Minimal size of cell assemblies coordinated by gamma oscillations

Physiological features of parvalbumin-expressing GABAergic interneurons contributing to high-frequency oscillations in the cerebral cortex

Parvalbumin-expressing (PV+) inhibitory interneurons drive gamma oscillations (30-80 Hz), which underlie higher cognitive functions. In this review, we discuss two groups/aspects of fundamental properties of PV+ interneurons. In the first group (dubbed Before Axon), we list properties representing optimal synaptic integration in PV+ interneurons designed to support fast oscillations. For example: [i] Information can neither enter nor leave the neocortex without the engagement of fast PV+ -mediated inhibition; [ii] Voltage responses in PV+ interneuron dendrites integrate linearly to reduce impact of the fluctuations in the afferent drive; and [iii] Reversed somatodendritic Rm gradient accelerates the time courses of synaptic potentials arriving at the soma. In the second group (dubbed After Axon), we list morphological and biophysical properties responsible for (a) short synaptic delays, and (b) efficient postsynaptic outcomes. For example: [i] Fast-spiking ability that allows PV+ interneurons to outpace other cortical neurons (pyramidal neurons). [ii] Myelinated axon (which is only found in the PV+ subclass of interneurons) to secure fast-spiking at the initial axon segment; and [iii] Inhibitory autapses - autoinhibition, which assures brief biphasic voltage transients and supports postinhibitory rebounds. Recent advent of scientific tools, such as viral strategies to target PV cells and the ability to monitor PV cells via in vivo imaging during behavior, will aid in defining the role of PV cells in the CNS. Given the link between PV+ interneurons and cognition, in the future, it would be useful to carry out physiological recordings in the PV+ cell type selectively and characterize if and how psychiatric and neurological diseases affect initiation and propagation of electrical signals in this cortical sub-circuit. Voltage imaging may allow fast recordings of electrical signals from many PV+ interneurons simultaneously.

Uncorrelated bilateral cortical input becomes timed across hippocampal subfields for long waves whereas gamma waves are largely ipsilateral

The role of interhemispheric connections along successive segments of cortico-hippocampal circuits is poorly understood. We aimed to obtain a global picture of spontaneous transfer of activity during non-theta states across several nodes of the bilateral circuit in anesthetized rats. Spatial discrimination techniques applied to bilateral laminar field potentials (FP) across the CA1/Dentate Gyrus provided simultaneous left and right readouts in five FP generators that reflect activity in specific hippocampal afferents and associative pathways. We used a battery of correlation and coherence analyses to extract complementary aspects at different time scales and frequency bands. FP generators exhibited varying bilateral correlation that was high in CA1 and low in the Dentate Gyrus. The submillisecond delays indicate coordination but not support for synaptic dependence of one side on another. The time and frequency characteristics of bilateral coupling were specific to each generator. The Schaffer generator was strongly bilaterally coherent for both sharp waves and gamma waves, although the latter maintained poor amplitude co-variation. The lacunosum-moleculare generator was composed of up to three spatially overlapping activities, and globally maintained high bilateral coherence for long but not short (gamma) waves. These two CA1 generators showed no ipsilateral relationship in any frequency band. In the Dentate Gyrus, strong bilateral coherence was observed only for input from the medial entorhinal areas, while those from the lateral entorhinal areas were largely asymmetric, for both alpha and gamma waves. Granger causality testing showed strong bidirectional relationships between all homonymous bilateral generators except the lateral entorhinal input and a local generator in the Dentate Gyrus. It also revealed few significant relationships between ipsilateral generators, most notably the anticipation of lateral entorhinal cortex toward all others. Thus, with the notable exception of the lateral entorhinal areas, there is a marked interhemispheric coherence primarily for slow envelopes of activity, but not for pulse-like gamma waves, except in the Schafer segment. The results are consistent with essentially different streams of activity entering from and returning to the cortex on each side, with slow waves reflecting times of increased activity exchange between hemispheres and fast waves generally reflecting ipsilateral processing.

Approaches to characterizing oscillatory burst detection algorithms for electrophysiological recordings

BACKGROUND

Cognitive processes are associated with fast oscillations of the local field potential and electroencephalogram. There is a growing interest in targeting them because these are disrupted by aging and disease. This has proven challenging because they often occur as short-lasting bursts. Moreover, they are obscured by broad-band aperiodic activity reflecting other neural processes. These attributes have made it exceedingly difficult to develop analytical tools for estimating the reliability of detection methods.

NEW METHOD

To address this challenge, we developed an open-source toolkit with four processing steps, that can be tailored to specific brain states and individuals. First, the power spectrum is decomposed into periodic and aperiodic components, each of whose properties are estimated. Second, the properties of the transient oscillatory bursts that contribute to the periodic component are derived and optimized to account for contamination from the aperiodic component. Third, using the burst properties and aperiodic power spectrum, surrogate neural signals are synthesized that match the observed signal's spectrotemporal properties. Lastly, oscillatory burst detection algorithms run on the surrogate signals are subjected to a receiver operating characteristic analysis, providing insight into their performance.

RESULTS

The characterization algorithm extracted features of oscillatory bursts across multiple frequency bands and brain regions, allowing for recording-specific evaluation of detection performance. For our dataset, the optimal detection threshold for gamma bursts was found to be lower than the one commonly used.

COMPARISON WITH EXISTING METHODS

Existing methods characterize the power spectrum, while ours evaluates the detection of oscillatory bursts.

