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

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.

Unpacking the navigation toolbox: insights from comparative cognition

The study of navigation is informed by ethological data from many species, laboratory investigation at behavioural and neurobiological levels, and computational modelling. However, the data are often species-specific, making it challenging to develop general models of how biology supports behaviour. Wiener et al. outlined a framework for organizing the results across taxa, called the 'navigation toolbox' (Wiener et al. In Animal thinking: contemporary issues in comparative cognition (eds R Menzel, J Fischer), pp. 51-76). This framework proposes that spatial cognition is a hierarchical process in which sensory inputs at the lowest level are successively combined into ever-more complex representations, culminating in a metric or quasi-metric internal model of the world (cognitive map). Some animals, notably humans, also use symbolic representations to produce an external representation, such as a verbal description, signpost or map that allows communication of spatial information or instructions between individuals. Recently, new discoveries have extended our understanding of how spatial representations are constructed, highlighting that the hierarchical relationships are bidirectional, with higher levels feeding back to influence lower levels. In the light of these new developments, we revisit the navigation toolbox, elaborate it and incorporate new findings. The toolbox provides a common framework within which the results from different taxa can be described and compared, yielding a more detailed, mechanistic and generalized understanding of navigation.

Grid cells: the missing link in understanding Parkinson's disease?

The mechanisms underlying Parkinson's disease (PD) are complex and not fully understood, and the box-and-arrow model among other current models present significant challenges. This paper explores the potential role of the allocentric brain and especially its grid cells in several PD motor symptoms, including bradykinesia, kinesia paradoxa, freezing of gait, the bottleneck phenomenon, and their dependency on cueing. It is argued that central hubs, like the locus coeruleus and the pedunculopontine nucleus, often narrowly interpreted in the context of PD, play an equally important role in governing the allocentric brain as the basal ganglia. Consequently, the motor and secondary motor (e.g., spatially related) symptoms of PD linked with dopamine depletion may be more closely tied to erroneous computation by grid cells than to the basal ganglia alone. Because grid cells and their associated central hubs introduce both spatial and temporal information to the brain influencing velocity perception they may cause bradykinesia or hyperkinesia as well. In summary, PD motor symptoms may primarily be an allocentric disturbance resulting from virtual faulty computation by grid cells revealed by dopamine depletion in PD.

Grid cells, border cells, and discrete complex analysis

We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity toward the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.

A Navigation Path Search and Optimization Method for Mobile Robots Based on the Rat Brain's Cognitive Mechanism

Rats possess exceptional navigational abilities, allowing them to adaptively adjust their navigation paths based on the environmental structure. This remarkable ability is attributed to the interactions and regulatory mechanisms among various spatial cells within the rat's brain. Based on these, this paper proposes a navigation path search and optimization method for mobile robots based on the rat brain's cognitive mechanism. The aim is to enhance the navigation efficiency of mobile robots. The mechanism of this method is based on developing a navigation habit. Firstly, the robot explores the environment to search for the navigation goal. Then, with the assistance of boundary vector cells, the greedy strategy is used to guide the robot in generating a locally optimal path. Once the navigation path is generated, a dynamic self-organizing model based on the hippocampal CA1 place cells is constructed to further optimize the navigation path. To validate the effectiveness of the method, this paper designs several 2D simulation experiments and 3D robot simulation experiments, and compares the proposed method with various algorithms. The experimental results demonstrate that the proposed method not only surpasses other algorithms in terms of path planning efficiency but also yields the shortest navigation path. Moreover, the method exhibits good adaptability to dynamic navigation tasks.

A map of spatial navigation for neuroscience

Spatial navigation has received much attention from neuroscientists, leading to the identification of key brain areas and the discovery of numerous spatially selective cells. Despite this progress, our understanding of how the pieces fit together to drive behavior is generally lacking. We argue that this is partly caused by insufficient communication between behavioral and neuroscientific researchers. This has led the latter to under-appreciate the relevance and complexity of spatial behavior, and to focus too narrowly on characterizing neural representations of space-disconnected from the computations these representations are meant to enable. We therefore propose a taxonomy of navigation processes in mammals that can serve as a common framework for structuring and facilitating interdisciplinary research in the field. Using the taxonomy as a guide, we review behavioral and neural studies of spatial navigation. In doing so, we validate the taxonomy and showcase its usefulness in identifying potential issues with common experimental approaches, designing experiments that adequately target particular behaviors, correctly interpreting neural activity, and pointing to new avenues of research.

