Grid cells are modulated by local head direction

Transformation of spatial representations along hippocampal circuits

The hippocampus is thought to provide the brain with a cognitive map of the external world by processing various types of spatial information. To understand how essential spatial variables such as direction, position, and distance are transformed along its circuits to construct this global map, we perform single-photon widefield microendoscope calcium imaging in the dentate gyrus and CA3 of mice freely navigating along a narrow corridor. We find that spatial activity maps in the dentate gyrus, but not in CA3, are correlated after aligning them to the running directions, suggesting that they represent the distance traveled along the track in egocentric coordinates. Together with population activity decoding, our data suggest that while spatial representations in the dentate gyrus and CA3 are anchored in both egocentric and allocentric coordinates, egocentric distance coding is more prevalent in the dentate gyrus than in CA3, providing insights into the assembly of the cognitive map.

Task-anchored grid cell firing is selectively associated with successful path integration-dependent behaviour

Grid firing fields have been proposed as a neural substrate for spatial localisation in general or for path integration in particular. To distinguish these possibilities, we investigate firing of grid and non-grid cells in the mouse medial entorhinal cortex during a location memory task. We find that grid firing can either be anchored to the task environment, or can encode distance travelled independently of the task reference frame. Anchoring varied between and within sessions, while spatial firing of non-grid cells was either coherent with the grid population, or was stably anchored to the task environment. We took advantage of the variability in task-anchoring to evaluate whether and when encoding of location by grid cells might contribute to behaviour. We find that when reward location is indicated by a visual cue, performance is similar regardless of whether grid cells are task-anchored or not, arguing against a role for grid representations when location cues are available. By contrast, in the absence of the visual cue, performance was enhanced when grid cells were anchored to the task environment. Our results suggest that anchoring of grid cells to task reference frames selectively enhances performance when path integration is required.

A topological deep learning framework for neural spike decoding

The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information are through head direction cells and grid cells. Brains use head direction cells to determine orientation, whereas grid cells consist of layers of decked neurons that overlay to provide environment-based navigation. These neurons fire in ensembles where several neurons fire at once to activate a single head direction or grid. We want to capture this firing structure and use it to decode head direction and animal location from head direction and grid cell activity. Understanding, representing, and decoding these neural structures require models that encompass higher-order connectivity, more than the one-dimensional connectivity that traditional graph-based models provide. To that end, in this work, we develop a topological deep learning framework for neural spike train decoding. Our framework combines unsupervised simplicial complex discovery with the power of deep learning via a new architecture we develop herein called a simplicial convolutional recurrent neural network. Simplicial complexes, topological spaces that use not only vertices and edges but also higher-dimensional objects, naturally generalize graphs and capture more than just pairwise relationships. Additionally, this approach does not require prior knowledge of the neural activity beyond spike counts, which removes the need for similarity measurements. The effectiveness and versatility of the simplicial convolutional neural network is demonstrated on head direction and trajectory prediction via head direction and grid cell datasets.

Grid codes underlie multiple cognitive maps in the human brain

Grid cells fire at multiple positions that organize the vertices of equilateral triangles tiling a 2D space and are well studied in rodents. The last decade witnessed rapid progress in two other research lines on grid codes-empirical studies on distributed human grid-like representations in physical and multiple non-physical spaces, and cognitive computational models addressing the function of grid cells based on principles of efficient and predictive coding. Here, we review the progress in these fields and integrate these lines into a systematic organization. We also discuss the coordinate mechanisms of grid codes in the human entorhinal cortex and medial prefrontal cortex and their role in neurological and psychiatric diseases.

Variational log-Gaussian point-process methods for grid cells

We present practical solutions to applying Gaussian-process (GP) methods to calculate spatial statistics for grid cells in large environments. GPs are a data efficient approach to inferring neural tuning as a function of time, space, and other variables. We discuss how to design appropriate kernels for grid cells, and show that a variational Bayesian approach to log-Gaussian Poisson models can be calculated quickly. This class of models has closed-form expressions for the evidence lower-bound, and can be estimated rapidly for certain parameterizations of the posterior covariance. We provide an implementation that operates in a low-rank spatial frequency subspace for further acceleration, and demonstrate these methods on experimental data.

