Toggling between gamma-frequency activity and suppression of cell assemblies

Shunting Inhibition Improves Synchronization in Heterogeneous Inhibitory Interneuronal Networks with Type 1 Excitability Whereas Hyperpolarizing Inhibition Is Better for Type 2 Excitability

All-to-all homogeneous networks of inhibitory neurons synchronize completely under the right conditions; however, many modeling studies have shown that biological levels of heterogeneity disrupt synchrony. Our fundamental scientific question is “how can neurons maintain partial synchrony in the presence of heterogeneity and noise?” A particular subset of strongly interconnected interneurons, the PV+ fast-spiking (FS) basket neurons, are strongly implicated in γ oscillations and in phase locking of nested γ oscillations to theta. Their excitability type apparently varies between brain regions: in CA1 and the dentate gyrus they have type 1 excitability, meaning that they can fire arbitrarily slowly, whereas in the striatum and cortex they have type 2 excitability, meaning that there is a frequency thresh old below which they cannot sustain repetitive firing. We constrained the models to study the effect of excitability type (more precisely bifurcation type) in isolation from all other factors. We use sparsely connected, heterogeneous, noisy networks with synaptic delays to show that synchronization properties, namely the resistance to suppression and the strength of theta phase to γ amplitude coupling, are strongly dependent on the pairing of excitability type with the type of inhibition. Shunting inhibition performs better for type 1 and hyperpolarizing inhibition for type 2. γ Oscillations and their nesting within theta oscillations are thought to subserve cognitive functions like memory encoding and recall; therefore, it is important to understand the contribution of intrinsic properties to these rhythms.

Neural gain control measured through cortical gamma oscillations is associated with sensory sensitivity

Gamma oscillations facilitate information processing by shaping the excitatory input/output of neuronal populations. Recent studies in humans and nonhuman primates have shown that strong excitatory drive to the visual cortex leads to suppression of induced gamma oscillations, which may reflect inhibitory-based gain control of network excitation. The efficiency of the gain control measured through gamma oscillations may in turn affect sensory sensitivity in everyday life. To test this prediction, we assessed the link between self-reported sensitivity and changes in magneto-encephalographic gamma oscillations as a function of motion velocity of high-contrast visual gratings. The induced gamma oscillations increased in frequency and decreased in power with increasing stimulation intensity. As expected, weaker suppression of the gamma response correlated with sensory hypersensitivity. Robustness of this result was confirmed by its replication in the two samples: neurotypical subjects and people with autism, who had generally elevated sensory sensitivity. We conclude that intensity-related suppression of gamma response is a promising biomarker of homeostatic control of the excitation-inhibition balance in the visual cortex.

Hippocampal network oscillations at the interplay between innate anxiety and learned fear

The hippocampus plays a central role as a hub for episodic memory and as an integrator of multimodal sensory information in time and space. Thereby, it critically determines contextual setting and specificity of episodic memories. It is also a key site for the control of innate anxiety states and involved in psychiatric diseases with heightened anxiety and generalized fear memory such as post-traumatic stress disorder (PTSD). Expression of both innate "unlearned" anxiety and "learned" fear requires contextual processing and engagement of a brain-wide network including the hippocampus together with the amygdala and medial prefrontal cortex. Strikingly, the hippocampus is also the site of emergence of oscillatory rhythms that coordinate information processing and filtering in this network. Here, we review data on how the hippocampal network oscillations and their coordination with amygdalar and prefrontal oscillations are engaged in innate threat evaluation. We further explore how such innate oscillatory communication might have an impact on contextualization and specificity of "learned" fear. We illustrate the partial overlap of fear and anxiety networks that are built by the hippocampus in conjunction with amygdala and prefrontal cortex. We further propose that (mal)-adaptive interplay via (dis)-balanced oscillatory communication between the anxiety network and the fear network may determine the strength of fear memories and their resistance to extinction.

Analyzing the competition of gamma rhythms with delayed pulse-coupled oscillators in phase representation

