Zhou Douglas, Xiao Yanyang, Zhang Yaoyu, Xu Zhiqin, Cai David
Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China ; Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York, United States of America ; NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.
PLoS One. 2014 Feb 19;9(2):e87636. doi: 10.1371/journal.pone.0087636. eCollection 2014.
Reconstruction of anatomical connectivity from measured dynamical activities of coupled neurons is one of the fundamental issues in the understanding of structure-function relationship of neuronal circuitry. Many approaches have been developed to address this issue based on either electrical or metabolic data observed in experiment. The Granger causality (GC) analysis remains one of the major approaches to explore the dynamical causal connectivity among individual neurons or neuronal populations. However, it is yet to be clarified how such causal connectivity, i.e., the GC connectivity, can be mapped to the underlying anatomical connectivity in neuronal networks. We perform the GC analysis on the conductance-based integrate-and-fire (I&F) neuronal networks to obtain their causal connectivity. Through numerical experiments, we find that the underlying synaptic connectivity amongst individual neurons or subnetworks, can be successfully reconstructed by the GC connectivity constructed from voltage time series. Furthermore, this reconstruction is insensitive to dynamical regimes and can be achieved without perturbing systems and prior knowledge of neuronal model parameters. Surprisingly, the synaptic connectivity can even be reconstructed by merely knowing the raster of systems, i.e., spike timing of neurons. Using spike-triggered correlation techniques, we establish a direct mapping between the causal connectivity and the synaptic connectivity for the conductance-based I&F neuronal networks, and show the GC is quadratically related to the coupling strength. The theoretical approach we develop here may provide a framework for examining the validity of the GC analysis in other settings.
从耦合神经元的测量动态活动重建解剖连接性是理解神经元回路结构 - 功能关系的基本问题之一。基于实验中观察到的电学或代谢数据，已经开发了许多方法来解决这个问题。格兰杰因果关系（GC）分析仍然是探索单个神经元或神经元群体之间动态因果连接性的主要方法之一。然而，尚不清楚这种因果连接性，即GC连接性，如何映射到神经元网络中的潜在解剖连接性。我们对基于电导的积分发放（I&F）神经元网络进行GC分析以获得它们的因果连接性。通过数值实验，我们发现可以通过由电压时间序列构建的GC连接性成功重建单个神经元或子网络之间的潜在突触连接性。此外，这种重建对动态状态不敏感，并且可以在不干扰系统和无需神经元模型参数先验知识的情况下实现。令人惊讶的是，甚至仅通过知道系统的发放模式，即神经元的放电时间，就可以重建突触连接性。使用脉冲触发相关技术，我们为基于电导的I&F神经元网络建立了因果连接性和突触连接性之间的直接映射，并表明GC与耦合强度呈二次相关。我们在此开发的理论方法可能为检验GC分析在其他情况下的有效性提供一个框架。
