Distance-dependent inhibition facilitates focality of gamma oscillations in the dentate gyrus

Imbalance between hippocampal projection cell and parvalbumin interneuron architecture increases epileptic susceptibility in mouse model of methyl CpG binding protein 2 duplication syndrome

OBJECTIVE

Methyl CpG-binding protein 2 (MECP2) duplication syndrome is a rare X-linked genomic disorder affecting predominantly males, which is usually manifested as epilepsy and autism spectrum disorder (ASD) comorbidity. The transgenic line MeCP2Tg1 was used for mimicking MECP2 duplication syndrome and showed autism-epilepsy co-occurrence. Previous works suggested that the excitatory/inhibitory (E/I) imbalance is a potential common mechanism for both epilepsy and ASD. The projection neurons and parvalbumin (PV) interneurons account for the majority of E/I balance in the hippocampus. Therefore, we explored how structural changes of projection and PV+ neurons occur in the hippocampus of MeCP2Tg1 mice and whether these morphological changes contribute to epilepsy susceptibility.

METHODS

We used the interneuron Designer receptors exclusively activated by designer drugs mouse model to inhibit inhibitory neurons in the hippocampus to verify the epilepsy susceptibility of MeCP2Tg1 (FVB, an inbred strain named as sensitivity to Friend leukemia virus) mice. Electroencephalograms were recorded for the definition of seizure. We performed retro-orbital injection of virus in MeCP2Tg1 (FVB):CaMKIIα-Cre (C57BL/6) mice or MeCP2Tg1:PV-Cre (C57BL/6) mice and their littermate controls to specifically label projection and PV+ neurons for structural analysis.

RESULTS

Epilepsy susceptibility was increased in MeCP2Tg1 mice. There was a reduced number of PV neurons and reduced dendritic complexity in the hippocampus of MeCP2Tg1 mice. The dendritic complexity in MeCP2Tg1 mice was increased compared to wild-type mice, and total dendritic spine density in dentate gyrus of MeCP2Tg1 mice was also increased. Total dendritic spine density was increased in CA1 of MeCP2Tg1 mice.

SIGNIFICANCE

Overexpression of MeCP2 may disrupt crucial signaling pathways, resulting in decreased dendritic complexity of PV interneurons and increased dendritic spine density of projection neurons. This reciprocal modulation of excitatory and inhibitory neuronal structures associated with MeCP2 implies its significance as a potential target in the development of epilepsy and offers a novel perspective on the co-occurrence of autism and epilepsy.

Dynamics of spike transmission and suppression between principal cells and interneurons in the hippocampus and entorhinal cortex

Synaptic excitation and inhibition are essential for neuronal communication. However, the variables that regulate synaptic excitation and inhibition in the intact brain remain largely unknown. Here, we examined how spike transmission and suppression between principal cells (PCs) and interneurons (INTs) are modulated by activity history, brain state, cell type, and somatic distance between presynaptic and postsynaptic neurons by applying cross-correlogram analyses to datasets recorded from the dorsal hippocampus and medial entorhinal cortex (MEC) of 11 male behaving and sleeping Long Evans rats. The strength, temporal delay, and brain-state dependency of the spike transmission and suppression depended on the subregions/layers. The spike transmission probability of PC-INT excitatory pairs that showed short-term depression versus short-term facilitation was higher in CA1 and lower in CA3. Likewise, the intersomatic distance affected the proportion of PC-INT excitatory pairs that showed short-term depression and facilitation in the opposite manner in CA1 compared with CA3. The time constant of depression was longer, while that of facilitation was shorter in MEC than in CA1 and CA3. During sharp-wave ripples, spike transmission showed a larger gain in the MEC than in CA1 and CA3. The intersomatic distance affected the spike transmission gain during sharp-wave ripples differently in CA1 versus CA3. A subgroup of MEC layer 3 (EC3) INTs preferentially received excitatory inputs from and inhibited MEC layer 2 (EC2) PCs. The EC2 PC-EC3 INT excitatory pairs, most of which showed short-term depression, exhibited higher spike transmission probabilities than the EC2 PC-EC2 INT and EC3 PC-EC3 INT excitatory pairs. EC2 putative stellate cells exhibited stronger spike transmission to and received weaker spike suppression from EC3 INTs than EC2 putative pyramidal cells. This study provides detailed comparisons of monosynaptic interaction dynamics in the hippocampal-entorhinal loop, which may help to elucidate circuit operations.