Dissociating two aspects of human 3D spatial perception by studying fighter pilots

Human perception of 3D space has been investigated extensively, but there are conflicting reports regarding its distortions. A possible solution to these discrepancies is that 3D perception is in fact comprised of two different processes-perception of traveled space, and perception of surrounding space. Here we tested these two aspects on the same subjects, for the first time. To differentiate these two aspects and investigate whether they emerge from different processes, we asked whether these two aspects are affected differently by the individual's experience of 3D locomotion. Using an immersive high-grade flight-simulator with realistic virtual-reality, we compared these two aspects of 3D perception in fighter pilots-individuals highly experienced in 3D locomotion-and in control subjects. We found that the two aspects of 3D perception were affected differently by 3D locomotion experience: the perception of 3D traveled space was plastic and experience-dependent, differing dramatically between pilots and controls, while the perception of surrounding space was rigid and unaffected by experience. This dissociation suggests that these two aspects of 3D spatial perception emerge from two distinct processes.

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.

An entorhinal-like region in food-caching birds

The mammalian entorhinal cortex routes inputs from diverse sources into the hippocampus. This information is mixed and expressed in the activity of many specialized entorhinal cell types, which are considered indispensable for hippocampal function. However, functionally similar hippocampi exist even in non-mammals that lack an obvious entorhinal cortex or, generally, any layered cortex. To address this dilemma, we mapped extrinsic hippocampal connections in chickadees, whose hippocampi are used for remembering numerous food caches. We found a well-delineated structure in these birds that is topologically similar to the entorhinal cortex and interfaces between the hippocampus and other pallial regions. Recordings of this structure revealed entorhinal-like activity, including border and multi-field grid-like cells. These cells were localized to the subregion predicted by anatomical mapping to match the dorsomedial entorhinal cortex. Our findings uncover an anatomical and physiological equivalence of vastly different brains, suggesting a fundamental nature of entorhinal-like computations for hippocampal function.

Grid Cells, Border Cells and Discrete Complex Analysis

We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity towards the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.

New Approaches to 3D Vision

New approaches to 3D vision are enabling new advances in artificial intelligence and autonomous vehicles, a better understanding of how animals navigate the 3D world, and new insights into human perception in virtual and augmented reality. Whilst traditional approaches to 3D vision in computer vision (SLAM: simultaneous localization and mapping), animal navigation (cognitive maps), and human vision (optimal cue integration) start from the assumption that the aim of 3D vision is to provide an accurate 3D model of the world, the new approaches to 3D vision explored in this issue challenge this assumption. Instead, they investigate the possibility that computer vision, animal navigation, and human vision can rely on partial or distorted models or no model at all. This issue also highlights the implications for artificial intelligence, autonomous vehicles, human perception in virtual and augmented reality, and the treatment of visual disorders, all of which are explored by individual articles. This article is part of a discussion meeting issue 'New approaches to 3D vision'.

Symmetries and asymmetries in the neural encoding of 3D space

The neural coding of space centres on three foundational cell types: place cells, head direction cells and grid cells. One notable characteristic of these neurons is the symmetry properties of their spatial firing patterns. In symmetric environments, firing patterns are often also symmetric: for example, place cells show translational symmetry in aligned sub-compartments of a multi-compartment environment. A single head direction cell has a mirror-symmetric firing pattern, while a sub-class of head direction cells can show multi-fold rotational symmetries in multi-compartment environments, matching the symmetry of the recently experienced environment. The entorhinal grid cells are notable for the symmetry of their firing patterns in both rotational and translational domains. However, these symmetries are broken in a variety of situations. These symmetry-making and -breaking observations shed light on the underlying computations that generate these firing patterns, and also invite speculation as to whether they may have a functional role. This article outlines these findings and speculates on the consequences of the resultant firing symmetries and asymmetries for spatial coding and cognition. This article is part of a discussion meeting issue 'New approaches to 3D vision'.

An entorhinal-like region in food-caching birds

The mammalian entorhinal cortex routes inputs from diverse sources into the hippocampus. This information is mixed and expressed in the activity of many specialized entorhinal cell types, which are considered indispensable for hippocampal function. However, functionally similar hippocampi exist even in non-mammals that lack an obvious entorhinal cortex, or generally any layered cortex. To address this dilemma, we mapped extrinsic hippocampal connections in chickadees, whose hippocampi are used for remembering numerous food caches. We found a well-delineated structure in these birds that is topologically similar to the entorhinal cortex and interfaces between the hippocampus and other pallial regions. Recordings of this structure revealed entorhinal-like activity, including border and multi-field grid-like cells. These cells were localized to the subregion predicted by anatomical mapping to match the dorsomedial entorhinal cortex. Our findings uncover an anatomical and physiological equivalence of vastly different brains, suggesting a fundamental nature of entorhinal-like computations for hippocampal function.

Excitatory-inhibitory recurrent dynamics produce robust visual grids and stable attractors

Spatially modulated grid cells have been recently found in the rat secondary visual cortex (V2) during active navigation. However, the computational mechanism and functional significance of V2 grid cells remain unknown. To address the knowledge gap, we train a biologically inspired excitatory-inhibitory recurrent neural network to perform a two-dimensional spatial navigation task with multisensory input. We find grid-like responses in both excitatory and inhibitory RNN units, which are robust with respect to spatial cues, dimensionality of visual input, and activation function. Population responses reveal a low-dimensional, torus-like manifold and attractor. We find a link between functional grid clusters with similar receptive fields and structured excitatory-to-excitatory connections. Additionally, multistable torus-like attractors emerged with increasing sparsity in inter- and intra-subnetwork connectivity. Finally, irregular grid patterns are found in recurrent neural network (RNN) units during a visual sequence recognition task. Together, our results suggest common computational mechanisms of V2 grid cells for spatial and non-spatial tasks.

