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

A spatial transformation-based CAN model for information integration within grid cell modules

The hippocampal-entorhinal circuit is considered to play an important role in the spatial cognition of animals. However, the mechanism of the information flow within the circuit and its contribution to the function of the grid-cell module are still topics of discussion. Prevailing theories suggest that grid cells are primarily influenced by self-motion inputs from the Medial Entorhinal Cortex, with place cells serving a secondary role by contributing to the visual calibration of grid cells. However, recent evidence suggests that both self-motion inputs and visual cues may collaboratively contribute to the formation of grid-like patterns. In this paper, we introduce a novel Continuous Attractor Network model based on a spatial transformation mechanism. This mechanism enables the integration of self-motion inputs and visual cues within grid-cell modules, synergistically driving the formation of grid-like patterns. From the perspective of individual neurons within the network, our model successfully replicates grid firing patterns. From the view of neural population activity within the network, the network can form and drive the activated bump, which describes the characteristic feature of grid-cell modules, namely, path integration. Through further exploration and experimentation, our model can exhibit significant performance in path integration. This study provides a new insight into understanding the mechanism of how the self-motion and visual inputs contribute to the neural activity within grid-cell modules. Furthermore, it provides theoretical support for achieving accurate path integration, which holds substantial implications for various applications requiring spatial navigation and mapping.

Modeling the grid cell activity based on cognitive space transformation

The grid cells in the medial entorhinal cortex are widely recognized as a critical component of spatial cognition within the entorhinal-hippocampal neuronal circuits. To account for the hexagonal patterns, several computational models have been proposed. However, there is still considerable debate regarding the interaction between grid cells and place cells. In response, we have developed a novel grid-cell computational model based on cognitive space transformation, which established a theoretical framework of the interaction between place cells and grid cells for encoding and transforming positions between the local frame and global frame. Our model not only can generate the firing patterns of the grid cells but also reproduces the biological experiment results about the grid-cell global representation of connected environments and supports the conjecture about the underlying reason. Moreover, our model provides new insights into how grid cells and place cells integrate external and self-motion cues.

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.

Spatial periodicity in grid cell firing is explained by a neural sequence code of 2-D trajectories

Spatial periodicity in grid cell firing has been interpreted as a neural metric for space providing animals with a coordinate system in navigating physical and mental spaces. However, the specific computational problem being solved by grid cells has remained elusive. Here, we provide mathematical proof that spatial periodicity in grid cell firing is the only possible solution to a neural sequence code of 2-D trajectories and that the hexagonal firing pattern of grid cells is the most parsimonious solution to such a sequence code. We thereby provide a teleological cause for the existence of grid cells and reveal the underlying nature of the global geometric organization in grid maps as a direct consequence of a simple local sequence code. A sequence code by grid cells provides intuitive explanations for many previously puzzling experimental observations and may transform our thinking about grid cells.

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.

Empirically validated theoretical analysis of visual-spatial perception under change of nervous system arousal

Introduction

Visual-spatial perception is a process for extracting the spatial relationship between objects in the environment. The changes in visual-spatial perception due to factors such as the activity of the sympathetic nervous system (hyperactivation) or parasympathetic nervous system (hypoactivation) can affect the internal representation of the external visual-spatial world. We formulated a quantitative model of the modulation of visual-perceptual space under action by hyperactivation or hypoactivation-inducing neuromodulating agents. We showed a Hill equation based relationship between neuromodulator agent concentration and alteration of visual-spatial perception utilizing the metric tensor to quantify the visual space.

Methods

We computed the dynamics of the psilocybin (hyperactivation-inducing agent) and chlorpromazine (hypoactivation-inducing agent) in brain tissue. Then, we validated our quantitative model by analyzing the findings of different independent behavioral studies where subjects were assessed for alterations in visual-spatial perception under the action of psilocybin and under chlorpromazine. To validate the neuronal correlates, we simulated the effect of the neuromodulating agent on the computational model of the grid-cell network, and also performed diffusion MRI-based tractography to find the neural tracts between the cortical areas involved: V2 and the entorhinal cortex.

Results

We applied our computational model to an experiment (where perceptual alterations were measured under psilocybin) and found that for n (Hill-coefficient) = 14.8 and k = 1.39, the theoretical prediction followed experimental observations very well (χ2 test robustly satisfied, p > 0.99). We predicted the outcome of another psilocybin-based experiment using these values (n = 14.8 and k = 1.39), whereby our prediction and experimental outcomes were well corroborated. Furthermore, we found that also under hypoactivation (chlorpromazine), the modulation of the visual-spatial perception follows our model. Moreover, we found neural tracts between the area V2 and entorhinal cortex, thus providing a possible brain network responsible for encoding visual-spatial perception. Thence, we simulated the altered grid-cell network activity, which was also found to follow the Hill equation.

