Distance coding strategies based on the entorhinal grid cell system

Abstract

Estimating and keeping track of the distance from salient points of the environment are important constituents of the spatial awareness and navigation. In rodents, the majority of principal cells in the hippocampus are known to be correlated with the position of the animal. However, the lack of topography in the hippocampal cognitive map does not support the assumption that connections between these cells are able to store and recall distances between coded positions. In contrast, the firing fields of the grid cells in the medial entorhinal cortex form triangular grids and are organized on metrical principles. We suggest a model in which a hypothesized ‘distance cell’ population is able to extract metrics from the activity of grid cells. We show that storing the momentary activity pattern of the grid cell system in a freely chosen position by one-shot learning and comparing it to the actual grid activity at other positions results in a distance dependent activity of these cells. The actual distance of the animal from the origin can be decoded directly by selecting the distance cell receiving the largest excitation or indirectly via transmission of local interneurons. We found that direct decoding works up to the longest grid spacing, but fails on smaller scales, while the indirect way provides precise distance determination up to the half of the longest grid spacing. In both cases, simulated distance cells have a multi-peaked, patchy spatial activity pattern consistent with the experimentally observed behavior of granule cells in the dentate gyrus.

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.