Adaptation and shunting inhibition leads to pyramidal/interneuron gamma with sparse firing of pyramidal cells

Tiagabine induced modulation of oscillatory connectivity and activity match PET-derived, canonical GABA-A receptor distributions

As the most abundant inhibitory neurotransmitter in the mammalian brain, γ-aminobutyric acid (GABA) plays a crucial role in shaping the frequency and amplitude of oscillations, which suggests a role for GABA in shaping the topography of functional connectivity and activity. This study explored the effects of pharmacologically blocking the reuptake of GABA (increasing local concentrations) using the GABA transporter 1 (GAT1) blocker, tiagabine (15 mg). In a placebo-controlled crossover design, we collected resting magnetoencephalography (MEG) recordings from 15 healthy individuals prior to, and at 1-, 3- and 5- hours post, administration of tiagabine and placebo. We quantified whole brain activity and functional connectivity in discrete frequency bands. Drug-by-session (2 × 4) analysis of variance in connectivity revealed interaction and main effects. Post-hoc permutation testing of each post-drug recording vs. respective pre-drug baseline revealed consistent reductions of a bilateral occipital network spanning theta, alpha and beta frequencies, across 1- 3- and 5- hour recordings following tiagabine only. The same analysis applied to activity revealed significant increases across frontal regions, coupled with reductions in posterior regions, across delta, theta, alpha and beta frequencies. Crucially, the spatial distribution of tiagabine-induced changes overlap with group-averaged maps of the distribution of GABA_A receptors, from flumazenil (FMZ-V_T) PET, demonstrating a link between GABA availability, GABA_A receptor distribution, and low-frequency network oscillations. Our results indicate that the relationship between PET receptor distributions and MEG effects warrants further exploration, since elucidating the nature of this relationship may uncover electrophysiologically-derived maps of oscillatory activity as sensitive, time-resolved, and targeted receptor-mapping tools for pharmacological imaging.

Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli : A mathematical and numerical study

In this paper, we investigate the dynamics of a neuron-glia cell system and the underlying mechanism for the occurrence of seizures. For our mathematical and numerical investigation of the cell model we will use bifurcation analysis and some computational methods. It turns out that an increase of the potassium concentration in the reservoir is one trigger for seizures and is related to a torus bifurcation. In addition, we will study potassium dynamics of the model by considering a reduced version and we will show how both mechanisms are linked to each other. Moreover, the reduction of the potassium leak current will also induce seizures. Our study will show that an enhancement of the extracellular potassium concentration, which influences the Nernst potential of the potassium current, may lead to seizures. Furthermore, we will show that an external forcing term (e.g. electroshocks as unidirectional rectangular pulses also known as electroconvulsive therapy) will establish seizures similar to the unforced system with the increased extracellular potassium concentration. To this end, we describe the unidirectional rectangular pulses as an autonomous system of ordinary differential equations. These approaches will explain the appearance of seizures in the cellular model. Moreover, seizures, as they are measured by electroencephalography (EEG), spread on the macro-scale (cm). Therefore, we extend the cell model with a suitable homogenised monodomain model, propose a set of (numerical) experiment to complement the bifurcation analysis performed on the single-cell model. Based on these experiments, we introduce a bidomain model for a more realistic modelling of white and grey matter of the brain. Performing similar (numerical) experiment as for the monodomain model leads to a suitable comparison of both models. The individual cell model, with its seizures explained in terms of a torus bifurcation, extends directly to corresponding results in both the monodomain and bidomain models where the neural firing spreads almost synchronous through the domain as fast traveling waves, for physiologically relevant paramenters.

Phase response theory explains cluster formation in sparsely but strongly connected inhibitory neural networks and effects of jitter due to sparse connectivity

We show how to predict whether a neural network will exhibit global synchrony (a one-cluster state) or a two-cluster state based on the assumption of pulsatile coupling and critically dependent upon the phase response curve (PRC) generated by the appropriate perturbation from a partner cluster. Our results hold for a monotonically increasing (meaning longer delays as the phase increases) PRC, which likely characterizes inhibitory fast-spiking basket and cortical low-threshold-spiking interneurons in response to strong inhibition. Conduction delays stabilize synchrony for this PRC shape, whereas they destroy two-cluster states, the former by avoiding a destabilizing discontinuity and the latter by approaching it. With conduction delays, stronger coupling strength can promote a one-cluster state, so the weak coupling limit is not applicable here. We show how jitter can destabilize global synchrony but not a two-cluster state. Local stability of global synchrony in an all-to-all network does not guarantee that global synchrony can be observed in an appropriately scaled sparsely connected network; the basin of attraction can be inferred from the PRC and must be sufficiently large. Two-cluster synchrony is not obviously different from one-cluster synchrony in the presence of noise and may be the actual substrate for oscillations observed in the local field potential (LFP) and the electroencephalogram (EEG) in situations where global synchrony is not possible. Transitions between cluster states may change the frequency of the rhythms observed in the LFP or EEG. Transitions between cluster states within an inhibitory subnetwork may allow more effective recruitment of pyramidal neurons into the network rhythm. NEW & NOTEWORTHY We show that jitter induced by sparse connectivity can destabilize global synchrony but not a two-cluster state with two smaller clusters firing alternately. On the other hand, conduction delays stabilize synchrony and destroy two-cluster states. These results hold if each cluster exhibits a phase response curve similar to one that characterizes fast-spiking basket and cortical low-threshold-spiking cells for strong inhibition. Either a two-cluster or a one-cluster state might provide the oscillatory substrate for neural computations.