Conclusion

We developed a computational model of visuospatial perceptual alterations under altered neural sympathetic/parasympathetic tone. We validated our model using analysis of behavioral studies, neuroimaging assessment, and neurocomputational evaluation. Our quantitative approach may be probed as a potential behavioral screening and monitoring methodology in neuropsychology to analyze perceptual misjudgment and mishaps by highly stressed workers.

The chicken and egg problem of grid cells and place cells

Place cells and grid cells are major building blocks of the hippocampal cognitive map. The prominent forward model postulates that grid-cell modules are generated by a continuous attractor network; that a velocity signal evoked during locomotion moves entorhinal activity bumps; and that place-cell activity constitutes summation of entorhinal grid-cell modules. Experimental data support the first postulate, but not the latter two. Several families of solutions that depart from these postulates have been put forward. We suggest a modified model (spatial modulation continuous attractor network; SCAN), whereby place cells are generated from spatially selective nongrid cells. Locomotion causes these cells to move the hippocampal activity bump, leading to movement of the entorhinal manifolds. Such inversion accords with the shift of hippocampal thought from navigation to more abstract functions.

A Spiking Neural Network Model of Rodent Head Direction Calibrated With Landmark Free Learning

Maintaining a stable estimate of head direction requires both self-motion (idiothetic) information and environmental (allothetic) anchoring. In unfamiliar or dark environments idiothetic drive can maintain a rough estimate of heading but is subject to inaccuracy, visual information is required to stabilize the head direction estimate. When learning to associate visual scenes with head angle, animals do not have access to the ‘ground truth' of their head direction, and must use egocentrically derived imprecise head direction estimates. We use both discriminative and generative methods of visual processing to learn these associations without extracting explicit landmarks from a natural visual scene, finding all are sufficiently capable at providing a corrective signal. Further, we present a spiking continuous attractor model of head direction (SNN), which when driven by idiothetic input is subject to drift. We show that head direction predictions made by the chosen model-free visual learning algorithms can correct for drift, even when trained on a small training set of estimated head angles self-generated by the SNN. We validate this model against experimental work by reproducing cue rotation experiments which demonstrate visual control of the head direction signal.

Fan cells in lateral entorhinal cortex directly influence medial entorhinal cortex through synaptic connections in layer 1

Standard models for spatial and episodic memory suggest that the lateral entorhinal cortex (LEC) and medial entorhinal cortex (MEC) send parallel independent inputs to the hippocampus, each carrying different types of information. Here, we evaluate the possibility that information is integrated between divisions of the entorhinal cortex prior to reaching the hippocampus. We demonstrate that, in mice, fan cells in layer 2 (L2) of LEC that receive neocortical inputs, and that project to the hippocampal dentate gyrus, also send axon collaterals to layer 1 (L1) of the MEC. Activation of inputs from fan cells evokes monosynaptic glutamatergic excitation of stellate and pyramidal cells in L2 of the MEC, typically followed by inhibition that contains fast and slow components mediated by GABA_A and GABA_B receptors, respectively. Inputs from fan cells also directly activate interneurons in L1 and L2 of MEC, with synaptic connections from L1 interneurons accounting for slow feedforward inhibition of L2 principal cell populations. The relative strength of excitation and inhibition following fan cell activation differs substantially between neurons and is largely independent of anatomical location. Our results demonstrate that the LEC, in addition to directly influencing the hippocampus, can activate or inhibit major hippocampal inputs arising from the MEC. Thus, local circuits in the superficial MEC may combine spatial information with sensory and higher order signals from the LEC, providing a substrate for integration of 'what' and 'where' components of episodic memories.