Networks of neurons can generate oscillatory activity as result of various types of coupling that lead to synchronization. A prominent type of oscillatory activity is gamma (30-80 Hz) rhythms, which may play an important role in neuronal information processing. Two mechanisms have mainly been proposed for their generation: (1) interneuron network gamma (ING) and (2) pyramidal-interneuron network gamma (PING). In vitro and in vivo experiments have shown that both mechanisms can exist in the same cortical circuits. This raises the questions: How do ING and PING interact when both can in principle occur? Are the network dynamics a superposition, or do ING and PING interact in a nonlinear way and if so, how? In this article, we first generalize the phase representation for nonlinear one-dimensional pulse coupled oscillators as introduced by Mirollo and Strogatz to type II oscillators whose phase response curve (PRC) has zero crossings. We then give a full theoretical analysis for the regular gamma-like oscillations of simple networks consisting of two neural oscillators, an "E neuron" mimicking a synchronized group of pyramidal cells, and an "I neuron" representing such a group of interneurons. Motivated by experimental findings, we choose the E neuron to have a type I PRC [leaky integrate-and-fire (LIF) neuron], while the I neuron has either a type I or type II PRC (LIF or "sine" neuron). The phase representation allows us to define in a simple manner scenarios of interaction between the two neurons, which are independent of the types and the details of the neuron models. The presence of delay in the couplings leads to an increased number of scenarios relevant for gamma-like oscillatory patterns. We analytically derive the set of such scenarios and describe their occurrence in terms of parameter values such as synaptic connectivity and drive to the E and I neurons. The networks can be tuned to oscillate in an ING or PING mode. We focus particularly on the transition region where both rhythms compete to govern the network dynamics and compare with oscillations in reduced networks, which can only generate either ING or PING. Our analytically derived oscillation frequency diagrams indicate that except for small coexistence regions, the networks generate ING if the oscillation frequency of the reduced ING network exceeds that of the reduced PING network, and vice versa. For networks with the LIF I neuron, the network oscillation frequency slightly exceeds the frequencies of corresponding reduced networks, while it lies between them for networks with the sine I neuron. In networks oscillating in ING (PING) mode, the oscillation frequency responds faster to changes in the drive to the I (E) neuron than to changes in the drive to the E (I) neuron. This finding suggests a method to analyze which mechanism governs an observed network oscillation. Notably, also when the network operates in ING mode, the E neuron can spike before the I neuron such that relative spike times of the pyramidal cells and the interneurons alone are not conclusive for distinguishing ING and PING.

Input-dependent modulation of MEG gamma oscillations reflects gain control in the visual cortex

Gamma-band oscillations arise from the interplay between neural excitation (E) and inhibition (I) and may provide a non-invasive window into the state of cortical circuitry. A bell-shaped modulation of gamma response power by increasing the intensity of sensory input was observed in animals and is thought to reflect neural gain control. Here we sought to find a similar input-output relationship in humans with MEG via modulating the intensity of a visual stimulation by changing the velocity/temporal-frequency of visual motion. In the first experiment, adult participants observed static and moving gratings. The frequency of the MEG gamma response monotonically increased with motion velocity whereas power followed a bell-shape. In the second experiment, on a large group of children and adults, we found that despite drastic developmental changes in frequency and power of gamma oscillations, the relative suppression at high motion velocities was scaled to the same range of values across the life-span. In light of animal and modeling studies, the modulation of gamma power and frequency at high stimulation intensities characterizes the capacity of inhibitory neurons to counterbalance increasing excitation in visual networks. Gamma suppression may thus provide a non-invasive measure of inhibitory-based gain control in the healthy and diseased brain.

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.

Resonant Interneurons Can Increase Robustness of Gamma Oscillations

Gamma oscillations are believed to play a critical role in in information processing, encoding, and retrieval. Inhibitory interneuronal network gamma (ING) oscillations may arise from a coupled oscillator mechanism in which individual neurons oscillate or from a population oscillator in which individual neurons fire sparsely and stochastically. All ING mechanisms, including the one proposed herein, rely on alternating waves of inhibition and windows of opportunity for spiking. The coupled oscillator model implemented with Wang-Buzsáki model neurons is not sufficiently robust to heterogeneity in excitatory drive, and therefore intrinsic frequency, to account for in vitro models of ING. Similarly, in a tightly synchronized regime, the stochastic population oscillator model is often characterized by sparse firing, whereas interneurons both in vivo and in vitro do not fire sparsely during gamma, but rather on average every other cycle. We substituted so-called resonator neural models, which exhibit class 2 excitability and postinhibitory rebound (PIR), for the integrators that are typically used. This results in much greater robustness to heterogeneity that actually increases as the average participation in spikes per cycle approximates physiological levels. Moreover, dynamic clamp experiments that show autapse-induced firing in entorhinal cortical interneurons support the idea that PIR can serve as a network gamma mechanism. Furthermore, parvalbumin-positive (PV(+)) cells were much more likely to display both PIR and autapse-induced firing than GAD2(+) cells, supporting the view that PV(+) fast-firing basket cells are more likely to exhibit class 2 excitability than other types of inhibitory interneurons.

SIGNIFICANCE STATEMENT

Gamma oscillations are believed to play a critical role in information processing, encoding, and retrieval. Networks of inhibitory interneurons are thought to be essential for these oscillations. We show that one class of interneurons with an abrupt onset of firing at a threshold frequency may allow more robust synchronization in the presence of noise and heterogeneity. The mechanism for this robustness depends on the intrinsic resonance at this threshold frequency. Moreover, we show experimentally the feasibility of the proposed mechanism and suggest a way to distinguish between this mechanism and another proposed mechanism: that of a stochastic population oscillator independent of the dynamics of individual neurons.

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.

