Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks

Synaptic interactions between stellate cells and parvalbumin interneurons in layer 2 of the medial entorhinal cortex are organized at the scale of grid cell clusters

Interactions between excitatory and inhibitory neurons are critical to computations in cortical circuits but their organization is difficult to assess with standard electrophysiological approaches. Within the medial entorhinal cortex, representation of location by grid and other spatial cells involves circuits in layer 2 in which excitatory stellate cells interact with each other via inhibitory parvalbumin expressing interneurons. Whether this connectivity is structured to support local circuit computations is unclear. Here, we introduce strategies to address the functional organization of excitatory-inhibitory interactions using crossed Cre- and Flp-driver mouse lines to direct targeted presynaptic optogenetic activation and postsynaptic cell identification. We then use simultaneous patch-clamp recordings from postsynaptic neurons to assess their shared input from optically activated presynaptic populations. We find that extensive axonal projections support spatially organized connectivity between stellate cells and parvalbumin interneurons, such that direct connections are often, but not always, shared by nearby neurons, whereas multisynaptic interactions coordinate inputs to neurons with greater spatial separation. We suggest that direct excitatory-inhibitory synaptic interactions may operate at the scale of grid cell clusters, with local modules defined by excitatory-inhibitory connectivity, while indirect interactions may coordinate activity at the scale of grid cell modules.

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal is to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software (version 1.0) is released as open source to enable broad community reuse and encourage novel applications.

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal was to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software is released as open source to enable broad community reuse and encourage novel applications.

Induced synchronization by endogenous noise modulation in finite-size random neural networks: A stochastic mean-field study

Event-related synchronization and desynchronization (ERS/ERD) are well-known features found experimentally in brain signals during cognitive tasks. Their understanding promises to have much better insights into neural information processes in cognition. Under the hypothesis that neural information affects the endogenous neural noise level in populations, we propose to employ a stochastic mean-field model to explain ERS/ERD in the γ-frequency range. The work extends previous mean-field studies by deriving novel effects from finite network size. Moreover, numerical simulations of ERS/ERD and their analytical explanation by the mean-field model suggest several endogenous noise modulation schemes, which may modulate the system's synchronization.

Simulation of oscillatory dynamics induced by an approximation of grid cell output

Grid cells, in entorhinal cortex (EC) and related structures, signal animal location relative to hexagonal tilings of 2D space. A number of modeling papers have addressed the question of how grid firing behaviors emerge using (for example) ideas borrowed from dynamical systems (attractors) or from coupled oscillator theory. Here we use a different approach: instead of asking how grid behavior emerges, we take as a given the experimentally observed intracellular potentials of superficial medial EC neurons during grid firing. Employing a detailed neural circuit model modified from a lateral EC model, we then ask how the circuit responds when group of medial EC principal neurons exhibit such potentials, simultaneously with a simulated theta frequency input from the septal nuclei. The model predicts the emergence of robust theta-modulated gamma/beta oscillations, suggestive of oscillations observed in an in vitro medial EC experimental model (Cunningham, M.O., Pervouchine, D.D., Racca, C., Kopell, N.J., Davies, C.H., Jones, R.S.G., Traub, R.D., and Whittington, M.A. (2006). Neuronal metabolism governs cortical network response state. Proc. Natl. Acad. Sci. U S A 103: 5597-5601). Such oscillations result because feedback interneurons tightly synchronize with each other - despite the varying phases of the grid cells - and generate a robust inhibition-based rhythm. The lack of spatial specificity of the model interneurons is consistent with the lack of spatial periodicity in parvalbumin interneurons observed by Buetfering, C., Allen, K., and Monyer, H. (2014). Parvalbumin interneurons provide grid cell-driven recurrent inhibition in the medial entorhinal cortex. Nat. Neurosci. 17: 710-718. If in vivo EC gamma rhythms arise during exploration as our model predicts, there could be implications for interpreting disrupted spatial behavior and gamma oscillations in animal models of Alzheimer's disease and schizophrenia. Noting that experimental intracellular grid cell potentials closely resemble cortical Up states and Down states, during which fast oscillations also occur during Up states, we propose that the co-occurrence of slow principal cell depolarizations and fast network oscillations is a general property of the telencephalon, in both waking and sleep states.

