Frequency control in synchronized networks of inhibitory neurons

Gamma oscillatory complexity conveys behavioral information in hippocampal networks

The hippocampus and entorhinal cortex exhibit rich oscillatory patterns critical for cognitive functions. In the hippocampal region CA1, specific gamma-frequency oscillations, timed at different phases of the ongoing theta rhythm, are hypothesized to facilitate the integration of information from varied sources and contribute to distinct cognitive processes. Here, we show that gamma elements -a multidimensional characterization of transient gamma oscillatory episodes- occur at any frequency or phase relative to the ongoing theta rhythm across all CA1 layers in male mice. Despite their low power and stochastic-like nature, individual gamma elements still carry behavior-related information and computational modeling suggests that they reflect neuronal firing. Our findings challenge the idea of rigid gamma sub-bands, showing that behavior shapes ensembles of irregular gamma elements that evolve with learning and depend on hippocampal layers. Widespread gamma diversity, beyond randomness, may thus reflect complexity, likely functional but invisible to classic average-based analyses.

Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain

Neurons in the brain are wired into adaptive networks that exhibit collective dynamics as diverse as scale-specific oscillations and scale-free neuronal avalanches. Although existing models account for oscillations and avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically or intractable to infer from data rigorously. Here we propose a feedback-driven Ising-like class of neural networks that captures avalanches and oscillations simultaneously and quantitatively. In the simplest yet fully microscopic model version, we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations to collective behaviors of extreme events and neuronal avalanches. Importantly, the inferred parameters indicate that the co-existence of scale-specific (oscillations) and scale-free (avalanches) dynamics occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations.

Local inhibition in a model of the indirect pathway globus pallidus network slows and deregularizes background firing, but sharpens and synchronizes responses to striatal input

The external segment of globus pallidus (GPe) is a network of oscillatory neurons connected by inhibitory synapses. We studied the intrinsic dynamic and the response to a shared brief inhibitory stimulus in a model GPe network. Individual neurons were simulated using a phase resetting model based on measurements from mouse GPe neurons studied in slices. The neurons showed a broad heterogeneity in their firing rates and in the shapes and sizes of their phase resetting curves. Connectivity in the network was set to match experimental measurements. We generated statistically equivalent neuron heterogeneity in a small-world model, in which 99% of connections were made with near neighbors and 1% at random, and in a model with entirely random connectivity. In both networks, the resting activity was slowed and made more irregular by the local inhibition, but it did not show any periodic pattern. Cross-correlations among neuron pairs were limited to directly connected neurons. When stimulated by a shared inhibitory input, the individual neuron responses separated into two groups: one with a short and stereotyped period of inhibition followed by a transient increase in firing probability, and the other responding with a sustained inhibition. Despite differences in firing rate, the responses of the first group of neurons were of fixed duration and were synchronized across cells.

Differential Contributions of Inhibitory Subnetwork to Visual Cortical Modulations Identified via Computational Model of Working Memory

Extrastriate visual neurons show no firing rate change during a working memory (WM) task in the absence of sensory input, but both αβ oscillations and spike phase locking are enhanced, as is the gain of sensory responses. This lack of change in firing rate is at odds with many models of WM, or attentional modulation of sensory networks. In this article we devised a computational model in which this constellation of results can be accounted for via selective activation of inhibitory subnetworks by a top-down working memory signal. We confirmed the model prediction of selective inhibitory activation by segmenting cells in the experimental neural data into putative excitatory and inhibitory cells. We further found that this inhibitory activation plays a dual role in influencing excitatory cells: it both modulates the inhibitory tone of the network, which underlies the enhanced sensory gain, and also produces strong spike-phase entrainment to emergent network oscillations. Using a phase oscillator model we were able to show that inhibitory tone is principally modulated through inhibitory network gain saturation, while the phase-dependent efficacy of inhibitory currents drives the phase locking modulation. The dual contributions of the inhibitory subnetwork to oscillatory and non-oscillatory modulations of neural activity provides two distinct ways for WM to recruit sensory areas, and has relevance to theories of cortical communication.

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.

Emergence of global synchronization in directed excitatory networks of type I neurons

The collective behaviour of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (PRC) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus is delivered to that neuron. The neuronal PRCs can be classified as having either purely positive values (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that feedforward loop motifs favour synchronization of type I excitatory and inhibitory neurons, while feedback loop motifs destroy their synchronization tendency. Moreover, large directed networks, either without feedback motifs or with many of them, have been constructed from the same undirected backbones, and a high synchronization level is observed for directed acyclic graphs with type I neurons. It has been shown that, the synchronizability of type I neurons depends on both the directionality of the network connectivity and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs.

A biophysical model of striatal microcircuits suggests gamma and beta oscillations interleaved at delta/theta frequencies mediate periodicity in motor control

Striatal oscillatory activity is associated with movement, reward, and decision-making, and observed in several interacting frequency bands. Local field potential recordings in rodent striatum show dopamine- and reward-dependent transitions between two states: a "spontaneous" state involving β (∼15-30 Hz) and low γ (∼40-60 Hz), and a state involving θ (∼4-8 Hz) and high γ (∼60-100 Hz) in response to dopaminergic agonism and reward. The mechanisms underlying these rhythmic dynamics, their interactions, and their functional consequences are not well understood. In this paper, we propose a biophysical model of striatal microcircuits that comprehensively describes the generation and interaction of these rhythms, as well as their modulation by dopamine. Building on previous modeling and experimental work suggesting that striatal projection neurons (SPNs) are capable of generating β oscillations, we show that networks of striatal fast-spiking interneurons (FSIs) are capable of generating δ/θ (ie, 2 to 6 Hz) and γ rhythms. Under simulated low dopaminergic tone our model FSI network produces low γ band oscillations, while under high dopaminergic tone the FSI network produces high γ band activity nested within a δ/θ oscillation. SPN networks produce β rhythms in both conditions, but under high dopaminergic tone, this β oscillation is interrupted by δ/θ-periodic bursts of γ-frequency FSI inhibition. Thus, in the high dopamine state, packets of FSI γ and SPN β alternate at a δ/θ timescale. In addition to a mechanistic explanation for previously observed rhythmic interactions and transitions, our model suggests a hypothesis as to how the relationship between dopamine and rhythmicity impacts motor function. We hypothesize that high dopamine-induced periodic FSI γ-rhythmic inhibition enables switching between β-rhythmic SPN cell assemblies representing the currently active motor program, and thus that dopamine facilitates movement in part by allowing for rapid, periodic shifts in motor program execution.

