Experimentally constrained CA1 fast-firing parvalbumin-positive interneuron network models exhibit sharp transitions into coherent high frequency rhythms

Persistent Interruption in Parvalbumin Positive Inhibitory Interneurons: Biophysical and Mathematical Mechanisms

Persistent activity in principal cells is a putative mechanism for maintaining memory traces during working memory. We recently demonstrated persistent interruption of firing in fast-spiking parvalbumin-expressing interneurons (PV-INs), a phenomenon which could serve as a substrate for persistent activity in principal cells through disinhibition lasting hundreds of milliseconds. Here, we find that hippocampal CA1 PV-INs exhibit type 2 excitability, like striatal and neocortical PV-INs. Modelling and mathematical analysis showed that the slowly inactivating potassium current Kv1 contributes to type 2 excitability, enables the multiple firing regimes observed experimentally in PV-INs, and provides a mechanism for robust persistent interruption of firing. Using a fast/slow separation of times scales approach with the Kv1 inactivation variable as a bifurcation parameter shows that the initial inhibitory stimulus stops repetitive firing by moving the membrane potential trajectory onto a co-existing stable fixed point corresponding to a non-spiking quiescent state. As Kv1 inactivation decays, the trajectory follows the branch of stable fixed points until it crosses a subcritical Hopf bifurcation then spirals out into repetitive firing. In a model describing entorhinal cortical PV-INs without Kv1, interruption of firing could be achieved by taking advantage of the bistability inherent in type 2 excitability based on a subcritical Hopf bifurcation, but the interruption was not robust to noise. Persistent interruption of firing is therefore broadly applicable to PV-INs in different brain regions but is only made robust to noise in the presence of a slow variable.

Volume-transmitted GABA waves pace epileptiform rhythms in the hippocampal network

Mechanisms that entrain and pace rhythmic epileptiform discharges remain debated. Traditionally, the quest to understand them has focused on interneuronal networks driven by synaptic GABAergic connections. However, synchronized interneuronal discharges could also trigger the transient elevations of extracellular GABA across the tissue volume, thus raising tonic conductance (Gtonic) of synaptic and extrasynaptic GABA receptors in multiple cells. Here, we monitor extracellular GABA in hippocampal slices using patch-clamp GABA "sniffer" and a novel optical GABA sensor, showing that periodic epileptiform discharges are preceded by transient, region-wide waves of extracellular GABA. Neural network simulations that incorporate volume-transmitted GABA signals point to a cycle of GABA-driven network inhibition and disinhibition underpinning this relationship. We test and validate this hypothesis using simultaneous patch-clamp recordings from multiple neurons and selective optogenetic stimulation of fast-spiking interneurons. Critically, reducing GABA uptake in order to decelerate extracellular GABA fluctuations-without affecting synaptic GABAergic transmission or resting GABA levels-slows down rhythmic activity. Our findings thus unveil a key role of extrasynaptic, volume-transmitted GABA in pacing regenerative rhythmic activity in brain networks.

NeuroML-DB: Sharing and characterizing data-driven neuroscience models described in NeuroML

As researchers develop computational models of neural systems with increasing sophistication and scale, it is often the case that fully de novo model development is impractical and inefficient. Thus arises a critical need to quickly find, evaluate, re-use, and build upon models and model components developed by other researchers. We introduce the NeuroML Database (NeuroML-DB.org), which has been developed to address this need and to complement other model sharing resources. NeuroML-DB stores over 1,500 previously published models of ion channels, cells, and networks that have been translated to the modular NeuroML model description language. The database also provides reciprocal links to other neuroscience model databases (ModelDB, Open Source Brain) as well as access to the original model publications (PubMed). These links along with Neuroscience Information Framework (NIF) search functionality provide deep integration with other neuroscience community modeling resources and greatly facilitate the task of finding suitable models for reuse. Serving as an intermediate language, NeuroML and its tooling ecosystem enable efficient translation of models to other popular simulator formats. The modular nature also enables efficient analysis of a large number of models and inspection of their properties. Search capabilities of the database, together with web-based, programmable online interfaces, allow the community of researchers to rapidly assess stored model electrophysiology, morphology, and computational complexity properties. We use these capabilities to perform a database-scale analysis of neuron and ion channel models and describe a novel tetrahedral structure formed by cell model clusters in the space of model properties and features. This analysis provides further information about model similarity to enrich database search.