Microcircuits for spatial coding in the medial entorhinal cortex

The hippocampal formation is critically involved in learning and memory and contains a large proportion of neurons encoding aspects of the organism's spatial surroundings. In the medial entorhinal cortex (MEC), this includes grid cells with their distinctive hexagonal firing fields as well as a host of other functionally defined cell types including head direction cells, speed cells, border cells, and object-vector cells. Such spatial coding emerges from the processing of external inputs by local microcircuits. However, it remains unclear exactly how local microcircuits and their dynamics within the MEC contribute to spatial discharge patterns. In this review we focus on recent investigations of intrinsic MEC connectivity, which have started to describe and quantify both excitatory and inhibitory wiring in the superficial layers of the MEC. Although the picture is far from complete, it appears that these layers contain robust recurrent connectivity that could sustain the attractor dynamics posited to underlie grid pattern formation. These findings pave the way to a deeper understanding of the mechanisms underlying spatial navigation and memory.

Arousal Fluctuations Govern Oscillatory Transitions Between Dominant γ and α Occipital Activity During Eyes Open/Closed Conditions

Arousal results in widespread activation of brain areas to increase their response in task and behavior relevant ways. Mediated by the Ascending Reticular Arousal System (ARAS), arousal-dependent inputs interact with neural circuitry to shape their dynamics. In the occipital cortex, such inputs may trigger shifts between dominant oscillations, whereα activity is replaced byγ activity, or vice versa. A salient example of this are spectral power alternations observed while eyes are opened and/or closed. These transitions closely follow fluctuations in arousal, suggesting a common origin. To better understand the mechanisms at play, we developed and analyzed a computational model composed of two modules: a thalamocortical feedback circuit coupled with a superficial cortical network. Upon activation by noise-like inputs originating from the ARAS, our model is able to demonstrate that noise-driven non-linear interactions mediate transitions in dominant peak frequency, resulting in the simultaneous suppression ofα limit cycle activity and the emergence ofγ oscillations through coherence resonance. Reduction in input provoked the reverse effect - leading to anticorrelated transitions betweenα andγ power. Taken together, these results shed a new light on how arousal shapes oscillatory brain activity.

Spiking Neural Networks and Hippocampal Function: A Web-Accessible Survey of Simulations, Modeling Methods, and Underlying Theories

Computational modeling has contributed to hippocampal research in a wide variety of ways and through a large diversity of approaches, reflecting the many advanced cognitive roles of this brain region. The intensively studied neuron type circuitry of the hippocampus is a particularly conducive substrate for spiking neural models. Here we present an online knowledge base of spiking neural network simulations of hippocampal functions. First, we overview theories involving the hippocampal formation in subjects such as spatial representation, learning, and memory. Then we describe an original literature mining process to organize published reports in various key aspects, including: (i) subject area (e.g., navigation, pattern completion, epilepsy); (ii) level of modeling detail (Hodgkin-Huxley, integrate-and-fire, etc.); and (iii) theoretical framework (attractor dynamics, oscillatory interference, self-organizing maps, and others). Moreover, every peer-reviewed publication is also annotated to indicate the specific neuron types represented in the network simulation, establishing a direct link with the Hippocampome.org portal. The web interface of the knowledge base enables dynamic content browsing and advanced searches, and consistently presents evidence supporting every annotation. Moreover, users are given access to several types of statistical reports about the collection, a selection of which is summarized in this paper. This open access resource thus provides an interactive platform to survey spiking neural network models of hippocampal functions, compare available computational methods, and foster ideas for suitable new directions of research.

Optogenetic pacing of medial septum parvalbumin-positive cells disrupts temporal but not spatial firing in grid cells

Grid cells in the medial entorhinal cortex (MEC) exhibit remarkable spatial activity patterns with spikes coordinated by theta oscillations driven by the medial septal area (MSA). Spikes from grid cells progress relative to the theta phase in a phenomenon called phase precession, which is suggested as essential to create the spatial periodicity of grid cells. Here, we show that optogenetic activation of parvalbumin-positive (PV+) cells in the MSA enabled selective pacing of local field potential (LFP) oscillations in MEC. During optogenetic stimulation, the grid cells were locked to the imposed pacing frequency but kept their spatial patterns. Phase precession was abolished, and speed information was no longer reflected in the LFP oscillations but was still carried by rate coding of individual MEC neurons. Together, these results support that theta oscillations are not critical to the spatial pattern of grid cells and do not carry a crucial velocity signal.