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Recent experimental literature has revealed that GABAergic interneurons exhibit increased activity prior to seizure onset, alongside additional evidence that such activity is synchronous and may arise abruptly. These findings have led some to hypothesize that this interneuronal activity may serve a causal role in driving the sudden change in brain activity that heralds seizure onset. However, the mechanisms predisposing an inhibitory network toward increased activity, specifically prior to ictogenesis, without a permanent change to inputs to the system remain unknown. We address this question by comparing simulated inhibitory networks containing control interneurons and networks containing hyperexcitable interneurons modeled to mimic treatment with 4-Aminopyridine (4-AP), an agent commonly used to model seizures in vivo and in vitro. Our in silico study demonstrates that model inhibitory networks with 4-AP interneurons are more prone than their control counterparts to exist in a bistable state in which asynchronously firing networks can abruptly transition into synchrony driven by a brief perturbation. This transition into synchrony brings about a corresponding increase in overall firing rate. We further show that perturbations driving this transition could arise in vivo from background excitatory synaptic activity in the cortex. Thus, we propose that bistability explains the increase in interneuron activity observed experimentally prior to seizure via a transition from incoherent to coherent dynamics. Moreover, bistability explains why inhibitory networks containing hyperexcitable interneurons are more vulnerable to this change in dynamics, and how such networks can undergo a transition without a permanent change in the drive. We note that while our comparisons are between networks of control and ictogenic neurons, the conclusions drawn specifically relate to the unusual dynamics that arise prior to seizure, and not seizure onset itself. However, providing a mechanistic explanation for this phenomenon specifically in a pro-ictogenic setting generates experimentally testable hypotheses regarding the role of inhibitory neurons in pre-ictal neural dynamics, and motivates further computational research into mechanisms underlying a newly hypothesized multi-step pathway to seizure initiated by inhibition.

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.

Electrical coupling between hippocampal neurons: contrasting roles of principal cell gap junctions and interneuron gap junctions

There is considerable experimental evidence, anatomical and physiological, that gap junctions exist in the hippocampus. Electrical coupling through these gap junctions may be divided into three types: between principal neurons, between interneurons and at mixed chemical (glutamatergic)/electrical synapses. An approach, combining in vitro experimental with modeling techniques, sheds some light on the functional consequences of electrical coupling, for network oscillations and for seizures. Additionally, in vivo experiments, using mouse connexin knockouts, suggest that the presence of electrical coupling is important for optimal performance on selected behavioral tasks; however, the interpretation of such data, in cellular terms, has so far proven difficult. Given that invertebrate central pattern generators so often depend on both chemical and electrical synapses, our hypothesis is that hippocampus-mediated and -influenced behaviors will act likewise. Experiments, likely hard ones, will be required to test this intuition.

Synchrony and so much more: Diverse roles for electrical synapses in neural circuits

Electrical synapses are neuronal gap junctions that are ubiquitous across brain regions and species. The biophysical properties of most electrical synapses are relatively simple-transcellular channels allow nearly ohmic, bidirectional flow of ionic current. Yet these connections can play remarkably diverse roles in different neural circuit contexts. Recent findings illustrate how electrical synapses may excite or inhibit, synchronize or desynchronize, augment or diminish rhythms, phase-shift, detect coincidences, enhance signals relative to noise, adapt, and interact with nonlinear membrane and transmitter-release mechanisms. Most of these functions are likely to be widespread in central nervous systems. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 77: 610-624, 2017.

Globally attracting synchrony in a network of oscillators with all-to-all inhibitory pulse coupling

The synchronization tendencies of networks of oscillators have been studied intensely. We assume a network of all-to-all pulse-coupled oscillators in which the effect of a pulse is independent of the number of oscillators that simultaneously emit a pulse and the normalized delay (the phase resetting) is a monotonically increasing function of oscillator phase with the slope everywhere less than 1 and a value greater than 2φ-1, where φ is the normalized phase. Order switching cannot occur; the only possible solutions are globally attracting synchrony and cluster solutions with a fixed firing order. For small conduction delays, we prove the former stable and all other possible attractors nonexistent due to the destabilizing discontinuity of the phase resetting at a phase of 0.

