Computational Neuroscience

Jochen Kerdels, Gabriele Peters

See also coverage of this project in Public Media and FernUni Media.

Summary

The entorhinal cortex of rats contains neurons, called grid cells, that exhibit a very peculiar behavior. Discovered about a decade ago, the activity of these cells was found to correlate with the allocentric position of the animal by forming a regular, hexagonal lattice of firing fields across the entire environment. Due to this unusual behavior and the proximity of the entorhinal cortex to other brain regions that also contain cells with spatially correlated activity grid cells are commonly recognized as an important element of a neuronal system for navigation. Existing computational models of grid cells share this view and typically describe the behavior of grid cells as a path integration component of such a system.
Complementary to this view, we presented a new computational model of grid cells that does not assume that grid cells are a specialized component of a navigational system. Instead, it assumes that the activity of grid cells reflects a general principle by which neurons in higher order parts of the cortex process information. The proposed model extends the growing neural gas (GNG) approach by Bernd Fritzke into a recursive algorithm (RGNG) that describes the joint behavior of grid cells in a group as well as the processes within each individual cell. We demonstrated that this approach is able to model the characteristic behavior of grid cells. In addition, it is also able to model the behavior of other cells, which also exhibit grid cell-like firing patterns but whose activity does not correlate with the animal's location in the environment.

Recursive Growing Neural Gas (RGNG)

Our model describes a putative general principle by which neurons in higher-order parts of the cortex process information of arbitrary input spaces. We argue, that each neuron tries to represent its entire input space as well as possible while being in competition with its peers. To model this behavior we employed a novel, two-layer recursive growing neural gas to describe a group or module of grid cells. The top layer represents the interaction between individual grid cells, while the bottom layer models the processes within each cell.

1. Results from Baseline Experiments

We evaluated the RGNG in a series of baseline experiments for various configurations. The obtained results show, that the RGNG is able to model the core properties of observed grid cell phenomena quantitatively as well as qualitatively covering phenomena like the distributions of gridness scores, grid spacings, or grid orientations within and across grid cell modules.

2. Results from Simulations on Real Movement Data of Rats

In addition to the baseline experiments we tested our model with realistic, publicly available movement data of rats provided by Sargolini et al., described in Conjunctive representation of position, direction, and velocity in entorhinal cortex, Science, 2006. We could show that our model is able to describe the activity of grid cells in this case as well. Furthermore, we demonstrated that the model can emulate two prominent grid cell phenomena: grid rescaling and grid rotation.

Grid Rescaling

Right: Artificial rate maps of a top layer unit of an RGNG within a single simulation run demonstrating the phenomenon of grid rescaling. The rate map on the right was sampled during a time period where the hypothetical original environment shown on the left was shrunk by 50% in one direction while simultaneously the assumed speed signal in that direction doubled, which is expected if the speed signal is derived from, e.g., optical flow.

Grid Rotation

Right: Artificial rate maps of a top layer unit of an RGNG and corresponding grid orientation distributions within a single simulation run demonstrating the phenomenon of grid rotation. The rate map and orientation distribution on the right were sampled during a time period where the input space coordinate system was rotated by 25 degrees from the 0 degree starting point shown on the left.

General Information Processing Scheme - Other Cells Than Grid Cells

Since the proposed model implements a general information processing scheme we are also able to model the behavior of non-grid cells that nevertheless exhibit hexagonal firing patterns. The activity of such cells does not correlate with the animal's allocentric position but, e.g., with their gaze position (Killian et al., A map of visual space in the primate entorhinal cortex, Nature, 2012). As far as we know our model is currently the only one that can describe the activity of such non-grid cell phenomena.