Gamma oscillation plasticity is mediated via parvalbumin interneurons

Understanding the plasticity of neuronal networks is an emerging field of (patho-) physiological research, yet the underlying cellular mechanisms remain poorly understood. Gamma oscillations (30 to 80 hertz), a biomarker of cognitive performance, require and potentiate glutamatergic transmission onto parvalbumin-positive interneurons (PVIs), suggesting an interface for cell-to-network plasticity. In ex vivo local field potential recordings, we demonstrate long-term potentiation of hippocampal gamma power. Gamma potentiation obeys established rules of PVI plasticity, requiring calcium-permeable AMPA receptors (CP-AMPARs) and metabotropic glutamate receptors (mGluRs). A microcircuit computational model of CA3 gamma oscillations predicts CP-AMPAR plasticity onto PVIs critically outperforms pyramidal cell plasticity in increasing gamma power and completely accounts for gamma potentiation. We reaffirm this ex vivo in three PVI-targeting animal models, demonstrating that gamma potentiation requires PVI-specific signaling via a Gq/PKC pathway comprising mGluR5 and a Gi-sensitive, PKA-dependent pathway. Gamma activity-dependent, metabotropically mediated CP-AMPAR plasticity on PVIs may serve as a guiding principle in understanding network plasticity in health and disease.

Oscillations in the dentate gyrus as a tool for the performance of the hippocampal functions: Healthy and epileptic brain

The dentate gyrus (DG) is part of the hippocampal formation and is essential for important cognitive processes such as navigation and memory. The oscillatory activity of the DG network is believed to play a critical role in cognition. DG circuits generate theta, beta, and gamma rhythms, which participate in the specific information processing performed by DG neurons. In the temporal lobe epilepsy (TLE), cognitive abilities are impaired, which may be due to drastic alterations in the DG structure and network activity during epileptogenesis. The theta rhythm and theta coherence are especially vulnerable in dentate circuits; disturbances in DG theta oscillations and their coherence may be responsible for general cognitive impairments observed during epileptogenesis. Some researchers suggested that the vulnerability of DG mossy cells is a key factor in the genesis of TLE, but others did not support this hypothesis. The aim of the review is not only to present the current state of the art in this field of research but to help pave the way for future investigations by highlighting the gaps in our knowledge to completely appreciate the role of DG rhythms in brain functions. Disturbances in oscillatory activity of the DG during TLE development may be a diagnostic marker in the treatment of this disease.

Connectivity concepts in neuronal network modeling

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.

Parvalbumin interneuron dendrites enhance gamma oscillations

Dendrites are essential determinants of the input-output relationship of single neurons, but their role in network computations is not well understood. Here, we use a combination of dendritic patch-clamp recordings and in silico modeling to determine how dendrites of parvalbumin (PV)-expressing basket cells contribute to network oscillations in the gamma frequency band. Simultaneous soma-dendrite recordings from PV basket cells in the dentate gyrus reveal that the slope, or gain, of the dendritic input-output relationship is exceptionally low, thereby reducing the cell's sensitivity to changes in its input. By simulating gamma oscillations in detailed network models, we demonstrate that the low gain is key to increase spike synchrony in PV basket cell assemblies when cells are driven by spatially and temporally heterogeneous synaptic inputs. These results highlight the role of inhibitory neuron dendrites in synchronized network oscillations.

Phase response approaches to neural activity models with distributed delay

In weakly coupled neural oscillator networks describing brain dynamics, the coupling delay is often distributed. We present a theoretical framework to calculate the phase response curve of distributed-delay induced limit cycles with infinite-dimensional phase space. Extending previous works, in which non-delayed or discrete-delay systems were investigated, we develop analytical results for phase response curves of oscillatory systems with distributed delay using Gaussian and log-normal delay distributions. We determine the scalar product and normalization condition for the linearized adjoint of the system required for the calculation of the phase response curve. As a paradigmatic example, we apply our technique to the Wilson-Cowan oscillator model of excitatory and inhibitory neuronal populations under the two delay distributions. We calculate and compare the phase response curves for the Gaussian and log-normal delay distributions. The phase response curves obtained from our adjoint calculations match those compiled by the direct perturbation method, thereby proving that the theory of weakly coupled oscillators can be applied successfully for distributed-delay-induced limit cycles. We further use the obtained phase response curves to derive phase interaction functions and determine the possible phase locked states of multiple inter-coupled populations to illuminate different synchronization scenarios. In numerical simulations, we show that the coupling delay distribution can impact the stability of the synchronization between inter-coupled gamma-oscillatory networks.