Intrinsic Cellular Properties and Connectivity Density Determine Variable Clustering Patterns in Randomly Connected Inhibitory Neural Networks

The plethora of inhibitory interneurons in the hippocampus and cortex play a pivotal role in generating rhythmic activity by clustering and synchronizing cell firing. Results of our simulations demonstrate that both the intrinsic cellular properties of neurons and the degree of network connectivity affect the characteristics of clustered dynamics exhibited in randomly connected, heterogeneous inhibitory networks. We quantify intrinsic cellular properties by the neuron's current-frequency relation (IF curve) and Phase Response Curve (PRC), a measure of how perturbations given at various phases of a neurons firing cycle affect subsequent spike timing. We analyze network bursting properties of networks of neurons with Type I or Type II properties in both excitability and PRC profile; Type I PRCs strictly show phase advances and IF curves that exhibit frequencies arbitrarily close to zero at firing threshold while Type II PRCs display both phase advances and delays and IF curves that have a non-zero frequency at threshold. Type II neurons whose properties arise with or without an M-type adaptation current are considered. We analyze network dynamics under different levels of cellular heterogeneity and as intrinsic cellular firing frequency and the time scale of decay of synaptic inhibition are varied. Many of the dynamics exhibited by these networks diverge from the predictions of the interneuron network gamma (ING) mechanism, as well as from results in all-to-all connected networks. Our results show that randomly connected networks of Type I neurons synchronize into a single cluster of active neurons while networks of Type II neurons organize into two mutually exclusive clusters segregated by the cells' intrinsic firing frequencies. Networks of Type II neurons containing the adaptation current behave similarly to networks of either Type I or Type II neurons depending on network parameters; however, the adaptation current creates differences in the cluster dynamics compared to those in networks of Type I or Type II neurons. To understand these results, we compute neuronal PRCs calculated with a perturbation matching the profile of the synaptic current in our networks. Differences in profiles of these PRCs across the different neuron types reveal mechanisms underlying the divergent network dynamics.

Identifying Anatomical Origins of Coexisting Oscillations in the Cortical Microcircuit

Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a close-to-irregular fashion at low rates. Using a combination of mean-field and linear response theory we predict the spectra generated in a layered microcircuit model of V1, composed of leaky integrate-and-fire neurons and based on connectivity compiled from anatomical and electrophysiological studies. The model exhibits low- and high-γ oscillations visible in all populations. Since locally generated frequencies are imposed onto other populations, the origin of the oscillations cannot be deduced from the spectra. We develop an universally applicable systematic approach that identifies the anatomical circuits underlying the generation of oscillations in a given network. Based on a theoretical reduction of the dynamics, we derive a sensitivity measure resulting in a frequency-dependent connectivity map that reveals connections crucial for the peak amplitude and frequency of the observed oscillations and identifies the minimal circuit generating a given frequency. The low-γ peak turns out to be generated in a sub-circuit located in layer 2/3 and 4, while the high-γ peak emerges from the inter-neurons in layer 4. Connections within and onto layer 5 are found to regulate slow rate fluctuations. We further demonstrate how small perturbations of the crucial connections have significant impact on the population spectra, while the impairment of other connections leaves the dynamics on the population level unaltered. The study uncovers connections where mechanisms controlling the spectra of the cortical microcircuit are most effective.

Recordings of brain activity show multiple coexisting oscillations. The generation of these oscillations has so far only been investigated in generic one- and two-population networks, neglecting their embedment into larger systems. We introduce a method that determines the mechanisms and sub-circuits generating oscillations in structured spiking networks. Analyzing a multi-layered model of the cortical microcircuit, we trace back characteristic oscillations to experimentally observed connectivity patterns. The approach exposes the influence of individual connections on frequency and amplitude of these oscillations and therefore reveals locations, where biological mechanisms controlling oscillations and experimental manipulations have the largest impact. The new analytical tool replaces parameter scans in computationally expensive models, guides circuit design, and can be employed to validate connectivity data.

Hippocampal CA1 Ripples as Inhibitory Transients

Memories are stored and consolidated as a result of a dialogue between the hippocampus and cortex during sleep. Neurons active during behavior reactivate in both structures during sleep, in conjunction with characteristic brain oscillations that may form the neural substrate of memory consolidation. In the hippocampus, replay occurs within sharp wave-ripples: short bouts of high-frequency activity in area CA1 caused by excitatory activation from area CA3. In this work, we develop a computational model of ripple generation, motivated by in vivo rat data showing that ripples have a broad frequency distribution, exponential inter-arrival times and yet highly non-variable durations. Our study predicts that ripples are not persistent oscillations but result from a transient network behavior, induced by input from CA3, in which the high frequency synchronous firing of perisomatic interneurons does not depend on the time scale of synaptic inhibition. We found that noise-induced loss of synchrony among CA1 interneurons dynamically constrains individual ripple duration. Our study proposes a novel mechanism of hippocampal ripple generation consistent with a broad range of experimental data, and highlights the role of noise in regulating the duration of input-driven oscillatory spiking in an inhibitory network.

Our memories are consolidated while we sleep through a bidirectional exchange of information between two brain areas called cortex and hippocampus. Neurons that were active in behavioral tasks reactivate again in both structures during sleep in a process of linking and modifying memories from the short term storage of the hippocampus to permanent storage in the neocortex. This process occurs mainly during short oscillatory hippocampal electrical events called sharp wave-ripples. We propose a novel mechanism of ripple generation consistent with a wide range of experimental data, to explain how hippocampal network properties shape ripple frequency and duration. Understanding the neuronal mechanism underlying ripples is crucial to explaining how the interaction between hippocampus and cortex during sleep enables memory consolidation.

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.

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.

Fluctuations in oscillation frequency control spike timing and coordinate neural networks

Neuroscience research spans multiple spatiotemporal scales, from subsecond dynamics of individual neurons to the slow coordination of billions of neurons during resting state and sleep. Here it is shown that a single functional principle-temporal fluctuations in oscillation peak frequency ("frequency sliding")-can be used as a common analysis approach to bridge multiple scales within neuroscience. Frequency sliding is demonstrated in simulated neural networks and in human EEG data during a visual task. Simulations of biophysically detailed neuron models show that frequency sliding modulates spike threshold and timing variability, as well as coincidence detection. Finally, human resting-state EEG data demonstrate that frequency sliding occurs endogenously and can be used to identify large-scale networks. Frequency sliding appears to be a general principle that regulates brain function on multiple spatial and temporal scales, from modulating spike timing in individual neurons to coordinating large-scale brain networks during cognition and resting state.

