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Reading the neural code for space

Munich scientists have put forward a mathematical theory that explains key features of grid cells, which are involved in spatial navigation (December 2015).

One year ago, the Nobel Prize in Physiology or Medicine went to the discoverers of the mammalian “GPS system” for spatial navigation. Measuring neural activity in cortex, these researchers had found that some cells represent space in a highly surprising manner: As the animal moves through its environment, distinct sets of cells are sequentially activated. Each individual “grid cell” responds to multiple positions in space that form a virtual hexagonal lattice tessellating the environment. This strikingly periodic and beautiful spatial pattern has caught the imagination of experimental and theoretical neuroscientists alike, and has been proposed to constitute the brain’s metric for space.

Theoretical neuroscientists from the Bernstein Center and Ludwig-Maximilians-Universität München (LMU) and from Harvard University have now dispelled the concept that the hexagonal grid’s periodic nature represents a universal metric for space.  In its place, Martin Stemmler (LMU), Alexander Mathis (Harvard) and Andreas V.M. Herz (LMU) put forward a comprehensive mathematical theory, proving that a spatial metric emerges only when reading out different grid cells simultaneously. This theory exploits and extends a computational principle well known from sensory systems and the brain’s motor cortex – population-vector decoding: physical quantities such as the angle of a visual stimulus or the direction of a movement can be easily read out from the activity of a population of neurons with different tuning properties if the neurons’ activities are combined in a particular, vector-like manner.

Thanks to the new theory, three basic questions can now be readily answered: Why are grid cells organized into discrete modules, within which all grid lattices share the same spatial scale and orientation, but have different spatial offsets? Why do the spatial scales of the grid lattices form a geometric progression? And why is the observed scale ratio close to 3/2? “If grid cells were not organized into modules with fixed grid scale and orientation, the brain could not use population vectors to represent spatial position,” explains Martin Stemmler. “The geometric progression in the grid scales maximizes the spatial resolution of the neural code, based on just a few bursts of neural activity. Finally, the scale ratio should be close to 3/2 to avoid catastrophic navigation errors when information from different grid modules is combined to calculate a single quantity, the animal’s position estimate.”

Not only can grid cells be used to estimate one’s own position in world-centered coordinates, but the proposed read-out mechanism converts the distance and direction to some goal directly into one’s own coordinate system, telling one which way to turn and how far to walk to get home, for instance. “Transiently silencing individual grid modules should lead to specific types of navigational errors – a prediction to be tested in future research”, says Alexander Mathis. Most significantly, the new mathematical framework imparts precision to the previously nebulous notion of a “neurobiological metric for space”. This settles also a recent controversy in the field – whether the observed distortions of grid patterns rule out the proposed role of grid cells as a metric for space: no, they do not.

The theory developed by Stemmler and colleagues goes beyond previous proposals for population-vector decoding, as the decoded quantity – the animal’s position – is not a circular variable like the angle of limb motion or the orientation of an object in one’s visual field. Animals move on two-dimensional surfaces or in three-dimensional spaces, so their position is no longer a one-dimensional variable, either. Moreover, the new approach shows how population-vector averages across different grid scales can be combined, by invoking the mathematical theory of self-similar scaling.  Not even the most sophisticated ideal observer can improve on this simple population-vector read-out. “The fact that population vector decoding is optimal results from the strict organization of grid cells into discrete modules with common lattice orientations and degrees of elliptic deformation,” explains Andreas Herz. “This suggests that population-vector decoding is a fundamental computational principle for brain function, even for higher cognitive functions such as memory and spatial navigation.”

Text: LMU Munich (modified)




Prof. Dr. Andreas Herz
Computational Neuroscience
Department Biology II
LMU Munich

Phone: +49 (0)89 - 2180 74801

M. Stemmler, A. Mathis & A.V.M. Herz (2015): Connecting Multiple Spatial Scales to Decode the Population Activity of Grid Cells. Science Advances 2015,1:e1500816