Parvalbumin expressing interneurons control spike-phase coupling of hippocampal cells to theta oscillations

Encoding of information by hippocampal neurons is defined by the number and the timing of action potentials generated relative to ongoing network oscillations in the theta (5–14 Hz), gamma (30–80 Hz) and ripple frequency range (150–200 Hz). The exact mechanisms underlying the temporal coupling of action potentials of hippocampal cells to the phase of rhythmic network activity are not fully understood. One critical determinant of action potential timing is synaptic inhibition provided by a complex network of Gamma-amino-hydroxy-butyric acid releasing (GABAergic) interneurons. Among the various GABAergic cell types, particularly Parvalbumin-expressing cells are powerful regulators of neuronal activity. Here we silenced Parvalbumin-expressing interneurons in hippocampal areas CA1 and the dentate gyrus in freely moving mice using the optogenetic silencing tool eNpHR to determine their influence on spike timing in principal cells. During optogenetic inhibition of Parvalbumin-expressing cells, local field potential recordings revealed no change in power or frequency of CA1 or dentate gyrus network oscillations. However, CA1 pyramidal neurons exhibited significantly reduced spike-phase coupling to CA1 theta, but not gamma or ripple oscillations. These data suggest that hippocampal Parvalbumin-expressing interneurons are particularly important for an intact theta-based temporal coding scheme of hippocampal principal cell populations.

Plasticity impairment exposes CA3 vulnerability in a hippocampal network model of mild traumatic brain injury

Proper function of the hippocampus is critical for executing cognitive tasks such as learning and memory. Traumatic brain injury (TBI) and other neurological disorders are commonly associated with cognitive deficits and hippocampal dysfunction. Although there are many existing models of individual subregions of the hippocampus, few models attempt to integrate the primary areas into one system. In this work, we developed a computational model of the hippocampus, including the dentate gyrus, CA3, and CA1. The subregions are represented as an interconnected neuronal network, incorporating well-characterized ex vivo slice electrophysiology into the functional neuron models and well-documented anatomical connections into the network structure. In addition, since plasticity is foundational to the role of the hippocampus in learning and memory as well as necessary for studying adaptation to injury, we implemented spike-timing-dependent plasticity among the synaptic connections. Our model mimics key features of hippocampal activity, including signal frequencies in the theta and gamma bands and phase-amplitude coupling in area CA1. We also studied the effects of spike-timing-dependent plasticity impairment, a potential consequence of TBI, in our model and found that impairment decreases broadband power in CA3 and CA1 and reduces phase coherence between these two subregions, yet phase-amplitude coupling in CA1 remains intact. Altogether, our work demonstrates characteristic hippocampal activity with a scaled network model of spiking neurons and reveals the sensitive balance of plasticity mechanisms in the circuit through one manifestation of mild traumatic injury.

Cholinergic modulation of dentate gyrus processing through dynamic reconfiguration of inhibitory circuits

The dentate gyrus (DG) of the hippocampus plays a key role in memory formation, and it is known to be modulated by septal projections. By performing electrophysiology and optogenetics, we evaluated the role of cholinergic modulation in the processing of afferent inputs in the DG. We show that mature granule cells (GCs), but not adult-born immature neurons, have increased responses to afferent perforant path stimuli upon cholinergic modulation. This is due to a highly precise reconfiguration of inhibitory circuits, differentially affecting Parvalbumin and Somatostatin interneurons, resulting in a nicotinic-dependent perisomatic disinhibition of GCs. This circuit reorganization provides a mechanism by which mature GCs could escape the strong inhibition they receive, creating a window of opportunity for plasticity. Indeed, coincident activation of perforant path inputs with optogenetic release of acetylcholine produces a long-term potentiated response in GCs, essential for memory formation.

