Gamma rhythmic bursts: coherence control in networks of cortical pyramidal neurons

The CAN-In network: A biologically inspired model for self-sustained theta oscillations and memory maintenance in the hippocampus

During working memory tasks, the hippocampus exhibits synchronous theta-band activity, which is thought to be correlated with the short-term memory maintenance of salient stimuli. Recent studies indicate that the hippocampus contains the necessary circuitry allowing it to generate and sustain theta oscillations without the need of extrinsic drive. However, the cellular and network mechanisms supporting synchronous rhythmic activity are far from being fully understood. Based on electrophysiological recordings from hippocampal pyramidal CA1 cells, we present a possible mechanism for the maintenance of such rhythmic theta-band activity in the isolated hippocampus. Our model network, based on the Hodgkin-Huxley formalism, comprising pyramidal neurons equipped with calcium-activated nonspecific cationic (CAN) ion channels, is able to generate and sustain synchronized theta oscillations (4-12 Hz), following a transient stimulation. The synchronous network activity is maintained by an intrinsic CAN current (I_CAN ), in the absence of constant external input. When connecting the pyramidal-CAN network to fast-spiking inhibitory interneurons, the dynamics of the model reveal that feedback inhibition improves the robustness of fast theta oscillations, by tightening the synchronization of the pyramidal CAN neurons. The frequency and power of the theta oscillations are both modulated by the intensity of the I_CAN , which allows for a wide range of oscillation rates within the theta band. This biologically plausible mechanism for the maintenance of synchronous theta oscillations in the hippocampus aims at extending the traditional models of septum-driven hippocampal rhythmic activity. © 2017 Wiley Periodicals, Inc.

Oscillatory synchrony as a mechanism of attentional processing

The question of how the brain selects which stimuli in our visual field will be given priority to enter into perception, to guide our actions and to form our memories has been a matter of intense research in studies of visual attention. Work in humans and animal models has revealed an extended network of areas involved in the control and maintenance of attention. For many years, imaging studies in humans constituted the main source of a systems level approach, while electrophysiological recordings in non-human primates provided insight into the cellular mechanisms of visual attention. Recent technological advances and the development of sophisticated analytical tools have allowed us to bridge the gap between the two approaches and assess how neuronal ensembles across a distributed network of areas interact in visual attention tasks. A growing body of evidence suggests that oscillatory synchrony plays a crucial role in the selective communication of neuronal populations that encode the attended stimuli. Here, we discuss data from theoretical and electrophysiological studies, with more emphasis on findings from humans and non-human primates that point to the relevance of oscillatory activity and synchrony for attentional processing and behavior. These findings suggest that oscillatory synchrony in specific frequencies reflects the biophysical properties of specific cell types and local circuits and allows the brain to dynamically switch between different spatio-temporal patterns of activity to achieve flexible integration and selective routing of information along selected neuronal populations according to behavioral demands. This article is part of a Special Issue entitled SI: Prediction and Attention.

Higher-order spike triggered analysis of neural oscillators

For the purpose of elucidating the neural coding process based on the neural excitability mechanism, researchers have recently investigated the relationship between neural dynamics and the spike triggered stimulus ensemble (STE). Ermentrout et al. analytically derived the relational equation between the phase response curve (PRC) and the spike triggered average (STA). The STA is the first cumulant of the STE. However, in order to understand the neural function as the encoder more explicitly, it is necessary to elucidate the relationship between the PRC and higher-order cumulants of the STE. In this paper, we give a general formulation to relate the PRC and the nth moment of the STE. By using this formulation, we derive a relational equation between the PRC and the spike triggered covariance (STC), which is the covariance of the STE. We show the effectiveness of the relational equation through numerical simulations and use the equation to identify the feature space of the rat hippocampal CA1 pyramidal neurons from their PRCs. Our result suggests that the hippocampal CA1 pyramidal neurons oscillating in the theta frequency range are commonly sensitive to inputs composed of theta and gamma frequency components.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

Weighted spike-triggered average of a fluctuating stimulus yielding the phase response curve

We demonstrate that the phase response curve (PRC) can be reconstructed using a weighted spike-triggered average of an injected fluctuating input. The key idea is to choose the weight to be proportional to the magnitude of the fluctuation of the oscillatory period. Particularly, when a neuron exhibits random switching behavior between two bursting modes, two corresponding PRCs can be simultaneously reconstructed, even from the data of a single trial. This method offers an efficient alternative to the experimental investigation of oscillatory systems, without the need for detailed modeling.

