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.

Spontaneous Dynamics of Hippocampal Place Fields in a Model of Combinatorial Competition among Stable Inputs.

We present computer simulations illustrating how the plastic integration of spatially stable inputs could contribute to the dynamic character of hippocampal spatial representations. In novel environments of slightly larger size than typical apparatus, the emergence of well-defined place fields in real place cells seems to rely on inputs from normally functioning grid cells. Theoretically, the grid-to-place transformation is possible if a place cell is able to respond selectively to a combination of suitably aligned grids. We previously identified the functional characteristics that allow a synaptic plasticity rule to accomplish this selection by synaptic competition during rat foraging behavior. Here, we show that the synaptic competition can outlast the formation of place fields, contributing to their spatial reorganization over time, when the model is run in larger environments and the topographical/modular organization of grid inputs is taken into account. Co-simulated cells that differ only by their randomly assigned grid inputs display different degrees and kinds of spatial reorganization-ranging from place-field remapping to more subtle in-field changes or lapses in firing. The model predicts a greater number of place fields and propensity for remapping in place cells recorded from more septal regions of the hippocampus and/or in larger environments, motivating future experimental standardization across studies and animal models. In sum, spontaneous remapping could arise from rapid synaptic learning involving inputs that are functionally homogeneous, spatially stable, and minimally stochastic.

Advantages of Persistent Cohomology in Estimating Animal Location From Grid Cell Population Activity.

Many cognitive functions are represented as cell assemblies. In the case of spatial navigation, the population activity of place cells in the hippocampus and grid cells in the entorhinal cortex represents self-location in the environment. The brain cannot directly observe self-location information in the environment. Instead, it relies on sensory information and memory to estimate self-location. Therefore, estimating low-dimensional dynamics, such as the movement trajectory of an animal exploring its environment, from only the high-dimensional neural activity is important in deciphering the information represented in the brain. Most previous studies have estimated the low-dimensional dynamics (i.e., latent variables) behind neural activity by unsupervised learning with Bayesian population decoding using artificial neural networks or gaussian processes. Recently, persistent cohomology has been used to estimate latent variables from the phase information (i.e., circular coordinates) of manifolds created by neural activity. However, the advantages of persistent cohomology over Bayesian population decoding are not well understood. We compared persistent cohomology and Bayesian population decoding in estimating the animal location from simulated and actual grid cell population activity. We found that persistent cohomology can estimate the animal location with fewer neurons than Bayesian population decoding and robustly estimate the animal location from actual noisy data.

Grid cells in rats deprived of geometric experience during development.

The medial entorhinal cortex (MEC) is part of the brain's network for dynamic representation of location. The most abundant class of neurons in this circuit is the grid cell, characterized by its periodic, hexagonally patterned firing fields. While in developing animals some MEC cell types express adult-like firing patterns already on the first exposure to an open spatial environment, only days after eye opening, grid cells mature more slowly, over a 1-to-2-wk period after the animals leave their nest. Whether the later emergence of a periodic grid pattern reflects a need for experience with spatial environments has not been determined. We here show that grid-like firing patterns continue to appear during exploration of open square environments in rats that are raised for the first months of their life in opaque spherical environments, in the absence of stable reference boundaries to guide spatial orientation. While strictly periodic firing fields were initially absent in these animals, clear grid patterns developed after only a few trials of training. In rats that were tested in the same open environment but raised for the first months of life in opaque cubes, with sharp vertical boundaries, grid-like firing was from the beginning indistinguishable from that of nondeprived control animals growing up in large enriched cages. Thus, although a minimum of experience with peripheral geometric boundaries is required for expression of regular grid patterns in a new environment, the effect of restricted spatial experience is overcome with short training, consistent with a preconfigured experience-independent basis for the grid pattern.

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.

Grid Cell Percolation.

Grid cells play a principal role in enabling cognitive representations of ambient environments. The key property of these cells-the regular arrangement of their firing fields-is commonly viewed as a means for establishing spatial scales or encoding specific locations. However, using grid cells' spiking outputs for deducing geometric orderliness proves to be a strenuous task due to fairly irregular activation patterns triggered by the animal's sporadic visits to the grid fields. This article addresses statistical mechanisms enabling emergent regularity of grid cell firing activity from the perspective of percolation theory. Using percolation phenomena for modeling the effect of the rat's moves through the lattices of firing fields sheds new light on the mechanisms of spatial information processing, spatial learning, path integration, and establishing spatial metrics. It is also shown that physiological parameters required for spiking percolation match the experimental range, including the characteristic 2/3 ratio between the grid fields' size and the grid spacing, pointing at a biological viability of the approach.

