Multiple origins of the cortical γ rhythm

Gamma rhythms (30-80 Hz) are a near-ubiquitous feature of neuronal population activity in mammalian cortices. Their dynamic properties permit the synchronization of neuronal responses to sensory input within spatially distributed networks, transient formation of local neuronal "cell assemblies," and coherent response patterns essential for intercortical regional communication. Each of these phenomena form part of a working hypothesis for cognitive function in cortex. All forms of physiological gamma rhythm are inhibition based, being characterized by rhythmic trains of inhibitory postsynaptic potentials in populations of principal neurons. It is these repeating periods of relative enhancement and attenuation of the responsivity of major cell groups in cortex that provides a temporal structure shared across many millions of neurons. However, when considering the origins of these repeating trains of inhibitory events considerable divergence is seen depending on cortical region studied and mode of activation of gamma rhythm generating networks. Here, we review the evidence for involvement of multiple subtypes of interneuron and focus on different modes of activation of these cells. We conclude that most massively parallel brain regions have different mechanisms of gamma rhythm generation, that different mechanisms have distinct functional correlates, and that switching between different local modes of gamma generation may be an effective way to direct cortical communication streams. Finally, we suggest that developmental disruption of the endophenotype for certain subsets of gamma-generating interneuron may underlie cognitive deficit in psychiatric illness.

Wave speed in excitable random networks with spatially constrained connections

Very fast oscillations (VFO) in neocortex are widely observed before epileptic seizures, and there is growing evidence that they are caused by networks of pyramidal neurons connected by gap junctions between their axons. We are motivated by the spatio-temporal waves of activity recorded using electrocorticography (ECoG), and study the speed of activity propagation through a network of neurons axonally coupled by gap junctions. We simulate wave propagation by excitable cellular automata (CA) on random (Erdös-Rényi) networks of special type, with spatially constrained connections. From the cellular automaton model, we derive a mean field theory to predict wave propagation. The governing equation resolved by the Fisher-Kolmogorov PDE fails to describe wave speed. A new (hyperbolic) PDE is suggested, which provides adequate wave speed that saturates with network degree , in agreement with intuitive expectations and CA simulations. We further show that the maximum length of connection is a much better predictor of the wave speed than the mean length. When tested in networks with various degree distributions, wave speeds are found to strongly depend on the ratio of network moments rather than on mean degree , which is explained by general network theory. The wave speeds are strikingly similar in a diverse set of networks, including regular, Poisson, exponential and power law distributions, supporting our theory for various network topologies. Our results suggest practical predictions for networks of electrically coupled neurons, and our mean field method can be readily applied for a wide class of similar problems, such as spread of epidemics through spatial networks.

Chemical synaptic and gap junctional interactions between principal neurons: partners in epileptogenesis

Field potential signals, corresponding to electrographic seizures in cortical structures, often contain two components, which sometimes appear to be separable and other times to be superimposed. The first component consists of low-amplitude very fast oscillations (VFO, >70-80 Hz); the second component consists of larger amplitude transients, lasting tens to hundreds of ms, and variously called population spikes, EEG spikes, or bursts--terms chosen in part because of the cellular correlates of the field events. To first approximation, the two components arise because of distinctive types of cellular interactions: gap junctions for VFO (a model of which is reviewed in the following), and recurrent synaptic excitation and/or inhibition for the transients. With in vitro studies of epileptic human neocortical tissue, it is possible to elicit VFO alone, or VFO superimposed on a large transient, but not a large transient without the VFO. If such observations prove to be general, they would imply that gap junction-mediated interactions are the primary factor in epileptogenesis. It appears to be the case then, that in the setting of seizure initiation (but not necessarily under physiological conditions), the gain of gap junction-mediated circuits can actually be larger than the gain in excitatory synaptic circuits.

