Uncovering 2-D toroidal representations in grid cell ensemble activity during 1-D behavior.

Minimal experiments, such as head-fixed wheel-running and sleep, offer experimental advantages but restrict the amount of observable behavior, making it difficult to classify functional cell types. Arguably, the grid cell, and its striking periodicity, would not have been discovered without the perspective provided by free behavior in an open environment. Here, we show that by shifting the focus from single neurons to populations, we change the minimal experimental complexity required. We identify grid cell modules and show that the activity covers a similar, stable toroidal state space during wheel running as in open field foraging. Trajectories on grid cell tori correspond to single trial runs in virtual reality and path integration in the dark, and the alignment of the representation rapidly shifts with changes in experimental conditions. Thus, we provide a methodology to discover and study complex internal representations in even the simplest of experiments.

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.

Visual boundary cues suffice to anchor place and grid cells in virtual reality.

The hippocampal formation contains neurons responsive to an animal's current location and orientation, which together provide the organism with a neural map of space.1,2,3 Spatially tuned neurons rely on external landmark cues and internally generated movement information to estimate position.4,5 An important class of landmark cue are the boundaries delimiting an environment, which can define place cell field position6,7 and stabilize grid cell firing.8 However, the precise nature of the sensory information used to detect boundaries remains unknown. We used 2-dimensional virtual reality (VR)9 to show that visual cues from elevated walls surrounding the environment are both sufficient and necessary to stabilize place and grid cell responses in VR, when only visual and self-motion cues are available. By contrast, flat boundaries formed by the edges of a textured floor did not stabilize place and grid cells, indicating only specific forms of visual boundary stabilize hippocampal spatial firing. Unstable grid cells retain internally coherent, hexagonally arranged firing fields, but these fields "drift" with respect to the virtual environment over periods >5 s. Optic flow from a virtual floor does not slow drift dynamics, emphasizing the importance of boundary-related visual information. Surprisingly, place fields are more stable close to boundaries even with floor and wall cues removed, suggesting invisible boundaries are inferred using the motion of a discrete, separate cue (a beacon signaling reward location). Subsets of place cells show allocentric directional tuning toward the beacon, with strength of tuning correlating with place field stability when boundaries are removed.

Evidence for grid-cell-like activity in the time domain.

The relation between the processing of space and time in the brain has been an enduring cross-disciplinary question. Grid cells have been recognized as a hallmark of the mammalian navigation system, with recent studies attesting to their involvement in the organization of conceptual knowledge in humans. To determine whether grid-cell-like representations support temporal processing, we asked subjects to mentally simulate changes in age and time-of-day, each constituting "trajectory" in an age-day space, while undergoing fMRI. We found that grid-cell-like representations supported trajecting across this age-day space. Furthermore, brain regions concurrently coding past-to-future orientation positively modulated the magnitude of grid-cell-like representation in the left entorhinal cortex. Finally, our findings suggest that temporal processing may be supported by spatially modulated systems, and that innate regularities of abstract domains may interface and alter grid-cell-like representations, similarly to spatial geometry.

Changes in spatial self-consciousness elicit grid cell-like representation in the entorhinal cortex.

Grid cells in the entorhinal cortex (EC) encode an individual's location in space, integrating both environmental and multisensory bodily cues. Notably, body-derived signals are also primary signals for the sense of self. While studies have demonstrated that continuous application of visuo-tactile bodily stimuli can induce perceptual shifts in self-location, it remains unexplored whether these illusory changes suffice to trigger grid cell-like representation (GCLR) within the EC, and how this compares to GCLR during conventional virtual navigation. To address this, we systematically induced illusory drifts in self-location toward controlled directions using visuo-tactile bodily stimulation, while maintaining the subjects' visual viewpoint fixed (absent conventional virtual navigation). Subsequently, we evaluated the corresponding GCLR in the EC through functional MRI analysis. Our results reveal that illusory changes in perceived self-location (independent of changes in environmental navigation cues) can indeed evoke entorhinal GCLR, correlating in strength with the magnitude of perceived self-location, and characterized by similar grid orientation as during conventional virtual navigation in the same virtual room. These data demonstrate that the same grid-like representation is recruited when navigating based on environmental, mainly visual cues, or when experiencing illusory forward drifts in self-location, driven by perceptual multisensory bodily cues.

Are grid cells used for navigation? On local metrics, subjective spaces, and black holes.

The symmetric, lattice-like spatial pattern of grid-cell activity is thought to provide a neuronal global metric for space. This view is compatible with grid cells recorded in empty boxes but inconsistent with data from more naturalistic settings. We review evidence arguing against the global-metric notion, including the distortion and disintegration of the grid pattern in complex and three-dimensional environments. We argue that deviations from lattice symmetry are key for understanding grid-cell function. We propose three possible functions for grid cells, which treat real-world grid distortions as a feature rather than a bug. First, grid cells may constitute a local metric for proximal space rather than a global metric for all space. Second, grid cells could form a metric for subjective action-relevant space rather than physical space. Third, distortions may represent salient locations. Finally, we discuss mechanisms that can underlie these functions. These ideas may transform our thinking about grid cells.