A putatively novel form of spontaneous coordination in neural activity

We simultaneously recorded local field potentials from three sites along the olfactory-entorhinal axis in rats lightly anesthetized with isoflurane, as part of another experiment. While analyzing the initial data from that experiment with spectrograms, we discovered a potentially novel form of correlated neural activity, with near-simultaneous occurrence across the three widely separated brain sites. After validating their existence further, we named these events Synchronous Frequency Bursts (SFBs). Here we report our initial investigations into their properties and their potential functional significance. In Experiment 1, we found that SFBs have highly regular properties, consisting of brief (approximately 250 ms), high amplitude bursts of LFP energy spanning frequency ranges from the delta band (1-4 Hz) to at least the low gamma band (30-50 Hz). SFBs occurred almost simultaneously across recording sites, usually with onsets <25 ms apart, and there was no clear pattern of temporal leading or lagging among the sites. While the SFBs had fairly typical, exponentially decaying power spectral density plots, their coherence structure was unusual, with high peaks in several narrow frequency ranges and little coherence in other bands. In Experiment 2, we found that SFBs occurred far more often under light anesthesia than deeper anesthetic states, and were especially prevalent as the animals regained consciousness. Finally, in Experiment 3 we showed that SFBs occur simultaneously at a significant rate across brain sites from putatively different functional subsystems--olfactory versus motor pathways. We suggest that SFBs do not carry information per se, but rather, play a role in coordinating activity in different frequency bands, potentially brain-wide, as animals progress from sleep or anesthesia toward full consciousness.

Synchrony-Induced Switching Behavior of Spike Pattern Attractors Created by Spike-Timing-Dependent Plasticity

Although context-dependent spike synchronization among populations of neurons has been experimentally observed, its functional role remains controversial. In this modeling study, we demonstrate that in a network of spiking neurons organized according to spike-timing-dependent plasticity, an increase in the degree of synchrony of a uniform input can cause transitions between memorized activity patterns in the order presented during learning. Furthermore, context-dependent transitions from a single pattern to multiple patterns can be induced under appropriate learning conditions. These findings suggest one possible functional role of neuronal synchrony in controlling the flow of information by altering the dynamics of the network.

Synchrony-Induced Attractor Transition in Cortical Neural Networks Organized by Spike-Timing Dependent Plasticity

Recent studies have shown that synchronous neural activity in the cortex area occurs related to behavior or recognition of animals, which suggests that such neural activity involves in information processing. Functions enabled by synchronous firing, however, are still unknown. Results reporting that a transition between recall states of associative memory is induced by external synchronous spikes in a neural network formed by spike-timing dependent plasticity indicate the possibility of a function of synchronous neural activity as a transition signal, requiring further examination using detailed cortical neuron models (AokiAoyagi). We introduced a mathematical model of pyramidal and fast-spiking cortical neurons based on Hodgkin-Huxley, and confirmed the transition between recall states through synchronous spike inputs in detailed neuron models.

Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex

It is postulated that synchronous firing of cortical neurons plays an active role in cognitive functions of the brain. An important issue is whether pyramidal neurons in different cortical layers exhibit similar tendencies to synchronise. To address this issue, we performed intracellular and whole-cell recordings of regular-spiking pyramidal neurons in slice preparations of the rat motor cortex (18-45 days old) and analysed the phase response curves of these pyramidal neurons in layers 2/3 and 5. The phase response curve represents how an external stimulus affects the timing of spikes immediately after the stimulus in repetitively firing neurons. The phase response curve can be classified into two categories, type 1 (the spike is always advanced) and type 2 (the spike is advanced or delayed depending on the stimulus phase), and are important determinants of whether or not rhythmic synchronization of neuron pairs occurs. We found that pyramidal neurons in layer 2/3 tend to display type-2 phase response curves whereas those in layer 5 tend to exhibit type-1 phase response curves. The differences were prominent particularly in the gamma-frequency range (20-45 Hz). Our results imply that the layer-2/3 pyramidal neurons, when coupled mutually through fast excitatory synapses, may exhibit a much stronger tendency for rhythmic synchronization than layer-5 neurons in the gamma-frequency range.