A transient postnatal quiescent period precedes emergence of mature cortical dynamics

Mature neural networks synchronize and integrate spatiotemporal activity patterns to support cognition. Emergence of these activity patterns and functions is believed to be developmentally regulated, but the postnatal time course for neural networks to perform complex computations remains unknown. We investigate the progression of large-scale synaptic and cellular activity patterns across development using high spatiotemporal resolution in vivo electrophysiology in immature mice. We reveal that mature cortical processes emerge rapidly and simultaneously after a discrete but volatile transition period at the beginning of the second postnatal week of rodent development. The transition is characterized by relative neural quiescence, after which spatially distributed, temporally precise, and internally organized activity occurs. We demonstrate a similar developmental trajectory in humans, suggesting an evolutionarily conserved mechanism that could facilitate a transition in network operation. We hypothesize that this transient quiescent period is a requisite for the subsequent emergence of coordinated cortical networks.

It can take several months, or even years, for the brain of a young animal to develop and refine the complex neural networks which underpin cognitive abilities such as memory, planning, and decision making. While the properties that support these functions have been well-documented, less is known about how they emerge during development.

Domínguez, Ma, Yu et al. therefore set out to determine when exactly these properties began to take shape in mice, using lightweight nets of electrodes to record brain activity in sleeping newborn pups. The nets were designed to avoid disturbing the animals or damaging their fragile brains.

The recordings showed that patterns of brain activity similar to those seen in adults emerged during the first couple of weeks after birth. Just before, however, the brains of the pups went through a brief period of reduced activity: this lull seemed to mark a transition from an immature to a more mature mode of operation. After this pause, neurons in the mouse brains showed coordinated patterns of firing reminiscent of those seen in adults. By monitoring the brains of human babies using scalp sensors, Domínguez, Ma, Yu et al. showed that a similar transition also occurs in infants during their first few months of life, suggesting that brains may mature via a process retained across species.

Overall, the relative lull in activity before transition may mark when neural networks gain mature properties; in the future, it could therefore potentially be used to diagnose and monitor individuals with delayed cognitive development.

GABAergic Inhibitory Interneuron Deficits in Alzheimer's Disease: Implications for Treatment

Alzheimer’s disease (AD) is a neurodegenerative disorder characterized clinically by severe cognitive deficits and pathologically by amyloid plaques, neuronal loss, and neurofibrillary tangles. Abnormal amyloid β-protein (Aβ) deposition in the brain is often thought of as a major initiating factor in AD neuropathology. However, gamma-aminobutyric acid (GABA) inhibitory interneurons are resistant to Aβ deposition, and Aβ decreases synaptic glutamatergic transmission to decrease neural network activity. Furthermore, there is now evidence suggesting that neural network activity is aberrantly increased in AD patients and animal models due to functional deficits in and decreased activity of GABA inhibitory interneurons, contributing to cognitive deficits. Here we describe the roles played by excitatory neurons and GABA inhibitory interneurons in Aβ-induced cognitive deficits and how altered GABA interneurons regulate AD neuropathology. We also comprehensively review recent studies on how GABA interneurons and GABA receptors can be exploited for therapeutic benefit. GABA interneurons are an emerging therapeutic target in AD, with further clinical trials urgently warranted.

Parvalbumin interneurons provide spillover to newborn and mature dentate granule cells

Parvalbumin-expressing interneurons (PVs) in the dentate gyrus provide activity-dependent regulation of adult neurogenesis as well as maintain inhibitory control of mature neurons. In mature neurons, PVs evoke GABA_A postsynaptic currents (GPSCs) with fast rise and decay phases that allow precise control of spike timing, yet synaptic currents with fast kinetics do not appear in adult-born neurons until several weeks after cell birth. Here we used mouse hippocampal slices to address how PVs signal to newborn neurons prior to the appearance of fast GPSCs. Whereas PV-evoked currents in mature neurons exhibit hallmark fast rise and decay phases, newborn neurons display slow GPSCs with characteristics of spillover signaling. We also unmasked slow spillover currents in mature neurons in the absence of fast GPSCs. Our results suggest that PVs mediate slow spillover signaling in addition to conventional fast synaptic signaling, and that spillover transmission mediates activity-dependent regulation of early events in adult neurogenesis.

