Grid cell

Related publications (9)

Bodily self and human grid cell-like activity: probing spatial representation with immersive virtual reality

Hyukjun Moon

Grid cells are place-modulated neurons that encode the location of an agent in space, relying on the integration of various sensorimotor signals from the body. Of note, the integration of those signals is also fundamental for the agent's conscious experience of selfhood, referred to as bodily self-consciousness (BSC). Although both grid cells and BSC systems are related to the brain mechanisms of self-location and are based on multimodal signal integration, their interplay has never been investigated. My thesis aimed at revealing their links in humans by assessing the impact of BSC modulations on grid cell-like representation (GCLR): an fMRI proxy of grid cell activity in entorhinal cortex (EC). In Study 1, I assessed whether manipulation on BSC, specifically enhancing self-identification, affects GCLR during spatial navigation in a virtual reality (VR) environment. I implemented a novel fMRI paradigm integrating a spatial navigation task with online BSC manipulation through a motion-mimicking avatar. The data showed a significant reduction of GCLR as well as improved spatial navigation performance in the condition with the self-identified avatar, linking entorhinal grid cell activity and BSC through bodily self-motion cues provided online during spatial navigation. These behavioral and neural changes were further associated with increased activity in posterior parietal and retrosplenial cortex, collectively suggesting the impact of BSC on a distributed spatial navigation networks in the human brain. Consistent with the previous BSC research, in Study1, I observed illusory drifts in experienced self-location toward the self-identified avatar. In Study2, I further investigated whether illusory self-location changes would be sufficient to elicit GCLR in the absence of active spatial navigation. Adopting the Full-body illusion (FBI) paradigm to the MRI scanner, my data extend changes in self-location related to multisensory stimulation and demonstrated that these indeed evoke GCLR. Although the amplitude of GCLR during the FBI was smaller than the one during virtual navigation, their grid orientations were similar. These data suggest that the brain mechanisms underlying the BSC-induced illusory self-location are similar and comparable, albeit weaker, to the ones during virtual navigation.Temporal Interference (TI) stimulation is a novel method that can excite or inhibit neurons in the deep brain by combining high-frequency electrical fields. Building on the previous studies, in study3, I probed the causal link between GCLR and spatial navigation by applying TI stimulation to EC of participants while they were performing a VR navigation task in the scanner. The preliminary results showed that their spatial navigation was improved by excitatory stimuli compared to the control, while it deteriorated during the inhibition. Besides, I found that modulated GCLR was also associated with improved performance in the excitatory condition. Together, these data provide the first causal link between GCLR and spatial navigation, showing potential future avenues for navigation enhancement in humans. To summarize, I investigated BSC and grid cell systems jointly in humans and, for the first time, uncovered their links through robust evidence based on both behavioral and neuroimaging data. My thesis shed new light on the research of both systems which are closely intermingled but have hitherto been considered separately.

EPFL2021

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

Olaf Blanke, Nathan Quentin Faivre, Baptiste Gauthier, Hyukjun Moon, Hyeongdong Park

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.

2022

Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns

Alexander Mathis

Lattices abound in nature—from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution, and cryptographic protocols. Do lattices also play a role in how the brain represents information? We focus on higher-dimensional stimulus domains, with particular emphasis on neural representations of physical space, and derive which neuronal lattice codes maximize spatial resolution. For mammals navigating on a surface, we show that the hexagonal activity patterns of grid cells are optimal. For species that move freely in three dimensions, a face-centered cubic lattice is best. This prediction could be tested experimentally in flying bats, arboreal monkeys, or marine mammals. More generally, our theory suggests that the brain encodes higher-dimensional sensory or cognitive variables with populations of grid-cell-like neurons whose activity patterns exhibit lattice structures at multiple, nested scales. The brain of a mammal has to store vast amounts of information. The ability of animals to navigate through their environment, for example, depends on a map of the space around them being encoded in the electrical activity of a finite number of neurons. In 2014 the Nobel Prize in Physiology or Medicine was awarded to neuroscientists who had provided insights into this process. Two of the winners had shown that, in experiments on rats, the neurons in a specific region of the brain ‘fired’ whenever the rat was at any one of a number of points in space. When these points were plotted in two dimensions, they made a grid of interlocking hexagons, thereby providing the rat with a map of its environment. However, many animals, such as bats and monkeys, navigate in three dimensions rather than two, and it is not clear whether these same hexagonal patterns are also used to represent three-dimensional space. Mathis et al. have now used mathematical analysis to search for the most efficient way for the brain to represent a three-dimensional region of space. This work suggests that the neurons need to fire at points that roughly correspond to the positions that individual oranges take up when they are stacked as tight as possible in a pile. Physicists call this arrangement a face-centered cubic lattice. At least one group of experimental neuroscientists is currently making measurements on the firing of neurons in freely flying bats, so it should soon be possible to compare the predictions of Mathis et al. with data from experiments.