Dichotomous Dynamics in E-I Networks with Strongly and Weakly Intra-connected Inhibitory Neurons

The interconnectivity between excitatory and inhibitory neural networks informs mechanisms by which rhythmic bursts of excitatory activity can be produced in the brain. One such mechanism, Pyramidal Interneuron Network Gamma (PING), relies primarily upon reciprocal connectivity between the excitatory and inhibitory networks, while also including intra-connectivity of inhibitory cells. The causal relationship between excitatory activity and the subsequent burst of inhibitory activity is of paramount importance to the mechanism and has been well studied. However, the role of the intra-connectivity of the inhibitory network, while important for PING, has not been studied in detail, as most analyses of PING simply assume that inhibitory intra-connectivity is strong enough to suppress subsequent firing following the initial inhibitory burst. In this paper we investigate the role that the strength of inhibitory intra-connectivity plays in determining the dynamics of PING-style networks. We show that networks with weak inhibitory intra-connectivity exhibit variations in burst dynamics of both the excitatory and inhibitory cells that are not obtained with strong inhibitory intra-connectivity. Networks with weak inhibitory intra-connectivity exhibit excitatory rhythmic bursts with weak excitatory-to-inhibitory synapses for which classical PING networks would show no rhythmic activity. Additionally, variations in dynamics of these networks as the excitatory-to-inhibitory synaptic weight increases illustrates the important role that consistent pattern formation in the inhibitory cells serves in maintaining organized and periodic excitatory bursts. Finally, motivated by these results and the known diversity of interneurons, we show that a PING-style network with two inhibitory subnetworks, one strongly intra-connected and one weakly intra-connected, exhibits organized and periodic excitatory activity over a larger parameter regime than networks with a homogeneous inhibitory population. Taken together, these results serve to better articulate the role of inhibitory intra-connectivity in generating PING-like rhythms, while also revealing how heterogeneity amongst inhibitory synapses might make such rhythms more robust to a variety of network parameters.

On Rhythms in Neuronal Networks with Recurrent Excitation

We investigate rhythms in networks of neurons with recurrent excitation, that is, with excitatory cells exciting each other. Recurrent excitation can sustain activity even when the cells in the network are driven below threshold, too weak to fire on their own. This sort of "reverberating" activity is often thought to be the basis of working memory. Recurrent excitation can also lead to "runaway" transitions, sudden transitions to high-frequency firing; this may be related to epileptic seizures. Not all fundamental questions about these phenomena have been answered with clarity in the literature. We focus on three questions here: (1) How much recurrent excitation is needed to sustain reverberating activity? How does the answer depend on parameters? (2) Is there a positive minimum frequency of reverberating activity, a positive "onset frequency"? How does it depend on parameters? (3) When do runaway transitions occur? For reduced models, we give mathematical answers to these questions. We also examine computationally to which extent our findings are reflected in the behavior of biophysically more realistic model networks. Our main results can be summarized as follows. (1) Reverberating activity can be fueled by extremely weak slow recurrent excitation, but only by sufficiently strong fast recurrent excitation. (2) The onset of reverberating activity, as recurrent excitation is strengthened or external drive is raised, occurs at a positive frequency. It is faster when the external drive is weaker (and the recurrent excitation stronger). It is slower when the recurrent excitation has a longer decay time constant. (3) Runaway transitions occur only with fast, not with slow, recurrent excitation. We also demonstrate that the relation between reverberating activity fueled by recurrent excitation and runaway transitions can be visualized in an instructive way by a (generalized) cusp catastrophe surface.

Theta-Gamma Coding Meets Communication-through-Coherence: Neuronal Oscillatory Multiplexing Theories Reconciled

Several theories have been advanced to explain how cross-frequency coupling, the interaction of neuronal oscillations at different frequencies, could enable item multiplexing in neural systems. The communication-through-coherence theory proposes that phase-matching of gamma oscillations between areas enables selective processing of a single item at a time, and a later refinement of the theory includes a theta-frequency oscillation that provides a periodic reset of the system. Alternatively, the theta-gamma neural code theory proposes that a sequence of items is processed, one per gamma cycle, and that this sequence is repeated or updated across theta cycles. In short, both theories serve to segregate representations via the temporal domain, but differ on the number of objects concurrently represented. In this study, we set out to test whether each of these theories is actually physiologically plausible, by implementing them within a single model inspired by physiological data. Using a spiking network model of visual processing, we show that each of these theories is physiologically plausible and computationally useful. Both theories were implemented within a single network architecture, with two areas connected in a feedforward manner, and gamma oscillations generated by feedback inhibition within areas. Simply increasing the amplitude of global inhibition in the lower area, equivalent to an increase in the spatial scope of the gamma oscillation, yielded a switch from one mode to the other. Thus, these different processing modes may co-exist in the brain, enabling dynamic switching between exploratory and selective modes of attention.