Cholinergic neuromodulation controls directed temporal communication in neocortex in vitro

Acetylcholine is the primary neuromodulator involved in cortical arousal in mammals. Cholinergic modulation is involved in conscious awareness, memory formation and attention – processes that involve intercommunication between different cortical regions. Such communication is achieved in part through temporal structuring of neuronal activity by population rhythms, particularly in the beta and gamma frequency ranges (12–80 Hz). Here we demonstrate, using in vitro and in silico models, that spectrally identical patterns of beta2 and gamma rhythms are generated in primary sensory areas and polymodal association areas by fundamentally different local circuit mechanisms: Glutamatergic excitation induced beta2 frequency population rhythms only in layer 5 association cortex whereas cholinergic neuromodulation induced this rhythm only in layer 5 primary sensory cortex. This region-specific sensitivity of local circuits to cholinergic modulation allowed for control of the extent of cortical temporal interactions. Furthermore, the contrasting mechanisms underlying these beta2 rhythms produced a high degree of directionality, favouring an influence of association cortex over primary auditory cortex.

Spatiotemporal patterns of electrocorticographic very fast oscillations (> 80 Hz) consistent with a network model based on electrical coupling between principal neurons

PURPOSE

We sought to characterize spatial and temporal patterns of electrocorticography (ECoG) very fast oscillations (> ∼80 Hz, VFOs) prior to seizures in human frontotemporal neocortex, and to develop a testable network model of these patterns.

METHODS

ECoG data were recorded with subdural grids from two preoperative patients with seizures of frontal lobe onset in an epilepsy monitoring unit. VFOs were recorded from rat neocortical slices. A "cellular automaton" model of network oscillations was developed, extending ideas of Traub et al. (Neuroscience, 92, 1999, 407) and Lewis & Rinzel (Network: Comput Neural Syst, 11, 2000, 299); this model is based on postulated electrical coupling between pyramidal cell axons.

RESULTS

Layer 5 of rat neocortex, in vitro, can generate VFOs when chemical synapses are blocked. Human epileptic neocortex, in situ, produces preseizure VFOs characterized by the sudden appearance of "blobs" of activity that evolve into spreading wavefronts. When wavefronts meet, they coalesce and propagate perpendicularly but never pass through each other. This type of pattern has been described by Lewis & Rinzel in cellular automaton models with spatially localized connectivity, and is demonstrated here with 120,000- to 5,760,000-cell models. We provide a formula for estimating VFO period from structural parameters and estimate the spatial scale of the connectivity.

DISCUSSION

These data provide further evidence, albeit indirect, that preseizure VFOs are generated by networks of pyramidal neurons coupled by gap junctions, each predominantly confined to pairs of neurons having somata separated by < ∼1-2 mm. Plausible antiepileptic targets are tissue mechanisms, such as pH regulation, that influence gap-junction conductance.

Temporal Interactions between Cortical Rhythms

Multiple local neuronal circuits support different, discrete frequencies of network rhythm in neocortex. Relationships between different frequencies correspond to mechanisms designed to minimise interference, couple activity via stable phase interactions, and control the amplitude of one frequency relative to the phase of another. These mechanisms are proposed to form a framework for spectral information processing. Individual local circuits can also transform their frequency through changes in intrinsic neuronal properties and interactions with other oscillating microcircuits. Here we discuss a frequency transformation in which activity in two co-active local circuits may combine sequentially to generate a third frequency whose period is the concatenation sum of the original two. With such an interaction, the intrinsic periodicity in each component local circuit is preserved – alternate, single periods of each original rhythm form one period of a new frequency – suggesting a robust mechanism for combining information processed on multiple concurrent spatiotemporal scales.

Model of very fast (> 75 Hz) network oscillations generated by electrical coupling between the proximal axons of cerebellar Purkinje cells

