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Properties


Grid cells are neurons that fire when a freely moving animal traverses a set of small regions (firing fields) which are roughly equal in size and arranged in a periodic triangular array that covers the entire available environment. Cells with this firing pattern have been found in all layers of the dorsocaudal medial entorhinal cortex (dMEC), but cells in different layers tend to differ in other respects. Layer II contains the largest density of pure grid cells, in the sense that they fire equally regardless of the direction in which an animal traverses a grid location. Grid cells from deeper layers are intermingled with conjunctive cells, head direction cells (i.e. in layers III, V and VI there are cells with a grid-like pattern that fire only when the animal is facing a particular direction) , boundary cells in the subiculum and entorhinal cortex that give information about how close an animal is to a border by increasing their firing rate as the animal moves closer to a wall or border, and entorhinal speed cells, which are cells in the entorhinal cortex found to correlate linearly with the speed of a moving rodent, purportedly giving the rodent information about its speed in the environment. Together, these cells in the hippocampal formation act as a GPS for animals, allowing them to orient and navigate the world, acting as an animal’s “cognitive map.”

Grid cells help establish an internal coordinate map of the external world. They can be described using 3 variables: phase, scale, and orientation. 1) A cell's phase refers to the x-y coordinates of the vertices of its firing field - the areas in space in which a the single grid cell fires. These vertices can be observed by recording from a single grid cell in a rodent moving around a cage. The areas in the cage in which the grid cell fires are the x-y coordinates of its firing field. Together, the firing of grid cells creates a hexagonal grid to map the spatial world. Grid cells with similar phases appear to be grouped together in small clusters, but the arrangement of these clusters is seemingly random across the entorhinal cortex (EC). Thus, the entorhinal cortex is scattered with randomly arranged clusters of similar-phase grid cells.

2) Scale refers to the size of a cell's firing fields and the spacing between them. Grid cells that lie next to one another (i.e., cells recorded from the same electrode) usually show the same grid spacing and orientation, but their grid vertices are displaced from one another by apparently random offsets. Cells recorded from separate electrodes at a distance from one another frequently show different grid spacings. Here in the entorhinal cortex, scale is organized in a topographic manner, meaning that both the size of cells' firing fields and the spacing between them increases as one moves dorsal to ventral. Cells that are located more ventrally (that is, farther from the dorsal border of the MEC) generally have larger firing fields at each grid vertex, and correspondingly greater spacing between the grid vertices. The total range of grid spacings is not well established: the initial report described a roughly twofold range of grid spacings (from 39 cm to 73 cm) across the dorsalmost part (upper 25%) of the MEC, but there are indications of considerably larger grid scales in more ventral zones. Brun et al. (2008) recorded grid cells from multiple levels in rats running along an 18-meter track, and found that the grid spacing expanded from about 25 cm in their dorsal most sites to about 3 m at the ventral most sites. These recordings only extended 3/4 of the way to the ventral tip, so it is possible that even larger grids exist. Interestingly, such multi-scale representations have been shown to be information theoretically desirable↵.

3) Orientation refers to the angle the grid of firing fields makes with respect to an external line. Grids have been found at a +/- 7.5 ̊ orientation. As opposed to having a 0 ̊ orientation, or no tilt relative to an axis, a +/-7.5 ̊ orientation results in asymmetric patterns along hypothetical axes surrounding the cells and thus greater variety of firing patterns than if the surrounding axes received symmetric input. Thus, this orientation appears to be advantageous as it allows for more disambiguation between many directions and orientations. The posited mechanism for this 7.5 ̊ orientation is shearing - deformation of cells on a plane at an amount proportional to the distance from the shearing axis.