Interneuronal network model of theta-nested fast oscillations predicts differential effects of heterogeneity, gap junctions and short term depression for hyperpolarizing versus shunting inhibition

Theta and gamma oscillations in the hippocampus have been hypothesized to play a role in the encoding and retrieval of memories. Recently, it was shown that an intrinsic fast gamma mechanism in medial entorhinal cortex can be recruited by optogenetic stimulation at theta frequencies, which can persist with fast excitatory synaptic transmission blocked, suggesting a contribution of interneuronal network gamma (ING). We calibrated the passive and active properties of a 100-neuron model network to capture the range of passive properties and frequency/current relationships of experimentally recorded PV+ neurons in the medial entorhinal cortex (mEC). The strength and probabilities of chemical and electrical synapses were also calibrated using paired recordings, as were the kinetics and short-term depression (STD) of the chemical synapses. Gap junctions that contribute a noticeable fraction of the input resistance were required for synchrony with hyperpolarizing inhibition; these networks exhibited theta-nested high frequency oscillations similar to the putative ING observed experimentally in the optogenetically-driven PV-ChR2 mice. With STD included in the model, the network desynchronized at frequencies above ~200 Hz, so for sufficiently strong drive, fast oscillations were only observed before the peak of the theta. Because hyperpolarizing synapses provide a synchronizing drive that contributes to robustness in the presence of heterogeneity, synchronization decreases as the hyperpolarizing inhibition becomes weaker. In contrast, networks with shunting inhibition required non-physiological levels of gap junctions to synchronize using conduction delays within the measured range.

Synaptic Role in Facilitating Synchronous Theta Oscillations in a Hybrid Hippocampal Neuronal Network

Theta rhythms (4–12 Hz) in the hippocampus are thought to be associated with cognitive functions such as memory processing and spatial navigation. Rhythmic oscillations in the neural system can be induced by synchronization of neural populations, while physiological mechanisms for the emergence, modulation, and regulation of such rhythms are not fully understood. Conceptual reduced models are promising in promoting current understandings toward neural synchronization because of high computational efficiency, while they appear less straightforward in biological relevance. In this study, we use a hybrid E-I network as a conceptual model of the hippocampus to investigate the dynamics of synchronous theta oscillations. Specifically, experimentally constrained Izhikevich neurons and preferential connections among neural groups specific to hippocampal CA1 are incorporated to enhance the biological relevance of the model network. Based on such a model, synaptic factors related to the balance of network excitation and inhibition are the main focus of present study. By careful parameter exploration, the distinct role of synaptic connections in theta rhythm generation, facilitation of synchronization, and induction of burst activities are clarified. It is revealed that theta rhythms can be present with AMPA mediated weak E-I couplings, or with strong NMDA current. Moreover, counter-inhibition, namely inhibition of inhibition, is found effective in modulating the degree of network synchronization, while has little effect on regulating network frequency in both regimes. Under pathological considerations where the effect of pyramidal sprouting is simulated, synchronized burst patterns are observed to be induced by elevated recurrent excitation among pyramidal cells. In the final part, we additionally perform a test on the robustness of our results under heterogeneous parameters. Our simulation results may provide insights into understanding how brain rhythms are generated and modulated, and the proposed model may serve as a useful template in probing mechanisms of hippocampal-related dynamics.