Population dynamics of the modified theta model: macroscopic phase reduction and bifurcation analysis link microscopic neuronal interactions to macroscopic gamma oscillation

Gamma oscillations of the local field potential are organized by collective dynamics of numerous neurons and have many functional roles in cognition and/or attention. To mathematically and physiologically analyse relationships between individual inhibitory neurons and macroscopic oscillations, we derive a modification of the theta model, which possesses voltage-dependent dynamics with appropriate synaptic interactions. Bifurcation analysis of the corresponding Fokker-Planck equation (FPE) enables us to consider how synaptic interactions organize collective oscillations. We also develop the adjoint method (infinitesimal phase resetting curve) for simultaneous equations consisting of ordinary differential equations representing synaptic dynamics and a partial differential equation for determining the probability distribution of the membrane potential. This method provides a macroscopic phase response function (PRF), which gives insights into how it is modulated by external perturbation or internal changes of parameters. We investigate the effects of synaptic time constants and shunting inhibition on these gamma oscillations. The sensitivity of rising and decaying time constants is analysed in the oscillatory parameter regions; we find that these sensitivities are not largely dependent on rate of synaptic coupling but, rather, on current and noise intensity. Analyses of shunting inhibition reveal that it can affect both promotion and elimination of gamma oscillations. When the macroscopic oscillation is far from the bifurcation, shunting promotes the gamma oscillations and the PRF becomes flatter as the reversal potential of the synapse increases, indicating the insensitivity of gamma oscillations to perturbations. By contrast, when the macroscopic oscillation is near the bifurcation, shunting eliminates gamma oscillations and a stable firing state appears. More interestingly, under appropriate balance of parameters, two branches of bifurcation are found in our analysis of the FPE. In this case, shunting inhibition can effect both promotion and elimination of the gamma oscillation depending only on the reversal potential.

Distinguishing mechanisms of gamma frequency oscillations in human current source signals using a computational model of a laminar neocortical network

Gamma frequency rhythms have been implicated in numerous studies for their role in healthy and abnormal brain function. The frequency band has been described to encompass as broad a range as 30-150 Hz. Crucial to understanding the role of gamma in brain function is an identification of the underlying neural mechanisms, which is particularly difficult in the absence of invasive recordings in macroscopic human signals such as those from magnetoencephalography (MEG) and electroencephalography (EEG). Here, we studied features of current dipole (CD) signals from two distinct mechanisms of gamma generation, using a computational model of a laminar cortical circuit designed specifically to simulate CDs in a biophysically principled manner (Jones et al., 2007, 2009). We simulated spiking pyramidal interneuronal gamma (PING) whose period is regulated by the decay time constant of GABAA-mediated synaptic inhibition and also subthreshold gamma driven by gamma-periodic exogenous excitatory synaptic drive. Our model predicts distinguishable CD features created by spiking PING compared to subthreshold driven gamma that can help to disambiguate mechanisms of gamma oscillations in human signals. We found that gamma rhythms in neocortical layer 5 can obscure a simultaneous, independent gamma in layer 2/3. Further, we arrived at a novel interpretation of the origin of high gamma frequency rhythms (100-150 Hz), showing that they emerged from a specific temporal feature of CDs associated with single cycles of PING activity and did not reflect a separate rhythmic process. Last we show that the emergence of observable subthreshold gamma required highly coherent exogenous drive. Our results are the first to demonstrate features of gamma oscillations in human current source signals that distinguish cellular and circuit level mechanisms of these rhythms and may help to guide understanding of their functional role.

Altered neural connectivity in excitatory and inhibitory cortical circuits in autism

Converging evidence from diverse studies suggests that atypical brain connectivity in autism affects in distinct ways short- and long-range cortical pathways, disrupting neural communication and the balance of excitation and inhibition. This hypothesis is based mostly on functional non-invasive studies that show atypical synchronization and connectivity patterns between cortical areas in children and adults with autism. Indirect methods to study the course and integrity of major brain pathways at low resolution show changes in fractional anisotropy (FA) or diffusivity of the white matter in autism. Findings in post-mortem brains of adults with autism provide evidence of changes in the fine structure of axons below prefrontal cortices, which communicate over short- or long-range pathways with other cortices and subcortical structures. Here we focus on evidence of cellular and axon features that likely underlie the changes in short- and long-range communication in autism. We review recent findings of changes in the shape, thickness, and volume of brain areas, cytoarchitecture, neuronal morphology, cellular elements, and structural and neurochemical features of individual axons in the white matter, where pathology is evident even in gross images. We relate cellular and molecular features to imaging and genetic studies that highlight a variety of polymorphisms and epigenetic factors that primarily affect neurite growth and synapse formation and function in autism. We report preliminary findings of changes in autism in the ratio of distinct types of inhibitory neurons in prefrontal cortex, known to shape network dynamics and the balance of excitation and inhibition. Finally we present a model that synthesizes diverse findings by relating them to developmental events, with a goal to identify common processes that perturb development in autism and affect neural communication, reflected in altered patterns of attention, social interactions, and language.

Active decorrelation in the basal ganglia

The cytoarchitecturally-homogeneous appearance of the globus pallidus, subthalamic nucleus and substantia nigra has long been said to imply a high degree of afferent convergence and sharing of inputs by nearby neurons. Moreover, axon collaterals of neurons in the external segment of the globus pallidus and the substantia nigra pars reticulata arborize locally and make inhibitory synapses on other cells of the same type. These features suggest that the connectivity of the basal ganglia may impose spike-time correlations among the cells, and it has been puzzling that experimental studies have failed to demonstrate such correlations. One possible solution arises from studies of firing patterns in basal ganglia cells, which reveal that they are nearly all pacemaker cells. Their high rate of firing does not depend on synaptic excitation, but they fire irregularly because a dense barrage of synaptic inputs normally perturbs the timing of their autonomous activity. Theoretical and computational studies show that the responses of repetitively-firing neurons to shared input or mutual synaptic coupling often defy classical intuitions about temporal synaptic integration. The patterns of spike-timing among such neurons depend on the ionic mechanism of pacemaking, the level of background uncorrelated cellular and synaptic noise, and the firing rates of the neurons, as well as the properties of their synaptic connections. Application of these concepts to the basal ganglia circuitry suggests that the connectivity and physiology of these nuclei may be configured to prevent the establishment of permanent spike-timing relationships between neurons. The development of highly synchronous oscillatory patterns of activity in Parkinson's disease may result from the loss of pacemaking by some basal ganglia neurons, and accompanying breakdown of the mechanisms responsible for active decorrelation.