CONCLUSIONS

This pipeline facilitates the evaluation of thresholds for detection algorithms from individual recordings.

Optimal flickering light stimulation for entraining gamma rhythms in older adults

With aging, optimal parameters of flickering light stimulation (FLS) for gamma entrainment may change in the eyes and brain. We investigated the optimal FLS parameters for gamma entrainment in 35 cognitively normal old adults by comparing event-related synchronization (ERS) and spectral Granger causality (sGC) of entrained gamma rhythms between different luminance intensities, colors, and flickering frequencies of FLSs. ERS entrained by 700 cd/m² FLS and 32 Hz or 34 Hz FLSs was stronger than that entrained by 400 cd/m² at Pz (p < 0.01) and 38 Hz or 40 Hz FLSs, respectively, at both Pz (p < 0.05) and Fz (p < 0.01). Parieto-occipital-to-frontotemporal connectivities of gamma rhythm entrained by 700 cd/m² FLS and 32 Hz or 34 Hz FLSs were also stronger than those entrained by 400 cd/m² at Pz (p < 0.01) and 38 Hz or 40 Hz FLSs, respectively (p < 0.001). ERS and parieto-occipital-to-frontotemporal connectivities of entrained gamma rhythms did not show significant difference between white and red lights. Adverse effects were comparable between different parameters. In older adults, 700 cd/m² FLS at 32 Hz or 34 Hz can entrain a strong gamma rhythm in the whole brain with tolerable adverse effects.

Network resonance can be generated independently at distinct levels of neuronal organization

Resonance is defined as maximal response of a system to periodic inputs in a limited frequency band. Resonance may serve to optimize inter-neuronal communication, and has been observed at multiple levels of neuronal organization. However, it is unknown how neuronal resonance observed at the network level is generated and how network resonance depends on the properties of the network building blocks. Here, we first develop a metric for quantifying spike timing resonance in the presence of background noise, extending the notion of spiking resonance for in vivo experiments. Using conductance-based models, we find that network resonance can be inherited from resonances at other levels of organization, or be intrinsically generated by combining mechanisms across distinct levels. Resonance of membrane potential fluctuations, postsynaptic potentials, and single neuron spiking can each be generated independently of resonance at any other level and be propagated to the network level. At all levels of organization, interactions between processes that give rise to low- and high-pass filters generate the observed resonance. Intrinsic network resonance can be generated by the combination of filters belonging to different levels of organization. Inhibition-induced network resonance can emerge by inheritance from resonance of membrane potential fluctuations, and be sharpened by presynaptic high-pass filtering. Our results demonstrate a multiplicity of qualitatively different mechanisms that can generate resonance in neuronal systems, and provide analysis tools and a conceptual framework for the mechanistic investigation of network resonance in terms of circuit components, across levels of neuronal organization.

How one part of the brain responds to periodic input from another part depends on resonant circuit properties. Resonance is a basic property of physical systems, and has been experimentally observed at various levels of neuronal organization both in vitro and in vivo. Yet how resonance is generated in neuronal networks is largely unknown. In particular, whether resonance can be generated directly at the level of a network of spiking neurons remains to be determined. Using detailed biophysical modeling, we develop a conceptual framework according to which resonance at a given level of organization is generated by the interplay of low- and high-pass filters, implemented at either the same or across levels of neuronal organization. We tease apart representative, biophysically-plausible generative mechanisms of resonance at four different levels of organization: membrane potential fluctuations, single neuron spiking, synaptic transmission, and neuronal networks. We identify conditions under which resonance at one level can be inherited to another level of organization, provide conclusive evidence that resonance at each level can be generated without resonance at any other level, and describe a number of representative routes to network resonance. The proposed framework facilitates the investigation of resonance in neuronal systems.

Loss of neuronal heterogeneity in epileptogenic human tissue impairs network resilience to sudden changes in synchrony

A myriad of pathological changes associated with epilepsy can be recast as decreases in cell and circuit heterogeneity. We thus propose recontextualizing epileptogenesis as a process where reduction in cellular heterogeneity, in part, renders neural circuits less resilient to seizure. By comparing patch clamp recordings from human layer 5 (L5) cortical pyramidal neurons from epileptogenic and non-epileptogenic tissue, we demonstrate significantly decreased biophysical heterogeneity in seizure-generating areas. Implemented computationally, this renders model neural circuits prone to sudden transitions into synchronous states with increased firing activity, paralleling ictogenesis. This computational work also explains the surprising finding of significantly decreased excitability in the population-activation functions of neurons from epileptogenic tissue. Finally, mathematical analyses reveal a bifurcation structure arising only with low heterogeneity and associated with seizure-like dynamics. Taken together, this work provides experimental, computational, and mathematical support for the theory that ictogenic dynamics accompany a reduction in biophysical heterogeneity.

Synaptic Variability and Cortical Gamma Oscillation Power in Schizophrenia

OBJECTIVE

Cognitive impairments in schizophrenia are associated with lower gamma oscillation power in the prefrontal cortex (PFC). Gamma power depends in part on excitatory drive to fast-spiking parvalbumin interneurons (PVIs). Excitatory drive to cortical neurons varies in strength, which could affect how these neurons regulate network oscillations. The authors investigated whether variability in excitatory synaptic strength across PVIs could contribute to lower prefrontal gamma power in schizophrenia.