Impaired Spatial Firing Representations of Neurons in the Medial Entorhinal Cortex of the Epileptic Rat Using Microelectrode Arrays

Epilepsy severely impairs the cognitive behavior of patients. It remains unclear whether epilepsy-induced cognitive impairment is associated with neuronal activities in the medial entorhinal cortex (MEC), a region known for its involvement in spatial cognition. To explore this neural mechanism, we recorded the spikes and local field potentials from MEC neurons in lithium-pilocarpine-induced epileptic rats using self-designed microelectrode arrays. Through the open field test, we identified spatial cells exhibiting spatially selective firing properties and assessed their spatial representations in relation to the progression of epilepsy. Meanwhile, we analyzed theta oscillations and theta modulation in both excitatory and inhibitory neurons. Furthermore, we used a novel object recognition test to evaluate changes in spatial cognitive ability of epileptic rats. After the epilepsy modeling, the spatial tuning of various types of spatial cells had suffered a rapid and pronounced damage during the latent period (1 to 5 d). Subsequently, the firing characteristics and theta oscillations were impaired. In the chronic period (>10 d), the performance in the novel object experiment deteriorated. In conclusion, our study demonstrates the detrimental effect on spatial representations and electrophysiological properties of MEC neurons in the epileptic latency, suggesting the potential use of these changes as a "functional biomarker" for predicting cognitive impairment caused by epilepsy.

cFOS as a biomarker of activity maturation in the hippocampal formation

We explored the potential for cFOS expression as a marker of functional development of "resting-state" waking activity in the extended network of the hippocampus and entorhinal cortex. We examined sleeping and awake mice at (P)ostnatal days 5, 9, 13, and 17 as well as in adulthood. We find that cFOS expression is state-dependent even at 5 days old, with reliable staining occurring only in the awake mice. Even during waking, cFOS expression was rare and weak at P5. The septal nuclei, entorhinal cortex layer (L)2, and anterodorsal thalamus were exceptional in that they had robust cFOS expression at P5 that was similar to or greater than in adulthood. Significant P5 expression was also observed in the dentate gyrus, entorhinal cortex L6, postsubiculum L4-6, ventral subiculum, supramammillary nucleus, and posterior hypothalamic nucleus. The expression in these regions grew stronger with age, and the expression in new regions was added progressively at P9 and P13 by which point the overall expression pattern in many regions was qualitatively similar to the adult. Six regions-CA1, dorsal subiculum, postsubiculum L2-3, reuniens nucleus, and perirhinal and postrhinal cortices-were very late developing, mostly achieving adult levels only after P17. Our findings support a number of developmental principles. First, early spontaneous activity patterns induced by muscle twitches during sleep do not induce robust cFOS expression in the extended hippocampal network. Second, the development of cFOS expression follows the progressive activation along the trisynaptic circuit, rather than birth date or cellular maturation. Third, we reveal components of the egocentric head-direction and theta-rhythm circuits as the earliest cFOS active circuits in the forebrain. Our results suggest that cFOS staining may provide a reliable and sensitive biomarker for hippocampal formation activity development, particularly in regard to the attainment of a normal waking state and synchronizing rhythms such as theta and gamma.

Cortical Integration of Vestibular and Visual Cues for Navigation, Visual Processing, and Perception

Despite increasing evidence of its involvement in several key functions of the cerebral cortex, the vestibular sense rarely enters our consciousness. Indeed, the extent to which these internal signals are incorporated within cortical sensory representation and how they might be relied upon for sensory-driven decision-making, during, for example, spatial navigation, is yet to be understood. Recent novel experimental approaches in rodents have probed both the physiological and behavioral significance of vestibular signals and indicate that their widespread integration with vision improves both the cortical representation and perceptual accuracy of self-motion and orientation. Here, we summarize these recent findings with a focus on cortical circuits involved in visual perception and spatial navigation and highlight the major remaining knowledge gaps. We suggest that vestibulo-visual integration reflects a process of constant updating regarding the status of self-motion, and access to such information by the cortex is used for sensory perception and predictions that may be implemented for rapid, navigation-related decision-making.