Very fast oscillations (VFO; > 75 Hz) occur transiently in vivo, in the cerebellum of mice genetically modified to model Angelman syndrome, and in a mouse model of fetal alcohol syndrome. We recently reported VFO in slices of mouse cerebellar cortex (Crus I and II of ansiform and paramedian lobules), either in association with gamma oscillations (approximately 40 Hz, evoked by nicotine) or in isolation [evoked by nicotine in combination with gamma-aminobutyric acid (GABA)(A) receptor blockade]. The experimental data suggest a role for electrical coupling between Purkinje cells (blockade of VFO by drugs reducing gap junction conductance and spikelets in some Purkinje cells); and the data suggest the specific involvement of Purkinje cell axons (because of field oscillation maxima in the granular layer). We show here that a detailed network model (1000 multicompartment Purkinje cells) replicates the experimental data when gap junctions are located on the proximal axons of Purkinje cells, provided sufficient spontaneous firing is present. Unlike other VFO models, most somatic spikelets do not correspond to axonal spikes in the parent axon, but reflect spikes in electrically coupled axons. The model predicts gating of VFO frequency by g(Na) inactivation, and experiments prolonging this inactivation time constant, with beta-pompilidotoxin, are consistent with this prediction. The model also predicts that cerebellar VFO can be explained as an electrically coupled system of axons that are not intrinsic oscillators: the electrically uncoupled cells do not individually oscillate (in the model) and axonal firing rates are much lower in the uncoupled state than in the coupled state.

Rhythm generation through period concatenation in rat somatosensory cortex

Rhythmic voltage oscillations resulting from the summed activity of neuronal populations occur in many nervous systems. Contemporary observations suggest that coexistent oscillations interact and, in time, may switch in dominance. We recently reported an example of these interactions recorded from in vitro preparations of rat somatosensory cortex. We found that following an initial interval of coexistent gamma ( approximately 25 ms period) and beta2 ( approximately 40 ms period) rhythms in the superficial and deep cortical layers, respectively, a transition to a synchronous beta1 ( approximately 65 ms period) rhythm in all cortical layers occurred. We proposed that the switch to beta1 activity resulted from the novel mechanism of period concatenation of the faster rhythms: gamma period (25 ms)+beta2 period (40 ms) = beta1 period (65 ms). In this article, we investigate in greater detail the fundamental mechanisms of the beta1 rhythm. To do so we describe additional in vitro experiments that constrain a biologically realistic, yet simplified, computational model of the activity. We use the model to suggest that the dynamic building blocks (or motifs) of the gamma and beta2 rhythms combine to produce a beta1 oscillation that exhibits cross-frequency interactions. Through the combined approach of in vitro experiments and mathematical modeling we isolate the specific components that promote or destroy each rhythm. We propose that mechanisms vital to establishing the beta1 oscillation include strengthened connections between a population of deep layer intrinsically bursting cells and a transition from antidromic to orthodromic spike generation in these cells. We conclude that neural activity in the superficial and deep cortical layers may temporally combine to generate a slower oscillation.

Region-specific changes in gamma and beta2 rhythms in NMDA receptor dysfunction models of schizophrenia

Cognitive disruption in schizophrenia is associated with altered patterns of spatiotemporal interaction associated with multiple electroencephalogram (EEG) frequency bands in cortex. In particular, changes in the generation of gamma (30-80 Hz) and beta2 (20-29 Hz) rhythms correlate with observed deficits in communication between different cortical areas. Aspects of these changes can be reproduced in animal models, most notably those involving acute or chronic reduction in glutamatergic synaptic communication mediated by N-methyl D-aspartate (NMDA) receptors. In vitro electrophysiological and immunocytochemical approaches afforded by such animal models continue to reveal a great deal about the mechanisms underlying EEG rhythm generation and are beginning to uncover which basic molecular, cellular, and network phenomena may underlie their disruption in schizophrenia. Here we briefly review the evidence for changes in gamma-aminobutyric acidergic (GABAergic) and glutamatergic function and address the problem of region specificity of changes with quantitative comparisons of effects of ketamine on gamma and beta2 rhythms in vitro. We conclude, from available evidence, that many observed changes in markers for GABAergic function in schizophrenia may be secondary to deficits in NMDA receptor-mediated excitatory synaptic activity. Furthermore, the broad range of changes in cortical dynamics seen in schizophrenia -- with contrasting effects seen in different brain regions and for different frequency bands -- may be more directly attributable to underlying deficits in glutamatergic neuronal communication rather than GABAergic inhibition alone.

New dynamics in cerebellar Purkinje cells: torus canards

We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that-after a saddle node bifurcation of limit cycles-the full model dynamics temporarily follow a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical applications: torus canards.