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 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.

Reduced grid-like theta modulation in schizophrenia.

The hippocampal formation has been implicated in the pathophysiology of schizophrenia, with patients showing impairments in spatial and relational cognition, structural changes in entorhinal cortex and reduced theta coherence with medial prefrontal cortex. Both the entorhinal cortex and medial prefrontal cortex exhibit a 6-fold (or 'hexadirectional') modulation of neural activity during virtual navigation that is indicative of grid cell populations and associated with accurate spatial navigation. Here, we examined whether these grid-like patterns are disrupted in schizophrenia. We asked 17 participants with diagnoses of schizophrenia and 23 controls (matched for age, sex and IQ) to perform a virtual reality spatial navigation task during magnetoencephalography. The control group showed stronger 4-10 Hz theta power during movement onset, as well as hexadirectional modulation of theta band oscillatory activity in the right entorhinal cortex whose directional stability across trials correlated with navigational accuracy. This hexadirectional modulation was absent in schizophrenia patients, with a significant difference between groups. These results suggest that impairments in spatial and relational cognition associated with schizophrenia may arise from disrupted grid firing patterns in entorhinal cortex.

An integrated deep learning-based model of spatial cells that combines self-motion with sensory information.

A special class of neurons in the hippocampal formation broadly known as the spatial cells, whose subcategories include place cells, grid cells, and head direction cells, are considered to be the building blocks of the brain's map of the spatial world. We present a general, deep learning-based modeling framework that describes the emergence of the spatial-cell responses and can also explain responses that involve a combination of path integration and vision. The first layer of the model consists of head direction (HD) cells that code for the preferred direction of the agent. The second layer is the path integration (PI) layer with oscillatory neurons: displacement of the agent in a given direction modulates the frequency of these oscillators. Principal component analysis (PCA) of the PI-cell responses showed the emergence of cells with grid-like spatial periodicity. We show that the Bessel functions could describe the response of these cells. The output of the PI layer is used to train a stack of autoencoders. Neurons of both the layers exhibit responses resembling grid cells and place cells. The paper concludes by suggesting the wider applicability of the proposed modeling framework beyond the two simulated studies.

Are Grid-Like Representations a Component of All Perception and Cognition?

Grid cells or grid-like responses have been reported in the rodent, bat and human brains during various spatial and non-spatial tasks. However, the functions of grid-like representations beyond the classical hippocampal formation remain elusive. Based on accumulating evidence from recent rodent recordings and human fMRI data, we make speculative accounts regarding the mechanisms and functional significance of the sensory cortical grid cells and further make theory-driven predictions. We argue and reason the rationale why grid responses may be universal in the brain for a wide range of perceptual and cognitive tasks that involve locomotion and mental navigation. Computational modeling may provide an alternative and complementary means to investigate the grid code or grid-like map. We hope that the new discussion will lead to experimentally testable hypotheses and drive future experimental data collection.

Toroidal topology of population activity in grid cells.

The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment1. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations2, and are organized in modules3 that collectively form a population code for the animal's allocentric position1. The invariance of the correlation structure of this population code across environments4,5 and behavioural states6,7, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,8-11. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models12. This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.

Effect of reward on electrophysiological signatures of grid cell population activity in human spatial navigation.

The regular equilateral triangular periodic firing pattern of grid cells in the entorhinal cortex is considered a regular metric for the spatial world, and the grid-like representation correlates with hexadirectional modulation of theta (4-8 Hz) power in the entorhinal cortex relative to the moving direction. However, researchers have not clearly determined whether grid cells provide only simple spatial measures in human behavior-related navigation strategies or include other factors such as goal rewards to encode information in multiple patterns. By analysing the hexadirectional modulation of EEG signals in the theta band in the entorhinal cortex of patients with epilepsy performing spatial target navigation tasks, we found that this modulation presents a grid pattern that carries target-related reward information. This grid-like representation is influenced by explicit goals and is related to the local characteristics of the environment. This study provides evidence that human grid cell population activity is influenced by reward information at the level of neural oscillations.

Locally ordered representation of 3D space in the entorhinal cortex.

As animals navigate on a two-dimensional surface, neurons in the medial entorhinal cortex (MEC) known as grid cells are activated when the animal passes through multiple locations (firing fields) arranged in a hexagonal lattice that tiles the locomotion surface1. However, although our world is three-dimensional, it is unclear how the MEC represents 3D space2. Here we recorded from MEC cells in freely flying bats and identified several classes of spatial neurons, including 3D border cells, 3D head-direction cells, and neurons with multiple 3D firing fields. Many of these multifield neurons were 3D grid cells, whose neighbouring fields were separated by a characteristic distance-forming a local order-but lacked any global lattice arrangement of the fields. Thus, whereas 2D grid cells form a global lattice-characterized by both local and global order-3D grid cells exhibited only local order, creating a locally ordered metric for space. We modelled grid cells as emerging from pairwise interactions between fields, which yielded a hexagonal lattice in 2D and local order in 3D, thereby describing both 2D and 3D grid cells using one unifying model. Together, these data and model illuminate the fundamental differences and similarities between neural codes for 3D and 2D space in the mammalian brain.