Linking minimal and detailed models of CA1 microcircuits reveals how theta rhythms emerge and their frequencies controlled

The wide variety of cell types and their biophysical complexities pose a challenge in our ability to understand oscillatory activities produced by cellular-based computational network models. This challenge stems from their high-dimensional and multiparametric natures. To overcome this, we implement a solution by linking minimal and detailed models of CA1 microcircuits that generate intrahippocampal (3-12 Hz) theta rhythms. We leverage insights from minimal models to guide explorations of more detailed models and obtain a cellular perspective of theta generation. Our findings distinguish the pyramidal cells as the theta rhythm initiators and reveal that their activity is regularized by the inhibitory cell populations, supporting a proposed hypothesis of an "inhibition-based tuning" mechanism. We find a strong correlation between input current to the pyramidal cells and the resulting local field potential theta frequency, indicating that intrinsic pyramidal cell properties underpin network frequency characteristics. This work provides a cellular-based foundation from which in vivo theta activities can be explored.

A Hypothesis for Theta Rhythm Frequency Control in CA1 Microcircuits

Computational models of neural circuits with varying levels of biophysical detail have been generated in pursuit of an underlying mechanism explaining the ubiquitous hippocampal theta rhythm. However, within the theta rhythm are at least two types with distinct frequencies associated with different behavioral states, an aspect that must be considered in pursuit of these mechanistic explanations. Here, using our previously developed excitatory-inhibitory network models that generate theta rhythms, we investigate the robustness of theta generation to intrinsic neuronal variability by building a database of heterogeneous excitatory cells and implementing them in our microcircuit model. We specifically investigate the impact of three key "building block" features of the excitatory cell model that underlie our model design: these cells' rheobase, their capacity for post-inhibitory rebound, and their spike-frequency adaptation. We show that theta rhythms at various frequencies can arise dependent upon the combination of these building block features, and we find that the speed of these oscillations are dependent upon the excitatory cells' response to inhibitory drive, as encapsulated by their phase response curves. Taken together, these findings support a hypothesis for theta frequency control that includes two aspects: (i) an internal mechanism that stems from the building block features of excitatory cell dynamics; (ii) an external mechanism that we describe as "inhibition-based tuning" of excitatory cell firing. We propose that these mechanisms control theta rhythm frequencies and underlie their robustness.

A new GABAergic somatostatin projection from the BNST onto accumbal parvalbumin neurons controls anxiety

The prevailing view is that parvalbumin (PV) interneurons play modulatory roles in emotional response through local medium spiny projection neurons (MSNs). Here, we show that PV activity within the nucleus accumbens shell (sNAc) is required for producing anxiety-like avoidance when mice are under anxiogenic situations. Firing rates of sNAc^PV neurons were negatively correlated to exploration time in open arms (threatening environment). In addition, sNAc^PV neurons exhibited high excitability in a chronic stress mouse model, which generated excessive maladaptive avoidance behavior in an anxiogenic context. We also discovered a novel GABAergic pathway from the anterior dorsal bed nuclei of stria terminalis (adBNST) to sNAc^PV neurons. Optogenetic activation of these afferent terminals in sNAc produced an anxiolytic effect via GABA transmission. Next, we further demonstrated that chronic stressors attenuated the inhibitory synaptic transmission at adBNST^GABA → sNAc^PV synapses, which in turn explains the hyperexcitability of sNAc PV neurons on stressed models. Therefore, activation of these GABAergic afferents in sNAc rescued the excessive avoidance behavior related to an anxious state. Finally, we identified that the majority GABAergic input neurons, which innervate sNAc^PV cells, were expressing somatostatin (SOM), and also revealed that coordination between SOM- and PV- cells functioning in the BNST → NAc circuit has an inhibitory influence on anxiety-like responses. Our findings provide a potentially neurobiological basis for therapeutic interventions in pathological anxiety.

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

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

Optogenetic activation of parvalbumin and somatostatin interneurons selectively restores theta-nested gamma oscillations and oscillation-induced spike timing-dependent long-term potentiation impaired by amyloid β oligomers

Background

Abnormal accumulation of amyloid β_1–42 oligomers (AβO_1–42), a hallmark of Alzheimer’s disease, impairs hippocampal theta-nested gamma oscillations and long-term potentiation (LTP) that are believed to underlie learning and memory. Parvalbumin-positive (PV) and somatostatin-positive (SST) interneurons are critically involved in theta-nested gamma oscillogenesis and LTP induction. However, how AβO_1–42 affects PV and SST interneuron circuits is unclear. Through optogenetic manipulation of PV and SST interneurons and computational modeling of the hippocampal neural circuits, we dissected the contributions of PV and SST interneuron circuit dysfunctions on AβO_1–42-induced impairments of hippocampal theta-nested gamma oscillations and oscillation-induced LTP.