Presynaptic GABAB receptors functionally uncouple somatostatin interneurons from the active hippocampal network

Information processing in cortical neuronal networks relies on properly balanced excitatory and inhibitory neurotransmission. A ubiquitous motif for maintaining this balance is the somatostatin interneuron (SOM-IN) feedback microcircuit. Here, we investigated the modulation of this microcircuit by presynaptic GABA_B receptors (GABA_BRs) in the rodent hippocampus. Whole-cell recordings from SOM-INs revealed that both excitatory and inhibitory synaptic inputs are strongly inhibited by GABA_BRs, while optogenetic activation of the interneurons shows that their inhibitory output is also strongly suppressed. Electron microscopic analysis of immunogold-labelled freeze-fracture replicas confirms that GABA_BRs are highly expressed presynaptically at both input and output synapses of SOM-INs. Activation of GABA_BRs selectively suppresses the recruitment of SOM-INs during gamma oscillations induced in vitro. Thus, axonal GABA_BRs are positioned to efficiently control the input and output synapses of SOM-INs and can functionally uncouple them from local network with implications for rhythmogenesis and the balance of entorhinal versus intrahippocampal afferents.

Dentate gyrus circuits for encoding, retrieval and discrimination of episodic memories

The dentate gyrus (DG) has a key role in hippocampal memory formation. Intriguingly, DG lesions impair many, but not all, hippocampus-dependent mnemonic functions, indicating that the rest of the hippocampus (CA1-CA3) can operate autonomously under certain conditions. An extensive body of theoretical work has proposed how the architectural elements and various cell types of the DG may underlie its function in cognition. Recent studies recorded and manipulated the activity of different neuron types in the DG during memory tasks and have provided exciting new insights into the mechanisms of DG computational processes, particularly for the encoding, retrieval and discrimination of similar memories. Here, we review these DG-dependent mnemonic functions in light of the new findings and explore mechanistic links between the cellular and network properties of, and the computations performed by, the DG.

Dendritic inhibition differentially regulates excitability of dentate gyrus parvalbumin-expressing interneurons and granule cells

Fast-spiking parvalbumin-expressing interneurons (PVIs) and granule cells (GCs) of the dentate gyrus receive layer-specific dendritic inhibition. Its impact on PVI and GC excitability is, however, unknown. By applying whole-cell recordings, GABA uncaging and single-cell-modeling, we show that proximal dendritic inhibition in PVIs is less efficient in lowering perforant path-mediated subthreshold depolarization than distal inhibition but both are highly efficient in silencing PVIs. These inhibitory effects can be explained by proximal shunting and distal strong hyperpolarizing inhibition. In contrast, GC proximal but not distal inhibition is the primary regulator of their excitability and recruitment. In GCs inhibition is hyperpolarizing along the entire somato-dendritic axis with similar strength. Thus, dendritic inhibition differentially controls input-output transformations in PVIs and GCs. Dendritic inhibition in PVIs is suited to balance PVI discharges in dependence on global network activity thereby providing strong and tuned perisomatic inhibition that contributes to the sparse representation of information in GC assemblies.

Fast-spiking parvalbumin-expressing interneurons (PVIs) and granule cells of the dentate gyrus receive layer-specific dendritic inhibition. The authors show that distal and proximal dendritic inhibition differentially control input-output transformations in PVIs and granule cells.

Tonic Resting State Hubness Supports High Gamma Activity Defined Verbal Memory Encoding Network in Epilepsy

High gamma activity (HGA) of verbal-memory encoding using invasive-electroencephalogram has laid the foundation for numerous studies testing the integrity of memory in diseased populations. Yet, the functional connectivity characteristics of networks subserving these memory linkages remains uncertain. By integrating this electrophysiological biomarker of memory encoding from IEEG with resting-state BOLD fluctuations, we estimated the segregation and hubness of HGA-memory regions in drug-resistant epilepsy patients and matched healthy controls. HGA-memory regions express distinctly different hubness compared to neighboring regions in health and in epilepsy, and this hubness was more relevant than segregation in predicting verbal memory encoding. The HGA-memory network comprised regions from both the cognitive control and primary processing networks, validating that effective verbal-memory encoding requires integrating brain functions, and is not dominated by a central cognitive core. Our results demonstrate a tonic intrinsic set of functional connectivity, which provides the necessary conditions for effective, phasic, task-dependent memory encoding.

