating overall suppression of synchronization. Still, for large coupling strengths, there exists an optimal noise level at which the periodic (ac) component of the order parameter reaches its maximum. The response of the phase velocity is also examined and found to display resonance behavior.Comment: 17 pages, 3 figure

Phase synchronization and noise-induced resonance in systems of coupled oscillators

We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures collective synchronization of the system, is investigated as the noise level and the coupling strength are varied, and hysteretic behavior is manifested. The power spectrum of the phase velocity is also examined and the quality factor as well as the response function is obtained to reveal noise-induced resonance behavior.Comment: to be published in Phys. Rev.

Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte

Biased competition through variations in amplitude of γ-oscillations

Experiments in visual cortex have shown that the firing rate of a neuron in response to the simultaneous presentation of a preferred and non-preferred stimulus within the receptive field is intermediate between that for the two stimuli alone (stimulus competition). Attention directed to one of the stimuli drives the response towards the response induced by the attended stimulus alone (selective attention). This study shows that a simple feedforward model with fixed synaptic conductance values can reproduce these two phenomena using synchronization in the gamma-frequency range to increase the effective synaptic gain for the responses to the attended stimulus. The performance of the model is robust to changes in the parameter values. The model predicts that the phase locking between presynaptic input and output spikes increases with attention