REHOVOT, ISRAEL—August 11, 2021—In a new study published in Nature, Weizmann Institute of Science researchers revealed, for the first time, how three-dimensional space is represented in the mammalian cortex by the brain’s “GPS” system. The team, led by Prof. Nachum Ulanovsky of Weizmann’s Department of Neurobiology and including scientists from the Hebrew University of Jerusalem, was surprised to find that this representation is very different from the way two-dimensional space is represented – a finding that turned several longstanding hypotheses on their heads.
Mammals, including humans, are aware of their position in space thanks to several types of specialized neurons in the hippocampus and the nearby entorhinal cortex – regions located deep inside the brain. Head-direction cells – the internal compasses of the brain – indicate to the animal the direction of its head. Place cells, believed to construct a mental map of the environment, are activated when an animal enters or crosses a specific location. In contrast, grid cells respond not to one location, but to multiples, and are thought to provide the brain with a GPS system of sorts.
The study of grid cells and the brain’s GPS was awarded the Nobel Prize in 2014. However, that and other research focused solely on how two dimensions are represented and said very little about the representation of three-dimensional space. To bridge this gap, Prof. Ulanovsky and colleagues set out to elucidate how grid cells act in three dimensions in freely behaving bats.
In the past, when grid cells were studied in rodents moving on two-dimensional surfaces, they were found to be activated in multiple circular areas, known as firing fields, which are arranged in a symmetrical hexagonal pattern – resembling millimeter graph paper – that tiles the surface. This unparalleled symmetry and periodicity suggest that grid cells may be involved in geometric spatial computations that form the core of the cerebral GPS. The entorhinal cortex, where grid cells are located, is the first area of the brain affected by Alzheimer’s disease, and it is possible that spatial disorientation, one of the early manifestations of Alzheimer’s, is due to the grid cells’ dysfunction and the loss of the hexagonal “millimeter paper” of grid cells.
Mathematically, the optimal way to pack circles in two dimensions is in a honeycomb-like hexagonal pattern; this may be why the grid cells’ circular firing fields are represented in the brain in a hexagonal lattice when animals walk over two-dimensional surfaces. Therefore, the researchers expected the activity pattern in three dimensions to be similarly symmetrical and hexagonal. “We and many other researchers hypothesized that we’d see hexagonally stacked balls, like oranges in a grocery store neatly stacked in a pyramid, or any other extremely ordered three-dimensional arrangement,” Prof. Ulanovsky says.
To test this hypothesis, the researchers, led by doctoral student Gily Ginosar, together with staff scientist Dr. Liora Las, recorded the activity of grid cells in bats that had small devices mounted on their heads. The bats were freely flying in a space the size of a large living room, and feeding stations at different heights ensured that each bat covered most of the room’s volume in every run. Once the data started coming in, the researchers saw that grid cells did not behave as expected in response to three-dimensional coordinates. “The well-ordered global grid that is the hallmark of their two-dimensional activity was altogether gone,” explains Prof. Ulanovsky.
Instead, the three-dimensional firing fields, shaped as spheres rather than circles, were packed like a box full of marbles. They were not completely disordered, but were certainly less organized than the three-dimensional equivalent of a hexagonal lattice – an arrangement that allowed the “marbles” some extra degrees of freedom. Whereas any noticeable global order was lacking, the spheres did commit to a local order wherein the distance between one sphere and its nearest neighbors remained constant.
To offer a mechanistic explanation of this phenomenon of local rather than global order, the experimental team – Ginosar, Dr. Las, and Prof. Ulanovsky – collaborated with theoreticians Dr. Johnatan Aljadeff, a former postdoctoral fellow at Weizmann and now a professor at the University of California in San Diego, and Profs. Haim Sompolinsky and Yoram Burak from the Hebrew University of Jerusalem. The teams constructed a model that uses principles borrowed from statistical physics in order to describe the interaction between particles. The model revealed that the spherical firing fields of grid cells seem to interact in almost the same way that particles do, meaning they are attracted to one another from a distance but repelled once they get too close. In particular, the balance of forces acting on particles could explain the local order that kept the spheres at constant local distances from one another, while avoiding any global lattice. Compared to previous models that were used to predict the three-dimensional organization of grid cells’ firing fields, the new one was the most loyal to the experimental data.
Taken together, the surprising experimental data and theoretical model offer a new way of looking at the neural basis of three-dimensional navigation and the role that grid cells play in this cognitive process. While previous models extrapolated a similar three-dimensional arrangement from the two-dimensional grid, the work of Prof. Ulanovsky and colleagues and their “box of marbles” model show that the situation is much more complex – and that since no periodic lattice is formed in three-dimensional space, classical theories for understanding the intriguing behavior of grid cells will need to be revised.
Prof. Nachum Ulanovsky’s research is supported by Dita & Yehuda L. Bronicki; the European Research Council; and the Israel Science Foundation. He is the incumbent of the Barbara and Morris L. Levinson Professorial Chair in Brain Research.
