Evidence has been presented that CA1 pyramidal cells, during spontaneous in vitro sharp wave/ripple (SPW-R) complexes, generate somatic action potentials that originate in axons. ‘Participating’ (somatically firing) pyramidal cells fire (almost always) at most once during a particular SPW-R whereas non-participating cells virtually never fire during an SPW-R. Somatic spikelets were small or absent, while ripple-frequency EPSCs and IPSCs occurred during the SPW-R in pyramidal neurons. These experimental findings could be replicated with a network model in which electrical coupling was present between small pyramidal cell axonal branches. Here, we explore this model in more depth. Factors that influence somatic participation include: (i) the diameter of axonal branches that contain coupling sites to other axons, because firing in larger branches injects more current into the main axon, increasing antidromic firing probability; (ii) axonal K+ currents; and (iii) somatic hyperpolarization and shunting. We predict that portions of axons fire at high frequency during SPW-R, while somata fire much less. In the model, somatic firing can occur by occasional generation of full action potentials in proximal axonal branches, which are excited by high-frequency spikelets. When the network contains phasic synaptic inhibition, at the axonal gap junction site, gamma oscillations result, again with more frequent axonal firing than somatic firing. Combining the models, so as to generate gamma followed by sharp waves, leads to strong overlap between the population of cells firing during gamma the population of cells firing during a subsequent sharp wave, as observed in vivo.
gap junction; axonal branch; transient K+ current; antidromic spike
Delta oscillations (1–4 Hz) associate with deep sleep and are implicated in memory consolidation and replay of cortical responses elicited during wake states. A potent local generator has been characterized in thalamus, and local generators in neocortex have been suggested. Here we demonstrate that isolated rat neocortex generates delta rhythms in conditions mimicking the neuromodulatory state during deep sleep (low cholinergic and dopaminergic tone). The rhythm originated in an NMDA receptor-driven network of intrinsic bursting (IB) neurons in layer 5, activating a source of GABAB receptor-mediated inhibition. In contrast, regular spiking (RS) neurons in layer 5 generated theta-frequency outputs. In layer 2/3 principal cells, outputs from IB cells associated with IPSPs, whereas those from layer 5 RS neurons related to nested bursts of theta-frequency EPSPs. Both interlaminar spike and field correlations revealed a sequence of events whereby sparse spiking in layer 2/3 was partially reflected back from layer 5 on each delta period. We suggest that these reciprocal, interlaminar interactions may represent a “Helmholtz machine”-like process to control synaptic rescaling during deep sleep.
Rhythmic activity in populations of cortical neurons accompanies, and may underlie, many aspects of primary sensory processing and short-term memory. Activity in the gamma band (30 Hz up to > 100 Hz) is associated with such cognitive tasks and is thought to provide a substrate for temporal coupling of spatially separate regions of the brain. However, such coupling requires close matching of frequencies in co-active areas, and because the nominal gamma band is so spectrally broad, it may not constitute a single underlying process. Here we show that, for inhibition-based gamma rhythms in vitro in rat neocortical slices, mechanistically distinct local circuit generators exist in different laminae of rat primary auditory cortex. A persistent, 30 – 45 Hz, gap-junction-dependent gamma rhythm dominates rhythmic activity in supragranular layers 2/3, whereas a tonic depolarization-dependent, 50 – 80 Hz, pyramidal/interneuron gamma rhythm is expressed in granular layer 4 with strong glutamatergic excitation. As a consequence, altering the degree of excitation of the auditory cortex causes bifurcation in the gamma frequency spectrum and can effectively switch temporal control of layer 5 from supragranular to granular layers. Computational modeling predicts the pattern of interlaminar connections may help to stabilize this bifurcation. The data suggest that different strategies are used by primary auditory cortex to represent weak and strong inputs, with principal cell firing rate becoming increasingly important as excitation strength increases.
