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Journal of Computational Neuroscience

, Volume 46, Issue 2, pp 211–232 | Cite as

A coarse-graining framework for spiking neuronal networks: from strongly-coupled conductance-based integrate-and-fire neurons to augmented systems of ODEs

  • Jiwei Zhang
  • Yuxiu Shao
  • Aaditya V. Rangan
  • Louis TaoEmail author
Article
  • 129 Downloads

Abstract

Homogeneously structured, fluctuation-driven networks of spiking neurons can exhibit a wide variety of dynamical behaviors, ranging from homogeneity to synchrony. We extend our partitioned-ensemble average (PEA) formalism proposed in Zhang et al. (Journal of Computational Neuroscience, 37(1), 81–104, 2014a) to systematically coarse grain the heterogeneous dynamics of strongly coupled, conductance-based integrate-and-fire neuronal networks. The population dynamics models derived here successfully capture the so-called multiple-firing events (MFEs), which emerge naturally in fluctuation-driven networks of strongly coupled neurons. Although these MFEs likely play a crucial role in the generation of the neuronal avalanches observed in vitro and in vivo, the mechanisms underlying these MFEs cannot easily be understood using standard population dynamic models. Using our PEA formalism, we systematically generate a sequence of model reductions, going from Master equations, to Fokker-Planck equations, and finally, to an augmented system of ordinary differential equations. Furthermore, we show that these reductions can faithfully describe the heterogeneous dynamic regimes underlying the generation of MFEs in strongly coupled conductance-based integrate-and-fire neuronal networks.

Keywords

Spiking neurons Synchrony Homogeneity Multiple firing events Partitioned-ensemble-average Maximum entropy principle Coarse-graining method 

Notes

Acknowledgments

This work was partially supported by the Natural Science Foundation of China through grants 11771035 (J.Z.), 91430216 (J.Z.), U1530401 (J.Z.), 31771147 (Y.S., L.T.) and 91232715 (L.T.), by the Open Research Fund of the State Key Laboratory of Cognitive Neuroscience and Learning grant CNLZD1404 (Y.S., L.T.), and by the Beijing Municipal Science andTechnology Commission under contract Z151100000915070 (Y.S., L.T.).

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina
  2. 2.Hubei Key Laboratory of Computational ScienceWuhan UniversityWuhanChina
  3. 3.Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life SciencesPeking UniversityBeijingChina
  4. 4.Center for Quantitative BiologyPeking UniversityBeijingChina
  5. 5.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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