Recruitment of parvalbumin-positive interneurons determines hippocampal function and associated behavior

Perisomatic inhibition provided by a subgroup of GABAergic interneurons plays a critical role in timing the output of pyramidal cells. To test their contribution at the network and the behavioral level, we generated genetically modified mice in which the excitatory drive was selectively reduced either by the knockout of the GluR-D or by conditional ablation of the GluR-A subunit in parvalbumin-positive cells. Comparable cell type-specific reductions of AMPA-mediated currents were obtained. Kainate-induced gamma oscillations exhibited reduced power in hippocampal slices from GluR-D-/- and GluR-A(PVCre-/-) mice. Experimental and modeling data indicated that this alteration could be accounted for by imprecise spike timing of fast-spiking cells (FS) caused by smaller interneuronal EPSPs. GluR-D-/- and GluR-A(PVCre-/-) mice exhibited similar impairments in hippocampus-dependent tasks. These findings directly show the effects of insufficient recruitment of fast-spiking cells at the network and behavioral level and demonstrate the role of this subpopulation for working and episodic-like memory.

Period concatenation underlies interactions between gamma and beta rhythms in neocortex

The neocortex generates rhythmic electrical activity over a frequency range covering many decades. Specific cognitive and motor states are associated with oscillations in discrete frequency bands within this range, but it is not known whether interactions and transitions between distinct frequencies are of functional importance. When coexpressed rhythms have frequencies that differ by a factor of two or more interactions can be seen in terms of phase synchronization. Larger frequency differences can result in interactions in the form of nesting of faster frequencies within slower ones by a process of amplitude modulation. It is not known how coexpressed rhythms, whose frequencies differ by less than a factor of two may interact. Here we show that two frequencies (gamma – 40 Hz and beta2 – 25 Hz), coexpressed in superficial and deep cortical laminae with low temporal interaction, can combine to generate a third frequency (beta1 – 15 Hz) showing strong temporal interaction. The process occurs via period concatenation, with basic rhythm-generating microcircuits underlying gamma and beta2 rhythms forming the building blocks of the beta1 rhythm by a process of addition. The mean ratio of adjacent frequency components was a constant – approximately the golden mean – which served to both minimize temporal interactions, and permit multiple transitions, between frequencies. The resulting temporal landscape may provide a framework for multiplexing – parallel information processing on multiple temporal scales.

Gap junctions on hippocampal mossy fiber axons demonstrated by thin-section electron microscopy and freeze fracture replica immunogold labeling

Gap junctions have been postulated to exist between the axons of excitatory cortical neurons based on electrophysiological, modeling, and dye-coupling data. Here, we provide ultrastructural evidence for axoaxonic gap junctions in dentate granule cells. Using combined confocal laser scanning microscopy, thin-section transmission electron microscopy, and grid-mapped freeze-fracture replica immunogold labeling, 10 close appositions revealing axoaxonic gap junctions ( approximately 30-70 nm in diameter) were found between pairs of mossy fiber axons ( approximately 100-200 nm in diameter) in the stratum lucidum of the CA3b field of the rat ventral hippocampus, and one axonal gap junction ( approximately 100 connexons) was found on a mossy fiber axon in the CA3c field of the rat dorsal hippocampus. Immunogold labeling with two sizes of gold beads revealed that connexin36 was present in that axonal gap junction. These ultrastructural data support computer modeling and in vitro electrophysiological data suggesting that axoaxonic gap junctions play an important role in the generation of very fast (>70 Hz) network oscillations and in the hypersynchronous electrical activity of epilepsy.

A beta2-frequency (20-30 Hz) oscillation in nonsynaptic networks of somatosensory cortex

Beta2 frequency (20-30 Hz) oscillations appear over somatosensory and motor cortices in vivo during motor preparation and can be coherent with muscle electrical activity. We describe a beta2 frequency oscillation occurring in vitro in networks of layer V pyramidal cells, the cells of origin of the corticospinal tract. This beta2 oscillation depends on gap junctional coupling, but it survives a cut through layer 4 and, hence, does not depend on apical dendritic electrogenesis. It also survives a blockade of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors or a blockade of GABA(A) receptors that is sufficient to suppress gamma (30-70 Hz) oscillations in superficial cortical layers. The oscillation period is determined by the M type of K+ current.