Results

Targeted whole-cell patch-clamp recordings and optogenetic manipulations of PV and SST interneurons during in vivo-like, optogenetically induced theta-nested gamma oscillations in vitro revealed that AβO_1–42 causes synapse-specific dysfunction in PV and SST interneurons. AβO_1–42 selectively disrupted CA1 pyramidal cells (PC)-to-PV interneuron and PV-to-PC synapses to impair theta-nested gamma oscillogenesis. In contrast, while having no effect on PC-to-SST or SST-to-PC synapses, AβO_1–42 selectively disrupted SST interneuron-mediated disinhibition to CA1 PC to impair theta-nested gamma oscillation-induced spike timing-dependent LTP (tLTP). Such AβO_1–42-induced impairments of gamma oscillogenesis and oscillation-induced tLTP were fully restored by optogenetic activation of PV and SST interneurons, respectively, further supporting synapse-specific dysfunctions in PV and SST interneurons. Finally, computational modeling of hippocampal neural circuits including CA1 PC, PV, and SST interneurons confirmed the experimental observations and further revealed distinct functional roles of PV and SST interneurons in theta-nested gamma oscillations and tLTP induction.

Conclusions

Our results reveal that AβO_1–42 causes synapse-specific dysfunctions in PV and SST interneurons and that optogenetic modulations of these interneurons present potential therapeutic targets for restoring hippocampal network oscillations and synaptic plasticity impairments in Alzheimer’s disease.

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

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

Dendritic NMDA receptors in parvalbumin neurons enable strong and stable neuronal assemblies

Parvalbumin-expressing (PV+) GABAergic interneurons mediate feedforward and feedback inhibition and have a key role in gamma oscillations and information processing. The importance of fast synaptic recruitment and action potential initiation and repolarization, and rapid synchronous GABA release by PV+ cells, is well established. In contrast, the functional significance of PV+ cell NMDA receptors (NMDARs), which generate relatively slow postsynaptic currents, is unclear. Underlining their potential importance, several studies implicate PV+ cell NMDAR disruption in impaired network function and circuit pathologies. Here, we show that dendritic NMDARs underlie supralinear integration of feedback excitation from local pyramidal neurons onto mouse CA1 PV+ cells. Furthermore, by incorporating NMDARs at feedback connections onto PV+ cells in spiking networks, we show that these receptors enable cooperative recruitment of PV+ interneurons, strengthening and stabilising principal cell assemblies. Failure of this phenomenon provides a parsimonious explanation for cognitive and sensory gating deficits in pathologies with impaired PV+ NMDAR signalling.

Open Source Brain: A Collaborative Resource for Visualizing, Analyzing, Simulating, and Developing Standardized Models of Neurons and Circuits

Computational models are powerful tools for exploring the properties of complex biological systems. In neuroscience, data-driven models of neural circuits that span multiple scales are increasingly being used to understand brain function in health and disease. But their adoption and reuse has been limited by the specialist knowledge required to evaluate and use them. To address this, we have developed Open Source Brain, a platform for sharing, viewing, analyzing, and simulating standardized models from different brain regions and species. Model structure and parameters can be automatically visualized and their dynamical properties explored through browser-based simulations. Infrastructure and tools for collaborative interaction, development, and testing are also provided. We demonstrate how existing components can be reused by constructing new models of inhibition-stabilized cortical networks that match recent experimental results. These features of Open Source Brain improve the accessibility, transparency, and reproducibility of models and facilitate their reuse by the wider community.