Membrane properties and the balance between excitation and inhibition control gamma-frequency oscillations arising from feedback inhibition

Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30-80 Hz gamma rhythm in which network oscillations arise through 'stochastic synchrony' capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs.

Modeling sharp wave-ripple complexes through a CA3-CA1 network model with chemical synapses

The hippocampus, and particularly the CA3 and CA1 areas, exhibit a variety of oscillatory rhythms that span frequencies from the slow theta range (4-10 Hz) up to fast ripples (200 Hz). Various computational models of different complexities have been developed in an effort to simulate such population oscillations. Nevertheless the mechanism that underlies the so called Sharp Wave-Ripple complex (SPWR), observed in extracellular recordings in CA1, still remains elusive. We present here, the combination of two simple but realistic models of the rat CA3 and CA1 areas, connected together in a feedforward scheme mimicking Schaffer collaterals. Both network models are computationally simple one-dimensional arrays of excitatory and inhibitory populations interacting only via fast chemical synapses. Connectivity schemes and postsynaptic potentials are based on physiological data, yielding a realistic network topology. The CA3 model exhibits quasi-synchronous population bursts, which give rise to sharp wave-like deep depolarizations in the CA1 dendritic layer accompanied by transient field oscillations at ≈ 150-200 Hz in the somatic layer. The frequency and synchrony of these oscillations is based on interneuronal activity and fast-decaying recurrent inhibition in CA1. Pyramidal cell spikes are sparse and come from a subset of cells receiving stronger than average excitatory input from CA3. The model is shown to accurately reproduce a large number of basic characteristics of SPWRs and yields a new mechanism for the generation of ripples, offering an interpretation to a range of neurophysiological observations, such as the ripple disruption by halothane and the selective firing of pyramidal cells during ripples, which may have implications for memory consolidation during SPWRs.

Network with shunting synapses as a non-linear frequency modulator

The role of 'noisy' excitation in synchronizing interneuron networks with shunting synapses was studied. The excitatory input was simulated as a Poisson pattern of presynaptic conductance with varying frequencies and amplitudes. We find that higher excitation frequencies induce stronger synchronisation of the network. Within the range of 1-10000 Hz, only frequencies between 20 Hz and 200 Hz affected network synchronisation. No detectable network synchronisation was found at excitation frequencies below 20 Hz, and the network's synchronisation was either almost independent of the external input or falling down to zero when the input frequency was greater than 200 Hz. Thus the network transformed the input signals with frequencies above 20 Hz into output signals with the network's synchronisation frequency. The network's synchronisation frequency in our model ranged from 20 to 68 Hz depending on the frequency of the excitatory input. We conclude that a network of interconnected interneurons is capable of converting an asynchronous excitatory input into a synchronous inhibitory output as a frequency amplifier with the amplification coefficient dependent on the number of converging excitatory inputs. Another important result of our work revealed that the external frequency may affect, in opposite ways, the frequency of the network with shunting synapses depending on the excitatory synaptic conductance and the magnitude of leak conductance.

Control of neural synchrony using channelrhodopsin-2: a computational study

In this paper, we present an optical stimulation based approach to induce 1:1 in-phase synchrony in a network of coupled interneurons wherein each interneuron expresses the light sensitive protein channelrhodopsin-2 (ChR2). We begin with a transition rate model for the channel kinetics of ChR2 in response to light stimulation. We then define "functional optical time response curve (fOTRC)" as a measure of the response of a periodically firing interneuron (transfected with ChR2 ion channel) to a periodic light pulse stimulation. We specifically consider the case of unidirectionally coupled (UCI) network and propose an open loop control architecture that uses light as an actuation signal to induce 1:1 in-phase synchrony in the UCI network. Using general properties of the spike time response curves (STRCs) for Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and fOTRC, we estimate the (open loop) optimal actuation signal parameters required to induce 1:1 in-phase synchrony. We then propose a closed loop controller architecture and a controller algorithm to robustly sustain stable 1:1 in-phase synchrony in the presence of unknown deviations in the network parameters. Finally, we test the performance of this closed-loop controller in a network of mutually coupled (MCI) interneurons.

Cascade-induced synchrony in stochastically driven neuronal networks

Perfect spike-to-spike synchrony is studied in all-to-all coupled networks of identical excitatory, current-based, integrate-and-fire neurons with delta-impulse coupling currents and Poisson spike-train external drive. This synchrony is induced by repeated cascading "total firing events," during which all neurons fire at once. In this regime, the network exhibits nearly periodic dynamics, switching between an effectively uncoupled state and a cascade-coupled total firing state. The probability of cascading total firing events occurring in the network is computed through a combinatorial analysis conditioned upon the random time when the first neuron fires and using the probability distribution of the subthreshold membrane potentials for the remaining neurons in the network. The probability distribution of the former is found from a first-passage-time problem described by a Fokker-Planck equation, which is solved analytically via an eigenfunction expansion. The latter is found using a central limit argument via a calculation of the cumulants of a single neuronal voltage. The influence of additional physiological effects that hinder or eliminate cascade-induced synchrony are also investigated. Conditions for the validity of the approximations made in the analytical derivations are discussed and verified via direct numerical simulations.