Simultaneous representation of multiple time horizons by entorhinal grid cells and CA1 place cells

Grid cells and place cells represent the spatiotemporal continuum of an animal's past, present, and future locations. However, their spatiotemporal relationship is unclear. Here, we co-record grid and place cells in freely foraging rats. We show that average time shifts in grid cells tend to be prospective and are proportional to their spatial scale, providing a nearly instantaneous readout of a spectrum of progressively increasing time horizons ranging hundreds of milliseconds. Average time shifts of place cells are generally larger compared to grid cells and also increase with place field sizes. Moreover, time horizons display nonlinear modulation by the animal's trajectories in relation to the local boundaries and locomotion cues. Finally, long and short time horizons occur at different parts of the theta cycle, which may facilitate their readout. Together, these findings suggest that population activity of grid and place cells may represent local trajectories essential for goal-directed navigation and planning.

Superficial-layer versus deep-layer lateral entorhinal cortex: Coding of allocentric space, egocentric space, speed, boundaries, and corners

Entorhinal cortex is the major gateway between the neocortex and the hippocampus and thus plays an essential role in subserving episodic memory and spatial navigation. It can be divided into the medial entorhinal cortex (MEC) and the lateral entorhinal cortex (LEC), which are commonly theorized to be critical for spatial (context) and non-spatial (content) inputs, respectively. Consistent with this theory, LEC neurons are found to carry little information about allocentric self-location, even in cue-rich environments, but they exhibit egocentric spatial information about external items in the environment. The superficial and deep layers of LEC are believed to mediate the input to and output from the hippocampus, respectively. As earlier studies mainly examined the spatial firing properties of superficial-layer LEC neurons, here we characterized the deep-layer LEC neurons and made direct comparisons with their superficial counterparts in single unit recordings from behaving rats. Because deep-layer LEC cells received inputs from hippocampal regions, which have strong selectivity for self-location, we hypothesized that deep-layer LEC neurons would be more informative about allocentric position than superficial-layer LEC neurons. We found that deep-layer LEC cells showed only slightly more allocentric spatial information and higher spatial consistency than superficial-layer LEC cells. Egocentric coding properties were comparable between these two subregions. In addition, LEC neurons demonstrated preferential firing at lower speeds, as well as at the boundary or corners of the environment. These results suggest that allocentric spatial outputs from the hippocampus are transformed in deep-layer LEC into the egocentric coding dimensions of LEC, rather than maintaining the allocentric spatial tuning of the CA1 place fields.

Effects of neuromodulation-inspired mechanisms on the performance of deep neural networks in a spatial learning task

In recent years, the biological underpinnings of adaptive learning have been modeled, leading to faster model convergence and various behavioral benefits in tasks including spatial navigation and cue-reward association. Furthermore, studies have investigated how the neuromodulatory system, a major driver of synaptic plasticity and state-dependent changes in the brain neuronal activities, plays a role in training deep neural networks (DNNs). In this study, we extended previous studies on neuromodulation-inspired DNNs and explored the effects of neuromodulatory components on learning and single unit activities in a spatial learning task. Under the multiscale neuromodulatory framework, plastic components, dropout probability modulation, and learning rate decay were added to the single unit, layer, and whole network levels of DNN models, respectively. We observed behavioral benefits including faster learning and smaller error of ambulation. We then concluded that neuromodulatory components can affect learning trajectories, outcomes, and single unit activities, in a component- and hyperparameter-dependent manner.

