Mathis Alexander, Stemmler Martin B, Herz Andreas Vm
Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States.
Bernstein Center for Computational Neuroscience, , , Germany.
Elife. 2015 Apr 24;4:e05979. doi: 10.7554/eLife.05979.
Lattices abound in nature-from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution, and cryptographic protocols. Do lattices also play a role in how the brain represents information? We focus on higher-dimensional stimulus domains, with particular emphasis on neural representations of physical space, and derive which neuronal lattice codes maximize spatial resolution. For mammals navigating on a surface, we show that the hexagonal activity patterns of grid cells are optimal. For species that move freely in three dimensions, a face-centered cubic lattice is best. This prediction could be tested experimentally in flying bats, arboreal monkeys, or marine mammals. More generally, our theory suggests that the brain encodes higher-dimensional sensory or cognitive variables with populations of grid-cell-like neurons whose activity patterns exhibit lattice structures at multiple, nested scales.
自然界中晶格无处不在——从矿物质的晶体结构到昆虫复眼中小眼的蜂窝状组织。这些排列为最优堆积、高效资源分配和加密协议提供了解决方案。晶格在大脑表征信息的方式中也起作用吗？我们专注于高维刺激域，特别强调物理空间的神经表征，并推导哪种神经元晶格编码能使空间分辨率最大化。对于在表面导航的哺乳动物，我们表明网格细胞的六边形活动模式是最优的。对于能在三维空间自由移动的物种，面心立方晶格是最佳的。这一预测可以在飞行的蝙蝠、树栖猴子或海洋哺乳动物身上进行实验验证。更一般地说，我们的理论表明，大脑用类似网格细胞的神经元群体对高维感觉或认知变量进行编码，这些神经元的活动模式在多个嵌套尺度上呈现出晶格结构。
