The hippocampus is a brain structure that is important for memorizing facts and episodes. In particular in rodents it is also essential for spatial navigation. For instance, it contains cells that only fire if the animal is at a particular location of its enclosure, largely independent of its orientation or any other factor. Such cells are referred to as place cells. In the entorhinal cortex, which provides the main input to the hippocampus, one finds cells that respond at regularly spaced locations of the enclosure. These cells are called grid cells. The question we address here is how place cells could emerge from grid cells.
We assume the simplest possible model in which the input from the grid cells is combined linearly, and if we optimize this linear transformation for sparseness, we naturally get place places. Sparseness means that the firing rate should be low most of the time and high only occasionally. Since sparseness is believed to be an important principle in the hippocampus, we think that our model provides a very simple but plausible mechanism for the emergence of place cells from grid cells.
Figure: One can record the activity of single grid cells in the entorhinal cortex of a rat while it is running in a circular enclosure. The mean firing rate of such a cell plotted as a function of the location of the rat in the enclosure looks like a hexagonal grid. The three plots on the left are three out of hundred simulated grid cells of different spatial spacing. If one combines the output of such grid cells linearly and optimizes for sparseness, one obtaines place cells, which have localized fields of high firing rate, as shown on the right.
The interesting question that remains is, of course, how do the grid cells emerge. This question is addressed in another project.