空间导航对动物和人类的生存至关重要。内嗅皮层的网格细胞是大脑执行空间导航功能的一种重要神经元，在定位生存资源、规划最优路线、路径整合等方面扮演了重要角色。网格细胞的空间编码机制研究是认知神经科学领域最前沿的科学问题之一。网格细胞和其所在脑区的功能异常是阿兹海默症的早期症状之一，对网格细胞的深入研究可以加深对阿兹海默症致病机理的理解，增强疾病的早期诊断和干预能力。揭开网格细胞的空间编码机制，对研发自主导航设备、开发类脑神经网络具有重大意义。经过十余年的探索，关于网格细胞如何编码空间已经取得了巨大的进展。然而，对于网格细胞集群如何加工空间信息，人们仍然知之甚少。当前一个前沿课题就是理解网格集群以及它们构成的环路结构在执行空间导航功能时的规律。本论文通过数学建模和临床实验深入研究了网格细胞集群的空间编码机制。 网格细胞集群如何编码空间，网格集群的偏向角与外在参照系存在何种联系是空间导航领域的研究前沿。大鼠和人类实验均发现，在正方形环境中，网格偏向角锚定边界，随着时间演化形成与边界的8度夹角。这个角度的生物学意义是当下的热点问题。本文先从信息编码入手，提出了基于信息熵的网格集群空间编码模型。通过数值模拟、几何解析以及强化学习等研究手段，发现8度偏角能够使得空间编码效率最大化。在模型中引入噪音后，可以进一步扩大最优偏角为8度时所对应的网格细胞数量的取值范围；网格细胞数量存在下界，当超过该下界时，最优偏角均为8度。模型还可以扩展到长方形环境，预测不同尺寸的长方形所对应的网格最优偏角。当前已有的网格细胞模型均无法预测这些现象。 上述研究建立了网格集群的空间编码模型。网格细胞的集群编码在神经系统中如何实现？目前主流假说认为大脑通过神经振荡完成网格集群的编码。但一直缺乏实验证据。研究发现动物和人类在空间导航过程中，海马系统存在清晰的theta(4-8Hz)振荡。因此课题组猜想，神经系统通过theta振荡编码网格集群信号。借助颅内电生理数据，本文第二个研究尝试在人类癫痫被试上验证该猜想。研究发现被试完成空间导航任务时，内嗅皮层的theta振荡展现出与被试运动方向之间的六周期调制模式。该模式是theta振荡携带网格集群信号的有力证据。同时研究还发现六周期调制模式独特的时空动态演化特性：时间上，六周期调制模式随着被试对环境熟悉程度的增加，逐渐增强；空间上，六周期调制模式对环境边界敏感，在边界区域的强度大于中心区域。一方面，该发现为网格细胞的振荡干涉模型以及振荡吸引子混合模型提供了实验证据。另一方面，该研究还拥有重要的临床价值。研究结果为网格集群提供了新的测量指标——神经振荡，它可以作为单细胞记录和核磁共振记录的有益补充，拓展了相关领域的研究范围，并为深部电刺激治疗与空间迷向有关的神经退行性疾病提供新的参数支持。 综上，本研究首先建立网格细胞集群的空间编码模型，揭示了网格细胞最优偏角的机理，回答了网格集群如何编码空间等问题。同时，借助临床实验数据探讨网格细胞如何通过神经振荡信号完成交互，实现对空间信息的群编码。本文的研究成果揭示了网格细胞在大脑介观尺度(神经元集群)的空间信息处理机制，构建起连接空间导航宏观尺度表征(脑区)和微观尺度表征(单细胞)之间的桥梁，进一步拓展了对网格细胞空间编码机制的理解。并且，网格信息加工的特定神经振荡模式将为阿尔茨海默症提供新的生物标记物，增强疾病的早期诊断和干预。最后，本文从系统科学视角出发，以空间导航为切入点，探讨了大脑如何“从局部作用涌现出高级功能”这个系统科学的核心问题。 本文的创新点主要包括： 从空间最优编码角度提出了网格细胞集群空间编码模型，研究网格细胞的最优偏角问题。模型解释了正方形环境中，网格偏向角呈现出与边界的8度夹角的实验现象。模型不仅能够预测网格细胞数量，还能预测长方形环境所对应的网格最优偏角。当前的网格细胞模型，包括连续吸引子模网络模型、振荡干涉模型以及前馈神经网络模型均无法预测这一现象。 借助临床实验数据，在人类被试中发现theta振荡的六周期调制，并揭示了调制的时间、空间动态演化特性，揭示了神经系统实现网格细胞集群空间编码的神经机制，并为阿尔茨海默症的诊断和治疗提供新的生物标记物。 关键词：网格细胞，theta经振荡，空间导航，网格偏向角，信息熵，六周期调制

 Spatial navigation is key to animal’s survival. Grid cells in entorhinal cortex are one type of neurons that involve in this process. Grid cells play fundamental role in locating food sources, planing optimal route, integrating path and so on. Given fact that grid cell and entorhinal cortex are among the first cortical structures affected by Alzheimer’s disease pathology, research on grid cell could help developing clinical markers of neurodegenerative disorders. Also, neuroscientific progress of grid cell could inspire self-piloting automobile algorithm and next generation artificial intelligence robots. After ten years of investigation, we have known a lot about coding mechanism of grid cell. However, the coding principle of grid cell assemblies is still lack. In this thesis, the issues will be discussed in detail and we will investigate it using two approach: computational modeling and clinical experiment. How do grid cell assemblies encode space and how grid orientation is associated with external environment? Recent experiments