Synchronous and asynchronous bursting states: role of intrinsic neural dynamics

Brain signals such as local field potentials often display gamma-band oscillations (30-70 Hz) in a variety of cognitive tasks. These oscillatory activities possibly reflect synchronization of cell assemblies that are engaged in a cognitive function. A type of pyramidal neurons, i.e., chattering neurons, show fast rhythmic bursting (FRB) in the gamma frequency range, and may play an active role in generating the gamma-band oscillations in the cerebral cortex. Our previous phase response analyses have revealed that the synchronization between the coupled bursting neurons significantly depends on the bursting mode that is defined as the number of spikes in each burst. Namely, a network of neurons bursting through a Ca(2+)-dependent mechanism exhibited sharp transitions between synchronous and asynchronous firing states when the neurons exchanged the bursting mode between singlet, doublet and so on. However, whether a broad class of bursting neuron models commonly show such a network behavior remains unclear. Here, we analyze the mechanism underlying this network behavior using a mathematically tractable neuron model. Then we extend our results to a multi-compartment version of the NaP current-based neuron model and prove a similar tight relationship between the bursting mode changes and the network state changes in this model. Thus, the synchronization behavior couples tightly to the bursting mode in a wide class of networks of bursting neurons.

Reproducing bursting interspike interval statistics of the gustatory cortex

Cortical neurons in vivo generate highly irregular spike sequences. Recently, it was experimentally found that the local variation of interspike intervals, LV, is nearly constant for every spike sequence for the same neurons. On the contrary, the coefficient of variation, CV, varies over different spike sequences. Here, we first show that these characteristic features are also applicable in bursting spike sequences that are obtained from the rat gustatory cortex. Next, we show that the conventional leaky integrate-and-fire model does not fully account for reproducing these statistical features in data of real bursting spike sequences. We resolve this difficulty by proposing an alternative neuron model which is a reduction of the bursting neuron model involving the persistent sodium current. Our study implies that (1) the characteristic features of CV and LV are the results of the endogenous bursting and (2) the bursting behavior in the gustatory cortex is caused mainly by the persistent sodium current.

Robustness and regularity of oscillations in neuronal populations

We study a biologically plausible but computationally simplified integrate-and-fire neuronal model. Oscillatory activity is analyzed in the networks with and without self-connections. We perform a detailed scan of four major parameters that represent the properties of neurons and synapses: connection ratio, connection strengths, post-synaptic potential decay rate and soma's potential decay rate. It is observed that networks with different properties exhibit different periods and different patterns of synchrony. We find that generally these oscillations are robust against changes of parameters, meanwhile we also locate the parametric boundaries where oscillations break down.

Event-related neural activities: what about phase?

The main topic of this overview is an analysis of the concepts of phase and synchrony, as used in neurophysiology, in their various meanings. A number of notions related to the concepts of phase and synchrony, which are incorporated in contemporary neurophysiology, particularly in the domain of neuro-cognitive physiology are discussed. These notions need a critical examination, since their use sometimes is not clear, or it may even be ambiguous. We present some of these concepts, namely (a) (des)synchronization, (b) phase resetting, (c) phase synchrony and phase/time delays, and (d) phase clustering within one signal, while discussing what type of neuronal activities may underlie these EEG phenomena.

Entrainment in a Chemical Oscillator Chain with a Pacemaker

Entrainment by a pacemaker was investigated experimentally and numerically in a chain of chemical oscillators using coupled discrete Belousov-Zhabotinsky reaction oscillators. The spontaneous frequency of each oscillator depended on the concentration of catalyst ions. The coupling strengths among the nearest neighbor oscillators were controlled by changing the spacing distance (d) between beads. When the coupling strength was sufficiently strong, the pacemaker entrained other oscillators in the chain. Subsequently, the trigger waves propagating from a pacemaker were observed. The range of trigger wave propagation area, i.e., the number of entrained oscillators, depended on d. Numerical simulation for the system described the experimental results well. Furthermore, photic noise maximized the strength of entrainment at an optimal noise intensity.

Microcircuits in action – from CPGs to neocortex

To understand the interface between global brain function and molecular neuroscience--that is, the microcircuit level--a major challenge. Such understanding is prerequisite if we are to account for neural function in cellular terms. Very few vertebrate microcircuits are yet understood because their analysis is demanding technically. In this review of the TINS Microcircuits Special Feature, we attempt to shed light on the problem by comparing the operation of four types of microcircuit, to identify common molecular and cellular components. Central pattern generator (CPG) networks underlying rhythmic movements and hippocampal microcircuits that generate gamma and theta rhythms are compared with the neocortical microcircuits used in cognitive tasks and a cerebellar network. The long-term goal is to identify the components of a molecular and synaptic tool kit for the design of different microcircuits.