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.

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.

Place cells dynamically refine grid cell activities to reduce error accumulation during path integration in a continuous attractor model.

Navigation is one of the most fundamental skills of animals. During spatial navigation, grid cells in the medial entorhinal cortex process speed and direction of the animal to map the environment. Hippocampal place cells, in turn, encode place using sensory signals and reduce the accumulated error of grid cells for path integration. Although both cell types are part of the path integration system, the dynamic relationship between place and grid cells and the error reduction mechanism is yet to be understood. We implemented a realistic model of grid cells based on a continuous attractor model. The grid cell model was coupled to a place cell model to address their dynamic relationship during a simulated animal's exploration of a square arena. The grid cell model processed the animal's velocity and place field information from place cells. Place cells incorporated salient visual features and proximity information with input from grid cells to define their place fields. Grid cells had similar spatial phases but a diversity of spacings and orientations. To determine the role of place cells in error reduction for path integration, the animal's position estimates were decoded from grid cell activities with and without the place field input. We found that the accumulated error was reduced as place fields emerged during the exploration. Place fields closer to the animal's current location contributed more to the error reduction than remote place fields. Place cells' fields encoding space could function as spatial anchoring signals for precise path integration by grid cells.

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.

Neural network based successor representations to form cognitive maps of space and language.

How does the mind organize thoughts? The hippocampal-entorhinal complex is thought to support domain-general representation and processing of structural knowledge of arbitrary state, feature and concept spaces. In particular, it enables the formation of cognitive maps, and navigation on these maps, thereby broadly contributing to cognition. It has been proposed that the concept of multi-scale successor representations provides an explanation of the underlying computations performed by place and grid cells. Here, we present a neural network based approach to learn such representations, and its application to different scenarios: a spatial exploration task based on supervised learning, a spatial navigation task based on reinforcement learning, and a non-spatial task where linguistic constructions have to be inferred by observing sample sentences. In all scenarios, the neural network correctly learns and approximates the underlying structure by building successor representations. Furthermore, the resulting neural firing patterns are strikingly similar to experimentally observed place and grid cell firing patterns. We conclude that cognitive maps and neural network-based successor representations of structured knowledge provide a promising way to overcome some of the short comings of deep learning towards artificial general intelligence.

Sense of self impacts spatial navigation and hexadirectional coding in human entorhinal cortex.

Grid cells in entorhinal cortex (EC) encode an individual's location in space and rely on environmental cues and self-motion cues derived from the individual's body. Body-derived signals are also primary signals for the sense of self and based on integrated sensorimotor signals (proprioceptive, tactile, visual, motor) that have been shown to enhance self-centered processing. However, it is currently unknown whether such sensorimotor signals that modulate self-centered processing impact grid cells and spatial navigation. Integrating the online manipulation of bodily signals, to modulate self-centered processing, with a spatial navigation task and an fMRI measure to detect grid cell-like representation (GCLR) in humans, we report improved performance in spatial navigation and decreased GCLR in EC. This decrease in entorhinal GCLR was associated with an increase in retrosplenial cortex activity, which was correlated with participants' navigation performance. These data link self-centered processes during spatial navigation to entorhinal and retrosplenial activity and highlight the role of different bodily factors at play when navigating in VR.

Grid-cell modules remain coordinated when neural activity is dissociated from external sensory cues.

The representation of an animal's position in the medial entorhinal cortex (MEC) is distributed across several modules of grid cells, each characterized by a distinct spatial scale. The population activity within each module is tightly coordinated and preserved across environments and behavioral states. Little is known, however, about the coordination of activity patterns across modules. We analyzed the joint activity patterns of hundreds of grid cells simultaneously recorded in animals that were foraging either in the light, when sensory cues could stabilize the representation, or in darkness, when such stabilization was disrupted. We found that the states of different modules are tightly coordinated, even in darkness, when the internal representation of position within the MEC deviates substantially from the true position of the animal. These findings suggest that internal brain mechanisms dynamically coordinate the representation of position in different modules, ensuring that they jointly encode a coherent and smooth trajectory.