Searching for autocoherence in the cortical network with a time-frequency analysis of the local field potential

Gamma-band peaks in the power spectrum of local field potentials (LFP) are found in multiple brain regions. It has been theorized that gamma oscillations may serve as a 'clock' signal for the purposes of precise temporal encoding of information and 'binding' of stimulus features across regions of the brain. Neurons in model networks may exhibit periodic spike firing or synchronized membrane potentials that give rise to a gamma-band oscillation that could operate as a 'clock'. The phase of the oscillation in such models is conserved over the length of the stimulus. We define these types of oscillations to be 'autocoherent'. We investigated the hypothesis that autocoherent oscillations are the basis of the experimentally observed gamma-band peaks: the autocoherent oscillator (ACO) hypothesis. To test the ACO hypothesis, we developed a new technique to analyze the autocoherence of a time-varying signal. This analysis used the continuous Gabor transform to examine the time evolution of the phase of each frequency component in the power spectrum. Using this analysis method, we formulated a statistical test to compare the ACO hypothesis with measurements of the LFP in macaque primary visual cortex, V1. The experimental data were not consistent with the ACO hypothesis. Gamma-band activity recorded in V1 did not have the properties of a 'clock' signal during visual stimulation. We propose instead that the source of the gamma-band spectral peak is the resonant V1 network driven by random inputs.

Synchrony with shunting inhibition in a feedforward inhibitory network

Recent experiments have shown that GABA(A) receptor mediated inhibition in adult hippocampus is shunting rather than hyperpolarizing. Simulation studies of realistic interneuron networks with strong shunting inhibition have been demonstrated to exhibit robust gamma band (20-80 Hz) synchrony in the presence of heterogeneity in the intrinsic firing rates of individual neurons in the network. In order to begin to understand how shunting can contribute to network synchrony in the presence of heterogeneity, we develop a general theoretical framework using spike time response curves (STRC's) to study patterns of synchrony in a simple network of two unidirectionally coupled interneurons (UCI network) interacting through a shunting synapse in the presence of heterogeneity. We derive an approximate discrete map to analyze the dynamics of synchronous states in the UCI network by taking into account the nonlinear contributions of the higher order STRC terms. We show how the approximate discrete map can be used to successfully predict the domain of synchronous 1:1 phase locked state in the UCI network. The discrete map also allows us to determine the conditions under which the two interneurons can exhibit in-phase synchrony. We conclude by demonstrating how the information from the study of the discrete map for the dynamics of the UCI network can give us valuable insight into the degree of synchrony in a larger feed-forward network of heterogeneous interneurons.

Cellular dynamical mechanisms for encoding the time and place of events along spatiotemporal trajectories in episodic memory

Understanding the mechanisms of episodic memory requires linking behavioral data and lesion effects to data on the dynamics of cellular membrane potentials and population interactions within brain regions. Linking behavior to specific membrane channels and neurochemicals has implications for therapeutic applications. Lesions of the hippocampus, entorhinal cortex and subcortical nuclei impair episodic memory function in humans and animals, and unit recording data from these regions in behaving animals indicate episodic memory processes. Intracellular recording in these regions demonstrates specific cellular properties including resonance, membrane potential oscillations and bistable persistent spiking that could underlie the encoding and retrieval of episodic trajectories. A model presented here shows how intrinsic dynamical properties of neurons could mediate the encoding of episodic memories as complex spatiotemporal trajectories. The dynamics of neurons allow encoding and retrieval of unique episodic trajectories in multiple continuous dimensions including temporal intervals, personal location, the spatial coordinates and sensory features of perceived objects and generated actions, and associations between these elements. The model also addresses how cellular dynamics could underlie unit firing data suggesting mechanisms for coding continuous dimensions of space, time, sensation and action.

Mechanisms of coherent activity in hippocampus and entorhinal cortex

We consider the mechanisms by which coherent activity arises in the hippocampus and entorhinal cortex, two brain areas that are associated with episodic memory in humans and similar forms of memory in animal models. Our approach relies upon techniques from the theory of coupled oscillators. We show that such techniques can yield accurate predictions of the behavior of synaptically coupled neurons. Future work will expand upon these techniques to include real-world complications that better mimic the in vivo state.

Inhibitory network of spiking neurons may express a sharp peak of synchrony at low frequency band

Spike synchronization remains an important issue in neuroscience, and inhibitory networks are the best candidates to provide such synchrony. Increasing evidence indicates that in many brain area inhibitory interneurons of similar properties make reciprocal connections. We found that a hybrid, as well as model network, consisting of two reciprocally inhibitory spiking neurons may express a peak of synchronization in a narrow range of low spiking frequencies in addition to classically described plateau of synchrony at a wide range of high frequencies. Occurrence of the low frequency peak of synchrony requires a moderate-to-strong inhibitory coupling and relatively fast synapses. This novel possibility of synchronization in a narrow range of network parameters may have an important implication in discrimination and encoding of signals of precise intensity, as well as in altering network ability to process information.

A phase code for memory could arise from circuit mechanisms in entorhinal cortex

Neurophysiological data reveals intrinsic cellular properties that suggest how entorhinal cortical neurons could code memory by the phase of their firing. Potential cellular mechanisms for this phase coding in models of entorhinal function are reviewed. This mechanism for phase coding provides a substrate for modeling the responses of entorhinal grid cells, as well as the replay of neural spiking activity during waking and sleep. Efforts to implement these abstract models in more detailed biophysical compartmental simulations raise specific issues that could be addressed in larger scale population models incorporating mechanisms of inhibition.

