[论文解读] Spatial Embedding Imposes Constraints on the Network Architectures of Neural Systems

Jennifer Stiso, Danielle S. Bassett|arXiv (Cornell University)|Jul 12, 2018

Functional Brain Connectivity Studies参考文献 4被引用 3

一句话总结

本文主张，物理空间嵌入通过塑造布线规则（如布线最小化和通信效率）从根本上限制了神经网络架构，导致具有高局部聚类性和稀疏长程连接的特定拓扑结构。这些空间约束影响功能动力学，解释了观察到的连接组特征，并对理解大脑功能与疾病中的功能障碍至关重要。

ABSTRACT

A fundamental understanding of the network architecture of the brain is necessary for the further development of theories explicating circuit function. Perhaps as a derivative of its initial application to abstract informational systems, network science provides many methods and summary statistics that address the network's topological characteristics with little or no thought to its physical instantiation. Recent progress has capitalized on quantitative tools from network science to parsimoniously describe and predict neural activity and connectivity across multiple spatial and temporal scales. Yet, for embedded systems, physical laws can directly constrain processes of network growth, development, and function, and an appreciation of those physical laws is therefore critical to an understanding of the system. Recent evidence demonstrates that the constraints imposed by the physical shape of the brain, and by the mechanical forces at play in its development, have marked effects on the observed network topology and function. Here, we review the rules imposed by space on the development of neural networks and show that these rules give rise to a specific set of complex topologies. We present evidence that these fundamental wiring rules affect the repertoire of neural dynamics that can emerge from the system, and thereby inform our understanding of network dysfunction in disease. We also discuss several computational tools, mathematical models, and algorithms that have proven useful in delineating the effects of spatial embedding on a given networked system and are important considerations for addressing future problems in network neuroscience. Finally, we outline several open questions regarding the network architectures that support circuit function, the answers to which will require a thorough and honest appraisal of the role of physical space in brain network anatomy and physiology.

研究动机与目标

• 确立物理空间嵌入对神经网络架构施加基本约束，影响连接模式与动力学。
• 证明空间约束（如布线最小化和通信效率）催生出特定的拓扑特征，例如高聚类性和稀疏长程连接。
• 强调在神经网络科学中整合几何与拓扑的重要性，以理解功能动力学与疾病机制。
• 回顾考虑空间嵌入的计算工具与模型，以改进对脑网络的分析。
• 识别在连接组发育、网络动力学与生物标志物发现方面，仍需深入考虑空间约束的开放性问题。

提出的方法

• 综述神经解剖学与连接组学中的实证证据，表明空间嵌入塑造了观察到的网络拓扑结构。
• 应用网络科学工具，区分拓扑属性（图的内在结构）与几何属性（空间嵌入）。
• 使用生成网络模型，整合空间约束，如距离依赖的连接概率与最小布线成本。
• 采用统计零模型与指标（如聚类系数、路径长度与模块性）量化空间约束下的拓扑结构。
• 整合应用代数拓扑方法，分析空间嵌入神经网络中的环路与高阶结构。
• 分析功能与结构连接数据，关联空间嵌入与功能梯度及动态基序。

实验结果

研究问题

• RQ1 空间受限的发育过程如何限制脑网络中环路的形成？
• RQ2 哪些连接组拓扑特征无法由布线最小化或通信效率完全解释，因而可能源于更细微的规则？
• RQ3 由物理生长规则产生的结构性拓扑如何支持功能梯度？
• RQ4 脑活动的不变特征与底层解剖结构之间的确切关系是什么？
• RQ5 连接组的发育如何决定皮层中活动的空间传播进程，无论在健康还是疾病状态下？

主要发现

• 空间嵌入对神经网络架构施加物理约束，导致具有高局部聚类性和稀疏长程连接的拓扑结构。
• 布线最小化与通信效率是相互竞争的规则，共同塑造脑网络的拓扑结构，尤其在皮层与皮层下系统中表现显著。
• 大脑中的功能连接模式与空间嵌入及由此产生的拓扑特征（如模块性与小世界组织）紧密关联。
• 脑网络的拓扑属性（如聚类与路径长度）在癫痫与精神分裂症等神经与精神疾病中发生广泛改变。
• 空间约束影响可涌现的神经动力学集合，从而影响正常功能与疾病相关的网络功能障碍。
• 一系列计算工具（包括零模型、生成模型与拓扑数据分析）正不断发展，使研究人员能够分离空间嵌入对观察到的神经网络现象的影响。