Grid cells in the medial entorhinal cortex ( mEC ) respond when an animal occupies a periodic lattice of "grid fields" in the environment. The grids URLanized in modules with spatial periods  clustered around discrete values separated by constant ratios reported in the range 1.3-1.8 . We propose a mechanism for dynamical URLanization in the mEC that can produce this modular structure  . In attractor network models of grid formation, the period of a single module is set by the length scale of recurrent inhibition between neurons. We show that grid cells will instead form a hierarchy of discrete modules if a continuous increase in inhibition distance along the dorso-ventral axis of the mEC is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids , whose lattice constants are separated by \sqrt{3 \approx 1.7, \sqrt{7}/2 \approx 1.3, or other ratios}  . We discuss how the interactions required by our model might be tested experimentally and realized by circuits in the mEC .
Grid cells in the medial entorhinal cortex ( MEC ) respond when an animal occupies a periodic lattice of "grid fields" in the environment. The grids URLanized in modules with spatial periods , or scales, clustered around discrete values separated by ratios in the range 1.2--2.0 . We propose a mechanism that produces this modular structure through dynamical URLanization in the MEC . In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids \approx 1.7, \sqrt{7}/2 \approx 1.3, or other ratios} and have values that fall within the observed range . We discuss how interactions required by our model might be tested experimentally .
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mEC
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constant ratios reported
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1.3-1.8
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for dynamical URLanization in the mEC that can produce
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through dynamical URLanization in the MEC
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period
grid scale
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length scale
distance
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grid cells will instead form
the MEC forms
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continuous
smooth
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the
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of the mEC
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, whose lattice constants are separated by \sqrt{3
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and have values that fall within the observed range
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and realized by circuits in the mEC