Gamma Oscillations in a Nonlinear Regime: A Minimal Model Approach Using Heterogeneous Integrate-and-Fire Networks

Fast oscillations and in particular gamma-band oscillation (20–80 Hz) are commonly observed during brain function and are at the center of several neural processing theories. In many cases, mathematical analysis of fast oscillations in neural networks has been focused on the transition between irregular and oscillatory firing viewed as an instability of the asynchronous activity. But in fact, brain slice experiments as well as detailed simulations of biological neural networks have produced a large corpus of results concerning the properties of fully developed oscillations that are far from this transition point. We propose here a mathematical approach to deal with nonlinear oscillations in a network of heterogeneous or noisy integrate-and-fire neurons connected by strong inhibition. This approach involves limited mathematical complexity and gives a good sense of the oscillation mechanism, making it an interesting tool to understand fast rhythmic activity in simulated or biological neural networks. A surprising result of our approach is that under some conditions, a change of the strength of inhibition only weakly influences the period of the oscillation. This is in contrast to standard theoretical and experimental models of interneuron network gamma oscillations (ING), where frequency tightly depends on inhibition strength, but it is similar to observations made in some in vitro preparations in the hippocampus and the olfactory bulb and in some detailed network models. This result is explained by the phenomenon of suppression that is known to occur in strongly coupled oscillating inhibitory networks but had not yet been related to the behavior of oscillation frequency.

A model of stimulus-specific neural assemblies in the insect antennal lobe

It has been proposed that synchronized neural assemblies in the antennal lobe of insects encode the identity of olfactory stimuli. In response to an odor, some projection neurons exhibit synchronous firing, phase-locked to the oscillations of the field potential, whereas others do not. Experimental data indicate that neural synchronization and field oscillations are induced by fast GABA(A)-type inhibition, but it remains unclear how desynchronization occurs. We hypothesize that slow inhibition plays a key role in desynchronizing projection neurons. Because synaptic noise is believed to be the dominant factor that limits neuronal reliability, we consider a computational model of the antennal lobe in which a population of oscillatory neurons interact through unreliable GABA(A) and GABA(B) inhibitory synapses. From theoretical analysis and extensive computer simulations, we show that transmission failures at slow GABA(B) synapses make the neural response unpredictable. Depending on the balance between GABA(A) and GABA(B) inputs, particular neurons may either synchronize or desynchronize. These findings suggest a wiring scheme that triggers stimulus-specific synchronized assemblies. Inhibitory connections are set by Hebbian learning and selectively activated by stimulus patterns to form a spiking associative memory whose storage capacity is comparable to that of classical binary-coded models. We conclude that fast inhibition acts in concert with slow inhibition to reformat the glomerular input into odor-specific synchronized neural assemblies.

High-frequency network oscillations in cerebellar cortex

Both cerebellum and neocortex receive input from the somatosensory system. Interaction between these regions has been proposed to underpin the correct selection and execution of motor commands, but it is not clear how such interactions occur. In neocortex, inputs give rise to population rhythms, providing a spatiotemporal coding strategy for inputs and consequent outputs. Here, we show that similar patterns of rhythm generation occur in cerebellum during nicotinic receptor subtype activation. Both gamma oscillations (30-80 Hz) and very fast oscillations (VFOs, 80-160 Hz) were generated by intrinsic cerebellar cortical circuitry in the absence of functional glutamatergic connections. As in neocortex, gamma rhythms were dependent on GABA(A) receptor-mediated inhibition, whereas VFOs required only nonsynaptically connected intercellular networks. The ability of cerebellar cortex to generate population rhythms within the same frequency bands as neocortex suggests that they act as a common spatiotemporal code within which corticocerebellar dialog may occur.

Correlation-induced synchronization of oscillations in olfactory bulb neurons

Oscillations are a common feature of odor-evoked and spontaneous activity in the olfactory system in vivo and in vitro and are thought to play an important role in information processing and memory in a variety of brain areas. Theoretical and experimental studies have described several mechanisms by which oscillations can be generated and synchronized. Here, we investigate the hypothesis that correlated noisy inputs are able to generate synchronous oscillations in olfactory bulb mitral cells in vitro. We consider several alternative mechanisms and conclude that olfactory bulb synchronous oscillations are likely to arise because of the response of uncoupled oscillating neurons to aperiodic but correlated inputs. This mechanism has been described theoretically, but we provide the first experimental evidence that such a mechanism may underlie synchronization in real neurons. In physiological experiments, we show that this mechanism can generate gamma-band oscillations in populations of olfactory bulb mitral cells. This mechanism synchronizes oscillatory firing by using shared fast fluctuations in stochastic inputs across neurons, without requiring any synaptic or electrical coupling. We discuss the properties and limitations of synchronization by this mechanism and suggest that it may underlie fast oscillations in many brain areas.

Phase resetting and coupling of noisy neural oscillators

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations.

Inhibitory coupling specifically generates emergent gamma oscillations in diverse cell types

Networks of inhibitory neurons regulate synchrony during many physiological and pathological oscillations. To explore how these effects depend on cellular, network, and synaptic factors, we developed and validated a semisynthetic inhibitory network that approximates simultaneous activity in multiple neurons by using consecutive responses from single cells. We recorded from three types of neurons, each of which forms interconnected networks in vivo, but has unique intrinsic properties. In all three cell types, fast inhibitory coupling generated emergent gamma oscillations. By contrast, inhibitory coupling desynchronized slower, spindle-frequency responses specifically in thalamic reticular neurons. The emergent gamma-frequency synchronization was also specific to tonic input and did not occur during responses to phasic inputs. These results illustrate how particular features of inhibitory networks (e.g., cell or input type) contribute to their synchronizing or desynchronizing functions. They also demonstrate phenomena (emergent gamma oscillations) that occur robustly in multiple cell types and may thus be a generic feature of inhibitory networks throughout the brain.