Combined experimental/simulation studies of cellular and network mechanisms of epileptogenesis in vitro and in vivo

The electrical correlates of clinical seizures, and of experimental models of seizures, are recognized because neurons behave differently than normal. Individual neurons do unusual things, and neuronal activities become correlated with each other in ways that are not observed under physiologic conditions. Single neurons may fire bursts of action potentials superimposed on large depolarizations, and the bursts may recur rhythmically over a wide range of frequencies (<1 Hz to 25 Hz); periods of noisy subthreshold activity can occur; and firing can even be suppressed in some neurons. At the population level, nearby neurons tend to fire action potentials, or generate bursts, that are temporally locked together on a few-milliseconds time scale, so that large voltage transients are generated in extracellular fields. Very fast oscillations (>80 Hz) in neuronal aggregates may occur before, during, or after such large field potentials. Finally, cellular activities may even be correlated across large brain regions. The authors review some of the means by which cellular intrinsic properties, synaptic interactions, and electrical coupling via gap junctions, all contribute to the anomalous population activities characteristic of seizures. Also reviewed are some of the data suggesting that the requisite gap junctions are located on the axons of glutamatergic neurons.

Orthogonal arrangement of rhythm-generating microcircuits in the hippocampus

As a structure involved in learning and memory, the hippocampus functions as a network. The functional differentiation along the longitudinal axis of the hippocampus is poorly demarcated in comparison with the transverse axis. Using patch clamp recordings in conjunction with post hoc anatomy, we have examined the pattern of connectivity and the functional differentiation along the long axis of the hippocampus. Here, we provide anatomical and physiological evidence that the prominent rhythmic network activities of the hippocampus, the behavior-specific gamma and theta oscillations, are seen predominantly along the transverse and longitudinal axes respectively. This orthogonal relationship is the result of the axonal field trajectories and the consequential interaction of the principal cells and major interneuron subtypes involved in generating each rhythm. Thus, the axonal arborization patterns of hippocampal inhibitory cells may represent a structural framework for the spatiotemporal distribution of activity observed within the hippocampus.

Transient depression of excitatory synapses on interneurons contributes to epileptiform bursts during gamma oscillations in the mouse hippocampal slice

Persistent gamma frequency (30-70 Hz) network oscillations occur in hippocampal slices under conditions of metabotropic glutamate receptor (mGluR) activation. Excessive mGluR activation generated a bistable pattern of network activity during which epochs of gamma oscillations of increasing amplitude were terminated by synchronized bursts and very fast oscillations (>70 Hz). We provide experimental evidence that, during this behavior, pyramidal cell-to-interneuron synaptic depression takes place, occurring spontaneously during the gamma rhythm and associated with the onset of epileptiform bursts. We further provide evidence that excitatory postsynaptic potentials (EPSPs) in pyramidal cells are potentiated during the interburst gamma oscillation. When these two types of synaptic plasticity are incorporated, phenomenologically, into a network model previously shown to account for many features of persistent gamma oscillations, we find that epochs of gamma do indeed alternate with epochs of very fast oscillations and epileptiform bursts. Thus the same neuronal network can generate either gamma oscillations or epileptiform bursts, in a manner depending on the degree of network drive and network-induced fluctuations in synaptic efficacies.

Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts

To better understand population phenomena in thalamocortical neuronal ensembles, we have constructed a preliminary network model with 3,560 multicompartment neurons (containing soma, branching dendrites, and a portion of axon). Types of neurons included superficial pyramids (with regular spiking [RS] and fast rhythmic bursting [FRB] firing behaviors); RS spiny stellates; fast spiking (FS) interneurons, with basket-type and axoaxonic types of connectivity, and located in superficial and deep cortical layers; low threshold spiking (LTS) interneurons, which contacted principal cell dendrites; deep pyramids, which could have RS or intrinsic bursting (IB) firing behaviors, and endowed either with nontufted apical dendrites or with long tufted apical dendrites; thalamocortical relay (TCR) cells; and nucleus reticularis (nRT) cells. To the extent possible, both electrophysiology and synaptic connectivity were based on published data, although many arbitrary choices were necessary. In addition to synaptic connectivity (by AMPA/kainate, NMDA, and GABA(A) receptors), we also included electrical coupling between dendrites of interneurons, nRT cells, and TCR cells, and--in various combinations--electrical coupling between the proximal axons of certain cortical principal neurons. Our network model replicates several observed population phenomena, including 1) persistent gamma oscillations; 2) thalamocortical sleep spindles; 3) series of synchronized population bursts, resembling electrographic seizures; 4) isolated double population bursts with superimposed very fast oscillations (>100 Hz, "VFO"); 5) spike-wave, polyspike-wave, and fast runs (about 10 Hz). We show that epileptiform bursts, including double and multiple bursts, containing VFO occur in rat auditory cortex in vitro, in the presence of kainate, when both GABA(A) and GABA(B) receptors are blocked. Electrical coupling between axons appears necessary (as reported previously) for persistent gamma and additionally plays a role in the detailed shaping of epileptogenic events. The degree of recurrent synaptic excitation between spiny stellate cells, and their tendency to fire throughout multiple bursts, also appears critical in shaping epileptogenic events.

Distinct roles for the kainate receptor subunits GluR5 and GluR6 in kainate-induced hippocampal gamma oscillations

Kainate receptors (KARs) play an important role in synaptic physiology, plasticity, and pathological phenomena such as epilepsy. However, the physiological implications for neuronal networks of the distinct expression patterns of KAR subunits are unknown. Using KAR knock-out mice, we show that subunits glutamate receptor (GluR) 5 and GluR6 play distinct roles in kainate-induced gamma oscillations and epileptiform burst activity. Ablation of GluR5 leads to a higher susceptibility of the network to the oscillogenic and epileptogenic effects of kainate, whereas lack of GluR6 prevents kainate-induced gamma oscillations or epileptiform bursts. Based on experimental and simulated neuronal network data as well as the consequences of GluR5 and GluR6 expression for cellular and synaptic physiology, we propose that the functional interplay of GluR5-containing KARs on axons of interneurons and GluR6-containing KARs in the somatodendritic region of both interneurons and pyramidal cells underlie the oscillogenic and epileptogenic effects of kainate.

Persistent gamma oscillations in superficial layers of rat auditory neocortex: experiment and model

Persistent in vitro gamma oscillations, induced by bath application of carbachol and kainate (amongst other drugs), were discovered by Eberhard Buhl and collaborators in 1998. The oscillations are robust, in that they can continue for hours; but the oscillations are also intricate in their mechanisms: they depend upon phasic synaptic excitation and inhibition, upon electrical coupling between interneurones and between pyramidal neurones, and--at least in neocortex--they depend upon complex intrinsic properties of some of the neurones.

Differential involvement of oriens/pyramidale interneurones in hippocampal network oscillations in vitro

Using whole-cell patch-clamp recordings in conjunction with post hoc anatomy we investigated the physiological properties of hippocampal stratum oriens and stratum pyramidale inhibitory interneurones, before and following the induction of pharmacologically evoked gamma frequency network oscillations. Prior to kainate-induced transient epochs of gamma activity, two distinct classes of oriens interneurones, oriens lacunosum-moleculare (O-LM) and trilaminar cells, showed prominent differences in their membrane and firing properties, as well as in the amplitude and kinetics of their excitatory postsynaptic events. In the active network both types of neurone received a phasic barrage of gamma frequency excitatory inputs but, due to their differential functional integration, showed clear differences in their output patterns. While O-LM cells fired intermittently at theta frequency, trilaminar interneurones discharged on every gamma cycle and showed a propensity to fire spike doublets. Two other classes of fast spiking interneurones, perisomatic targeting basket and bistratified cells, in the active network discharged predominantly single action potentials on every gamma cycle. Thus, within a locally excited network, O-LM cells are likely to provide a theta-frequency patterned output to distal dendritic segments, whereas basket and bistratified cells are involved in the generation of locally synchronous gamma band oscillations. The anatomy and output profile of trilaminar cells suggest they are involved in the projection of locally generated gamma rhythms to distal sites. Therefore a division of labour appears to exist whereby different frequencies and spatiotemporal properties of hippocampal rhythms are mediated by different interneurone subtypes.