What Are Grid Cells?

A grid cell is a place-modulated neuron whose multiple firing locations define a periodic triangular array covering the entire available surface of an open two-dimensional environment. Grid cells are thought to form an essential part of the brain’s coordinate system for metric navigation.

They have attracted attention because the crystal-like structure underlying their firing fields is not imported from the outside world, but created within the nervous system. Understanding the origin and properties of grid cells is an attractive challenge for anybody wanting to know how brain circuits compute.

History

The experimental study of spatial representations in the brain entered a new era with the discovery of place cells in the 1970s (O’Keefe & Dostrovsky, 1971) and head-direction cells in the 1980s (Ranck, 1985; Taube et al., 1990). Discharging whenever the rat is in a certain place in the environment, or whenever the rat’s head points in a certain direction, these cells are likely to contribute to the brain’s systems for local navigation.

Soon after their discovery, place cells were suggested to be the elements of a neural representation of allocentric space and the animal’s own position within it which the animal could use to find its way from one place to another (O’Keefe & Nadel, 1978; McNaughton et al., 1996). The representation was thought to form a map-like framework for storage of experience in memory, a framework referred to as the ‘cognitive map’ (O’Keefe & Nadel, 1978).

During the years that followed, the conception of the hippocampus as a single dynamic spatial map was challenged by accumulating evidence suggesting that the very same place cells participate in a number of representations, even in the same spatial location (Bostock et al., 1991). Researchers also showed that place-specific firing persisted in CA1 neurons even after removal of all intrahippocampal input from CA3 (Brun et al., 2002). Because only direct perforant-path inputs from the entorhinal cortex were left by these lesions, it was concluded that spatial signals were either computed either in CA1 itself or, more likely, in a general metric navigational system upstream of the hippocampus (Brun et al., 2002), a possibility raised early on (O’Keefe, 1976).

Grid cell in entorhinal cortex.

Figure 1: Grid cell in entorhinal cortex.
Left: Trajectory of the rat (black) with spike locations superimposed (red).
Right: Colour-coded map showing firing rate distribution for the same cell. The colour scale is from blue (silent) to red (peak rate).

In response to these challenges, Fyhn and colleagues (2004) recorded directly from layers II and III of the medial entorhinal cortex, in the area that provided the strongest projections to the place cells of the dorsal hippocampus (Witter et al., 1989; Dolorfo & Amaral, 1998). Principal neurons in this area had multiple sharply tuned firing fields which collectively signalled the rat’s changing position with a precision similar to that of place cells in the hippocampus.

When these cells were recorded in sufficiently large two-dimensional environments, it became clear that the many fields of each neuron formed a periodic triangular array, or a ‘’’grid’’’, that tiled the entirety of the animal’s environment, like the cross-points of graph paper (Hafting et al., 2005) (Figure 1).

Grid Cells And Neural Circuits For Path Integration

A key property of the entorhinal representation is its apparently universal nature (Hafting et al., 2005; Fyhn et al., 2007; see Redish & Touretzky, 1997 and Sharp, 1999, for theoretical suggestions consistent with this observation). Unlike place cells in the hippocampus, the entorhinal grid map is activated in a stereotypic manner across environments, irrespective of the environment’s particular landmarks, suggesting that the same neural map is applied wherever the animal is walking.

The rigid structure of the map and its independence of particular landmarks suggest that firing positions must be integrated in these cells from speed and direction signals, without reference to the external environment. This process is referred to as ‘’’path integration’’’.

While path integration is likely to determine the basic structure of the dynamic firing matrix, the stability of grid vertices and grid orientations relative to cues in the external environment implies that the grid map must be associated with geometric boundaries and landmarks (Hafting et al., 2005). Under certain conditions, such as when the boundaries of a familiar recording box are displaced slightly, these associations may override the concurrent path integration-driven processes (Barry et al., 2007).

How path integration signals are integrated with external sensory input has not been determined.

An Entorhinal Spatial Map

The grid of each cell can be described by three parameters:

  • spacing (the distance between fields),
  • orientation (the tilt of the grid relative to a reference axis), and
  • spatial phase (displacement in the x and y directions relative to an external reference point).

These parameters are mapped differently onto the entorhinal map (Hafting et al., 2005).

Neighbouring cells in layer II of medial entorhinal cortex have similar spacing and orientation. Their spacing increases monotonically from the dorsomedial pole of the medial entorhinal cortex to more ventrolateral positions of the same area (Figure 2.), just like the spatial scale of place cells increases from the dorsal to the ventral pole of the hippocampus (Jung et al., 1994).

Firing fields of cells at different positions along the dorsomedial-to-ventrolateral axis of the medial entorhinal cortex.