Oscillatory Synchronization Requires Precise and Balanced Feedback Inhibition in a Model of the Insect Antennal Lobe

In the insect olfactory system, odor-evoked transient synchronization of antennal lobe (AL) projection neurons (PNs) is phase-locked to the oscillations of the local field potential. Sensory information is contained in the spatiotemporal synchronization pattern formed by the identities of the phase-locked PNs. This article investigates the role of feedback inhibition from the local neurons (LNs) in this coding. First, experimental biological results are reproduced with a reduced computational spiking neural network model of the AL. Second, the low complexity of the model leads to a mathematical analysis from which a lower bound on the phase-locking probability is derived. Parameters involved in the bound indicate that PN phase locking depends not only on the number of LN-evoked inhibitory postsynaptic potentials (IPSPs) previously received, but also on their temporal jitter. If the inhibition received by a PN at the current oscillatory cycle is both perfectly balanced (i.e., equal to the mean inhibitory drive) and precise (without any jitter), then the PN will be phase-locked at the next oscillatory cycle with probability one.

Detailed and abstract phase-locked attractor network models of early olfactory systems

Across species, primary olfactory centers show similarities both in their cellular organization and their types of olfactory information coding. In this article, we consider an excitatory-inhibitory spiking neural network as a model of early olfactory systems (antennal lobe for insects, olfactory bulb for vertebrates). In line with experimental results, we show that, in our network, odor-like stimuli evoke synchronization of excitatory cells, phase-locked to the oscillations of the local field potential. As revealed by a mathematical analysis, the phase-locking probability of excitatory cells is given by an inverted-U function and the firing probability of inhibitory cells is well described by a sigmoid function. These neural response functions are used to reduce the spiking model to a more abstract model with discrete-time dynamics (oscillatory cycles) and binary-state neurons (phase-locked or not). An iterative map, built for explaining the dynamics of the binary model, reveals that it converges to fixed point attractors similar to those obtained with the spiking model. This result is consistent with odor-specific attractors found in recent experimental studies. It also provides insights for designing bio-inspired olfactory associative memories applicable for data analysis in electronic noses.

Slow and Fast Inhibition and an H-Current Interact to Create a Theta Rhythm in a Model of CA1 Interneuron Network

The oriens-lacunosum moleculare (O-LM) subtype of interneuron is a key component in the formation of the theta rhythm (8–12 Hz) in the hippocampus. It is known that the CA1 region of the hippocampus can produce theta rhythms in vitro with all ionotropic excitation blocked, but the mechanisms by which this rhythmicity happens were previously unknown. Here we present a model suggesting that individual O-LM cells, by themselves, are capable of producing a single-cell theta-frequency firing, but coupled O-LM cells are not capable of producing a coherent population theta. By including in the model fast-spiking (FS) interneurons, which give rise to IPSPs that decay faster than those of the O-LM cells, coherent theta rhythms are produced. The inhibition to O-LM cells from the FS cells synchronizes the O-LM cells, but only when the FS cells themselves fire at a theta frequency. Reciprocal connections from the O-LM cells to the FS cells serve to parse the FS cell firing into theta bursts, which can then synchronize the O-LM cells. A component of the model O-LM cell critical to the synchronization mechanism is the hyperpolarization-activated h-current. The model can robustly reproduce relative phases of theta frequency activity in O-LM and FS cells.

Chaos synchronization in gap-junction-coupled neurons

Depending on temperature, the modified Hodgkin-Huxley (MHH) equations exhibit a variety of dynamical behaviors, including intrinsic chaotic firing. We analyze synchronization in a large ensemble of MHH neurons that are interconnected with gap junctions. By evaluating tangential Lyapunov exponents we clarify whether the synchronous state of neurons is chaotic or periodic. Then, we evaluate transversal Lyapunov exponents to elucidate if this synchronous state is stable against infinitesimal perturbations. Our analysis elucidates that with weak gap junctions, the stability of the synchronization of MHH neurons shows rather complicated changes with temperature. We, however, find that with strong gap junctions, the synchronous state is stable over the wide range of temperature irrespective of whether synchronous state is chaotic or periodic. It turns out that strong gap junctions realize the robust synchronization mechanism, which well explains synchronization in interneurons in the real nervous system.

Beyond Two-Cell Networks: Experimental Measurement of Neuronal Responses to Multiple Synaptic Inputs

Oscillations of large populations of neurons are thought to be important in the normal functioning of the brain. We have used phase response curve (PRC) methods to characterize the dynamics of single neurons and predict population dynamics. Our past experimental work was limited to special circumstances (e.g., 2-cell networks of periodically firing neurons). Here, we explore the feasibility of extending our methods to predict the synchronization properties of stellate cells (SCs) in the rat entorhinal cortex under broader conditions. In particular, we test the hypothesis that PRCs in SCs scale linearly with changes in synaptic amplitude, and measure how well responses to Poisson process-driven inputs can be predicted in terms of PRCs. Although we see nonlinear responses to excitatory and inhibitory inputs, we find that models based on weak coupling account for scaling and Poisson process-driven inputs reasonably accurately.

Background gamma rhythmicity and attention in cortical local circuits: a computational study

We describe a simple computational model, based on generic features of cortical local circuits, that links cholinergic neuromodulation, gamma rhythmicity, and attentional selection. We propose that cholinergic modulation, by reducing adaptation currents in principal cells, induces a transition from asynchronous spontaneous activity to a "background" gamma rhythm (resembling the persistent gamma rhythms evoked in vitro by cholinergic agonists) in which individual principal cells participate infrequently and irregularly. We suggest that such rhythms accompany states of preparatory attention or vigilance and report simulations demonstrating that their presence can amplify stimulus-specific responses and enhance stimulus competition within a local circuit.