Reconstruction of post-synaptic potentials by reverse modeling of local field potentials

OBJECTIVE

Among electrophysiological signals, local field potentials (LFPs) are extensively used to study brain activity, either in vivo or in vitro. LFPs are recorded with extracellular electrodes implanted in brain tissue. They reflect intermingled excitatory and inhibitory processes in neuronal assemblies. In cortical structures, LFPs mainly originate from the summation of post-synaptic potentials (PSPs), either excitatory (ePSPs) or inhibitory (iPSPs) generated at the level of pyramidal cells. The challenging issue, addressed in this paper, is to estimate, from a single extracellularly-recorded signal, both ePSP and iPSP components of the LFP.

APPROACH

The proposed method is based on a model-based reverse engineering approach in which the measured LFP is fed into a physiologically-grounded neural mass model (mesoscopic level) to estimate the synaptic activity of a sub-population of pyramidal cells interacting with local GABAergic interneurons.

MAIN RESULTS

The method was first validated using simulated LFPs for which excitatory and inhibitory components are known a priori and can thus serve as a ground truth. It was then evaluated on in vivo data (PTZ-induced seizures, rat; PTZ-induced excitability increase, mouse; epileptiform discharges, mouse) and on in clinico data (human seizures recorded with depth-EEG electrodes).

SIGNIFICANCE

Under these various conditions, results showed that the proposed reverse engineering method provides a reliable estimation of the average excitatory and inhibitory post-synaptic potentials originating of the measured LFPs. They also indicated that the method allows for monitoring of the excitation/inhibition ratio. The method has potential for multiple applications in neuroscience, typically when a dynamical tracking of local excitability changes is required.

Deciphering the Contribution of Oriens-Lacunosum/Moleculare (OLM) Cells to Intrinsic θ Rhythms Using Biophysical Local Field Potential (LFP) Models

Oscillations in local field potentials (LFPs) are prevalent and contribute to brain function. An understanding of the cellular correlates and pathways affecting LFPs is needed, but many overlapping pathways in vivo make this difficult to achieve. A prevalent LFP rhythm in the hippocampus associated with memory processing and spatial navigation is the θ (3–12 Hz) oscillation. θ rhythms emerge intrinsically in an in vitro whole hippocampus preparation and this reduced preparation makes it possible to assess the contribution of different cell types to LFP generation. We focus on oriens-lacunosum/moleculare (OLM) cells as a major class of interneurons in the hippocampus. OLM cells can influence pyramidal (PYR) cells through two distinct pathways: by direct inhibition of PYR cell distal dendrites, and by indirect disinhibition of PYR cell proximal dendrites. We use previous inhibitory network models and build biophysical LFP models using volume conductor theory. We examine the effect of OLM cells to ongoing intrinsic LFP θ rhythms by directly comparing our model LFP features with experiment. We find that OLM cell inputs regulate the robustness of LFP responses without affecting their average power and that this robust response depends on coactivation of distal inhibition and basal excitation. We use our models to estimate the spatial extent of the region generating LFP θ rhythms, leading us to predict that about 22,000 PYR cells participate in intrinsic θ generation. Besides obtaining an understanding of OLM cell contributions to intrinsic LFP θ rhythms, our work can help decipher cellular correlates of in vivo LFPs.

Hippocampal Ripple Oscillations and Inhibition-First Network Models: Frequency Dynamics and Response to GABA Modulators