METHODS

In postmortem PFC from 20 matched pairs of comparison and schizophrenia subjects, levels of vesicular glutamate transporter 1 (VGlut1) and postsynaptic density 95 (PSD95) proteins were quantified to assess variability in excitatory synaptic strength across PVIs. A computational model network was then used to simulate how variability in excitatory synaptic strength across fast-spiking (a defining feature of PVIs) interneurons (FSIs) regulates gamma power.

RESULTS

The variability of VGlut1 and PSD95 levels at excitatory inputs across PVIs was larger in schizophrenia relative to comparison subjects. This alteration was not influenced by schizophrenia-associated comorbid factors, was not present in monkeys chronically exposed to antipsychotic medications, and was not present in calretinin interneurons. In the model network, variability in excitatory synaptic strength across FSIs regulated gamma power by affecting network synchrony. Finally, greater synaptic variability interacted synergistically with other synaptic alterations in schizophrenia (i.e., fewer excitatory inputs to FSIs and lower inhibitory strength from FSIs) to robustly reduce gamma power.

CONCLUSIONS

The study findings suggest that greater variability in excitatory synaptic strength across PVIs, in combination with other modest synaptic alterations in these neurons, can markedly lower PFC gamma power in schizophrenia.

From mechanisms to functions: The role of theta and gamma coherence in the intrahippocampal circuits

Brain rhythms are essential for information processing in neuronal networks. Oscillations recorded in different brain regions can be synchronized and have a constant phase difference, that is, they can be coherent. Coherence between local field potential (LFP) signals from different brain regions may be correlated with the performance of cognitive tasks, indicating that these regions of the brain are jointly involved in the information processing. Why does coherence occur and how is it related to the information transfer between different regions of the hippocampal formation? In this article, we discuss possible mechanisms of theta and gamma coherence and its role in the hippocampus-dependent attention and memory processes, since theta and gamma rhythms are most pronounced in these processes. We review in vivo studies of interactions between different regions of the hippocampal formation in theta and gamma frequency bands. The key propositions of the review are as follows: (1) coherence emerges from synchronous postsynaptic currents in principal neurons as a result of synchronization of neuronal spike activity; (2) the synchronization of neuronal spike patterns in two regions of the hippocampal formation can be realized through induction or resonance; (3) coherence at a specific time point reflects the transfer of information between the regions of the hippocampal formation; (4) the physiological roles of theta and gamma coherence are different due to their different functions and mechanisms of generation. All hippocampal neurons are involved in theta activity, and theta coherence arranges the firing order of principal neurons throughout the hippocampal formation. In contrast, gamma coherence reflects the coupling of active neuronal ensembles. Overall, the coherence of LFPs between different areas of the brain is an important physiological process based on the synchronized neuronal firing, and it is essential for cooperative information processing.

A Model of the CA1 Field Rhythms

We propose a model of the main rhythms in the hippocampal CA1 field: theta rhythm; slow, middle, and fast gamma rhythms; and ripple oscillations. We have based this on data obtained from animals behaving freely. We have considered the modes of neuronal discharges and the occurrence of local field potential oscillations in the theta and non-theta states at different inputs from the CA3 field, the medial entorhinal cortex, and the medial septum. In our work, we tried to reproduce the main experimental phenomena about rhythms in the CA1 field: the coupling of neurons to the phase of rhythms, cross-rhythm phase–phase coupling, and phase–amplitude coupling. Using computational experiments, we have proved the hypothesis that the descending phase of the theta rhythm in the CA1 field is formed by the input from the CA3 field via the Shaffer collaterals, and the ascending phase of the theta rhythm is formed by the IPSPs from CCK basket cells. The slow gamma rhythm is coupled to the descending phase of the theta rhythm, since it also depends on the arrival of the signal via the Shaffer collaterals. The middle gamma rhythm is formed by the EPSPs of the principal neurons of the third layer of the entorhinal cortex, corresponds to experimental data. We were able to unite in a single mathematical model several theoretical ideas about the mechanisms of rhythmic processes in the CA1 field of the hippocampus.

Temporal patterns of synchrony in a pyramidal-interneuron gamma (PING) network

Synchronization in neural systems plays an important role in many brain functions. Synchronization in the gamma frequency band (30-100 Hz) is involved in a variety of cognitive phenomena; abnormalities of the gamma synchronization are found in schizophrenia and autism spectrum disorder. Frequently, the strength of synchronization is not high, and synchronization is intermittent even on short time scales (few cycles of oscillations). That is, the network exhibits intervals of synchronization followed by intervals of desynchronization. Neural circuit dynamics may show different distributions of desynchronization durations even if the synchronization strength is fixed. We use a conductance-based neural network exhibiting pyramidal-interneuron gamma rhythm to study the temporal patterning of synchronized neural oscillations. We found that changes in the synaptic strength (as well as changes in the membrane kinetics) can alter the temporal patterning of synchrony. Moreover, we found that the changes in the temporal pattern of synchrony may be independent of the changes in the average synchrony strength. Even though the temporal patterning may vary, there is a tendency for dynamics with short (although potentially numerous) desynchronizations, similar to what was observed in experimental studies of neural synchronization in the brain. Recent studies suggested that the short desynchronizations dynamics may facilitate the formation and the breakup of transient neural assemblies. Thus, the results of this study suggest that changes of synaptic strength may alter the temporal patterning of the gamma synchronization as to make the neural networks more efficient in the formation of neural assemblies and the facilitation of cognitive phenomena.

