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The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment 1 . Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations 2 , and are organized in modules 3 that collectively form a population code for the animal’s allocentric position 1 . The invariance of the correlation structure of this population code across environments 4 , 5 and behavioural states 6 , 7 , independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern 1 , 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 models 12 . This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells. Simultaneous recordings from hundreds of grid cells in rats, combined with topological data analysis, show that network activity in grid cells resides on a toroidal manifold that is invariant across environments and brain states.

Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is −1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA. Long before the invention of GPS systems, ships used a technique called dead reckoning to navigate at sea. By tracking the ship’s speed and direction of movement away from a starting point, the crew could estimate their position at any given time. Many believe that some animals, including rats and humans, can use a similar process to navigate in the absence of external landmarks. This process is referred to as “path integration”. It is commonly believed that the brain’s navigation system is based on such path integration in two key regions: the entorhinal cortex and the hippocampus. Most models of navigation assume that a network of grid cells in the entorhinal cortex processes information about an animal’s speed and direction of movement. The grid cell network estimates the animal’s future position and relays this information to cells in the hippocampus called place cells. Individual place cells then fire whenever the animal reaches a specific location. However, recent work has shown that information also flows from place cells back to grid cells. Further experiments have suggested that place cells develop before grid cells. Also, inactivating place cells eliminates the hexagonal patterns that normally appear in the activity of the grid cells. Using a computational model, Dordek, Soudry et al. now show that place cell activity could in principle trigger the formation of the grid cell network, rather than vice versa. This is achieved using a process that resembles a common statistical algorithm called principal component analysis (PCA). However, this only works if place cells only excite grid cells and never inhibit their activity, similar to what is known from the anatomy of these brain regions. Under these circumstances, the model shows hexagonal patterns emerging in the activity of the grid cells, with similar properties to those patterns observed experimentally. These results suggest that navigation may not depend solely on grid cells processing information about speed and direction of movement, as assumed by path integration models. Instead grid cells may rely on position-based input from place cells. The next step is to create a single model that combines the flow of information from place cells to grid cells and vice versa.

How the neocortex works is a mystery. In this paper we propose a novel framework for understanding its function. Grid cells are neurons in the entorhinal cortex that represent the location of an animal in its environment. Recent evidence suggests that grid cell-like neurons may also be present in the neocortex. We propose that grid cells exist throughout the neocortex, in every region and in every cortical column. They define a location-based framework for how the neocortex functions. Whereas grid cells in the entorhinal cortex represent the location of one thing, the body relative to its environment, we propose that cortical grid cells simultaneously represent the location of many things. Cortical columns in somatosensory cortex track the location of tactile features relative to the object being touched and cortical columns in visual cortex track the location of visual features relative to the object being viewed. We propose that mechanisms in the entorhinal cortex and hippocampus that evolved for learning the structure of environments are now used by the neocortex to learn the structure of objects. Having a representation of location in each cortical column suggests mechanisms for how the neocortex represents object compositionality and object behaviors. It leads to the hypothesis that every part of the neocortex learns complete models of objects and that there are many models of each object distributed throughout the neocortex. The similarity of circuitry observed in all cortical regions is strong evidence that even high-level cognitive tasks are learned and represented in a location-based framework.

In familiar environments, the firing fields of entorhinal grid cells form regular triangular lattices. However, when the geometric shape of the environment is deformed, these time-averaged grid patterns are distorted in a grid scale-dependent and local manner. We hypothesized that this distortion in part reflects dynamic anchoring of the grid code to displaced boundaries, possibly through border cell-grid cell interactions. To test this hypothesis, we first reanalyzed two existing rodent grid rescaling datasets to identify previously unrecognized boundary-tethered shifts in grid phase that contribute to the appearance of rescaling. We then demonstrated in a computational model that boundary-tethered phase shifts, as well as scale-dependent and local distortions of the time-averaged grid pattern, could emerge from border-grid interactions without altering inherent grid scale. Together, these results demonstrate that environmental deformations induce history-dependent shifts in grid phase, and implicate border-grid interactions as a potential mechanism underlying these dynamics.

Hippocampal place cells are spatially tuned neurons that serve as elements of a ‘cognitive map’ in the mammalian brain 1 . To detect the animal’s location, place cells are thought to rely upon two interacting mechanisms: sensing the position of the animal relative to familiar landmarks 2 , 3 and measuring the distance and direction that the animal has travelled from previously occupied locations 4 – 7 . The latter mechanism—known as path integration—requires a finely tuned gain factor that relates the animal’s self-movement to the updating of position on the internal cognitive map, as well as external landmarks to correct the positional error that accumulates 8 , 9 . Models of hippocampal place cells and entorhinal grid cells based on path integration treat the path-integration gain as a constant 9 – 14 , but behavioural evidence in humans suggests that the gain is modifiable 15 . Here we show, using physiological evidence from rat hippocampal place cells, that the path-integration gain is a highly plastic variable that can be altered by persistent conflict between self-motion cues and feedback from external landmarks. In an augmented-reality system, visual landmarks were moved in proportion to the movement of a rat on a circular track, creating continuous conflict with path integration. Sustained exposure to this cue conflict resulted in predictable and prolonged recalibration of the path-integration gain, as estimated from the place cells after the landmarks were turned off. We propose that this rapid plasticity keeps the positional update in register with the movement of the rat in the external world over behavioural timescales. These results also demonstrate that visual landmarks not only provide a signal to correct cumulative error in the path-integration system 4 , 8 , 16 – 19 , but also rapidly fine-tune the integration computation itself. Evidence from hippocampal place cells shows that path-integration gain, previously thought to be a constant factor in the computation of location, is flexible and can be rapidly fine-tuned.