A unified theory for the computational and mechanistic origins of grid cells

The discovery of entorhinal grid cells has generated considerable interest in how and why hexagonal firing fields might emerge in a generic manner from neural circuits, and what their computational significance might be. Here, we forge a link between the problem of path integration and the existence of hexagonal grids, by demonstrating that such grids arise in neural networks trained to path integrate under simple biologically plausible constraints. Moreover, we develop a unifying theory for why hexagonal grids are ubiquitous in path-integrator circuits. Such trained networks also yield powerful mechanistic hypotheses, exhibiting realistic levels of biological variability not captured by hand-designed models. We furthermore develop methods to analyze the connectome and activity maps of our networks to elucidate fundamental mechanisms underlying path integration. These methods provide a road map to go from connectomic and physiological measurements to conceptual understanding in a manner that could generalize to other settings.

Grid cell remapping under three-dimensional object and social landmarks detected by implantable microelectrode arrays for the medial entorhinal cortex

Grid cells with stable hexagonal firing patterns in the medial entorhinal cortex (MEC) carry the vital function of serving as a metric for the surrounding environment. Whether this mechanism processes only spatial information or involves nonspatial information remains elusive. Here, we fabricated an MEC-shaped microelectrode array (MEA) to detect the variation in neural spikes and local field potentials of the MEC when rats forage in a square enclosure with a planar, three-dimensional object and social landmarks in sequence. The results showed that grid cells exhibited rate remapping under social conditions in which spike firing fields closer to the social landmark had a higher firing rate. Furthermore, global remapping showed that hexagonal firing patterns were rotated and scaled when the planar landmark was replaced with object and social landmarks. In addition, when grid cells were activated, the local field potentials were dominated by the theta band (5-8 Hz), and spike phase locking was observed at troughs of theta oscillations. Our results suggest the pattern separation mechanism of grid cells in which the spatial firing structure and firing rate respond to spatial and social information, respectively, which may provide new insights into how the brain creates a cognitive map.

Spatial representation by ramping activity of neurons in the retrohippocampal cortex

Neurons in the retrohippocampal cortices play crucial roles in spatial memory. Many retrohippocampal neurons have firing fields that are selectively active at specific locations, with memory for rewarded locations associated with reorganization of these firing fields. Whether this is the sole strategy for representing spatial memories is unclear. Here, we demonstrate that during a spatial memory task retrohippocampal neurons encode location through ramping activity that extends across segments of a linear track approaching and following a reward, with the rewarded location represented by offsets or switches in the slope of the ramping activity. Ramping representations could be maintained independently of trial outcome and cues marking the reward location, indicating that they result from recall of the track structure. When recorded in an open arena, neurons that generated ramping activity during the spatial memory task were more numerous than grid or border cells, with a majority showing spatial firing that did not meet criteria for classification as grid or border representations. Encoding of rewarded locations through offsets and switches in the slope of ramping activity also emerged in recurrent neural network models trained to solve a similar spatial memory task. Impaired performance of model networks following disruption of outputs from ramping neurons is consistent with this coding strategy supporting navigation to recalled locations of behavioral significance. Our results suggest that encoding of learned spaces by retrohippocampal networks employs both discrete firing fields and continuous ramping representations. We hypothesize that retrohippocampal ramping activity mediates readout of learned models for goal-directed navigation.

Natural switches in behaviour rapidly modulate hippocampal coding

Throughout their daily lives, animals and humans often switch between different behaviours. However, neuroscience research typically studies the brain while the animal is performing one behavioural task at a time, and little is known about how brain circuits represent switches between different behaviours. Here we tested this question using an ethological setting: two bats flew together in a long 135 m tunnel, and switched between navigation when flying alone (solo) and collision avoidance as they flew past each other (cross-over). Bats increased their echolocation click rate before each cross-over, indicating attention to the other bat^1–9. Hippocampal CA1 neurons represented the bat’s own position when flying alone (place coding^10–14). Notably, during cross-overs, neurons switched rapidly to jointly represent the interbat distance by self-position. This neuronal switch was very fast—as fast as 100 ms—which could be revealed owing to the very rapid natural behavioural switch. The neuronal switch correlated with the attention signal, as indexed by echolocation. Interestingly, the different place fields of the same neuron often exhibited very different tuning to interbat distance, creating a complex non-separable coding of position by distance. Theoretical analysis showed that this complex representation yields more efficient coding. Overall, our results suggest that during dynamic natural behaviour, hippocampal neurons can rapidly switch their core computation to represent the relevant behavioural variables, supporting behavioural flexibility.