The Generation and Modulation of Distinct Gamma Oscillations with Local, Horizontal, and Feedback Connections in the Primary Visual Cortex: A Model Study on Large-Scale Networks

Gamma oscillation (GAMMA) in the local field potential (LFP) is a synchronized activity commonly found in many brain regions, and it has been thought as a functional signature of network connectivity in the brain, which plays important roles in information processing. Studies have shown that the response property of GAMMA is related to neural interaction through local recurrent connections (RC), feed-forward (FF), and feedback (FB) connections. However, the relationship between GAMMA and long-range horizontal connections (HC) in the brain remains unclear. Here, we aimed to understand this question in a large-scale network model for the primary visual cortex (V1). We created a computational model composed of multiple excitatory and inhibitory units with biologically plausible connectivity patterns for RC, FF, FB, and HC in V1; then, we quantitated GAMMA in network models at different strength levels of HC and other connection types. Surprisingly, we found that HC and FB, the two types of large-scale connections, play very different roles in generating and modulating GAMMA. While both FB and HC modulate a fast gamma oscillation (around 50-60 Hz) generated by FF and RC, HC generates a new GAMMA oscillating around 30 Hz, whose power and peak frequency can also be modulated by FB. Furthermore, response properties of the two GAMMAs in a network with both HC and FB are different in a way that is highly consistent with a recent experimental finding for distinct GAMMAs in macaque V1. The results suggest that distinct GAMMAs are signatures for neural connections in different spatial scales and they might be related to different functions for information integration. Our study, for the first time, pinpoints the underlying circuits for distinct GAMMAs in a mechanistic model for macaque V1, which might provide a new framework to study multiple gamma oscillations in other cortical regions.

Empirically constrained network models for contrast-dependent modulation of gamma rhythm in V1

Gamma oscillations are thought to play a key role in neuronal network function and neuronal communication, yet the underlying generating mechanisms have not been fully elucidated to date. At least partly, this may be due to the fact that even in simple network models of interconnected inhibitory (I) and excitatory (E) neurons, many parameters remain unknown and are set based on practical considerations or by convention. Here, we mitigate this problem by requiring PING (Pyramidal Interneuron Network Gamma) models to simultaneously satisfy a broad set of criteria for realistic behaviour based on empirical data spanning both the single unit (spikes) and local population (LFP) levels while unknown parameters are varied. By doing so, we were able to constrain the parameter ranges and select empirically valid models. The derived model constraints implied weak rather than strong PING as the generating mechanism for gamma, connectivity between E and I neurons within specific bounds, and variations of the external input to E but not I neurons. Constrained models showed valid behaviours, including gamma frequency increases with contrast and power saturation or decay at high contrasts. Using an empirically-validated model we studied the route to gamma instability at high contrasts. This involved increased heterogeneity of E neurons with increasing input triggering a breakdown of I neuron pacemaker function. Further, we illustrate the model's capacity to resolve disputes in the literature concerning gamma oscillation properties and GABA conductance proxies. We propose that the models derived in our study will be useful for other modelling studies, and that our approach to the empirical constraining of PING models can be expanded when richer empirical datasets become available. As local gamma networks are the building blocks of larger networks that aim to understand complex cognition through their interactions, there is considerable value in improving our models of these building blocks.

Auditory Cortex Volume and Gamma Oscillation Abnormalities in Schizophrenia

We investigated whether the gray matter volume of primary auditory cortex (Heschl's gyrus [HG]) was associated with abnormal patterns of auditory γ activity in schizophrenia, namely impaired γ synchronization in the 40-Hz auditory steady-state response (ASSR) and increased spontaneous broadband γ power. (The γ data were previously reported in Hirano et al, JAMA Psychiatry, 2015;72:813-821). Participants were 24 healthy controls (HC) and 23 individuals with chronic schizophrenia (SZ). The ASSR was obtained from the electroencephalogram to click train stimulation at 20, 30, and 40 Hz rates. Dipole source localization of the ASSR was used to provide a spatial filter of auditory cortex activity, from which ASSR evoked power and phase locking factor (PLF), and induced γ power were computed. HG gray matter volume was derived from structural magnetic resonance imaging at 3 T with manually traced regions of interest. As expected, HG gray matter volume was reduced in SZ compared with HC. In SZ, left hemisphere ASSR PLF and induced γ power during the 40-Hz stimulation condition were positively and negatively correlated with left HG gray matter volume, respectively. These results provide evidence that cortical gray matter structure, possibly resulting from reduced synaptic connectivity at the microcircuit level, is related to impaired γ synchronization and increased spontaneous γ activity in schizophrenia.

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.

Relation between gamma oscillations and neuronal plasticity in the visual cortex

Learning is thought to be mediated by activity-dependent modification of neuronal interactions. To avoid maladaptive modifications of synaptic transmission by spurious activity, synaptic plasticity has to be gated. In the case of supervised learning, these gating functions are accomplished by reinforcement through value-assigning systems. Here we show that the dynamic state of local circuits correlates with the occurrence of activity-dependent long-term changes in neuronal response properties. We find that repeated visual stimuli induce long-term changes of orientation preference of neuronal populations in visual cortex if stimuli induce synchronized population responses oscillating at ɣ-frequencies. This suggests that neuronal plasticity is controlled by a hierarchy of gating systems and assigns critical gating functions to resonance properties of local circuits.