Kinetics and Connectivity Properties of Parvalbumin- and Somatostatin-Positive Inhibition in Layer 2/3 Medial Entorhinal Cortex

Parvalbumin-positive (Pvalb⁺) and somatostatin-positive (Sst⁺) cells are the two largest subgroups of inhibitory interneurons. Studies in visual cortex indicate that synaptic connections between Pvalb⁺ cells are common while connections between Sst⁺ interneurons have not been observed. The inhibitory connectivity and kinetics of these two interneuron subpopulations, however, have not been characterized in medial entorhinal cortex (mEC). Using fluorescence-guided paired recordings in mouse brain slices from interneurons and excitatory cells in layer 2/3 mEC, we found that, unlike neocortical measures, Sst⁺ cells inhibit each other, albeit with a lower probability than Pvalb⁺ cells (18% vs 36% for unidirectional connections). Gap junction connections were also more frequent between Pvalb⁺ cells than between Sst⁺ cells. Pvalb⁺ cells inhibited each other with larger conductances, smaller decay time constants, and shorter delays. Similarly, synaptic connections between Pvalb⁺ and excitatory cells were more likely and expressed faster decay times and shorter delays than those between Sst⁺ and excitatory cells. Inhibitory cells exhibited smaller synaptic decay time constants between interneurons than on their excitatory targets. Inhibition between interneurons also depressed faster, and to a greater extent. Finally, inhibition onto layer 2 pyramidal and stellate cells originating from Pvalb⁺ interneurons were very similar, with no significant differences in connection likelihood, inhibitory amplitude, and decay time. A model of short-term depression fitted to the data indicates that recovery time constants for refilling the available pool are in the range of 50-150 ms and that the fraction of the available pool released on each spike is in the range 0.2-0.5.

A Model of Spatial Cell Development in Rat Hippocampus Based on Artificial Neural Network

Physiological studies have shown that the hippocampal structure of rats develops at different stages, in which the place cells continue to develop during the whole juvenile period of rats and mature after the juvenile period. As the main information source of place cells, grid cells should mature earlier than place cells. In order to make better use of the biological information exhibited by the rat brain hippocampus in the environment, we propose a position cognition model based on the spatial cell development mechanism of rat hippocampus. The model uses a recurrent neural network with parametric bias (RNNPB) to simulate changes in the discharge characteristics during the development of a single stripe cell. The oscillatory interference mechanism is able to fuse the developing stripe waves, thus indirectly simulating the developmental process of the grid cells. The output of the grid cells is then used as the information input of the place cells, whose development process is simulated by BP neural network. After the place cells matured, the position matrix generated by the place cell group was used to realize the position cognition of rats in a given spatial region. The experimental results show that this model can simulate the development process of grid cells and place cells, and it can realize high precision positioning in the given space area. Moreover, the experimental effect of cognitive map construction using this model is basically consistent with the effect of RatSLAM, which verifies the validity and accuracy of the model.

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.

The grid code for ordered experience

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have presented a challenge to existing models of entorhinal function. In this Perspective, we propose that hippocampal input provides a key informative drive to the grid network in both spatial and non-spatial circumstances, particularly around salient events. We build on previous models in which neural activity propagates through the entorhinal-hippocampal network in time. This temporal contiguity in network activity points to temporal order as a necessary characteristic of representations generated by the hippocampal formation. We advocate that interactions in the entorhinal-hippocampal loop build a topological representation that is rooted in the temporal order of experience. In this way, the structure of grid cell firing supports a learned topology rather than a rigid coordinate frame that is bound to measurements of the physical world.

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.

Spatially structured inhibition defined by polarized parvalbumin interneuron axons promotes head direction tuning

In cortical microcircuits, it is generally assumed that fast-spiking parvalbumin interneurons mediate dense and nonselective inhibition. Some reports indicate sparse and structured inhibitory connectivity, but the computational relevance and the underlying spatial organization remain unresolved. In the rat superficial presubiculum, we find that inhibition by fast-spiking interneurons is organized in the form of a dominant super-reciprocal microcircuit motif where multiple pyramidal cells recurrently inhibit each other via a single interneuron. Multineuron recordings and subsequent 3D reconstructions and analysis further show that this nonrandom connectivity arises from an asymmetric, polarized morphology of fast-spiking interneuron axons, which individually cover different directions in the same volume. Network simulations assuming topographically organized input demonstrate that such polarized inhibition can improve head direction tuning of pyramidal cells in comparison to a "blanket of inhibition." We propose that structured inhibition based on asymmetrical axons is an overarching spatial connectivity principle for tailored computation across brain regions.