For things needing your attention: the role of neocortical gamma in sensory perception

Two general classes of hypotheses for the role for gamma oscillations in sensation are those that predict gamma facilitates signal amplification through local synchronization of a distinct ensemble, and those that predict gamma modulates fine temporal relationships between neurons to represent information. Correlative evidence has been offered for and against these hypotheses. A recent study in which gamma was optogenetically entrained by driving fast-spiking interneurons showed enhanced sensory detection of harder-to-perceive stimuli, those that benefit most from attention, in agreement with the amplification hypotheses. These findings are supported by similar studies employing less specific optogenetic patterns or single neuron stimulation, but contrast with findings based on direct optogenetic stimulation of pyramidal neurons. Key next steps for this topic are described.

Interplay of intrinsic and synaptic conductances in the generation of high-frequency oscillations in interneuronal networks with irregular spiking

High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.

Neurons in the brain engage in collective oscillations at different frequencies. Gamma and high-gamma oscillations (30–100 Hz and higher) have been associated with cognitive functions, and are altered in psychiatric disorders such as schizophrenia and autism. Our understanding of how high-frequency oscillations are orchestrated in the brain is still limited, but it is necessary for the development of effective clinical approaches to the treatment of these disorders. Some neuron types exhibit dynamical properties that can favour synchronization. The theory of weakly coupled oscillators showed how the phase response of individual neurons can predict the patterns of phase relationships that are observed at the network level. However, neurons in vivo do not behave like regular oscillators, but fire irregularly in a regime dominated by fluctuations. Hence, which intrinsic dynamical properties matter for synchronization, and in which regime, is still an open question. Here, we show how single-cell damped subthreshold oscillations enhance synchrony in interneuronal networks by introducing a depolarizing component, mediated by post-inhibitory rebound, that is correlated among neurons due to common inhibitory input.

Neurosystems: brain rhythms and cognitive processing

Neuronal rhythms are ubiquitous features of brain dynamics, and are highly correlated with cognitive processing. However, the relationship between the physiological mechanisms producing these rhythms and the functions associated with the rhythms remains mysterious. This article investigates the contributions of rhythms to basic cognitive computations (such as filtering signals by coherence and/or frequency) and to major cognitive functions (such as attention and multi-modal coordination). We offer support to the premise that the physiology underlying brain rhythms plays an essential role in how these rhythms facilitate some cognitive operations.

Seizure-induced alterations in fast-spiking basket cell GABA currents modulate frequency and coherence of gamma oscillation in network simulations

Gamma frequency oscillations have been proposed to contribute to memory formation and retrieval. Fast-spiking basket cells (FS-BCs) are known to underlie development of gamma oscillations. Fast, high amplitude GABA synapses and gap junctions have been suggested to contribute to gamma oscillations in FS-BC networks. Recently, we identified that, apart from GABAergic synapses, FS-BCs in the hippocampal dentate gyrus have GABAergic currents mediated by extrasynaptic receptors. Our experimental studies demonstrated two specific changes in FS-BC GABA currents following experimental seizures [Yu et al., J. Neurophysiol. 109, 1746 (2013)]: increase in the magnitude of extrasynaptic (tonic) GABA currents and a depolarizing shift in GABA reversal potential (E(GABA)). Here, we use homogeneous networks of a biophysically based model of FS-BCs to examine how the presence of extrasynaptic GABA conductance (g(GABA-extra)) and experimentally identified, seizure-induced changes in g(GABA-extra) and E(GABA) influence network activity. Networks of FS-BCs interconnected by fast GABAergic synapses developed synchronous firing in the dentate gamma frequency range (40-100 Hz). Systematic investigation revealed that the biologically realistic range of 30 to 40 connections between FS-BCs resulted in greater coherence in the gamma frequency range when networks were activated by Poisson-distributed dendritic synaptic inputs rather than by homogeneous somatic current injections, which were balanced for FS-BC firing frequency in unconnected networks. Distance-dependent conduction delay enhanced coherence in networks with 30-40 FS-BC interconnections while inclusion of gap junctional conductance had a modest effect on coherence. In networks activated by somatic current injections resulting in heterogeneous FS-BC firing, increasing g(GABA-extra) reduced the frequency and coherence of FS-BC firing when E(GABA) was shunting (-74 mV), but failed to alter average FS-BC frequency when E(GABA) was depolarizing (-54 mV). When FS-BCs were activated by biologically based dendritic synaptic inputs, enhancing g(GABA-extra) reduced the frequency and coherence of FS-BC firing when E(GABA) was shunting and increased average FS-BC firing when E(GABA) was depolarizing. Shifting E(GABA) from shunting to depolarizing potentials consistently increased network frequency to and above high gamma frequencies (>80 Hz). Since gamma oscillations may contribute to learning and memory processing [Fell et al., Nat. Neurosci. 4, 1259 (2001); Jutras et al., J. Neurosci. 29, 12521 (2009); Wang, Physiol. Rev. 90, 1195 (2010)], our demonstration that network oscillations are modulated by extrasynaptic inhibition in FS-BCs suggests that neuroactive compounds that act on extrasynaptic GABA receptors could impact memory formation by modulating hippocampal gamma oscillations. The simulation results indicate that the depolarized FS-BC GABA reversal, observed after experimental seizures, together with enhanced spillover extrasynaptic GABA currents are likely to promote generation of focal high frequency activity associated with epileptic networks.