Use-dependent long-term changes of neuronal response properties must be gated to prevent irrelevant activity from inducing inappropriate modifications. Here we test the hypothesis that local network dynamics contribute to such gating. As synaptic modifications depend on temporal contiguity between presynaptic and postsynaptic activity, we examined the effect of synchronized gamma (ɣ) oscillations on stimulation-dependent modifications of orientation selectivity in adult cat visual cortex. Changes of orientation maps were induced by pairing visual stimulation with electrical activation of the mesencephalic reticular formation. Changes in orientation selectivity were assessed with optical recording of intrinsic signals and multiunit recordings. When conditioning stimuli were associated with strong ɣ-oscillations, orientation domains matching the orientation of the conditioning grating stimulus became more responsive and expanded, because neurons with preferences differing by less than 30° from the orientation of the conditioning grating shifted their orientation preference toward the conditioned orientation. When conditioning stimuli induced no or only weak ɣ-oscillations, responsiveness of neurons driven by the conditioning stimulus decreased. These differential effects depended on the power of oscillations in the low ɣ-band (20 Hz to 48 Hz) and not on differences in discharge rate of cortical neurons, because there was no correlation between the discharge rates during conditioning and the occurrence of changes in orientation preference. Thus, occurrence and polarity of use-dependent long-term changes of cortical response properties appear to depend on the occurrence of ɣ-oscillations during induction and hence on the degree of temporal coherence of the change-inducing network activity.

Progressive reduction of auditory evoked gamma in first episode schizophrenia but not clinical high risk individuals

The early auditory-evoked gamma band response (EAGBR) may serve as an index of the integrity of fast recurrent inhibition or synaptic connectivity in the auditory cortex, where abnormalities in individuals with schizophrenia have been consistently found. The EAGBR has been rarely investigated in first episode schizophrenia patients (FESZ) and individuals at clinical high risk (CHR) for schizophrenia, and never been compared directly between these populations nor evaluated longitudinally. Here we examined the EAGBR in FESZ, CHR, and matched healthy controls (HC) at baseline and 1-year follow-up assessments to determine whether the EAGBR was affected in these clinical groups, and whether any EAGBR abnormalities changed over time. The electroencephalogram was recorded with a dense electrode array while subjects (18 FESZ, 18 CHR, and 40 HC) performed an auditory oddball task. Event-related spectral measures (phase locking factor [PLF] and evoked power) were computed on Morlet-wavelet-transformed single epochs from the standard trials. At baseline, EAGBR PLF and evoked power did not differ between groups. FESZ showed progressive reductions of PLF and evoked power from baseline to follow-up, and deficits in PLF at follow-up compared to HC. EAGBR peak frequency also increased at temporal sites in FESZ from baseline to follow-up. Longitudinal effects on the EAGBR were not found in CHR or HC, nor did these groups differ at follow-up. In conclusion, we detected neurophysiological changes of auditory cortex function in FESZ during a one-year period, which were not observed in CHR. These findings are discussed within the context of neurodevelopmental models of schizophrenia.

Training and Spontaneous Reinforcement of Neuronal Assemblies by Spike Timing Plasticity

The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations. A simple analytic account for how fast spike time correlations affect both microscopic and macroscopic network structure is lacking. We develop a low-dimensional mean field theory for STDP in recurrent networks and show the emergence of assemblies of strongly coupled neurons with shared stimulus preferences. After training, this connectivity is actively reinforced by spike train correlations during the spontaneous dynamics. Furthermore, the stimulus coding by cell assemblies is actively maintained by these internally generated spiking correlations, suggesting a new role for noise correlations in neural coding. Assembly formation has often been associated with firing rate-based plasticity schemes; our theory provides an alternative and complementary framework, where fine temporal correlations and STDP form and actively maintain learned structure in cortical networks.

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.

Gamma Oscillations in the Basolateral Amygdala: Biophysical Mechanisms and Computational Consequences

The basolateral nucleus of the amygdala (BL) is thought to support numerous emotional behaviors through specific microcircuits. These are often thought to be comprised of feedforward networks of principal cells (PNs) and interneurons. Neither well-understood nor often considered are recurrent and feedback connections, which likely engender oscillatory dynamics within BL. Indeed, oscillations in the gamma frequency range (40 − 100 Hz) are known to occur in the BL, and yet their origin and effect on local circuits remains unknown. To address this, we constructed a biophysically and anatomically detailed model of the rat BL and its local field potential (LFP) based on the physiological and anatomical literature, along with in vivo and in vitro data we collected on the activities of neurons within the rat BL. Remarkably, the model produced intermittent gamma oscillations (∼50 − 70 Hz) whose properties matched those recorded in vivo, including their entrainment of spiking. BL gamma-band oscillations were generated by the intrinsic circuitry, depending upon reciprocal interactions between PNs and fast-spiking interneurons (FSIs), while connections within these cell types affected the rhythm’s frequency. The model allowed us to conduct experimentally impossible tests to characterize the synaptic and spatial properties of gamma. The entrainment of individual neurons to gamma depended on the number of afferent connections they received, and gamma bursts were spatially restricted in the BL. Importantly, the gamma rhythm synchronized PNs and mediated competition between ensembles. Together, these results indicate that the recurrent connectivity of BL expands its computational and communication repertoire.