Morphological and electrophysiological studies have shown that granule cell axons, the mossy fibers (MFs), establish gap junctions and, therefore, electrical communication among them. That granule cells express gap junctional proteins in their axons suggests the possibility that their terminals express them as well. If this were to be the case, mixed electrical-chemical communication could be supported, as MF terminals normally use glutamate for fast communication with their target cells. Here we present electrophysiological and modeling studies consistent with this hypothesis. We show that MF activation produced fast spikelets followed by excitatory postsynaptic potentials in pyramidal cells (PCs), which, unlike the spikelets, underwent frequency potentiation and were strongly depressed by activation of metabotropic glutamate receptors, as expected from transmission of MF origin. The spikelets, which persisted during blockade of chemical transmission, wee potentiated by dopamine and suppressed by the gap junction blocker carbenoxolone. The various waveforms evoked by MF stimulation were replicated in a multi-compartment model of a PC by brief current pulse injections into the proximal apical dendritic compartment, where MFs are known to contact PCs. Mixed electrical and glutamatergic communication between granule cells and some PCs in CA3 may ensure the activation of sets of PCs, bypassing the strong action of concurrent feed-forward inhibition that granule cells activate. Importantly, MF-to-PC electrical coupling may allow bidirectional, possibly graded communication that can be faster than chemical synapses and subject to different forms of modulation.
CA3; mossy fibers; spikelets; mixed transmission; electrical communication
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.
synchronized burst; very fast oscillation; recurrent excitation; electrical coupling; seizure; in vitro model
Very fast oscillations, 80 Hz and greater (designated here VFOs or “ripples”) have been observed in the hippocampus and neocortex, under a variety of conditions that are summarized briefly later. VFOs may be of relevance for normal brain function (1, 2, 3, 4) and could also be of relevance in the initiation of focal epileptic seizures (5, 6). To determine whether such relevance indeed exists, an understanding of the cellular mechanisms of VFOs is essential. For purposes of this commentary, I shall assume that all forms of VFOs are governed by a few common basic underlying principles. Future experimental data may show that assumption to be false, but for now, the assumption at least allows the formulation of straightforward hypotheses that could stimulate experiments.
High-frequency oscillations (HFOs) are an important part of brain activity in health and disease. However, their origins remain obscure and controversial. One possible mechanism depends on the presence of sparsely distributed gap junctions that electrically couple the axons of principal cells. A plexus of electrically coupled axons is modeled as a random network with bi-directional connections between its nodes. Under certain conditions the network can demonstrate one of two types of oscillatory activity. Type I oscillations (100–200 Hz) are predicted to be caused by spontaneously spiking axons in a network with strong (high conductance) gap junctions. Type II oscillations (200–300 Hz) require no spontaneous spiking and relatively weak (low-conductance) gap junctions, across which spike propagation failures occur. The type II oscillations are reentrant and self-sustained. Here we examine what determines the frequency of type II oscillations. Using simulations we show that the distribution of loop lengths is the key factor for determining frequency in type II network oscillations. We first analyze spike failure between two electrically coupled cells using a model of anatomically reconstructed CA1 pyramidal neuron. Then network oscillations are studied by a cellular automaton model with random network connectivity, in which we control loop statistics. We show that oscillation periods can be predicted from the network’s loop statistics. The shortest loop, around which a spike can travel, is the most likely pacemaker candidate. The principle of one loop as a pacemaker is remarkable, because random networks contain a large number of loops juxtaposed and superimposed, and their number rapidly grows with network size. This principle allows us to predict the frequency of oscillations from network connectivity and visa versa. We finally propose that type I oscillations may correspond to ripples, while type II oscillations correspond to so-called fast ripples.
network; loop; pacemaker; gap junction; axon; pyramidal neuron
Dendrodendritic electrical signaling via gap junctions is now an accepted feature of neuronal communication in mammalian brain, whereas axodendritic and axosomatic gap junctions have rarely been described. We present ultrastructural, immunocytochemical, and dye-coupling evidence for “mixed” (electrical/chemical) synapses on both principal cells and interneurons in adult rat hippocampus. Thin-section electron microscopic images of small gap junction-like appositions were found at mossy fiber (MF) terminals on thorny excrescences of CA3 pyramidal neurons (CA3pyr), apparently forming glutamatergic mixed synapses. Lucifer Yellow injected into weakly fixed CA3pyr was detected in MF axons that contacted four injected CA3pyr, supporting gap junction-mediated coupling between those two types of principal cells. Freeze-fracture replica immunogold labeling revealed diverse sizes and morphologies of connexin-36-containing gap junctions throughout hippocampus. Of 20 immunogold-labeled gap junctions, seven were large (328–1140 connexons), three of which were consistent with electrical synapses between interneurons; but nine were at axon terminal synapses, three of which were immediately adjacent to distinctive glutamate receptor-containing postsynaptic densities, forming mixed glutamatergic synapses. Four others were adjacent to small clusters of immunogold-labeled 10-nm E-face intramembrane particles, apparently representing extrasynaptic glutamate receptor particles. Gap junctions also were on spines in stratum lucidum, stratum oriens, dentate gyrus, and hilus, on both interneurons and unidentified neurons. In addition, one putative GABAergic mixed synapse was found in thin-section images of a CA3pyr, but none were found by immunogold labeling, suggesting the rarity of GABAergic mixed synapses. Cx36-containing gap junctions throughout hippocampus suggest the possibility of reciprocal modulation of electrical and chemical signals in diverse hippocampal neurons.