Biomimetic FPGA-based spatial navigation model with grid cells and place cells

The mammalian spatial navigation system is characterized by an initial divergence of internal representations, with disparate classes of neurons responding to distinct features including location, speed, borders and head direction; an ensuing convergence finally enables navigation and path integration. Here, we report the algorithmic and hardware implementation of biomimetic neural structures encompassing a feed-forward trimodular, multi-layer architecture representing grid-cell, place-cell and decoding modules for navigation. The grid-cell module comprised of neurons that fired in a grid-like pattern, and was built of distinct layers that constituted the dorsoventral span of the medial entorhinal cortex. Each layer was built as an independent continuous attractor network with distinct grid-field spatial scales. The place-cell module comprised of neurons that fired at one or few spatial locations, organized into different clusters based on convergent modular inputs from different grid-cell layers, replicating the gradient in place-field size along the hippocampal dorso-ventral axis. The decoding module, a two-layer neural network that constitutes the convergence of the divergent representations in preceding modules, received inputs from the place-cell module and provided specific coordinates of the navigating object. After vital design optimizations involving all modules, we implemented the tri-modular structure on Zynq Ultrascale+ field-programmable gate array silicon chip, and demonstrated its capacity in precisely estimating the navigational trajectory with minimal overall resource consumption involving a mere 2.92% Look Up Table utilization. Our implementation of a biomimetic, digital spatial navigation system is stable, reliable, reconfigurable, real-time with execution time of about 32 s for 100k input samples (in contrast to 40 minutes on Intel Core i7-7700 CPU with 8 cores clocking at 3.60 GHz) and thus can be deployed for autonomous-robotic navigation without requiring additional sensors.

Parvalbumin Interneurons Are Differentially Connected to Principal Cells in Inhibitory Feedback Microcircuits along the Dorsoventral Axis of the Medial Entorhinal Cortex

The medial entorhinal cortex (mEC) shows a high degree of spatial tuning, predominantly grid cell activity, which is reliant on robust, dynamic inhibition provided by local interneurons (INs). In fact, feedback inhibitory microcircuits involving fast-spiking parvalbumin (PV) basket cells (BCs) are believed to contribute dominantly to the emergence of grid cell firing in principal cells (PrCs). However, the strength of PV BC-mediated inhibition onto PrCs is not uniform in this region, but high in the dorsal and weak in the ventral mEC. This is in good correlation with divergent grid field sizes, but the underlying morphologic and physiological mechanisms remain unknown. In this study, we examined PV BCs in layer (L)2/3 of the mEC characterizing their intrinsic physiology, morphology and synaptic connectivity in the juvenile rat. We show that while intrinsic physiology and morphology are broadly similar over the dorsoventral axis, PV BCs form more connections onto local PrCs in the dorsal mEC, independent of target cell type. In turn, the major PrC subtypes, pyramidal cell (PC) and stellate cell (SC), form connections onto PV BCs with lower, but equal probability. These data thus identify inhibitory connectivity as source of the gradient of inhibition, plausibly explaining divergent grid field formation along this dorsoventral axis of the mEC.

Somatostatin expressing GABAergic interneurons in the medial entorhinal cortex preferentially inhibit layerIII-V pyramidal cells

GABA released from heterogeneous types of interneurons acts in a complex spatio-temporal manner on postsynaptic targets in the networks. In addition to GABA, a large fraction of GABAergic cells also express neuromodulator peptides. Somatostatin (SOM) containing interneurons, in particular, have been recognized as key players in several brain circuits, however, the action of SOM and its downstream network effects remain largely unknown. Here, we used optogenetics, electrophysiologic, anatomical and behavioral experiments to reveal that the dendrite-targeting, SOM⁺ GABAergic interneurons demonstrate a unique layer-specific action in the medial entorhinal cortex (MEC) both in terms of GABAergic and SOM-related properties. We show that GABAergic and somatostatinergic neurotransmission originating from SOM⁺ local interneurons preferentially inhibit layer_III-V pyramidal cells, known to be involved in memory formation. We propose that this dendritic GABA–SOM dual inhibitory network motif within the MEC serves to selectively modulate working-memory formation without affecting the retrieval of already learned spatial navigation tasks.

Miklós Kecskés et al. show that somatostatin-expressing interneurons in the medial entorhinal cortex regulate deep-layer pyramidal neurons and impact short-term memory in mice.

Robustness Improvement of Visual Templates Matching Based on Frequency-Tuned Model in RatSLAM

This paper describes an improved brain-inspired simultaneous localization and mapping (RatSLAM) that extracts visual features from saliency maps using a frequency-tuned (FT) model. In the traditional RatSLAM algorithm, the visual template feature is organized as a one-dimensional vector whose values only depend on pixel intensity; therefore, this feature is susceptible to changes in illumination intensity. In contrast to this approach, which directly generates visual templates from raw RGB images, we propose an FT model that converts RGB images into saliency maps to obtain visual templates. The visual templates extracted from the saliency maps contain more of the feature information contained within the original images. Our experimental results demonstrate that the accuracy of loop closure detection was improved, as measured by the number of loop closures detected by our method compared with the traditional RatSLAM system. We additionally verified that the proposed FT model-based visual templates improve the robustness of familiar visual scene identification by RatSLAM.

