Controlling phase noise in oscillatory interference models of grid cell firing

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 broadband power shifts in entorhinal EEG are related to the firing of grid cells

The relationship between the firing of the grid cell and mesoscopic neural oscillations is one of the key issues to understand the neural mechanism of grid cells. Previous studies have focused more on the correspondence between neuronal firing and phases of oscillations, such as phase precession. There are also some conclusions about the relationship between the activity of grid cells and the intensity of neural oscillations, such as the disappearance of grid pattern caused by the blocking of theta rhythm, but the correlation between the firing rates of grid cells and the narrowband power of neural oscillations or the broadband LFP power is still scarce. Through analyzing the records of spike times of grid cells and local entorhinal EEG obtained by Hafting et al., in the spatial navigation experiment, we find that grid cells are, to a large proportion, a kind of broadband-shift neurons, and the positive correlation between grid cell activity and power of low theta and gamma bands was observed. These results have well verified, promoted, and connected many scattered research conclusions, such as the broadband shift phenomenon of hippocampal neurons, the influence of low theta activity on the firing pattern of grid cells, and the positive correlation between single-cell activity and gamma-band activity. This work is of great significance for the study of the neural mechanism of grid cells at the micro and mesoscopic levels, and may also inspire the use of indicators such as broadband power as markers for grid cell activity.

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.

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.

Entorhinal Neurons Exhibit Cue Locking in Rodent VR

The regular firing pattern exhibited by medial entorhinal (mEC) grid cells of locomoting rodents is hypothesized to provide spatial metric information relevant for navigation. The development of virtual reality (VR) for head-fixed mice confers a number of experimental advantages and has become increasingly popular as a method for investigating spatially-selective cells. Recent experiments using 1D VR linear tracks have shown that some mEC cells have multiple fields in virtual space, analogous to grid cells on real linear tracks. We recorded from the mEC as mice traversed virtual tracks featuring regularly spaced repetitive cues and identified a population of cells with multiple firing fields, resembling the regular firing of grid cells. However, further analyses indicated that many of these were not, in fact, grid cells because: (1) when recorded in the open field they did not display discrete firing fields with six-fold symmetry; and (2) in different VR environments their firing fields were found to match the spatial frequency of repetitive environmental cues. In contrast, cells identified as grid cells based on their open field firing patterns did not exhibit cue locking. In light of these results we highlight the importance of controlling the periodicity of the visual cues in VR and the necessity of identifying grid cells from real open field environments in order to correctly characterize spatially modulated neurons in VR experiments.

Spatial synchronization codes from coupled rate-phase neurons

During spatial navigation, the frequency and timing of spikes from spatial neurons including place cells in hippocampus and grid cells in medial entorhinal cortex are temporally organized by continuous theta oscillations (6-11 Hz). The theta rhythm is regulated by subcortical structures including the medial septum, but it is unclear how spatial information from place cells may reciprocally organize subcortical theta-rhythmic activity. Here we recorded single-unit spiking from a constellation of subcortical and hippocampal sites to study spatial modulation of rhythmic spike timing in rats freely exploring an open environment. Our analysis revealed a novel class of neurons that we termed 'phaser cells,' characterized by a symmetric coupling between firing rate and spike theta-phase. Phaser cells encoded space by assigning distinct phases to allocentric isocontour levels of each cell's spatial firing pattern. In our dataset, phaser cells were predominantly located in the lateral septum, but also the hippocampus, anteroventral thalamus, lateral hypothalamus, and nucleus accumbens. Unlike the unidirectional late-to-early phase precession of place cells, bidirectional phase modulation acted to return phaser cells to the same theta-phase along a given spatial isocontour, including cells that characteristically shifted to later phases at higher firing rates. Our dynamical models of intrinsic theta-bursting neurons demonstrated that experience-independent temporal coding mechanisms can qualitatively explain (1) the spatial rate-phase relationships of phaser cells and (2) the observed temporal segregation of phaser cells according to phase-shift direction. In open-field phaser cell simulations, competitive learning embedded phase-code entrainment maps into the weights of downstream targets, including path integration networks. Bayesian phase decoding revealed error correction capable of resetting path integration at subsecond timescales. Our findings suggest that phaser cells may instantiate a subcortical theta-rhythmic loop of spatial feedback. We outline a framework in which location-dependent synchrony reconciles internal idiothetic processes with the allothetic reference points of sensory experience.

The Preferred Directions of Conjunctive Grid X Head Direction Cells in the Medial Entorhinal Cortex Are Periodically Organized

The discovery of speed-modulated grid, head direction, and conjunctive grid x head direction cells in the medial entorhinal cortex has led to the hypothesis that path integration, the updating of one’s spatial representation based on movement, may be carried out within this region. This hypothesis has been formalized by many computational models, including a class known as attractor network models. While many of these models propose specific mechanisms by which path integration might occur, predictions of these specific mechanisms have not been tested. Here I derive and test a key prediction of one attractor network path integration mechanism. Specifically, I first demonstrate that this mechanism predicts a periodic distribution of conjunctive cell preferred directions in order to minimize drift. Next, I test whether conjunctive cell preferred directions are in fact periodically organized. Results indicate that conjunctive cells are preferentially tuned to increments of 36°, consistent with drift minimization in this path integration mechanism. By contrast, no periodicity was observed in the preferred directions of either pure grid or pure head direction cells. These results provide the first neural evidence of a nonuniform structure in the directional preferences of any head direction representation found in the brain.

Using Grid Cells for Navigation

Mammals are able to navigate to hidden goal locations by direct routes that may traverse previously unvisited terrain. Empirical evidence suggests that this “vector navigation” relies on an internal representation of space provided by the hippocampal formation. The periodic spatial firing patterns of grid cells in the hippocampal formation offer a compact combinatorial code for location within large-scale space. Here, we consider the computational problem of how to determine the vector between start and goal locations encoded by the firing of grid cells when this vector may be much longer than the largest grid scale. First, we present an algorithmic solution to the problem, inspired by the Fourier shift theorem. Second, we describe several potential neural network implementations of this solution that combine efficiency of search and biological plausibility. Finally, we discuss the empirical predictions of these implementations and their relationship to the anatomy and electrophysiology of the hippocampal formation.

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Grid cells (GCs) are believed to provide a path integration input to place cells

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However, GCs also provide a powerful context-independent metric for large-scale space

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Hence, we show how GCs can be used for vector navigation between arbitrary locations

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We simulate various neural implementations and make testable experimental predictions

A hybrid oscillatory interference/continuous attractor network model of grid cell firing

Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account for experimental data. The oscillatory interference model proposes that the grid pattern is formed from linear interference patterns or "periodic bands" in which velocity-controlled oscillators integrate self-motion to code displacement along preferred directions. However, it also allows the use of symmetric recurrent connectivity between grid cells to provide relative stability and continuous attractor dynamics. Here, we present simulations of this type of hybrid model, demonstrate that it generates intracellular membrane potential profiles that closely match those observed in vivo, addresses several criticisms aimed at pure oscillatory interference and continuous attractor models, and provides testable predictions for future empirical studies.