Department of Biomedical Engineering, Tufts University, Medford, MA, USA.
Eur J Neurosci. 2021 Jan;53(2):485-498. doi: 10.1111/ejn.14937. Epub 2020 Sep 15.
The analysis of real-world networks of neurons is biased by the current ability to measure just a subsample of the entire network. It is thus relevant to understand if the information gained in the subsamples can be extended to the global network to improve functional interpretations. Here we showed how average clustering coefficient (CC), average path length (PL), and small-world propensity (SWP) scale when spatial sampling is applied to small-world networks. This extraction mimics the measurement of physical neighbors by means of electrical and optical techniques, both used to study neuronal networks. We applied this method to in silico and in vivo data and we found that the analyzed properties scale with the size of the sampled network and the global network topology. By means of mathematical manipulations, the topology dependence was reduced during scaling. We highlighted the behaviors of the descriptors that, qualitatively, are shared by all the analyzed networks and that allowed an approximated prediction of those descriptors in the global graph using the subgraph information. In contrast, below a spatial threshold, any extrapolation failed; the subgraphs no longer contain enough information to make predictions. In conclusion, the size of the chosen subgraphs is critical to extend the findings to the global network.
对神经元真实网络的分析受到当前仅能测量整个网络子样本的能力的限制。因此，了解在子样本中获得的信息是否可以扩展到全局网络以改善功能解释是很重要的。在这里，我们展示了当对小世界网络进行空间采样时，平均聚类系数（CC）、平均路径长度（PL）和小世界倾向（SWP）如何进行缩放。这种提取模拟了通过电和光技术测量物理邻居的方式，这两种技术都被用于研究神经元网络。我们将这种方法应用于模拟和体内数据，并发现所分析的特性与采样网络和全局网络拓扑的大小有关。通过数学运算，在缩放过程中减少了拓扑依赖性。我们强调了描述符的行为，这些行为在性质上是所有分析网络共有的，并且允许使用子图信息在全局图中对这些描述符进行近似预测。相比之下，低于空间阈值时，任何外推都失败了；子图不再包含足够的信息来进行预测。总之，选择的子图的大小对于将发现扩展到全局网络至关重要。
