Neural Comput - Optimal population codes for space: grid cells outperform place cells.


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Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial "tuning curves" for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

Resumo Limpo

rodent use two distinct neuron coordin system estim posit place field hippocampus grid field entorhin cortex wherea place cell spike one particular spatial locat grid cell fire multipl site correspond point imaginari hexagon lattic studi best construct place grid code take probabilist natur neural spike account spatial encod properti individu neuron confer highest resolut decod anim posit neuron popul respons priori estim spatial posit grid code ambigu regular period lattic possess translat symmetri solut problem requir lattic grid cell differ space spatial resolut crucial depend choos right ratio space across popul comput expect error estim posit asymptot limit use fisher inform low spike count use maximum likelihood estim achiev high spatial resolut cover larg rang space grid code lead tradeoff best grid code spatial resolut built nest modul differ spatial period one insid wherea maxim spatial rang requir distinct spatial period pairwis incommensur optim spatial resolut predict two grid cell properti experiment observ first short lattic space outnumb long lattic space second grid code selfsimilar across differ lattic space grid field alway cover fix fraction lattic period condit satisfi spatial tune curv neuron span rang fire rate resolut grid code easili exceed best possibl place code number neuron

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