There is a growing consensus that neuronal oscillations constitute a fundamental computational mechanism in the brain. Beyond this, recent experimental evidence has highlighted interactions between oscillations at high and low frequencies (e.g. gamma oscillations, 40–80 Hz, are modulated by theta oscillations, 4–10 Hz), and two major theories have developed regarding the functional role of this kind of cross-frequency coupling. Here, we present a computational modelling study of these theories with strong implications for biological studies. Firstly, we demonstrate for the first time that each of these theories is physiologically plausible, in that they can be implemented in a spiking network model with parameters guided by experimental data. Secondly, we show that they are each computationally useful, able to overcome a feature-binding ambiguity in a presented stimulus. Finally, we implement both theories within a single network model, and find that only a single parameter change is required to switch between the two processing states. This leads to the exciting new proposal that both theories may be correct, both implemented in the brain, with dynamic switching between modes according to processing and attentional requirements.

Interplay of orientation selectivity and the power of low- and high-gamma bands in the cat primary visual cortex

Gamma oscillations are ubiquitous in brain and are believed to be inevitable for information processing in brain. Here, we report that distinct bands (low, 30-40Hz and high gamma, 60-80Hz) of stimulus-triggered gamma oscillations are systematically linked to the orientation selectivity index (OSI) of neurons in the cat primary visual cortex. The gamma-power is high for the highly selective neurons in the low-gamma band, whereas it is high for the broadly selective neurons in the high-gamma band. We suggest that the low-gamma band is principally implicated in feed-forward excitatory flow, whereas the high-gamma band governs the flow of this excitation.

Cooperation and competition of gamma oscillation mechanisms

Oscillations of neuronal activity in different frequency ranges are thought to reflect important aspects of cortical network dynamics. Here we investigate how various mechanisms that contribute to oscillations in neuronal networks may interact. We focus on networks with inhibitory, excitatory, and electrical synapses, where the subnetwork of inhibitory interneurons alone can generate interneuron gamma (ING) oscillations and the interactions between interneurons and pyramidal cells allow for pyramidal-interneuron gamma (PING) oscillations. What type of oscillation will such a network generate? We find that ING and PING oscillations compete: The mechanism generating the higher oscillation frequency "wins"; it determines the frequency of the network oscillation and suppresses the other mechanism. For type I interneurons, the network oscillation frequency is equal to or slightly above the higher of the ING and PING frequencies in corresponding reduced networks that can generate only either of them; if the interneurons belong to the type II class, it is in between. In contrast to ING and PING, oscillations mediated by gap junctions and oscillations mediated by inhibitory synapses may cooperate or compete, depending on the type (I or II) of interneurons and the strengths of the electrical and chemical synapses. We support our computer simulations by a theoretical model that allows a full theoretical analysis of the main results. Our study suggests experimental approaches to deciding to what extent oscillatory activity in networks of interacting excitatory and inhibitory neurons is dominated by ING or PING oscillations and of which class the participating interneurons are.

Coherent and intermittent ensemble oscillations emerge from networks of irregular spiking neurons

Local field potential (LFP) recordings from spatially distant cortical circuits reveal episodes of coherent gamma oscillations that are intermittent, and of variable peak frequency and duration. Concurrently, single neuron spiking remains largely irregular and of low rate. The underlying potential mechanisms of this emergent network activity have long been debated. Here we reproduce such intermittent ensemble oscillations in a model network, consisting of excitatory and inhibitory model neurons with the characteristics of regular-spiking (RS) pyramidal neurons, and fast-spiking (FS) and low-threshold spiking (LTS) interneurons. We find that fluctuations in the external inputs trigger reciprocally connected and irregularly spiking RS and FS neurons in episodes of ensemble oscillations, which are terminated by the recruitment of the LTS population with concurrent accumulation of inhibitory conductance in both RS and FS neurons. The model qualitatively reproduces experimentally observed phase drift, oscillation episode duration distributions, variation in the peak frequency, and the concurrent irregular single-neuron spiking at low rate. Furthermore, consistent with previous experimental studies using optogenetic manipulation, periodic activation of FS, but not RS, model neurons causes enhancement of gamma oscillations. In addition, increasing the coupling between two model networks from low to high reveals a transition from independent intermittent oscillations to coherent intermittent oscillations. In conclusion, the model network suggests biologically plausible mechanisms for the generation of episodes of coherent intermittent ensemble oscillations with irregular spiking neurons in cortical circuits.