Hippocampal ripples are involved in memory consolidation, but the mechanisms underlying their generation remain unclear. Models relying on interneuron networks in the CA1 region disagree on the predominant source of excitation to interneurons: either "direct," via the Schaffer collaterals that provide feedforward input from CA3 to CA1, or "indirect," via the local pyramidal cells in CA1, which are embedded in a recurrent excitatory-inhibitory network. Here, we used physiologically constrained computational models of basket-cell networks to investigate how they respond to different conditions of transient, noisy excitation. We found that direct excitation of interneurons could evoke ripples (140-220 Hz) that exhibited intraripple frequency accommodation and were frequency-insensitive to GABA modulators, as previously shown in in vitro experiments. In addition, the indirect excitation of the basket-cell network enabled the expression of intraripple frequency accommodation in the fast-gamma range (90-140 Hz), as in vivo In our model, intraripple frequency accommodation results from a hysteresis phenomenon in which the frequency responds differentially to the rising and descending phases of the transient excitation. Such a phenomenon predicts a maximum oscillation frequency occurring several milliseconds before the peak of excitation. We confirmed this prediction for ripples in brain slices from male mice. These results suggest that ripple and fast-gamma episodes are produced by the same interneuron network that is recruited via different excitatory input pathways, which could be supported by the previously reported intralaminar connectivity bias between basket cells and functionally distinct subpopulations of pyramidal cells in CA1. Together, our findings unify competing inhibition-first models of rhythm generation in the hippocampus.SIGNIFICANCE STATEMENT The hippocampus is a part of the brain of humans and other mammals that is critical for the acquisition and consolidation of memories. During deep sleep and resting periods, the hippocampus generates high-frequency (∼200 Hz) oscillations called ripples, which are important for memory consolidation. The mechanisms underlying ripple generation are not well understood. A prominent hypothesis holds that the ripples are generated by local recurrent networks of inhibitory neurons. Using computational models and experiments in brain slices from rodents, we show that the dynamics of interneuron networks clarify several previously unexplained characteristics of ripple oscillations, which advances our understanding of hippocampus-dependent memory consolidation.

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.

Hippocampal GABAergic Inhibitory Interneurons

In the hippocampus GABAergic local circuit inhibitory interneurons represent only ~10-15% of the total neuronal population; however, their remarkable anatomical and physiological diversity allows them to regulate virtually all aspects of cellular and circuit function. Here we provide an overview of the current state of the field of interneuron research, focusing largely on the hippocampus. We discuss recent advances related to the various cell types, including their development and maturation, expression of subtype-specific voltage- and ligand-gated channels, and their roles in network oscillations. We also discuss recent technological advances and approaches that have permitted high-resolution, subtype-specific examination of their roles in numerous neural circuit disorders and the emerging therapeutic strategies to ameliorate such pathophysiological conditions. The ultimate goal of this review is not only to provide a touchstone for the current state of the field, but to help pave the way for future research by highlighting where gaps in our knowledge exist and how a complete appreciation of their roles will aid in future therapeutic strategies.

Feedback Inhibition Shapes Emergent Computational Properties of Cortical Microcircuit Motifs

Cortical microcircuits are very complex networks, but they are composed of a relatively small number of stereotypical motifs. Hence, one strategy for throwing light on the computational function of cortical microcircuits is to analyze emergent computational properties of these stereotypical microcircuit motifs. We are addressing here the question how spike timing-dependent plasticity shapes the computational properties of one motif that has frequently been studied experimentally: interconnected populations of pyramidal cells and parvalbumin-positive inhibitory cells in layer 2/3. Experimental studies suggest that these inhibitory neurons exert some form of divisive inhibition on the pyramidal cells. We show that this data-based form of feedback inhibition, which is softer than that of winner-take-all models that are commonly considered in theoretical analyses, contributes to the emergence of an important computational function through spike timing-dependent plasticity: The capability to disentangle superimposed firing patterns in upstream networks, and to represent their information content through a sparse assembly code.SIGNIFICANCE STATEMENT We analyze emergent computational properties of a ubiquitous cortical microcircuit motif: populations of pyramidal cells that are densely interconnected with inhibitory neurons. Simulations of this model predict that sparse assembly codes emerge in this microcircuit motif under spike timing-dependent plasticity. Furthermore, we show that different assemblies will represent different hidden sources of upstream firing activity. Hence, we propose that spike timing-dependent plasticity enables this microcircuit motif to perform a fundamental computational operation on neural activity patterns.

