2009 Special IssueDistance coding strategies based on the entorhinal grid cell system
Introduction
Behavioral experiments have shown that rodents (Siegrist, Etienne, Boulens, Maurer, & Rowe, 2003), cats (Poucet, Thinus-Blanc, & Chapuis, 1983) and chimpanzees (Menzel, 1973) are able to learn the layout of their environment, make detours and find shortcuts if they face obstacles or have to cross unknown areas while they navigate. To achieve these metric navigation tasks, the animal has to possess metric information, i.e. distance among places and direction from specific points in the environment. Orientation of the animal is coded by head direction cells that were first discovered in the dorsal presubiculum (Ranck, 1984) but was later found in many other brain regions, including thalamus (Taube, 1995), mammillary nucleus (Stackman & Taube, 1998), retrosplenial cortex (Chen, Lin, Green, Barnes, & McNaughton, 1994), striatum (Wiener, 1993) and layer III of the entorhinal cortex (Sargolini et al., 2006). However, neurons representing distance from specific points have not been described yet.
The majority of principal cells in the hippocampus are place cells that show spatially correlated activity, representing specific positions of the environment. In the CA3 region of the hippocampus, there is a significant number of lateral cross connections between principal cells, therefore, a natural assumption of computational models (Trullier & Meyer, 2000) was that the connection strengths between CA3 place cells could represent distances between positions. However, place cells are not topographically organized, they randomly re-map in a new environment, therefore distance between positions represented by any two place cells is not constant, it depends on the environment. This makes hard to implement metrics by the CA3 recurrent collaterals, since the connection strengths in the whole connection system should be reorganized in each environment for correct distance representation.
The attention has been recently drawn to the medial entorhinal cortex (MEC) layer II pyramidal cells (Fyhn et al., 2007, Fyhn et al., 2004, Hafting et al., 2005, Moser et al., 2008, Sargolini et al., 2006) that show a topographic organization. These grid cells were shown to be active on the vertices of triangular grids tessellating the plane and each cell is characterized by the spacing (spatial periodicity), orientation and the 2 dimensional phase value of its grid (Fig. 1C). The cells were found to be topographically organized along the dorsoventral axis of MEC according to their spacing value. This grid cell system is considered as an explicit example of metric space representation in the central nervous system (Jeffery and Burgess, 2006, Moser and Moser, 2008), and according to the present view (Fuhs and Touretzky, 2006, Guanella et al., 2007), the function of grid cell system is to perform path integration. These properties make the grid cell system a possible source of metric information.
However, due to the periodic nature of their spatial code, extraction of the distance information from these cells is not straightforward, further computations are necessary to perform this task. In this paper we extend the analysis of our previously proposed model that generates metrics via grid cells (Huhn, Somogyvári, Kiss, & Érdi, 2009). This model system has to solve two tasks: first, it should refer to or address two positions, between which distance is measured, second, the distance between these points should be decoded from the activity pattern of the grid cell system. In our model, the general task of estimating the distance between any two positions in the environment was simplified so that the position of the animal is compared to an already visited and stored significant position. The distance of the animal from this origin is encoded by the populational activity of hypothesized ‘distance cells’ (DCs) that receive input both directly and indirectly (through inhibitory cells) from the grid cell system. We study two variants of the general model: in one of them, the direct input is dominant, while in the other one it is negligible and distance cell activity is mainly determined by the indirect input. Distance coding capabilities and the estimation precision of the two model variants are analyzed in this paper.
Section snippets
Model
The general model architecture is the following: grid cells innervate both DCs and feed-forward inhibitory neurons (FFINs) projecting to distance cells, and a competition among distance cells is executed by feed-back inhibitory cells (Fig. 1A, B). Each distance cell and feed-forward inhibitory neuron is innervated by grid cells that share a common spacing, i.e. has a scale equaling this spatial periodicity and each inhibitory neuron projects to a distance cell that has the same scale. The two
Results
The task that the model has to execute is to represent the distance of the animal from the origin by the populational activity of distance cells. In model A, the activity of a DC depends on the summed input received from its presynaptic grid cells, since effects from FFINs are assumed to be negligible. The constrain that a DC receives input from grid cells of a given spacing results that the net input of the DC changes periodically with the distance from the origin, creating concentric rings
Discussion
In the short history of grid cells, most papers discuss their possible role in navigation in connection with hippocampal place representation. Up to now these articles attributed more or less the same role to the grid cell system: being involved in path integration it facilitates the creation of place cells in the hippocampus even in the absence of allothetic information (Fiete et al., 2008, Franzius et al., 2006, Fuhs and Touretzky, 2006, Rolls and Kesner, 2006, Solstad et al., 2006). It is
Acknowledgement
Authors are grateful for the useful discussions held at the Budapest Computational Neuroscience Forum. The research was funded by the EU Framework 6 ICEA project (IST 027819). PE thanks the Henry Luce Foundation for general support.
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