During rapid behavioural switches in flying bats, hippocampal neurons can rapidly switch their core computation to represent the relevant behavioural variables, supporting behavioural flexibility.

Modular microcircuit organization of the presubicular head-direction map

Our internal sense of direction is thought to rely on the activity of head-direction (HD) neurons. We find that the mouse dorsal presubiculum (PreS), a key structure in the cortical representation of HD, displays a modular "patch-matrix" organization, which is conserved across species (including human). Calbindin-positive layer 2 neurons within the "matrix" form modular recurrent microcircuits, while inputs from the anterodorsal and laterodorsal thalamic nuclei are non-overlapping and target the "patch" and "matrix" compartments, respectively. The apical dendrites of identified HD cells are largely restricted within the "matrix," pointing to a non-random sampling of patterned inputs and to a precise structure-function architecture. Optogenetic perturbation of modular recurrent microcircuits results in a drastic tonic suppression of firing only in a subpopulation of HD neurons. Altogether, our data reveal a modular microcircuit organization of the PreS HD map and point to the existence of cell-type-specific microcircuits that support the cortical HD representation.

Orientation Invariant Sensorimotor Object Recognition Using Cortical Grid Cells

Grid cells enable efficient modeling of locations and movement through path integration. Recent work suggests that the brain might use similar mechanisms to learn the structure of objects and environments through sensorimotor processing. This work is extended in our network to support sensor orientations relative to learned allocentric object representations. The proposed mechanism enables object representations to be learned through sensorimotor sequences, and inference of these learned object representations from novel sensorimotor sequences produced by rotated objects through path integration. The model proposes that orientation-selective cells are present in each column in the neocortex, and provides a biologically plausible implementation that echoes experimental measurements and fits in with theoretical predictions of previous studies.

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.

Deep entorhinal cortex: from circuit organization to spatial cognition and memory

The deep layers of the entorhinal cortex are important for spatial cognition, as well as memory storage, consolidation and retrieval. A long-standing hypothesis is that deep-layer neurons relay spatial and memory-related signals between the hippocampus and telencephalon. We review the implications of recent circuit-level analyses that suggest more complex roles. The organization of deep entorhinal layers is consistent with multi-stage processing by specialized cell populations; in this framework, hippocampal, neocortical, and subcortical inputs are integrated to generate representations for use by targets in the telencephalon and for feedback to the superficial entorhinal cortex and hippocampus. Addressing individual sublayers of the deep entorhinal cortex in future experiments and models will be important for establishing systems-level mechanisms for spatial cognition and episodic memory.

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.

Identification of predictors for mini-mental state examination and revised Hasegawa's Dementia Scale scores using MR-based brain morphometry

Purpose

The early detection of cognitive function decline is crucial to help manage or slow the progression of symptoms. The Mini-Mental State Examination (MMSE) and revised Hasegawa's Dementia Scale (HDS-R) are widely used in screening for cognitive impairment. The purpose of this study was to explore common predictors of the two different cognitive testing systems using MR-based brain morphometry.

Materials and Methods

This retrospective study included 200 subjects with clinical suspicion of cognitive impairment who underwent 3D T1-weighted MRI at our institution between February 2019 and August 2020. Variables related to the volume of deep gray matter and 70 cortical thicknesses were obtained from the MR images using voxel-based specific regional analysis system for Alzheimer's disease (VSRAD) and FreeSurfer software. The correlation between each variable including age and MMSE/HDS-R scores was evaluated using uni- and multi-variate logistic regression analyses.

Results

In univariate analysis, parameters include hippocampal volume and bilateral entorhinal cortex (ERC) thickness showed moderate correlation coefficients with both MMSE and HDS-R scores. Multivariate analysis demonstrated the right ERC thickness was the common parameter which significantly correlates with both MMSE and HDS-R scores (p < 0.05).

Conclusion

Right ERC thickness appears to offer a useful predictive biomarker for both MMSE and HDS-R scores.