Relationship between the mechanisms of gamma rhythm generation and the magnitude of the macroscopic phase response function in a population of excitatory and inhibitory modified quadratic integrate-and-fire neurons

Gamma oscillations are thought to play an important role in brain function. Interneuron gamma (ING) and pyramidal interneuron gamma (PING) mechanisms have been proposed as generation mechanisms for these oscillations. However, the relation between the generation mechanisms and the dynamical properties of the gamma oscillation are still unclear. Among the dynamical properties of the gamma oscillation, the phase response function (PRF) is important because it encodes the response of the oscillation to inputs. Recently, the PRF for an inhibitory population of modified theta neurons that generate an ING rhythm was computed by the adjoint method applied to the associated Fokker-Planck equation (FPE) for the model. The modified theta model incorporates conductance-based synapses as well as the voltage and current dynamics. Here, we extended this previous work by creating an excitatory-inhibitory (E-I) network using the modified theta model and described the population dynamics with the corresponding FPE. We conducted a bifurcation analysis of the FPE to find parameter regions which generate gamma oscillations. In order to label the oscillatory parameter regions by their generation mechanisms, we defined ING- and PING-type gamma oscillation in a mathematically plausible way based on the driver of the inhibitory population. We labeled the oscillatory parameter regions by these generation mechanisms and derived PRFs via the adjoint method on the FPE in order to investigate the differences in the responses of each type of oscillation to inputs. PRFs for PING and ING mechanisms are derived and compared. We found the amplitude of the PRF for the excitatory population is larger in the PING case than in the ING case. Finally, the E-I population of the modified theta neuron enabled us to analyze the PRFs of PING-type gamma oscillation and the entrainment ability of E and I populations. We found a parameter region in which PRFs of E and I are both purely positive in the case of PING oscillations. The different entrainment abilities of E and I stimulation as governed by the respective PRFs was compared to direct simulations of finite populations of model neurons. We find that it is easier to entrain the gamma rhythm by stimulating the inhibitory population than by stimulating the excitatory population as has been found experimentally.

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.

The right hippocampus leads the bilateral integration of gamma-parsed lateralized information

It is unclear whether the two hippocampal lobes convey similar or different activities and how they cooperate. Spatial discrimination of electric fields in anesthetized rats allowed us to compare the pathway-specific field potentials corresponding to the gamma-paced CA3 output (CA1 Schaffer potentials) and CA3 somatic inhibition within and between sides. Bilateral excitatory Schaffer gamma waves are generally larger and lead from the right hemisphere with only moderate covariation of amplitude, and drive CA1 pyramidal units more strongly than unilateral waves. CA3 waves lock to the ipsilateral Schaffer potentials, although bilateral coherence was weak. Notably, Schaffer activity may run laterally, as seen after the disruption of the connecting pathways. Thus, asymmetric operations promote the entrainment of CA3-autonomous gamma oscillators bilaterally, synchronizing lateralized gamma strings to converge optimally on CA1 targets. The findings support the view that interhippocampal connections integrate different aspects of information that flow through the left and right lobes.

DOI:http://dx.doi.org/10.7554/eLife.16658.001

In humans and other backboned animals, the brain is divided into the left and right hemispheres, which are connected by several large bundles of nerve fibers. Thanks to these fiber tracts, sensory information from each side of the body can reach both sides of the brain. However, although many areas of the brain work with a counterpart on the opposite hemisphere to process this sensory information, they do not necessarily perform the same tasks, or perform them at the same time as their partner.

The hippocampus is a brain region that helps to support navigation, to detect novelty, and to produce memories. In fact, our brains contain two hippocampi – one in each hemisphere. Previous studies of the hippocampus have tended to record from only one side of the brain. Benito, Martín-Vázquez, Makarova et al. now compare the activity of the left and right hippocampi, and consider how the two structures might work together.

Recordings of the electrical activity of the hippocampi of anesthetized rats show that different groups of neurons fire in rhythmic sequence, forming waves called gamma waves. Successive waves have different amplitudes, and can be thought to form ‘strings’. The recordings made by Benito et al. show that the two hippocampi produce parallel strings of waves, although the waves that originate in the right hemisphere are generally larger than those that originate in the left. Right-hemisphere waves also tend to begin slightly earlier than their left-hemisphere counterparts.

Further experiments revealed that disrupting the fiber tracts between the hemispheres uncouples the waves that no longer occur at the same time, and the strings of waves may remain constrained to one side of the brain. In healthy animals, however, the right-hand dominance acts as a master-slave device, and makes the waves from the two hemispheres pair up and merge in the neurons that receive them both. Thus the information running in both hippocampi can be integrated or compared before sending to the cortex for task execution or storage.

Overall, the findings reported by Benito et al. suggest that different types of information flow through the left and right hemispheres, and that the brain integrates these two streams using asymmetric connections. The next challenge is to identify how the information in the two streams differs: whether each stream reflects different sensory stimuli, different features of a scene, or the difference between recalled and perceived information.

DOI:http://dx.doi.org/10.7554/eLife.16658.002

Potential Mechanisms Underlying Intercortical Signal Regulation via Cholinergic Neuromodulators

The dynamical behavior of the cortex is extremely complex, with different areas and even different layers of a cortical column displaying different temporal patterns. A major open question is how the signals from different layers and different brain regions are coordinated in a flexible manner to support function. Here, we considered interactions between primary auditory cortex and adjacent association cortex. Using a biophysically based model, we show how top-down signals in the beta and gamma regimes can interact with a bottom-up gamma rhythm to provide regulation of signals between the cortical areas and among layers. The flow of signals depends on cholinergic modulation: with only glutamatergic drive, we show that top-down gamma rhythms may block sensory signals. In the presence of cholinergic drive, top-down beta rhythms can lift this blockade and allow signals to flow reciprocally between primary sensory and parietal cortex.