Irregular distribution of grid cell firing fields in rats exploring a 3D volumetric space.

We investigated how entorhinal grid cells encode volumetric space. On a horizontal surface, grid cells usually produce multiple, spatially focal, approximately circular firing fields that are evenly sized and spaced to form a regular, close-packed, hexagonal array. This spatial regularity has been suggested to underlie navigational computations. In three dimensions, theoretically the equivalent firing pattern would be a regular, hexagonal close packing of evenly sized spherical fields. In the present study, we report that, in rats foraging in a cubic lattice, grid cells maintained normal temporal firing characteristics and produced spatially stable firing fields. However, although most grid fields were ellipsoid, they were sparser, larger, more variably sized and irregularly arranged, even when only fields abutting the lower surface (equivalent to the floor) were considered. Thus, grid self-organization is shaped by the environment's structure and/or movement affordances, and grids may not need to be regular to support spatial computations.

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.

Resonating neurons stabilize heterogeneous grid-cell networks.

A central theme that governs the functional design of biological networks is their ability to sustain stable function despite widespread parametric variability. Here, we investigated the impact of distinct forms of biological heterogeneities on the stability of a two-dimensional continuous attractor network (CAN) implicated in grid-patterned activity generation. We show that increasing degrees of biological heterogeneities progressively disrupted the emergence of grid-patterned activity and resulted in progressively large perturbations in low-frequency neural activity. We postulated that targeted suppression of low-frequency perturbations could ameliorate heterogeneity-induced disruptions of grid-patterned activity. To test this, we introduced intrinsic resonance, a physiological mechanism to suppress low-frequency activity, either by adding an additional high-pass filter (phenomenological) or by incorporating a slow negative feedback loop (mechanistic) into our model neurons. Strikingly, CAN models with resonating neurons were resilient to the incorporation of heterogeneities and exhibited stable grid-patterned firing. We found CAN models with mechanistic resonators to be more effective in targeted suppression of low-frequency activity, with the slow kinetics of the negative feedback loop essential in stabilizing these networks. As low-frequency perturbations (1/f noise) are pervasive across biological systems, our analyses suggest a universal role for mechanisms that suppress low-frequency activity in stabilizing heterogeneous biological networks.

A computational grid-to-place-cell transformation model indicates a synaptic driver of place cell impairment in early-stage Alzheimer's Disease.

Alzheimer's Disease (AD) is characterized by progressive neurodegeneration and cognitive impairment. Synaptic dysfunction is an established early symptom, which correlates strongly with cognitive decline, and is hypothesised to mediate the diverse neuronal network abnormalities observed in AD. However, how synaptic dysfunction contributes to network pathology and cognitive impairment in AD remains elusive. Here, we present a grid-cell-to-place-cell transformation model of long-term CA1 place cell dynamics to interrogate the effect of synaptic loss on network function and environmental representation. Synapse loss modelled after experimental observations in the APP/PS1 mouse model was found to induce firing rate alterations and place cell abnormalities that have previously been observed in AD mouse models, including enlarged place fields and lower across-session stability of place fields. Our results support the hypothesis that synaptic dysfunction underlies cognitive deficits, and demonstrate how impaired environmental representation may arise in the early stages of AD. We further propose that dysfunction of excitatory and inhibitory inputs to CA1 pyramidal cells may cause distinct impairments in place cell function, namely reduced stability and place map resolution.

Subjective value, not a gridlike code, describes neural activity in ventromedial prefrontal cortex during value-based decision-making.

Across many studies, ventromedial prefrontal cortex (vmPFC) activity has been found to correlate with subjective value during value-based decision-making. Recently, however, vmPFC has also been shown to reflect a hexagonal gridlike code during navigation through physical and conceptual space, and such gridlike codes have been proposed to enable value-based choices between novel options. Here, we first show that, in theory, a hexagonal gridlike code can in some cases mimic vmPFC activity previously attributed to subjective value, raising the possibility that the subjective value correlates previously observed in vmPFC may have actually been a misconstrued gridlike signal. We then compare the two accounts empirically, using fMRI data from a large number of subjects performing an intertemporal choice task. We find clear and unambiguous evidence that subjective value is a better description of vmPFC activity in this task than a hexagonal gridlike code. In fact, we find no significant evidence at all for a hexagonal gridlike code in vmPFC activity during intertemporal choice. This result limits the generality of gridlike modulation as description of vmPFC activity. We suggest that vmPFC may flexibly switch representational schemes so as to encode the most relevant information for the current task.

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.