Grid cells display the same firing patterns regardless of environment or state (sleep, wake, etc.). They maintain their phase, shape, and orientation. Grid patterns appear on the first entrance of an animal into a novel environment, and usually remain stable thereafter. When an animal is moved into a completely different environment, grid cells maintain their grid spacing, and the grids of neighboring cells maintain their relative offsets. Thus, grid cells have a very rigid function, which is helpful in creating a stable map of the environment. This rigid firing can be contrasted to the firing of another type of hippocampal formation cell, known as the place cell. Within individual environments, place cells have one area within the environment in which they fire. For example, in laboratory settings in which a rodent is placed in a cage, a single place cell will fire only when the rodent is in one part of the cage vs. in other parts. Thus, depending on the environment and the location of the animal in the environment, the identity of the place cells that fire changes. This non-rigidity of firing is expected for cells that may play a role in memories of locations, as memory is not a rigid function and involves constant modulation. On the other hand, the rigidity of grid cell firing is expected for their posited function of maintaining a spatial map of the world. Grid cell activity does not require visual input, since grid patterns remain unchanged when all the lights in an environment are turned off. When visual cues are present, however, they exert strong control over the alignment of the grids: Rotating a cue card on the wall of a cylinder causes grid patterns to rotate by the same amount.

Theta rhythmicity
Neural activity in nearly every part of the hippocampal system is modulated by the limbic theta rhythm, which has a frequency range of about 6–9 Hz in rats. The entorhinal cortex is no exception: like the hippocampus, it receives cholinergic and GABAergic input from the medial septal area, the central controller of theta. Grid cells, like hippocampal place cells, show strong theta modulation. Grid cells from layer II of the MEC also resemble hippocampal place cells in that they show phase precession—that is, their spike activity advances from late to early phases of the theta cycle as an animal passes through a grid vertex. Most grid cells from layer III do not precess, but their spike activity is largely confined to half of the theta cycle. The grid cell phase precession is not derived from the hippocampus, because it continues to appear in animals whose hippocampus has been inactivated by an agonist of GABA. copied from Grid cell Grid cell modulation by theta rhythms is a component of one proposed model of grid cell hexagonal firing - the oscillatory interference model. In general, this model posits that the hexagonal firing is a result of the interference of three dendritic spike oscillations, each at 60˚ from the other, in addition to a constant general theta oscillation in the background. This mechanism has been called into question by many recent findings, including observing MEC grid cells that don't show theta modulation, recordings from MEC grid cells that lack theta waves, and the implausibility of independent dendritic oscillations.

Theta rhythms were originally heavily studied in rodents. Later studies found the existence of grid cells in other mammals, such as bats. Yartsev et al. found the existence of grid cells without theta rhythmicity, suggesting that theta rhythms are not necessary for grid cell firing. More specifically, they found grid cells in the Egyptian fruit bat analogous to those in rodents. Their analogous properties implied to researchers that findings from bat grid cells would hold to rodent grid cells. However, it should be noted that these grid cells in medial entorhinal cortex (MEC) had different properties than those in rodents. The grid cells did not have continuous theta oscillations in the local potential field (LFP) nor the MEC. There did not appear to be any correlation between grid cell firing and velocity or echolocation rate - that is, no apparent relation between speed of movement and grid cell firing, unlike in rodents (grid cells appeared to fire more when rodents moved faster). The grid cells were found to exist without theta rhythms – in fact, 24 out of the 25 tested MEC grid cells were not modulated by theta. In layers II and III (layers with more grid cells) MEC grid cells, no theta modulation was found in the 35 neurons tested. The researchers further removed theta-bout epochs from grid cell firing to see if any recalculation - changes in grid cell firing patterns - would take place. It did not, thus further calling into question the notion that theta rhythms cause grid formation. These results suggested that grid cells may not need theta rhythms for normal functioning and further call into question the oscillatory interference model.

