Optimal Population Codes for Space: Grid Cells Outperform Place Cells
Optimal Population Codes for Space: Grid Cells Outperform Place Cells
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DOI：
10.1162/neco_a_00319
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发表时间：
2012-09-01
影响因子：
2.9
通讯作者：
Stemmler, Martin
中科院分区：
文献类型：
--
作者：
Mathis, Alexander;Herz, Andreas V. M.;Stemmler, Martin
啮齿类动物使用两个不同的神经元坐标系来估计它们的位置：海马体中的位置域和内嗅皮层中的网格域。放置细胞仅在一个特定的空间位置处出现尖峰，而网格细胞则在与假想的六边形晶格的点相对应的多个位置处放电。我们研究如何最好地构建位置和网格代码，同时考虑神经尖峰的概率性质。当从神经元群体反应中解码动物的位置时，单个神经元的哪些空间编码特性赋予了最高分辨率？先验地，根据网格代码估计空间位置可能是不明确的，因为规则的周期晶格具有平移对称性。解决这个问题需要不同间距的网格单元格；空间分辨率关键取决于在总体中选择这些间距的正确比率。我们使用 Fisher 信息计算估计渐近极限位置的预期误差，并使用最大似然估计计算低峰值计数的预期误差。在网格代码中实现高空间分辨率和覆盖大范围的空间需要权衡：空间分辨率的最佳网格代码是由具有不同空间周期的嵌套模块构建的，一个在另一个内部，而最大化空间范围需要成对不相称的不同空间周期。优化空间分辨率可以预测通过实验观察到的两个网格单元属性。首先，短晶格间距的数量应多于长晶格间距的数量。其次，网格码在不同的晶格间距上应该是自相似的，以便网格场始终覆盖晶格周期的固定部分。如果满足这些条件并且每个神经元的空间“调谐曲线”跨越相同的放电率范围，则网格代码的分辨率很容易超过具有相同数量神经元的最佳可能位置代码的分辨率。
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.