Combining Theory, Model, and Experiment to Explain How Intrinsic Theta Rhythms Are Generated in an In Vitro Whole Hippocampus Preparation without Oscillatory Inputs

Scientists have observed local field potential theta rhythms (3-12 Hz) in the hippocampus for decades, but understanding the mechanisms underlying their generation is complicated by their diversity in pharmacological and frequency profiles. In addition, interactions with other brain structures and oscillatory drives to the hippocampus during distinct brain states has made it difficult to identify hippocampus-specific properties directly involved in theta generation. To overcome this, we develop cellular-based network models using a whole hippocampus in vitro preparation that spontaneously generates theta rhythms. Building on theoretical and computational analyses, we find that spike frequency adaptation and postinhibitory rebound constitute a basis for theta generation in large, minimally connected CA1 pyramidal (PYR) cell network models with fast-firing parvalbumin-positive (PV⁺) inhibitory cells. Sparse firing of PYR cells and large excitatory currents onto PV⁺ cells are present as in experiments. The particular theta frequency is more controlled by PYR-to-PV⁺ cell interactions rather than PV⁺-to-PYR cell interactions. We identify two scenarios by which theta rhythms can emerge, and they can be differentiated by the ratio of excitatory to inhibitory currents to PV⁺ cells, but not to PYR cells. Only one of the scenarios is consistent with data from the whole hippocampus preparation, which leads to the prediction that the connection probability from PV⁺ to PYR cells needs to be larger than from PYR to PV⁺ cells. Our models can serve as a platform on which to build and develop an understanding of in vivo theta generation.

Interneuronal mechanisms of hippocampal theta oscillations in a full-scale model of the rodent CA1 circuit

The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the rodent CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct interneuronal types spontaneously emerged from the isolated CA1 circuit without rhythmic inputs. Perturbation experiments identified parvalbumin-expressing interneurons and neurogliaform cells, as well as interneuronal diversity itself, as important factors in theta generation. These simulations reveal new insights into the spatiotemporal organization of the CA1 circuit during theta oscillations.

Interneuronal mechanisms of hippocampal theta oscillations in a full-scale model of the rodent CA1 circuit

The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the rodent CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct interneuronal types spontaneously emerged from the isolated CA1 circuit without rhythmic inputs. Perturbation experiments identified parvalbumin-expressing interneurons and neurogliaform cells, as well as interneuronal diversity itself, as important factors in theta generation. These simulations reveal new insights into the spatiotemporal organization of the CA1 circuit during theta oscillations.

DOI:http://dx.doi.org/10.7554/eLife.18566.001

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

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

Resonant Interneurons Can Increase Robustness of Gamma Oscillations

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

SIGNIFICANCE STATEMENT

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

Network models provide insights into how oriens-lacunosum-moleculare and bistratified cell interactions influence the power of local hippocampal CA1 theta oscillations

Hippocampal theta is a 4–12 Hz rhythm associated with episodic memory, and although it has been studied extensively, the cellular mechanisms underlying its generation are unclear. The complex interactions between different interneuron types, such as those between oriens–lacunosum-moleculare (OLM) interneurons and bistratified cells (BiCs), make their contribution to network rhythms difficult to determine experimentally. We created network models that are tied to experimental work at both cellular and network levels to explore how these interneuron interactions affect the power of local oscillations. Our cellular models were constrained with properties from patch clamp recordings in the CA1 region of an intact hippocampus preparation in vitro. Our network models are composed of three different types of interneurons: parvalbumin-positive (PV+) basket and axo-axonic cells (BC/AACs), PV+ BiCs, and somatostatin-positive OLM cells. Also included is a spatially extended pyramidal cell model to allow for a simplified local field potential representation, as well as experimentally-constrained, theta frequency synaptic inputs to the interneurons. The network size, connectivity, and synaptic properties were constrained with experimental data. To determine how the interactions between OLM cells and BiCs could affect local theta power, we explored how the number of OLM-BiC connections and connection strength affected local theta power. We found that our models operate in regimes that could be distinguished by whether OLM cells minimally or strongly affected the power of network theta oscillations due to balances that, respectively, allow compensatory effects or not. Inactivation of OLM cells could result in no change or even an increase in theta power. We predict that the dis-inhibitory effect of OLM cells to BiCs to pyramidal cell interactions plays a critical role in the resulting power of network theta oscillations. Overall, our network models reveal a dynamic interplay between different classes of interneurons in influencing local theta power.