Barry, Bush, O'Keefe, and Burgess, the pioneers of grid cell theta rhythm studies on rodents and original supporters of the oscillatory interference model, did not agree with Yartsev et al.'s conclusions, saying that the speed at which the bats were moving was not fast enough to have theta rhythm detected. The reason for this is two-fold - theta rhythm was thought to be present only at faster speeds, and it is difficult to detect theta rhythms at slow speeds regardless of their existence. To demonstrate this, the group replicated their rodent data analysis to concentrate only on grid cell firing in which the rodent was moving as slowly as the bats in Yartsev et al.'s study. They reported findings of no theta rhythm, concluding that Yartsev et al. detected no theta rhythm due to their use of slow-moving data. Yartsev, Witter, and Ulanovsky responded to this by arguing that the speeds at which their bats were moving were speeds at which theta should have been detected, if it existed. They argued that the speeds that Barry et al. were testing in their data analysis were those close to near immobility of rats - a state of movement in which no theta rhythm is expected to be detected in any species.

One possible alternative explanation supported by Yartsev et al.'s evidence is a model known as the attractor model. It explains both local individual spikes and the general hexagonal spiking pattern. To explain local firing spikes, it has been suggested that cells with similar firing fields activate (fire), spreading and causing their neighbors to activate, resulting in a bump of activity – that is, one of the observed hexagons of activity. This activation spreading is stopped from spreading across the entire field by surrounding inhibition. To explain the hexagonal pattern overall, it has been posited that cells fire in groups across the entire entorhinal network. The entire network is not activated by this spreading thanks to competitive inhibition between the firing areas, that compete and spread out so that there is a maximal amount of distance between the firing areas. Indirect support for this is the multitude of grid cells that exist, that connections between grid cells are strongest amongst those most similar, and their rigid arrangement. Currently, this model is more supported than the oscillatory interference model. --

Research findings
Theta-frequency activity arising from the hippocampus is manifested during some short-term memory tasks (Vertes, 2005). Studies suggest that these rhythms reflect the "on-line" state of the hippocampus; one of readiness to process incoming signals (Buzsáki, 2002). Conversely, theta oscillations have been correlated to various voluntary behaviors (exploration, spatial navigation, etc.) and alert states (goose bumps, etc.) in rats (Vanderwolf, 1969), suggesting that it may reflect the integration of sensory information with motor output (for review, see Bland & Oddie, 2001). A large body of evidence indicates that theta rhythm is likely involved in spatial learning and navigation (Buzsáki, 2005).

Theta rhythms are very strong in rodent hippocampi and entorhinal cortex during learning and memory retrieval, and are believed to be vital to the induction of long-term potentiation, a potential cellular mechanism of learning and memory. Based on evidence from electrophysiological studies showing that both synaptic plasticity and strength of inputs to hippocampal region CA1 vary systematically with ongoing theta oscillations (Hyman et al., 2003; Brankack et al., 1993), it has been suggested that the theta rhythm functions to separate periods of encoding of current sensory stimuli and retrieval of episodic memory cued by current stimuli so as to avoid interference that would occur if encoding and retrieval were simultaneous. copied from Theta wave

Theta rhythms are also thought to play a role in grid cell activity. Found in the layers of the medial entorhinal cortex (MEC), grid cells are thought to encode a spatial representation of the environment in hexagonal grids, the exact mechanism of which is unknown. Possible explanations include oscillatory interference models and network models.

Oscillatory interference models involve the theta rhythm modulated oscillations, specifically global theta and velocity-controlled cell-specific theta oscillations. This idea was pioneered by O’Keefe and Reece’s finding of theta precession as a rat moves through an experimental field from one location to another. This model was then updated to one that described interference between three velocity-controlled cell-specific theta oscillations, each 60˚ from the other, and a global theta oscillation. It was suspected that the interference of these theta oscillations resulted in the spatially periodic hexagonal grid cell firing map observed. This model has been called into question by later findings such as the existence of grid firing without theta oscillations and recordings from the MEC of grid cells without theta oscillations. Others found the idea of isolated dendritic isolations implausible.

Currently, a competing model, network models (specifically path-integration-based attractor models), is more, albeit not fully, supported. It involves similar-phase cells firing together resulting in more activity, accompanied by inhibition of other cells. Support for this includes the existence of multiple types of grid cells, similar grid cells having the strongest connections, grid cells’ physical arrangement in separate grids for separate functions, and their maintained arrangement regardless of type of external stimuli.