title: Granger causality network reconstruction of conductance-based integrate-and-fire neuronal systems.
abstract: 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.
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Douglas
authors.initials: D
authors.lastname: Zhou
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Yanyang
authors.initials: Y
authors.lastname: Xiao
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Yaoyu
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.
authors.forename: Zhiqin
authors.initials: Z
authors.lastname: Xu
authors.affiliation: 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.
authors.forename: David
authors.initials: D
authors.lastname: Cai
mesh_terms: D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology*; D009474:Neurons / Q000166:cytology*