TY - JOUR
T1 - A coarse-graining framework for spiking neuronal networks
T2 - from strongly-coupled conductance-based integrate-and-fire neurons to augmented systems of ODEs
AU - Zhang, Jiwei
AU - Shao, Yuxiu
AU - Rangan, Aaditya V.
AU - Tao, Louis
N1 - Funding Information:
ural 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.).
Funding Information:
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.).
Funding Information:
Acknowledgments This work was partially supported by the Nat-
Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/4/15
Y1 - 2019/4/15
N2 - 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.
AB - 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.
KW - Coarse-graining method
KW - Homogeneity
KW - Maximum entropy principle
KW - Multiple firing events
KW - Partitioned-ensemble-average
KW - Spiking neurons
KW - Synchrony
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U2 - 10.1007/s10827-019-00712-w
DO - 10.1007/s10827-019-00712-w
M3 - Article
C2 - 30788694
AN - SCOPUS:85061930801
SN - 0929-5313
VL - 46
SP - 211
EP - 232
JO - Journal of Computational Neuroscience
JF - Journal of Computational Neuroscience
IS - 2
ER -