Figure 2: Firing fields of cells at different positions along the dorsomedial-to-ventrolateral axis of the medial entorhinal cortex.
The figure shows a parvalbumin-stained sagittal brain section with the dorsocaudal parts of the medial entorhinal cortex (heavily stained).
Representative grid fields are arranged along the dorso-ventral axis where they were recorded. Grid scale (spacing and field size) increases with distance from the dorsomedial border with the postrhinal cortex (arrow).

Whether grid cells are organized with respect to orientation has not been firmly determined, although preliminary observations suggest that grid cells in different regions of the left and right medial entorhinal cortex may have different orientation (Hafting et al., 2005; Fyhn et al., 2007). In contrast to spacing and orientation, the spatial phase of the grid is distributed, i.e. the firing vertices of co-localized grid cells are shifted randomly (Figure 3.), in the same way that neighbouring place cells in the hippocampus have different place fields.

Firing fields of three co-localized grid cells

Figure 3: Firing fields of three co-localized grid cells recorded simultaneously while a rat ran around in a large circular enclosure (2 m diameter).
Left: The rat’s trajectory is shown in black; spike locations for each cell (t1c1, t2c1 and t2c2) are shown in blue, red, and green, respectively.
Middle: Peak firing locations for each of the three cells.
Right: Peaks are offset to visualize difference in spatial phase but similarity in spacing and orientation.
Reproduced, with permission, from Hafting et al. (2005).

The functional significance of this mixed topographic-nontopographic organization has not been established. A key objective for future research will be to determine whether the entorhinal spatial map has discrete subdivisions.

Architectonic features of the entorhinal cortex are suggestive of a modular organization (Witter & Moser, 2006), but whether the apparent anatomical cell clusters of this brain region correspond to functionally segregated grid maps, each with their own spacing and orientation, remains to be determined.

The Relation Between Grid Cells And Place Cells

The majority of the principal cells in layers II and III of medial entorhinal cortex have grid properties (Sargolini et al., 2006). Thus, most of the spatially selective cortical input to hippocampal place cells is likely to originate from entorhinal grid cells.

Model for transformation of periodic grid fields to non-periodic place fields.

Figure 4: Model for transformation of periodic grid fields to non-periodic place fields.
Place cells receive input from grid cells with similar spatial phase (a common central peak) but a diversity of spacings and orientations.
Connection weights are indicated by the thickness of the arrows. Interneurons (red) provide non-specific inhibition. Colour code as in Figure 1.
Adapted, with permission, from Solstad et al. (2006).

An important question raised by this possibility is how the periodic spatial firing pattern of the grid cells is transformed to a non-periodic signal in place cells. If all grid cells projecting to a particular place cell had a single, common scale, the hippocampal place field would be expected to repeat itself at intervals similar to the grid spacing.

If the inputs vary in spacing and orientation, however, linear summation would result in firing fields with very large repetition cycles, much beyond the scale of any laboratory environment (O’Keefe & Burgess, 2005; Fuhs & Touretzky, 2006; McNaughton et al., 2006; Solstad et al., 2006) (Figure 4.).

In such cells, only a single field would be seen in standard recording boxes. Because a given location in the hippocampus may receive inputs from more than 25% of the dorsomedial-to-ventrolateral axis of the medial entorhinal cortex (Witter et al., 1989; Dolorfo & Amaral, 1998), the latter possibility is more likely.

One potential concern for these models is the observation that the set of grids in a given hemisphere may cover only a single orientation and a discrete set of scales (Barry et al., 2007). This might impede their simple summation to form place cells, and suggests that grids might implement something analogous to modulo arithmetic to represent location over a large scale with high efficiency (Burak et al., 2006; Gorchetchnikov & Grossberg, 2007).

Whether the grid cell population has multiple orientations and whether scales are continuous or discontinuous needs further experimental study, however.

The above models also rely on the unproven assumption that the spatial phase of the contributing grid cells overlaps significantly. This assumption may not be necessary. Place fields could be generated merely from random connectivity by a competitive Hebbian learning process, provided that there is enough variability in orientation, phase and spacing of the afferent grid cell population (Rolls et al., 2006).

Current experimental data are not conclusive as to whether and to what extent plasticity is required for grid to place transformations. While synaptic plasticity is necessary for shaping and stabilizing the hippocampal spatial representation in a novel environment, modifications in the connectivity matrix may not be required for manifestation of place-specific firing as such.

Spatially confined firing fields can still be seen in CA1 pyramidal neurons after deletion of NMDA receptors in CA3 or CA1 (McHugh et al., 1996; Nakazawa et al., 2002), suggesting that, at short time scales, place fields can be generated and maintained by pre-existing connections or by non-NMDA-receptor-dependent plasticity, at least in some hippocampal areas.

Authors: Edvard Moser, Centre for the Biology of Memory, Norwegian University of Science and Technology, Trondheim, Norway, May-Britt Moser, Professor, Centre for the Biology of Memory, NTNU, Norway.

Excerpted from Edvard Moser and May-Britt Moser (2007), Scholarpedia, 2(7):3394.