Episodic Memories: How do the Hippocampus and the Entorhinal Ring Attractors Cooperate to Create Them?

The brain is capable of registering a constellation of events, encountered only once, as an episodic memory that can last for a lifetime. As evidenced by the clinical case of the patient HM, memories preserving their episodic nature still depend on the hippocampal formation, several years after being created, while semantic memories are thought to reside in neocortical areas. The neurobiological substrate of one-time learning and life-long storing in the brain, that must exist at the cellular and circuit level, is still undiscovered. The breakthrough is delayed by the fact that studies jointly investigating the rodent hippocampus and entorhinal cortex are mostly targeted at understanding the spatial aspect of learning. Here, we present the concept of an entorhinal cortical module, termed EPISODE module, that could explain how the representations of different elements constituting episodic memories can be linked together at the stage of encoding. The new model that we propose here reconciles the structural and functional observations made in the entorhinal cortex and explains how the downstream hippocampal processing organizes the representations into meaningful sequences.

Inter- and intra-animal variation in the integrative properties of stellate cells in the medial entorhinal cortex

Distinctions between cell types underpin organizational principles for nervous system function. Functional variation also exists between neurons of the same type. This is exemplified by correspondence between grid cell spatial scales and the synaptic integrative properties of stellate cells (SCs) in the medial entorhinal cortex. However, we know little about how functional variability is structured either within or between individuals. Using ex-vivo patch-clamp recordings from up to 55 SCs per mouse, we found that integrative properties vary between mice and, in contrast to the modularity of grid cell spatial scales, have a continuous dorsoventral organization. Our results constrain mechanisms for modular grid firing and provide evidence for inter-animal phenotypic variability among neurons of the same type. We suggest that neuron type properties are tuned to circuit-level set points that vary within and between animals.

Transition Scale-Spaces: A Computational Theory for the Discretized Entorhinal Cortex

Although hippocampal grid cells are thought to be crucial for spatial navigation, their computational purpose remains disputed. Recently, they were proposed to represent spatial transitions and convey this knowledge downstream to place cells. However, a single scale of transitions is insufficient to plan long goal-directed sequences in behaviorally acceptable time.

Here, a scale-space data structure is suggested to optimally accelerate retrievals from transition systems, called transition scale-space (TSS). Remaining exclusively on an algorithmic level, the scale increment is proved to be ideally [Formula: see text] for biologically plausible receptive fields. It is then argued that temporal buffering is necessary to learn the scale-space online. Next, two modes for retrieval of sequences from the TSS are presented: top down and bottom up. The two modes are evaluated in symbolic simulations (i.e., without biologically plausible spiking neurons). Additionally, a TSS is used for short-cut discovery in a simulated Morris water maze. Finally, the results are discussed in depth with respect to biological plausibility, and several testable predictions are derived. Moreover, relations to other grid cell models, multiresolution path planning, and scale-space theory are highlighted. Summarized, reward-free transition encoding is shown here, in a theoretical model, to be compatible with the observed discretization along the dorso-ventral axis of the medial entorhinal cortex. Because the theoretical model generalizes beyond navigation, the TSS is suggested to be a general-purpose cortical data structure for fast retrieval of sequences and relational knowledge.

Source code for all simulations presented in this paper can be found at https://github.com/rochus/transitionscalespace .

Identifying Core Regions for Path Integration on Medial Entorhinal Cortex of Hippocampal Formation

Path integration is one of the functions that support the self-localization ability of animals. Path integration outputs position information after an animal’s movement when initial-position and movement information is input. The core region responsible for this function has been identified as the medial entorhinal cortex (MEC), which is part of the hippocampal formation that constitutes the limbic system. However, a more specific core region has not yet been identified. This research aims to clarify the detailed structure at the cell-firing level in the core region responsible for path integration from fragmentarily accumulated experimental and theoretical findings by reviewing 77 papers. This research draws a novel diagram that describes the MEC, the hippocampus, and their surrounding regions by focusing on the MEC’s input/output (I/O) information. The diagram was created by summarizing the results of exhaustively scrutinizing the papers that are relative to the I/O relationship, the connection relationship, and cell position and firing pattern. From additional investigations, we show function information related to path integration, such as I/O information and the relationship between multiple functions. Furthermore, we constructed an algorithmic hypothesis on I/O information and path-integration calculation method from the diagram and the information of functions related to path integration. The algorithmic hypothesis is composed of regions related to path integration, the I/O relations between them, the calculation performed there, and the information representations (cell-firing pattern) in them. Results of examining the hypothesis confirmed that the core region responsible for path integration was either stellate cells in layer II or pyramidal cells in layer III of the MEC.