Stellate Cells in the Medial Entorhinal Cortex Are Required for Spatial Learning

Spatial learning requires estimates of location that may be obtained by path integration or from positional cues. Grid and other spatial firing patterns of neurons in the superficial medial entorhinal cortex (MEC) suggest roles in behavioral estimation of location. However, distinguishing the contributions of path integration and cue-based signals to spatial behaviors is challenging, and the roles of identified MEC neurons are unclear. We use virtual reality to dissociate linear path integration from other strategies for behavioral estimation of location. We find that mice learn to path integrate using motor-related self-motion signals, with accuracy that decreases steeply as a function of distance. We show that inactivation of stellate cells in superficial MEC impairs spatial learning in virtual reality and in a real world object location recognition task. Our results quantify contributions of path integration to behavior and corroborate key predictions of models in which stellate cells contribute to location estimation.

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Mice learn to estimate location by path integration and cue-based strategies

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Motor-related self-motion signals are used for path integration

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Accuracy of path integration decreases with distance

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Stellate cells in medial entorhinal cortex are required for spatial learning

Control of clustered action potential firing in a mathematical model of entorhinal cortex stellate cells

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An SDE model of entorhinal cortex (EC) stellate cells is proposed.

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Experimentally observed action potential clustering is investigated in the model.

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Clusters are generated by subcritical-Hopf/homoclinic type bursting.

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Potential mechanisms underlying changes in EC dynamics in dementia are presented.

The entorhinal cortex is a crucial component of our memory and spatial navigation systems and is one of the first areas to be affected in dementias featuring tau pathology, such as Alzheimer’s disease and frontotemporal dementia. Electrophysiological recordings from principle cells of medial entorhinal cortex (layer II stellate cells, mEC-SCs) demonstrate a number of key identifying properties including subthreshold oscillations in the theta (4–12 Hz) range and clustered action potential firing. These single cell properties are correlated with network activity such as grid firing and coupling between theta and gamma rhythms, suggesting they are important for spatial memory. As such, experimental models of dementia have revealed disruption of organised dorsoventral gradients in clustered action potential firing.

To better understand the mechanisms underpinning these different dynamics, we study a conductance based model of mEC-SCs. We demonstrate that the model, driven by extrinsic noise, can capture quantitative differences in clustered action potential firing patterns recorded from experimental models of tau pathology and healthy animals. The differential equation formulation of our model allows us to perform numerical bifurcation analyses in order to uncover the dynamic mechanisms underlying these patterns. We show that clustered dynamics can be understood as subcritical Hopf/homoclinic bursting in a fast-slow system where the slow sub-system is governed by activation of the persistent sodium current and inactivation of the slow A-type potassium current. In the full system, we demonstrate that clustered firing arises via flip bifurcations as conductance parameters are varied. Our model analyses confirm the experimentally suggested hypothesis that the breakdown of clustered dynamics in disease occurs via increases in AHP conductance.

Structural modularity and grid activity in the medial entorhinal cortex

Following the groundbreaking discovery of grid cells, the medial entorhinal cortex (MEC) has become the focus of intense anatomical, physiological, and computational investigations. Whether and how grid activity maps onto cell types and cortical architecture is still an open question. Fundamental similarities in microcircuits, function, and connectivity suggest a homology between rodent MEC and human posteromedial entorhinal cortex. Both are specialized for spatial processing and display similar cellular organization, consisting of layer 2 pyramidal/calbindin cell patches superimposed on scattered stellate neurons. Recent data indicate the existence of a further nonoverlapping modular system (zinc patches) within the superficial MEC layers. Zinc and calbindin patches have been shown to receive largely segregated inputs from the presubiculum and parasubiculum. Grid cells are also clustered in the MEC, and we discuss possible structure-function schemes on how grid activity could map onto cortical patch systems. We hypothesize that in the superficial layers of the MEC, anatomical location can be predictive of function; thus relating functional properties and neuronal morphologies to the cortical modules will be necessary for resolving how grid activity maps onto cortical architecture. Imaging or cell identification approaches in freely moving animals will be required for testing this hypothesis.

Anatomical and Electrophysiological Clustering of Superficial Medial Entorhinal Cortex Interneurons