Theta oscillations by synaptic excitation in a neocortical circuit model

Neocortical theta-band oscillatory activity is associated with cognitive tasks involving learning and memory. This oscillatory activity is proposed to originate from the synchronization of interconnected layer V intrinsic bursting (IB) neurons by recurrent excitation. To test this hypothesis, a sparsely connected spiking circuit model based on empirical data was simulated using Hodgkin-Huxley-type bursting neurons and use-dependent depressing synaptic connections. In response to a heterogeneous tonic current stimulus, the model generated coherent and robust oscillatory activity throughout the theta-band (4-12 Hz). These oscillations were not, however, self-sustaining without a driving current, and not dependent on N-methyl-D-aspartate receptor synaptic currents. At realistic connection strengths, synaptic depression was necessary to avoid instability and expanded the basin of attraction for theta oscillations by controlling the gain of recurrent excitation. These results support the hypothesis that IB neuron networks can generate robust and coherent theta-band oscillations in neocortex.

Toward a developmental neurobiology of autism

Autism is a complex, behaviorally defined, developmental brain disorder with an estimated prevalence of 1 in 1,000. It is now clear that autism is not a disease, but a syndrome with a strong genetic component. The etiology of autism is poorly defined both at the cellular and the molecular levels. Based on the fact that seizure activity is frequently associated with autism and that abnormal evoked potentials have been observed in autistic individuals in response to tasks that require attention, several investigators have recently proposed that autism might be caused by an imbalance between excitation and inhibition in key neural systems including the cortex. Despite considerable ongoing effort toward the identification of chromosome regions affected in autism and the characterization of many potential gene candidates, only a few genes have been reproducibly shown to display specific mutations that segregate with autism, likely because of the complex polygenic nature of this syndrome. Among those, several candidate genes have been shown to control the early patterning and/or the late synaptic maturation of specific neuronal subpopulations controlling the balance between excitation and inhibition in the developing cortex and cerebellum. In the present article, we review our current understanding of the developmental mechanisms patterning the balance between excitation and inhibition in the context of the neurobiology of autism.

Rapid temporal modulation of synchrony by competition in cortical interneuron networks

The synchrony of neurons in extrastriate visual cortex is modulated by selective attention even when there are only small changes in firing rate (Fries, Reynolds, Rorie, & Desimone, 2001). We used Hodgkin-Huxley type models of cortical neurons to investigate the mechanism by which the degree of synchrony can be modulated independently of changes in firing rates. The synchrony of local networks of model cortical interneurons interacting through GABA(A) synapses was modulated on a fast timescale by selectively activating a fraction of the interneurons. The activated interneurons became rapidly synchronized and suppressed the activity of the other neurons in the network but only if the network was in a restricted range of balanced synaptic background activity. During stronger background activity, the network did not synchronize, and for weaker background activity, the network synchronized but did not return to an asynchronous state after synchronizing. The inhibitory output of the network blocked the activity of pyramidal neurons during asynchronous network activity, and during synchronous network activity, it enhanced the impact of the stimulus-related activity of pyramidal cells on receiving cortical areas (Salinas & Sejnowski, 2001). Synchrony by competition provides a mechanism for controlling synchrony with minor alterations in rate, which could be useful for information processing. Because traditional methods such as cross-correlation and the spike field coherence require several hundred milliseconds of recordings and cannot measure rapid changes in the degree of synchrony, we introduced a new method to detect rapid changes in the degree of coincidence and precision of spike timing.

Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses

Fast-spiking (FS) interneurons have specific types (Kv3.1/3.2 type) of the delayed potassium channel, which differ from the conventional Hodgkin-Huxley (HH) type potassium channel (Kv1.3 type) in several aspects. In this study, we show dramatic effects of the Kv3.1/3.2 potassium channel on the synchronization of the FS interneurons. We show analytically that two identical electrically coupled FS interneurons modeled with Kv3.1/3.2 channel fire synchronously at arbitrary firing frequencies, unlike similarly coupled FS neurons modeled with Kv1.3 channel that show frequency-dependent synchronous and antisynchronous firing states. Introducing GABA(A) receptor-mediated synaptic connections into an FS neuron pair tends to induce an antisynchronous firing state, even if the chemical synapses are bidirectional. Accordingly, an FS neuron pair connected simultaneously by electrical and chemical synapses achieves both synchronous firing state and antisynchronous firing state in a physiologically plausible range of the conductance ratio between electrical and chemical synapses. Moreover, we find that a large-scale network of FS interneurons connected by gap junctions and bidirectional GABAergic synapses shows similar bistability in the range of gamma frequencies (30-70 Hz).