Do we expect periodic grid cells to emerge in bats, or perhaps dolphins, exploring a three-dimensional environment? How long will it take? Our self-organizing model, based on ring-rate adaptation, points at a complex answer. The mathematical analysis leads to asymptotic states resembling face centered cubic (FCC) and hexagonal close packed (HCP) crystal structures, which are calculated to be very close to each other in terms of cost function. The simulation of the full model, however, shows that the approach to such asymptotic states involves several sub-processes over distinct time scales. The smoothing of the initially irregular multiple fields of individual units and their arrangement into hexagonal grids over certain best planes are observed to occur relatively quickly, even in large 3D volumes. The correct mutual orientation of the planes, though, and the coordinated arrangement of different units, take a longer time, with the network showing no sign of convergence towards either a pure FCC or HCP ordering.
Our ability to navigate through our environment depends on a region of the brain called the hippocampus. In the 1990s it was shown that this structure, which takes its name from the Greek word for ‘seahorse’ owing to its shape, was larger in London taxi drivers than it was in the general population. However, as early as the 1960s, experiments in rats had revealed that specific cells within the hippocampus—called place cells—fire whenever an animal is in a particular location, and thus enable the animal to build up a map of its environment.
In 2014, the scientist who discovered place cells shared the Nobel Prize in Physiology or Medicine with two neuroscientists who had discovered an additional type of cell that is involved in navigation. These grid cells, which are located in a region of the brain that provides input to the hippocampus, ‘fire’ at multiple points in space. When the scientists who discovered grid cells plotted these points in two dimensions, they formed a grid of tessellating triangles that spanned the entire area.
However, many animals, including aquatic mammals, monkeys and bats, navigate in three dimensions rather than two. This raises an obvious question: can grid cells also represent three-dimensional space? Stella and Treves have addressed this issue by constructing a computer model that simulates grid cell activity in a virtual bat flying through a virtual room. The model reveals that grid cells switch from firing largely at random to firing in some semblance of a three-dimensional pattern relatively quickly.
However, this pattern bears little resemblance to the highly ordered arrangement seen in two dimensions. Indeed, the model suggests that a bat flying at 1 metre per second around a room that measured 2.5 × 2.5 × 2.5 metres would need to fly continuously for a very long time (at least 80 hours) before such a pattern could be established in three dimensions. This suggests that the regular tessellation shown by grid cells in two dimensions might not be routinely established in three dimensions. Instead, simpler ‘precursor’ firing patterns may form over shorter periods of time, providing a looser mapping of three-dimensional space.