SIGNIFICANCE STATEMENT

Flexible coordination of multiple cortical areas is critical for complex cognitive functions, but how this is accomplished is not understood. Using computational models, we studied the interactions between primary auditory cortex (A1) and association cortex (Par2). Our model is capable of replicating interaction patterns observed in vitro and the simulations predict that the coordination between top-down gamma and beta rhythms is central to the gating process regulating bottom-up sensory signaling projected from A1 to Par2 and that cholinergic modulation allows this coordination to occur.

Robust network oscillations during mammalian respiratory rhythm generation driven by synaptic dynamics

How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address this question in the preBötzinger complex (preBötC), a brainstem neural network that paces robust, yet labile, inspiration in mammals. The preBötC is composed of a few hundred neurons that alternate bursting activity with silent periods, but the mechanism underlying this vital rhythm remains elusive. Using a computational approach to model a randomly connected neuronal network that relies on short-term synaptic facilitation (SF) and depression (SD), we show that synaptic fluctuations can initiate population activities through recurrent excitation. We also show that a two-step SD process allows activity in the network to synchronize (bursts) and generate a population refractory period (silence). The model was validated against an array of experimental conditions, which recapitulate several processes the preBötC may experience. Consistent with the modeling assumptions, we reveal, by electrophysiological recordings, that SF/SD can occur at preBötC synapses on timescales that influence rhythmic population activity. We conclude that nondeterministic neuronal spiking and dynamic synaptic strengths in a randomly connected network are sufficient to give rise to regular respiratory-like rhythmic network activity and lability, which may play an important role in generating the rhythm for breathing and other coordinated motor activities in mammals.

Dynamics of the functional link between area MT LFPs and motion detection

The evolution of a visually guided perceptual decision results from multiple neural processes, and recent work suggests that signals with different neural origins are reflected in separate frequency bands of the cortical local field potential (LFP). Spike activity and LFPs in the middle temporal area (MT) have a functional link with the perception of motion stimuli (referred to as neural-behavioral correlation). To cast light on the different neural origins that underlie this functional link, we compared the temporal dynamics of the neural-behavioral correlations of MT spikes and LFPs. Wide-band activity was simultaneously recorded from two locations of MT from monkeys performing a threshold, two-stimuli, motion pulse detection task. Shortly after the motion pulse occurred, we found that high-gamma (100-200 Hz) LFPs had a fast, positive correlation with detection performance that was similar to that of the spike response. Beta (10-30 Hz) LFPs were negatively correlated with detection performance, but their dynamics were much slower, peaked late, and did not depend on stimulus configuration or reaction time. A late change in the correlation of all LFPs across the two recording electrodes suggests that a common input arrived at both MT locations prior to the behavioral response. Our results support a framework in which early high-gamma LFPs likely reflected fast, bottom-up, sensory processing that was causally linked to perception of the motion pulse. In comparison, late-arriving beta and high-gamma LFPs likely reflected slower, top-down, sources of neural-behavioral correlation that originated after the perception of the motion pulse.

Interconnection and synchronization of neuronal populations in the mouse medial septum/diagonal band of Broca

The medial septum/diagonal band of Broca (MS/DBB) is crucial for hippocampal theta rhythm generation (4-12 Hz). However, the mechanisms behind theta rhythmogenesis are still under debate. The MS/DBB consists, in its majority, of three neuronal populations that use acetylcholine, GABA, or glutamate as neurotransmitter. While the firing patterns of septal neurons enable the MS/DBB to generate rhythmic output critical for the generation of the hippocampal theta rhythm, the ability to synchronize these action potentials is dependent on the interconnectivity between the three major MS/DBB neuronal populations, yet little is known about intraseptal connections. Here we assessed the connectivity between pairs of MS/DBB neurons with paired patch-clamp recordings. We found that glutamatergic and GABAergic neurons provide intraseptal connections and produce sizable currents in MS/DBB postsynaptic cells. We also analyzed linear and nonlinear relationships between the action potentials fired by pairs of neurons belonging to various MS/DBB neuronal populations. Our results show that while the synchrony index for action potential firing was significantly higher in pairs of GABAergic neurons, coherence of action potential firing in the theta range was similarly low in all pairs analyzed. Recurrence analysis demonstrated that individual action potentials were more recurrent in cholinergic neurons than in other cell types. Implementing sparse connectivity in a computer model of the MS/DBB network reproduced our experimental data. We conclude that the interplay between the intrinsic membrane properties of different MS/DBB neuronal populations and the connectivity among these populations underlie the ability of the MS/DBB network to critically contribute to hippocampal theta rhythmogenesis.

Neocortical calretinin neurons in primates: increase in proportion and microcircuitry structure

In this article we first point at the expansion of associative cortical areas in primates, as well as at the intrinsic changes in the structure of the cortical column. There is a huge increase in proportion of glutamatergic cortical projecting neurons located in the upper cortical layers (II/III). Inside this group, a novel class of associative neurons becomes recognized for its growing necessity in both inter-areal and intra-areal columnar integration. Equally important to the changes in glutamatergic population, we found that literature data suggest a 50% increase in the proportion of neocortical GABAergic neurons between primates and rodents. This seems to be a result of increase in proportion of calretinin interneurons in layers II/III, population which in associative areas represents 15% of all neurons forming those layers. Evaluating data about functional properties of their connectivity we hypothesize that such an increase in proportion of calretinin interneurons might lead to supra-linear growth in memory capacity of the associative neocortical network. An open question is whether there are some new calretinin interneuron subtypes, which might substantially change micro-circuitry structure of the primate cerebral cortex.