Cyfip1 Haploinsufficiency Does Not Alter GABAA Receptor δ-Subunit Expression and Tonic Inhibition in Dentate Gyrus PV+ Interneurons and Granule Cells

Copy number variation (CNV) at chromosomal region 15q11.2 is linked to increased risk of neurodevelopmental disorders including autism and schizophrenia. A significant gene at this locus is cytoplasmic fragile X mental retardation protein (FMRP) interacting protein 1 (CYFIP1). CYFIP1 protein interacts with FMRP, whose monogenic absence causes fragile X syndrome (FXS). Fmrp knock-out has been shown to reduce tonic GABAergic inhibition by interacting with the δ-subunit of the GABAA receptor (GABAAR). Using in situ hybridization (ISH), qPCR, Western blotting techniques, and patch clamp electrophysiology in brain slices from a Cyfip1 haploinsufficient mouse, we examined δ-subunit mediated tonic inhibition in the dentate gyrus (DG). In wild-type (WT) mice, DG granule cells (DGGCs) responded to the δ-subunit-selective agonist THIP with significantly increased tonic currents. In heterozygous mice, no significant difference was observed in THIP-evoked currents in DGGCs. Phasic GABAergic inhibition in DGGC was also unaltered with no difference in properties of spontaneous IPSCs (sIPSCs). Additionally, we demonstrate that DG granule cell layer (GCL) parvalbumin-positive interneurons (PV+-INs) have functional δ-subunit-mediated tonic GABAergic currents which, unlike DGGC, are also modulated by the α1-selective drug zolpidem. Similar to DGGC, both IPSCs and THIP-evoked currents in PV+-INs were not different between Cyfip1 heterozygous and WT mice. Supporting our electrophysiological data, we found no significant change in hippocampal δ-subunit mRNA expression or protein level and no change in α1/α4-subunit mRNA expression. Thus, Cyfip1 haploinsufficiency, mimicking human 15q11.2 microdeletion syndrome, does not alter hippocampal phasic or tonic GABAergic inhibition, substantially differing from the Fmrp knock-out mouse model.

Macroscopic phase resetting-curves determine oscillatory coherence and signal transfer in inter-coupled neural circuits

Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated in routing information. While multiple cellular mechanisms influence the network oscillatory dynamics and structure the macroscopic firing motifs, one of the key questions is to identify the biophysical neuronal and synaptic properties that permit such motifs to arise. A second important issue is how the different neural activity coherence states determine the communication between the neural circuits. Here we analyse the emergence of phase-locking within bidirectionally delayed-coupled spiking circuits in which global gamma band oscillations arise from synaptic coupling among largely excitable neurons. We consider both the interneuronal (ING) and the pyramidal-interneuronal (PING) population gamma rhythms and the inter coupling targeting the pyramidal or the inhibitory neurons. Using a mean-field approach together with an exact reduction method, we reduce each spiking network to a low dimensional nonlinear system and derive the macroscopic phase resetting-curves (mPRCs) that determine how the phase of the global oscillation responds to incoming perturbations. This is made possible by the use of the quadratic integrate-and-fire model together with a Lorentzian distribution of the bias current. Depending on the type of gamma (PING vs. ING), we show that incoming excitatory inputs can either speed up the macroscopic oscillation (phase advance; type I PRC) or induce both a phase advance and a delay (type II PRC). From there we determine the structure of macroscopic coherence states (phase-locking) of two weakly synaptically-coupled networks. To do so we derive a phase equation for the coupled system which links the synaptic mechanisms to the coherence states of the system. We show that a synaptic transmission delay is a necessary condition for symmetry breaking, i.e. a non-symmetric phase lag between the macroscopic oscillations. This potentially provides an explanation to the experimentally observed variety of gamma phase-locking modes. Our analysis further shows that symmetry-broken coherence states can lead to a preferred direction of signal transfer between the oscillatory networks where this directionality also depends on the timing of the signal. Hence we suggest a causal theory for oscillatory modulation of functional connectivity between cortical circuits.