Dendritic distributions of I h channels in experimentally-derived multi-compartment models of oriens-lacunosum/moleculare (O-LM) hippocampal interneurons

The O-LM cell type mediates feedback inhibition onto hippocampal pyramidal cells and gates information flow in the CA1. Its functions depend on the presence of voltage-gated channels (VGCs), which affect its integrative properties and response to synaptic input. Given the challenges associated with determining densities and distributions of VGCs on interneuron dendrites, we take advantage of computational modeling to consider different possibilities. In this work, we focus on hyperpolarization-activated channels (h-channels) in O-LM cells. While h-channels are known to be present in O-LM cells, it is unknown whether they are present on their dendrites. In previous work, we used ensemble modeling techniques with experimental data to obtain insights into potentially important conductance balances. We found that the best O-LM models that included uniformly distributed h-channels in the dendrites could not fully capture the “sag” response. This led us to examine activation kinetics and non-uniform distributions of h-channels in the present work. In tuning our models, we found that different kinetics and non-uniform distributions could better reproduce experimental O-LM cell responses. In contrast to CA1 pyramidal cells where higher conductance densities of h-channels occur in more distal dendrites, decreasing conductance densities of h-channels away from the soma were observed in O-LM models. Via an illustrative scenario, we showed that having dendritic h-channels clearly speeds up back-propagating action potentials in O-LM cells, unlike when h-channels are present only in the soma. Although the present results were morphology-dependent, our work shows that it should be possible to determine the distributions and characteristics of O-LM cells with recordings and morphologies from the same cell. We hypothesize that h-channels are distributed in O-LM cell dendrites and endow them with particular synaptic integration properties that shape information flow in hippocampus.

Cognitive impairment in temporal lobe epilepsy: role of online and offline processing of single cell information

Cognitive impairment is a common comorbidity in temporal lobe epilepsy (TLE) and is often considered more detrimental to quality of life than seizures. While it has been previously shown that the encoding of memory during behavior is impaired in the pilocarpine model of TLE in rats, how this information is consolidated during the subsequent sleep period remains unknown. In this study, we first report marked deficits in spatial memory performance and severe cell loss in the CA1 layer of the hippocampus lower spatial coherence of firing in TLE rats. We then present the first evidence that the reactivation of behavior-driven patterns of activity of CA1 place cells in the hippocampus is intact in TLE rats. Using a template-matching method, we discovered that real-time (3-5 s) reactivation structure was intact in TLE rats. Furthermore, we estimated the entropy rate of short time scale (∼250 ms) bursting activity using block entropies and found that significant, extended temporal correlations exist in both TLE and control rats. Fitting a first-order Markov Chain model to these bursting time series, we found that long sequences derived from behavior were significantly enriched in the Markov model over corresponding models fit on randomized data confirming the presence of replay in shorter time scales. We propose that the persistent consolidation of poor spatial information in both real time and during bursting activity may contribute to memory impairments in TLE rats.

Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context

The hippocampus is a heavily studied brain structure due to its involvement in learning and memory. Detailed models of excitatory, pyramidal cells in hippocampus have been developed using a range of experimental data. These models have been used to help us understand, for example, the effects of synaptic integration and voltage gated channel densities and distributions on cellular responses. However, these cellular outputs need to be considered from the perspective of the networks in which they are embedded. Using modeling approaches, if cellular representations are too detailed, it quickly becomes computationally unwieldy to explore large network simulations. Thus, simple models are preferable, but at the same time they need to have a clear, experimental basis so as to allow physiologically based understandings to emerge. In this article, we describe the development of simple models of CA1 pyramidal cells, as derived in a well-defined experimental context of an intact, whole hippocampus preparation expressing population oscillations. These models are based on the intrinsic properties and frequency-current profiles of CA1 pyramidal cells, and can be used to build, fully examine, and analyze large networks.