Neurons of the medial entorhinal cortex (MEC) provide spatial representations critical for navigation. In this network, the periodic firing fields of grid cells act as a metric element for position. The location of the grid firing fields depends on interactions between self-motion information, geometrical properties of the environment and nonmetric contextual cues. Here, we test whether visual information, including nonmetric contextual cues, also regulates the firing rate of MEC neurons. Removal of visual landmarks caused a profound impairment in grid cell periodicity. Moreover, the speed code of MEC neurons changed in darkness and the activity of border cells became less confined to environmental boundaries. Half of the MEC neurons changed their firing rate in darkness. Manipulations of nonmetric visual cues that left the boundaries of a 1D environment in place caused rate changes in grid cells. These findings reveal context specificity in the rate code of MEC neurons.

Place and grid cells in the hippocampal formation provide foundational representations of environmental location, and potentially of locations within conceptual spaces. Some accounts predict that environmental sensory information and self-motion are encoded in complementary representations, while other models suggest that both features combine to produce a single coherent representation. Here, we use virtual reality to dissociate visual environmental from physical motion inputs, while recording place and grid cells in mice navigating virtual open arenas. Place cell firing patterns predominantly reflect visual inputs, while grid cell activity reflects a greater influence of physical motion. Thus, even when recorded simultaneously, place and grid cell firing patterns differentially reflect environmental information (or ‘states’) and physical self-motion (or ‘transitions’), and need not be mutually coherent. Place cells and grid cells are known to encode spatial information about an animal’s location relative to the surrounding environment. Here, the authors show that place cells predominantly encode environmental sensory inputs, while grid cell activity reflects a greater influence of physical motion.

We present a mouse virtual reality (VR) system which restrains head-movements to horizontal rotations, compatible with multi-photon imaging. This system allows expression of the spatial navigation and neuronal firing patterns characteristic of real open arenas (R). Comparing VR to R: place and grid, but not head-direction, cell firing had broader spatial tuning; place, but not grid, cell firing was more directional; theta frequency increased less with running speed, whereas increases in firing rates with running speed and place and grid cells' theta phase precession were similar. These results suggest that the omni-directional place cell firing in R may require local-cues unavailable in VR, and that the scale of grid and place cell firing patterns, and theta frequency, reflect translational motion inferred from both virtual (visual and proprioceptive) and real (vestibular translation and extra-maze) cues. By contrast, firing rates and theta phase precession appear to reflect visual and proprioceptive cues alone.

The entorhinal cortex contains a network of grid cells that play a fundamental part in the brain’s spatial system, supporting tasks such as path integration and spatial memory. In rodents, grid cells are thought to rely on network theta oscillations, but such signals are not evident in all species, challenging our understanding of the physiological basis of the grid network. We analyzed intracranial recordings from neurosurgical patients during virtual navigation to identify oscillatory characteristics of the human entorhinal grid network. The power of entorhinal theta oscillations showed six-fold modulation according to the virtual heading during navigation, which is a hypothesized signature of grid representations. Furthermore, modulation strength correlated with spatial memory performance. These results demonstrate the connection between theta oscillations and the human entorhinal grid network and show that features of grid-like neuronal representations can be identified from population electrophysiological recordings.

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of ‘grid fields’ in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4–1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally. In a room, we have a sense of our location relative to the doors and to objects within the room. This is because the brain constructs a mental map of our current environment. As we move around the room, neurons called grid cells fire whenever we are in specific locations. But these locations are not random. They correspond to the corners of a grid of tessellating triangles on the floor, a little like the dots in a regular polka-dot pattern. Grid cells fire whenever we stand on one of the dots. This enables the brain to keep track of where we are and where we are heading. But the brain does not use just a single grid cell map to represent a room. Instead, it uses multiple maps with different spatial scales. These maps differ in the distance between the points at which each grid cell fires, that is, the distance between the polka dots. Some maps have many small triangles, providing high resolution spatial information. Others have fewer, larger triangles. This is similar to how we use maps with different spatial scales when driving between cities versus walking around a single neighborhood. A set of grid cell maps with the same spatial scale—and the same orientation—is known as a grid cell module. Animal experiments suggest that different individuals use a similar combination of grid cell modules that can efficiently map rooms. But how can the brain reliably produce this particular combination? Using a computer model to simulate networks of grid cells, Kang and Balasubramanian identify a mechanism that enables the brain to spontaneously organize into the previously observed combination. The interactions between networks—in particular the balance of inhibitory and excitatory activity—determine the arrangement of grid cell modules. This process still works even with random fluctuations in network activity. Grid cells occupy a brain region that degenerates early in the course of Alzheimer's disease. This may explain why some patients experience difficulty finding their way around as one of their first symptoms. To develop effective treatments, scientists need to understand how neural circuits within this brain region work, and how the disease process disrupts them. The computer model of Kang and Balasubramanian brings the research community a step closer to achieving this. It also provides insights into how neuronal networks self-organize, which is relevant to other brain functions too.