Large scale brain oscillations emerge from synaptic interactions within neuronal circuits. Over the past years, such macroscopic rhythms have been suggested to play a crucial role in routing the flow of information across cortical regions, resulting in a functional connectome. The underlying mechanism is cortical oscillations that bind together following a well-known motif called phase-locking. While there is significant experimental support for multiple phase-locking modes in the brain, it is still unclear what is the underlying mechanism that permits macroscopic rhythms to phase lock. In the present paper we take up with this issue, and to show that, one can study the emergent macroscopic phase-locking within the mathematical framework of weakly coupled oscillators. We find that under synaptic delays, fully symmetrically coupled networks can display symmetry-broken states of activity, where one network starts to lead in phase the second (also sometimes known as stuttering states). When we analyse how incoming transient signals affect the coupled system, we find that in the symmetry-broken state, the effect depends strongly on which network is targeted (the leader or the follower) as well as the timing of the input. Hence we show how the dynamics of the emergent phase-locked activity imposes a functional directionality on how signals are processed. We thus offer clarification on the synaptic and circuit properties responsible for the emergence of multiple phase-locking patterns and provide support for its functional implication in information transfer.

Parvalbumin+ interneurons obey unique connectivity rules and establish a powerful lateral-inhibition microcircuit in dentate gyrus

Parvalbumin-positive (PV⁺) GABAergic interneurons in hippocampal microcircuits are thought to play a key role in several higher network functions, such as feedforward and feedback inhibition, network oscillations, and pattern separation. Fast lateral inhibition mediated by GABAergic interneurons may implement a winner-takes-all mechanism in the hippocampal input layer. However, it is not clear whether the functional connectivity rules of granule cells (GCs) and interneurons in the dentate gyrus are consistent with such a mechanism. Using simultaneous patch-clamp recordings from up to seven GCs and up to four PV⁺ interneurons in the dentate gyrus, we find that connectivity is structured in space, synapse-specific, and enriched in specific disynaptic motifs. In contrast to the neocortex, lateral inhibition in the dentate gyrus (in which a GC inhibits neighboring GCs via a PV⁺ interneuron) is ~ 10-times more abundant than recurrent inhibition (in which a GC inhibits itself). Thus, unique connectivity rules may enable the dentate gyrus to perform specific higher-order computations.

GABAergic interneurons are known to provide inhibition to allow computational function of neuronal network. Here, Espinoza and colleagues show that connectivity of granule cells and interneurons in the dentate gyrus of mouse hippocampus are consistent with the circuit architecture capable of performing a winners-take-all mechanism.

Inhibitory Interneurons Regulate Temporal Precision and Correlations in Cortical Circuits

GABAergic interneurons, which are highly diverse, have long been thought to contribute to the timing of neural activity as well as to the generation and shaping of brain rhythms. GABAergic activity is crucial not only for entrainment of oscillatory activity across a neural population, but also for precise regulation of the timing of action potentials and the suppression of slow-timescale correlations. The diversity of inhibition provides the potential for flexible regulation of patterned activity, but also poses a challenge to identifying the elements of excitatory-inhibitory interactions underlying network engagement. This review highlights the key roles of inhibitory interneurons in spike correlations and brain rhythms, describes several scales on which GABAergic inhibition regulates timing in neural networks, and identifies potential consequences of inhibitory dysfunction.

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.

Recording Spatially Restricted Oscillations in the Hippocampus of Behaving Mice

The local field potential (LFP) emerges from ion movements across neural membranes. Since the voltage recorded by LFP electrodes reflects the summed electrical field of a large volume of brain tissue, extracting information about local activity is challenging. Studying neuronal microcircuits, however, requires a reliable distinction between truly local events and volume-conducted signals originating in distant brain areas. Current source density (CSD) analysis offers a solution for this problem by providing information about current sinks and sources in the vicinity of the electrodes. In brain areas with laminar cytoarchitecture such as the hippocampus, one-dimensional CSD can be obtained by estimating the second spatial derivative of the LFP. Here, we describe a method to record multilaminar LFPs using linear silicon probes implanted into the dorsal hippocampus. CSD traces are computed along individual shanks of the probe. This protocol thus describes a procedure to resolve spatially restricted neuronal network oscillations in the hippocampus of freely moving mice.