Department of Physics, University of Milan and INFN, Via Celoria 13, 20133 Milano, Italy.
Department of Physics, University of California San Diego, La Jolla, California 92093-0374, USA.
Phys Rev E. 2016 Dec;94(6-1):062409. doi: 10.1103/PhysRevE.94.062409. Epub 2016 Dec 20.
Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation, and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e., there are groups of neurons which have grids with similar periodicity, orientation, and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e., without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed comodularity of grid cell periodicity, orientation, and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.
网格细胞在动物探索特定空间区域时会放电，此时这些动物占据了跨越环境的三角形网格的顶点。不同的神经元具有不同周期性、方向和椭圆度的三角形网格。这些网格共同允许动物保持对物理空间的内部、心理表示。实验表明，网格细胞是模块化的，即存在具有相似周期性、方向和椭圆度的网格的神经元群。我们使用统计物理方法来推导出模块内网格属性的可变性与网格系统完全覆盖（即没有间隙）的空间范围之间的关系，网格系统的概率很高。较大的可变性缩小了表示范围，为实验观察到的网格细胞周期性、方向和椭圆度的共调制提供了功能基础。我们获得了在给定变异性和覆盖范围的情况下，神经元数量和模块周期之间的缩放关系。具体来说，我们预测了在较小的网格尺度下比在较大的网格尺度下需要增加多少个神经元。