Neural Correlates of Spatial Navigation in Primate Hippocampus

The hippocampus has been extensively implicated in spatial navigation in rodents and more recently in bats. Numerous studies have revealed that various kinds of spatial information are encoded across hippocampal regions. In contrast, investigations of spatial behavioral correlates in the primate hippocampus are scarce and have been mostly limited to head-restrained subjects during virtual navigation. However, recent advances made in freely-moving primates suggest marked differences in spatial representations from rodents, albeit some similarities. Here, we review empirical studies examining the neural correlates of spatial navigation in the primate (including human) hippocampus at the levels of local field potentials and single units. The lower frequency theta oscillations are often intermittent. Single neuron responses are highly mixed and task-dependent. We also discuss neuronal selectivity in the eye and head coordinates. Finally, we propose that future studies should focus on investigating both intrinsic and extrinsic population activity and examining spatial coding properties in large-scale hippocampal-neocortical networks across tasks.

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.

Large-scale two-photon calcium imaging in freely moving mice

We developed a miniaturized two-photon microscope (MINI2P) for fast, high-resolution, multiplane calcium imaging of over 1,000 neurons at a time in freely moving mice. With a microscope weight below 3 g and a highly flexible connection cable, MINI2P allowed stable imaging with no impediment of behavior in a variety of assays compared to untethered, unimplanted animals. The improved cell yield was achieved through a optical system design featuring an enlarged field of view (FOV) and a microtunable lens with increased z-scanning range and speed that allows fast and stable imaging of multiple interleaved planes, as well as 3D functional imaging. Successive imaging across multiple, adjacent FOVs enabled recordings from more than 10,000 neurons in the same animal. Large-scale proof-of-principle data were obtained from cell populations in visual cortex, medial entorhinal cortex, and hippocampus, revealing spatial tuning of cells in all areas.

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We made a light-weight 2-photon miniscope for calcium imaging in freely moving mice

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Stable high-quality imaging was observed during a wide spectrum of behaviors

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Activity can be monitored in volumes of over 1,000 visual or entorhinal-cortex cells

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A custom-designed z-scanning module allows fast imaging across multiple planes

A Plane-Dependent Model of 3D Grid Cells for Representing Both 2D and 3D Spaces Under Various Navigation Modes

Grid cells are crucial in path integration and representation of the external world. The spikes of grid cells spatially form clusters called grid fields, which encode important information about allocentric positions. To decode the information, studying the spatial structures of grid fields is a key task for both experimenters and theorists. Experiments reveal that grid fields form hexagonal lattice during planar navigation, and are anisotropic beyond planar navigation. During volumetric navigation, they lose global order but possess local order. How grid cells form different field structures behind these different navigation modes remains an open theoretical question. However, to date, few models connect to the latest discoveries and explain the formation of various grid field structures. To fill in this gap, we propose an interpretive plane-dependent model of three-dimensional (3D) grid cells for representing both two-dimensional (2D) and 3D space. The model first evaluates motion with respect to planes, such as the planes animals stand on and the tangent planes of the motion manifold. Projection of the motion onto the planes leads to anisotropy, and error in the perception of planes degrades grid field regularity. A training-free recurrent neural network (RNN) then maps the processed motion information to grid fields. We verify that our model can generate regular and anisotropic grid fields, as well as grid fields with merely local order; our model is also compatible with mode switching. Furthermore, simulations predict that the degradation of grid field regularity is inversely proportional to the interval between two consecutive perceptions of planes. In conclusion, our model is one of the few pioneers that address grid field structures in a general case. Compared to the other pioneer models, our theory argues that the anisotropy and loss of global order result from the uncertain perception of planes rather than insufficient training.

How environmental movement constraints shape the neural code for space

Study of the neural code for space in rodents has many insights to offer for how mammals, including humans, construct a mental representation of space. This code is centered on the hippocampal place cells, which are active in particular places in the environment. Place cells are informed by numerous other spatial cell types including grid cells, which provide a signal for distance and direction and are thought to help anchor the place cell signal. These neurons combine self-motion and environmental information to create and update their map-like representation. Study of their activity patterns in complex environments of varying structure has revealed that this "cognitive map" of space is not a fixed and rigid entity that permeates space, but rather is variably affected by the movement constraints of the environment. These findings are pointing toward a more flexible spatial code in which the map is adapted to the movement possibilities of the space. An as-yet-unanswered question is whether these different forms of representation have functional consequences, as suggested by an enactivist view of spatial cognition.