Essays on Science and SocietyNeuroscience

Brain crystals

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Science  02 Oct 2015:
Vol. 350, Issue 6256, pp. 47-48
DOI: 10.1126/science.aad3002

I have been enthralled with crystals ever since I was a child. Growing up, I was fortunate enough to have a neighbor who was a geologist with a mesmerizing collection of colorful minerals. My first personal exploration of crystal formation came with watching icicles growing on the eaves of our roof. They came in different shapes and sizes and made me wonder: “How?” Later, I was surprised to discover that there was a whole field of “icicle physics” that dealt with precisely this question (1, 2).

Imagine my renewed excitement when, as a budding neuroscientist at university, I learned that there was crystal-like neural activity in the brain. There is a group of neurons in the parahippocampal formation named “grid cells” that fire in hexagonal symmetry (3) (see the figure, panel A, left). Grid neurons themselves are not necessarily arranged in a crystal-like pattern in the brain [although some argue this could be the case (4)]. Rather, each cell acts as a crystal “generator,” where the fundamental blocks are fields of neural activity.

Grid cell firing appears to be invariant to properties of the enclosure (e.g., size, shape), as well as an animal's behavior (e.g., running speed, grooming), which prompts the suggestion that they represent an internally generated path integration system for navigation (3). The universal metric of space had been found (3, 5, 6)!

I became curious as to whether the hexagonal grid was the only crystal structure in the brain. For instance, engineers and architects often prefer a square grid for constructing space—it is the periodicity rather than a particular symmetry that is a key prerequisite for a metric system to work. I recorded from neurons in the rat parahippocampal region to see if cells with other firing patterns could be found there. To my delight, I found another class of spatially tuned cells that fired in response to multiple discrete locations in the environment. The pattern was not random but failed to exhibit the hexagonal symmetry observed in grid cells (figure, panel A, right) (7).

Breaking grid symmetry.

(A) Firing-rate maps of a grid cell (left) and a bandlike spatially periodic cell (right). (B) Occasionally, cell f ring altered for grid (left) and nongrid (right) patterns between trials. (C) A schematic of the force–boundary interaction model. Place cells (blue, PC) and border cells (tan, BC) are interconnected via an inhibitory theta interneuron network (orange, θ). The place cells drive the f ring pattern of the grid cell (light brown, GC). (D) Recorded (top) and predicted (bottom) grid cell in a trapezoidal enclosure. (E) An example of right-to-left grid expansion and rotation in a trapezoid (left). Such transformation was not observed in a square environment (right).


I developed an analysis method based on the two-dimensional Fourier transform to quantify the properties of all spatial cells in the parahippocampal region (including grid cells) and proposed a possible underlying mechanism for grid cell formation. Our results suggest that grid cells form the most stable subset of a larger continuum of locational cells whose firing properties can be described as a weighted sum of a small number (from 1 to 4) of periodic, bandlike inputs. We noticed that under certain circumstances grid cells lost their hexagonal symmetry and became more irregular, on some occasions even acquiring a bandlike firing pattern (figure, panel B). The geometry of the enclosure in which the rat was tested seemed to play a major role in facilitating such pattern transitions.

The geometry of an enclosure is defined by the arrangement of its boundaries. Indeed, “border cells” located in close anatomical proximity to grid cells are active along the boundaries of the enclosure (8, 9). We thought that perhaps border cells could play an important role in shaping grid cell pattern. We tested this idea by developing a model in which a grid cell firing pattern was generated by interacting place cells (cells in the hippocampus that are active in a particular place of the enclosure) and border cells (10). We called this a field-boundary interaction model (figure, panel C). We postulated that the strength of interaction of individual place fields would be proportional to the distance between the grid cells in a winner-take-all manner and that the role of border cells is to “push” the fields away. The model predicted that grid cells would exhibit hexagonal symmetry in square and circular enclosures but that this pattern would break down in more polarized enclosures, such as trapezoids. It also indicated that the grid orientations would be aligned to the walls of the enclosure.

FINALIST: Julija Krupic

Julija Krupic received her undergraduate degree from Vilnius University and a Ph.D. from University College London (UCL). She is currently a Sir Henry Wellcome Fellow at UCL, where she conducts research on how place cell activity guides animal behavior. In 2016, Julija will move to the Salk Institute where she will study how connectivity affects the functional properties of place cells.

We went on to test this model experimentally by recording grid cells in rats that were placed in square, circular, hexagonal, and trapezoidal enclosures (11). Our results confirmed both predictions: grid cell orientations were clustered in square, but not circular, enclosures, and the perfect grid pattern seen in the square enclosures did not exist in trapezoidal enclosures. In trapezoids, the grid became more elliptical and nonhomogeneous: It was larger and rotated toward the narrower part of the trapezoid compared with the wider part (figure, panels D and E). Such profound distortions were not observed in the square or circular enclosures where the symmetrical and consistent pattern was similar to those observed in most previous studies. The results challenge the idea that the grid cell system can act as a universal spatial metric for the cognitive map, as grid patterns changed remarkably between enclosures and even within the same enclosure. It is possible that grid cells may still be measuring distance in trapezoids, albeit in a distorted fashion, and this finding leads to the intriguing idea that our brains perceive distance differently in environments with polarized geometry.

These results made us wonder what the grid cell system is really used for: Is it a metric system with some limitations or is it a matrix of locations, and has the metric property emerged as a side effect?


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