Local GABAergic interneurons regulate the activity of spatially-modulated principal cells in the medial entorhinal cortex (MEC), mediating stellate-to-stellate connectivity and possibly enabling grid formation via recurrent inhibitory circuitry. Despite the important role interneurons seem to play in the MEC cortical circuit, the combination of low cell counts and functional diversity has made systematic electrophysiological studies of these neurons difficult. For these reasons, there remains a paucity of knowledge on the electrophysiological profiles of superficial MEC interneuron populations. Taking advantage of glutamic acid decarboxylase 2 (GAD2)-IRES-tdTomato and PV-tdTomato transgenic mice, we targeted GABAergic interneurons for whole-cell patch-clamp recordings and characterized their passive membrane features, basic input/output properties and action potential (AP) shape. These electrophysiologically characterized cells were then anatomically reconstructed, with emphasis on axonal projections and pial depth. K-means clustering of interneuron anatomical and electrophysiological data optimally classified a population of 106 interneurons into four distinct clusters. The first cluster is comprised of layer 2- and 3-projecting, slow-firing interneurons. The second cluster is comprised largely of PV+ fast-firing interneurons that project mainly to layers 2 and 3. The third cluster contains layer 1- and 2-projecting interneurons, and the fourth cluster is made up of layer 1-projecting horizontal interneurons. These results, among others, will provide greater understanding of the electrophysiological characteristics of MEC interneurons, help guide future in vivo studies, and may aid in uncovering the mechanism of grid field formation.

Layer-Specific Organization of Local Excitatory and Inhibitory Synaptic Connectivity in the Rat Presubiculum

The presubiculum is part of the parahippocampal spatial navigation system and contains head direction and grid cells upstream of the medial entorhinal cortex. This position within the parahippocampal cortex renders the presubiculum uniquely suited for analyzing the circuit requirements underlying the emergence of spatially tuned neuronal activity. To identify the local circuit properties, we analyzed the topology of synaptic connections between pyramidal cells and interneurons in all layers of the presubiculum by testing 4250 potential synaptic connections using multiple whole-cell recordings of up to 8 cells simultaneously. Network topology showed layer-specific organization of microcircuits consistent with the prevailing distinction of superficial and deep layers. While connections among pyramidal cells were almost absent in superficial layers, deep layers exhibited an excitatory connectivity of 3.9%. In contrast, synaptic connectivity for inhibition was higher in superficial layers though markedly lower than in other cortical areas. Finally, synaptic amplitudes of both excitatory and inhibitory connections showed log-normal distributions suggesting a nonrandom functional connectivity. In summary, our study provides new insights into the microcircuit organization of the presubiculum by revealing area- and layer-specific connectivity rules and sets new constraints for future models of the parahippocampal navigation system.

Modeling the differentiation of A- and C-type baroreceptor firing patterns

The baroreceptor neurons serve as the primary transducers of blood pressure for the autonomic nervous system and are thus critical in enabling the body to respond effectively to changes in blood pressure. These neurons can be separated into two types (A and C) based on the myelination of their axons and their distinct firing patterns elicited in response to specific pressure stimuli. This study has developed a comprehensive model of the afferent baroreceptor discharge built on physiological knowledge of arterial wall mechanics, firing rate responses to controlled pressure stimuli, and ion channel dynamics within the baroreceptor neurons. With this model, we were able to predict firing rates observed in previously published experiments in both A- and C-type neurons. These results were obtained by adjusting model parameters determining the maximal ion-channel conductances. The observed variation in the model parameters are hypothesized to correspond to physiological differences between A- and C-type neurons. In agreement with published experimental observations, our simulations suggest that a twofold lower potassium conductance in C-type neurons is responsible for the observed sustained basal firing, where as a tenfold higher mechanosensitive conductance is responsible for the greater firing rate observed in A-type neurons. A better understanding of the difference between the two neuron types can potentially be used to gain more insight about pathophysiology and treatment of diseases related to baroreflex function, e.g. in patients with autonomic failure, a syndrome that is difficult to diagnose in terms of its pathophysiology.

Continuous attractor network models of grid cell firing based on excitatory-inhibitory interactions

Neurons in the medial entorhinal cortex encode location through spatial firing fields that have a grid‐like organisation. The challenge of identifying mechanisms for grid firing has been addressed through experimental and theoretical investigations of medial entorhinal circuits. Here, we discuss evidence for continuous attractor network models that account for grid firing by synaptic interactions between excitatory and inhibitory cells. These models assume that grid‐like firing patterns are the result of computation of location from velocity inputs, with additional spatial input required to oppose drift in the attractor state. We focus on properties of continuous attractor networks that are revealed by explicitly considering excitatory and inhibitory neurons, their connectivity and their membrane potential dynamics. Models at this level of detail can account for theta‐nested gamma oscillations as well as grid firing, predict spatial firing of interneurons as well as excitatory cells, show how gamma oscillations can be modulated independently from spatial computations, reveal critical roles for neuronal noise, and demonstrate that only a subset of excitatory cells in a network need have grid‐like firing fields. Evaluating experimental data against predictions from detailed network models will be important for establishing the mechanisms mediating grid firing.