Dendritic nonlinearities reduce network size requirements and mediate ON and OFF states of persistent activity in a PFC microcircuit model

Technological advances have unraveled the existence of small clusters of co-active neurons in the neocortex. The functional implications of these microcircuits are in large part unexplored. Using a heavily constrained biophysical model of a L5 PFC microcircuit, we recently showed that these structures act as tunable modules of persistent activity, the cellular correlate of working memory. Here, we investigate the mechanisms that underlie persistent activity emergence (ON) and termination (OFF) and search for the minimum network size required for expressing these states within physiological regimes. We show that (a) NMDA-mediated dendritic spikes gate the induction of persistent firing in the microcircuit. (b) The minimum network size required for persistent activity induction is inversely proportional to the synaptic drive of each excitatory neuron. (c) Relaxation of connectivity and synaptic delay constraints eliminates the gating effect of NMDA spikes, albeit at a cost of much larger networks. (d) Persistent activity termination by increased inhibition depends on the strength of the synaptic input and is negatively modulated by dADP. (e) Slow synaptic mechanisms and network activity contain predictive information regarding the ability of a given stimulus to turn ON and/or OFF persistent firing in the microcircuit model. Overall, this study zooms out from dendrites to cell assemblies and suggests a tight interaction between dendritic non-linearities and network properties (size/connectivity) that may facilitate the short-memory function of the PFC.

Working memory, the ability to retain information for a short period of time, is a fundamental cognitive function that shapes behavior. The cellular correlate of working memory is the prolonged spiking (persistent) activity of neurons in the prefrontal cortex. Impairments of prefrontal cortex functionalities and working memory have been associated with a variety of cognitive disorders, such as schizophrenia, the attention deficit hyperactivity disorder, and drug addiction. Hence, understanding how neurons embedded in the local circuitry support and maintain persistent activity is of outmost importance. Our work uses a multi-level integrative approach spanning from the dendritic, to the neuronal and network levels to identify the key biophysical and anatomical mechanisms contributing to persistent activity, leading to a number of high impact findings: it predicts a tradeoff between dendritic regenerative events and the size of a network expressing persistent activity. It also proposes when and how the persistent state can be stabilized, opening new avenues for pharmacological interventions. Finally, it describes decoding mechanisms for upcoming ON/OFF state transitions, furthering our understanding of information processing in the PFC and shedding new light on the emergence of anticipatory behaviors.

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.

Abrupt and gradual transitions between low and hyperexcited firing frequencies in neuronal models with fast synaptic excitation: a comparative study

Hyperexcitability of neuronal networks is one of the hallmarks of epileptic brain seizure generation, and results from a net imbalance between excitation and inhibition that promotes excessive abnormal firing frequencies. The transition between low and high firing frequencies as the levels of recurrent AMPA excitation change can occur either gradually or abruptly. We used modeling, numerical simulations, and dynamical systems tools to investigate the biophysical and dynamic mechanisms that underlie these two identified modes of transition in recurrently connected neurons via AMPA excitation. We compare our results and demonstrate that these two modes of transition are qualitatively different and can be linked to different intrinsic properties of the participating neurons.

Toggling between gamma-frequency activity and suppression of cell assemblies

Gamma (30–80 Hz) rhythms in hippocampus and neocortex resulting from the interaction of excitatory and inhibitory cells (E- and I-cells), called Pyramidal-Interneuronal Network Gamma (PING), require that the I-cells respond to the E-cells, but don't fire on their own. In idealized models, there is a sharp boundary between a parameter regime where the I-cells have weak-enough drive for PING, and one where they have so much drive that they fire without being prompted by the E-cells. In the latter regime, they often de-synchronize and suppress the E-cells; the boundary was therefore called the “suppression boundary” by Börgers and Kopell (2005). The model I-cells used in the earlier work by Börgers and Kopell have a “type 1” phase response, i.e., excitatory input always advances them. However, fast-spiking inhibitory basket cells often have a “type 2” phase response: Excitatory input arriving soon after they fire delays them. We study the effect of the phase response type on the suppression transition, under the additional assumption that the I-cells are kept synchronous by gap junctions. When many E-cells participate on a given cycle, the resulting excitation advances the I-cells on the next cycle if their phase response is of type 1, and this can result in suppression of more E-cells on the next cycle. Therefore, strong E-cell spike volleys tend to be followed by weaker ones, and vice versa. This often results in erratic fluctuations in the strengths of the E-cell spike volleys. When the phase response of the I-cells is of type 2, the opposite happens: strong E-cell spike volleys delay the inhibition on the next cycle, therefore tend to be followed by yet stronger ones. The strengths of the E-cell spike volleys don't oscillate, and there is a nearly abrupt transition from PING to ING (a rhythm involving I-cells only).

Rates and rhythms: a synergistic view of frequency and temporal coding in neuronal networks

In the CNS, activity of individual neurons has a small but quantifiable relationship to sensory representations and motor outputs. Coactivation of a few 10s to 100s of neurons can code sensory inputs and behavioral task performance within psychophysical limits. However, in a sea of sensory inputs and demand for complex motor outputs how is the activity of such small subpopulations of neurons organized? Two theories dominate in this respect: increases in spike rate (rate coding) and sharpening of the coincidence of spiking in active neurons (temporal coding). Both have computational advantages and are far from mutually exclusive. Here, we review evidence for a bias in neuronal circuits toward temporal coding and the coexistence of rate and temporal coding during population rhythm generation. The coincident expression of multiple types of gamma rhythm in sensory cortex suggests a mechanistic substrate for combining rate and temporal codes on the basis of stimulus strength.