NeuroSLAM: a brain-inspired SLAM system for 3D environments

Roboticists have long drawn inspiration from nature to develop navigation and simultaneous localization and mapping (SLAM) systems such as RatSLAM. Animals such as birds and bats possess superlative navigation capabilities, robustly navigating over large, three-dimensional environments, leveraging an internal neural representation of space combined with external sensory cues and self-motion cues. This paper presents a novel neuro-inspired 4DoF (degrees of freedom) SLAM system named NeuroSLAM, based upon computational models of 3D grid cells and multilayered head direction cells, integrated with a vision system that provides external visual cues and self-motion cues. NeuroSLAM's neural network activity drives the creation of a multilayered graphical experience map in a real time, enabling relocalization and loop closure through sequences of familiar local visual cues. A multilayered experience map relaxation algorithm is used to correct cumulative errors in path integration after loop closure. Using both synthetic and real-world datasets comprising complex, multilayered indoor and outdoor environments, we demonstrate NeuroSLAM consistently producing topologically correct three-dimensional maps.

Origin and role of path integration in the cognitive representations of the hippocampus: computational insights into open questions

Path integration is a straightforward concept with varied connotations that are important to different disciplines concerned with navigation, such as ethology, cognitive science, robotics and neuroscience. In studying the hippocampal formation, it is fruitful to think of path integration as a computation that transforms a sense of motion into a sense of location, continuously integrated with landmark perception. Here, we review experimental evidence that path integration is intimately involved in fundamental properties of place cells and other spatial cells that are thought to support a cognitive abstraction of space in this brain system. We discuss hypotheses about the anatomical and computational origin of path integration in the well-characterized circuits of the rodent limbic system. We highlight how computational frameworks for map-building in robotics and cognitive science alike suggest an essential role for path integration in the creation of a new map in unfamiliar territory, and how this very role can help us make sense of differences in neurophysiological data from novel versus familiar and small versus large environments. Similar computational principles could be at work when the hippocampus builds certain non-spatial representations, such as time intervals or trajectories defined in a sensory stimulus space.

Self-motion processing in visual and entorhinal cortices: inputs, integration, and implications for position coding

The sensory signals generated by self-motion are complex and multimodal, but the ability to integrate these signals into a unified self-motion percept to guide navigation is essential for animal survival. Here, we summarize classic and recent work on self-motion coding in the visual and entorhinal cortices of the rodent brain. We compare motion processing in rodent and primate visual cortices, highlighting the strengths of classic primate work in establishing causal links between neural activity and perception, and discuss the integration of motor and visual signals in rodent visual cortex. We then turn to the medial entorhinal cortex (MEC), where calculations using self-motion to update position estimates are thought to occur. We focus on several key sources of self-motion information to MEC: the medial septum, which provides locomotor speed information; visual cortex, whose input has been increasingly recognized as essential to both position and speed-tuned MEC cells; and the head direction system, which is a major source of directional information for self-motion estimates. These inputs create a large and diverse group of self-motion codes in MEC, and great interest remains in how these self-motion codes might be integrated by MEC grid cells to estimate position. However, which signals are used in these calculations and the mechanisms by which they are integrated remain controversial. We end by proposing future experiments that could further our understanding of the interactions between MEC cells that code for self-motion and position and clarify the relationship between the activity of these cells and spatial perception.

Hexagonal Grid Fields Optimally Encode Transitions in Spatiotemporal Sequences

Grid cells of the rodent entorhinal cortex are essential for spatial navigation. Although their function is commonly believed to be either path integration or localization, the origin or purpose of their hexagonal firing fields remains disputed. Here they are proposed to arise as an optimal encoding of transitions in sequences. First, storage requirements for transitions in general episodic sequences are examined using propositional logic and graph theory. Subsequently, transitions in complete metric spaces are considered under the assumption of an ideal sampling of an input space. It is shown that memory capacity of neurons that have to encode multiple feasible spatial transitions is maximized by a hexagonal pattern. Grid cells are proposed to encode spatial transitions in spatiotemporal sequences, with the entorhinal-hippocampal loop forming a multitransition system.

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.