in rats and humans revealed that grid orientation is anchored to environmental boundaries. More specifically, these results revealed a slight yet consistent offset of 8 degrees relative to boundaries of a square environment. The causes and possible functional roles of this orientation are still unclear. Here we propose that this phenomenon maximizes the spatial information conveyed by grid cell assemblies. Computer simulations of the grid cell assemblies network reveal that the universal grid orientation at 8 degrees optimizes spatial coding specifically in the presence of noise. Our model also predicts the minimum number of grid cells in each module. In addition, analytical results and a dynamical reinforcement learning model reveal the mechanism underlying the noise-induced orientation preference at 8 degrees. Together, these results suggest that the experimentally observed orientation of grid cells serves to maximize spatial information in the presence of noise. The above work proposes a scheme that how grid cell assemblies encodes space. How does nervous system achieve this coding scheme? Computational models of grid cells have assumed that they rely on neural oscillations. However, it still lacks supporting from experiment data. Theta frequency (4-8Hz) oscillations are a prominent mesoscopic phenomenon during navigation in both rodents and humans. We suspect that theta oscillations may play the role and thus carry grid-like signal. We examined intracranial EEG recordings of epilepsy patients performing a virtual navigation task. We found that the power of theta oscillations exhibits 6-fold rotational modulation by movement direction, reminiscent of grid cell-like representations detected using fMRI. Modulation of theta power was specific to 6-fold rotational symmetry and to the entorhinal cortex. Hexadirectional modulation of theta power by movement direction only emerged during fast movements, stabilized over the course of the experiment, and showed sensitivity to the environmental boundary. Our results suggest that oscillatory power in the theta frequency range carries an imprint of sum grid cell activity (grid cell assemblies). Taken together, this thesis focus on coding mechanism of grid cell in mesoscopic representation (neuron assemblies), which bridges the gap between macroscopic representation and microscopic representation of spatial navigation and contributes to a better understanding of the principles governing the neuronal representation by grid cell. And the specific pattern of neural oscillation could provide a new clinical markers of Alzheimer’s disease and new parameter of deep brain stimulation for memory-deficit disorders. KEY WORDS: grid cell, theta oscillation, spatial navigation, grid orientation, information entropy, hexadirectional modulation