2015

Decoding the Population Activity of Grid Cells for Spatial Localization and Goal-Directed Navigation

Alexander Mathis

Mammalian grid cells fire whenever an animal crosses the points of an imaginary, hexagonal grid tessellating the environment. Here, we show how animals can localize themselves and navigate by reading-out a simple population vector of grid cell activity across multiple scales, even though this activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into modules with equal lattice scale and orientation. Computing the homing vector is least error-prone when the ratio of successive grid scales is around 3/2. Silencing intermediate-scale modules should cause systematic errors in navigation, while knocking out the module at the smallest scale will only affect navigational precision. Read-out neurons should behave like goal-vector cells subject to nonlinear gain fields.

Neuroscience2015

Connecting multiple spatial scales to decode the population activity of grid cells

Alexander Mathis

Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.

2015

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

Alexander Mathis

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial “tuning curves” for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

2012

Resolution of Nested Neuronal Representations Can Be Exponential in the Number of Neurons

Alexander Mathis

Collective computation is typically polynomial in the number of computational elements, such as transistors or neurons, whether one considers the storage capacity of a memory device or the number of floating-point operations per second of a CPU. However, we show here that the capacity of a computational network to resolve real-valued signals of arbitrary dimensions can be exponential in N, even if the individual elements are noisy and unreliable. Nested, modular codes that achieve such high resolutions mirror the properties of grid cells in vertebrates, which underlie spatial navigation.

2012

Multiscale codes in the nervous system: The problem of noise correlations and the ambiguity of periodic scales

Alexander Mathis

Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise [Mathis, Herz, and Stemmler, Phys. Rev. Lett. 109, 018103 (2012)]. Indeed, the cortex seems to use periodic, multiscale grid codes to represent position accurately. Here we show how such codes can be read out without taking the long-term limit; even on short time scales, the precision of such codes scales exponentially in the number N of neurons. Does this finding also hold for neurons that are not firing in a statistically independent fashion? To assess the extent to which biological grid codes are subject to statistical dependences, we first analyze the noise correlations between pairs of grid code neurons in behaving rodents. We find that if the grids of two neurons align and have the same length scale, the noise correlations between the neurons can reach values as high as 0.8. For increasing mismatches between the grids of the two neurons, the noise correlations fall rapidly. Incorporating such correlations into a population coding model reveals that the correlations lessen the resolution, but the exponential scaling of resolution with N is unaffected.

2013

A connectionist model of spatial learning in the rat

Thomas Strösslin

When animals explore an environment, they store useful spatial information in their brains. In subsequent visits, they can recall this information and thus avoid dangerous places or find again a food location. This ability, which may be crucial for the animal's survival, is termed "spatial learning". In the late 1940s, theoretical considerations have led researchers to the conclusion that rats establish a "cognitive map" of their environment. This spatial representation can then be used by the animal in order to navigate towards a rewarding location. In 1971, researchers have for the first time found direct evidence that the hippocampus, a brain area in the limbic system, may contain such a cognitive map. The activity of neurons in the hippocampus of rats tends to be highly correlated with the animal's position within the environment. These "place cells" have since been the target of a large body of research. Apart from spatial learning, the hippocampus seems to be involved in a more general type of learning, namely in the formation of so-called "episodic memories". Models of hippocampal function could thus provide valuable insights for the understanding of memory processes in general. Insights from animal navigation could also prove beneficial for the design of autonomous mobile robots. constructing a consistent map of the environment from experience, and using it for solving navigation problems are difficult tasks. Incorporating principles borrowed from animal navigation may help building more robust and autonomous robots. The main objective of this thesis is to develop a neural network model of spatial learning in the rat. The system should be capable of learning how to navigate to a hidden reward location based on realistic sensory input. The system is validated on a mobile robot. Our model consists of several interconnected brain regions, each represented by a population of neurons. The model closely follows experimental results on functional, anatomical and neurophysiological properties of these regions. One population, for instance, models the hippocampal place cells. A head-direction system closely interacts with the place cells and endows the robot with a sense of direction. A population of motor-related cells codes for the direction of the next movement. Associations are learnt between place cells and motor cells in order to navigate towards a goal location. This study allows us to make experimental predictions on functional and neurophysiological properties of the modelled brain regions. In our validation experiments, the robot successfully establishes a spatial representation. The robot can localise itself in the environment and quickly learns to navigate to the hidden goal location.

EPFL2004