A diversity of localized timescales in network activity.
A diversity of localized timescales in network activity.
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作者：
Chaudhuri R;Bernacchia A;Wang XJ
神经元表现出不同的时间尺度，因此网络的不同部分以不同的时间动态响应。当比较大脑区域和局部人群中的细胞之间的时间尺度时，都观察到了这种多样性;潜在的电路机制仍然未知。我们研究的条件下，空间局部连接可以产生这样不同的时间行为。在线性网络中，如果连接矩阵的特征向量被定位到网络的不同部分，则时间尺度是分离的。我们开发了一个框架来预测局部特征向量的形状。值得注意的是，对于单独的时间尺度而言，仅本地连通性是不够的。然而，本地化的时间尺度可以实现异质性的连接配置文件，我们展示了两类网络架构，允许这样的本地化。我们的研究结果提出了一个框架，结构异质性功能多样性，超越神经动力学，一般适用于生物网络的结构和动力学之间的关系。DOI：http://dx.doi.org/10.7554/eLife.01239.001许多生物系统可以被认为是网络，其中大量的元素，称为“节点”，相互连接。例如，大脑是一个由相互连接的神经元组成的网络，这个网络不断变化的活动模式是我们对周围世界的体验的基础。在大脑中，不同的部分可以以不同的速度处理信息：大脑的感觉区域对当前环境做出快速反应，而大脑的认知区域参与复杂的思维过程，能够在更长的时间内收集信息。然而，网络的哪些属性允许不同区域在不同的时间尺度上处理信息，以及结构属性的变化如何转化为网络部分可以运行的时间尺度的差异，在很大程度上是未知的。现在，Chaudhuri等人使用一种简单但普遍存在的网络来解决这些问题，这种网络称为线性网络。线性网络的活动可以分解成更简单的模式，称为特征向量，可以组合起来预测整个网络的响应。如果这些特征向量“映射”到网络的不同部分，这就可以解释不同的区域如何在不同的时间尺度上处理信息。Chaudhuri等人开发了一种数学理论来预测什么性质会导致这些特征向量彼此分离，并将其应用于具有类似于大脑布线的架构的网络。这表明，网络中连通性的梯度，使得节点与相邻节点共享的属性比远距离节点多，加上节点间连接强度的随机差异，是产生这种分离活动模式的一般性基序。有趣的是，这种梯度和随机性都是生物系统的共同特征。DOI：http://dx.doi.org/10.7554/eLife.01239.002网站
Neurons show diverse timescales, so that different parts of a network respond with disparate temporal dynamics. Such diversity is observed both when comparing timescales across brain areas and among cells within local populations; the underlying circuit mechanism remains unknown. We examine conditions under which spatially local connectivity can produce such diverse temporal behavior. In a linear network, timescales are segregated if the eigenvectors of the connectivity matrix are localized to different parts of the network. We develop a framework to predict the shapes of localized eigenvectors. Notably, local connectivity alone is insufficient for separate timescales. However, localization of timescales can be realized by heterogeneity in the connectivity profile, and we demonstrate two classes of network architecture that allow such localization. Our results suggest a framework to relate structural heterogeneity to functional diversity and, beyond neural dynamics, are generally applicable to the relationship between structure and dynamics in biological networks. DOI: http://dx.doi.org/10.7554/eLife.01239.001 Many biological systems can be thought of as networks in which a large number of elements, called ‘nodes’, are connected to each other. The brain, for example, is a network of interconnected neurons, and the changing activity patterns of this network underlie our experience of the world around us. Within the brain, different parts can process information at different speeds: sensory areas of the brain respond rapidly to the current environment, while the cognitive areas of the brain, involved in complex thought processes, are able to gather information over longer periods of time. However, it has been largely unknown what properties of a network allow different regions to process information over different timescales, and how variations in structural properties translate into differences in the timescales over which parts of a network can operate. Now Chaudhuri et al. have addressed these issues using a simple but ubiquitous class of networks called linear networks. The activity of a linear network can be broken down into simpler patterns called eigenvectors that can be combined to predict the responses of the whole network. If these eigenvectors ‘map’ to different parts of the network, this could explain how distinct regions process information on different timescales. Chaudhuri et al. developed a mathematical theory to predict what properties would cause such eigenvectors to be separated from each other and applied it to networks with architectures that resemble the wiring of the brain. This revealed that gradients in the connectivity across the network, such that nodes share more properties with neighboring nodes than distant nodes, combined with random differences in the strength of inter-node connections, are general motifs that give rise to such separated activity patterns. Intriguingly, such gradients and randomness are both common features of biological systems. DOI: http://dx.doi.org/10.7554/eLife.01239.002