CA3; dentate gyrus; interneuron; pyramidal neuron; principal cell; mossy fiber; gap junction
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.
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, 12000, 299); this model is based on postulated electrical coupling between pyramidal cell axons.
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.
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.
Ripple; Gap junction; Cellular automaton
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.
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.
EEG; oscillation; interneuron; coherence; attention; auditory
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 (~40 Hz, evoked by nicotine), or in isolation (evoked by nicotine in combination with GABAA 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 (1,000 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 gNa inactivation, and experiments prolonging this inactivation time constant, with β-pompilidotoxin, are consistent with this prediction. The model also predicts that cerebellar VFO can be explained as an electrically coupled system of axons which 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.
gap junction; network model; cerebellar cortex
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 γ-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.
schizophrenia; EEG; gamma; beta; inhibition; NMDA
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 follow temporarily a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical applications: torus canards.
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.
EEG; neocortex; gamma rhythm; beta rhythm; inhibition
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 (∼25 ms period) and beta2 (∼40 ms period) rhythms in the superficial and deep cortical layers, respectively, a transition to a synchronous beta1 (∼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.
Since the late 19th century, rhythmic electrical activity has been observed in the mammalian brain. Although subject to intense scrutiny, only a handful of these rhythms are understood in terms of the biophysical elements that produce the oscillations. Even less understood are the mechanisms that underlie interactions between rhythms; how do rhythms of different frequencies coexist and affect one another in the dynamic environment of the brain? In this article, we consider a recent proposal for a novel mechanism of cortical rhythm generation: period concatenation, in which the periods of faster rhythms sum to produce a slower oscillation. To model this phenomenon, we implement simple—yet biophysical—computational models of the individual neurons that produce the brain's voltage activity. We utilize established models for the faster rhythms, and unite these in a particular way to generate a slower oscillation. Through the combined approach of experimental recordings (from thin sections of rat cortex) and mathematical modeling, we identify the cell types, synaptic connections, and ionic currents involved in rhythm generation through period concatenation. In this way the brain may generate new activity through the combination of preexisting elements.
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.
EEG; neocortex; gamma rhythm; beta rhythm; inhibition
We describe a form of very fast oscillation (VFO) in patient electrocorticographic (ECoG) recordings, that can occur prior to ictal events, in which the frequency increases steadily from ~30–40 Hz to >120 Hz, over a period of seconds. We dub these events “glissandi” and describe a possible model for them.
Four patients with epilepsy had presurgical evaluations (with ECoG obtained in two of them), and excised tissue was studied in vitro, from 3 of the patients. Glissandi were seen spontaneously in vitro, associated with ictal events; using acute slices of rat neocortex; and they were simulated using a network model of 15,000 detailed layer V pyramidal neurons, coupled by gap junctions.
Glissandi were observed to arise from human temporal neocortex. In vitro, they lasted 0.2 to 4.1 seconds, prior to ictal onset. Similar events were observed in the rat in vitro, in layer V of frontal neocortex, when alkaline solution was pressure-ejected; glissandi persisted when GABAA, GABAB, and NMDA and AMPA receptors were blocked. Non-alkaline conditions, prevented glissando generation. In network simulations, it was found that steadily increasing gap junction conductance would lead to the observed steady increase in VFO field frequency. This occurred because increasing gap junction conductance shortened the time required for an action potential to cross from cell to cell.
The in vitro and modeling data are consistent with the hypothesis that glissandi arise when pyramidal cell gap junction conductances rise over time, possibly as a result of an alkaline fluctuation in brain pH.
very fast oscillations; electrocorticography; gap junction; pH; epilepsy model