TY - JOUR
T1 - Coarse-grained event tree analysis for quantifying Hodgkin-Huxley neuronal network dynamics
AU - Sun, Yi
AU - Rangan, Aaditya V.
AU - Zhou, Douglas
AU - Cai, David
N1 - Funding Information:
Acknowledgements The work was supported by NSF grants DMS-0506396, DMS-0507901, DMS-1009575 and a grant from the Swartz foundation. Y. Sun was supported by NSF Joint Institutes’ Postdoctoral Fellowship through SAMSI. D. Zhou was supported by Shanghai Pujiang Program (Grant No. 10PJ1406300) and NSFC (Grant No. 11026052). We thank two anonymous referees for helpful comments on the manuscript.
PY - 2012/2
Y1 - 2012/2
N2 - We present an event tree analysis of studying the dynamics of the Hodgkin-Huxley (HH) neuronal networks. Our study relies on a coarse-grained projection to event trees and to the event chains that comprise these trees by using a statistical collection of spatial-temporal sequences of relevant physiological observables (such as sequences of spiking multiple neurons). This projection can retain information about network dynamics that covers multiple features, swiftly and robustly. We demonstrate that for even small differences in inputs, some dynamical regimes of HH networks contain sufficiently higher order statistics as reflected in event chains within the event tree analysis. Therefore, this analysis is effective in discriminating small differences in inputs. Moreover, we use event trees to analyze the results computed from an efficient library-based numerical method proposed in our previous work, where a pre-computed high resolution data library of typical neuronal trajectories during the interval of an action potential (spike) allows us to avoid resolving the spikes in detail. In this way, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable statistical accuracy in terms of average firing rate and power spectra of voltage traces. Our numerical simulation results show that the library method is efficient in the sense that the results generated by using this numerical method with much larger time steps contain sufficiently high order statistical structure of firing events that are similar to the ones obtained using a regular HH solver. We use our event tree analysis to demonstrate these statistical similarities.
AB - We present an event tree analysis of studying the dynamics of the Hodgkin-Huxley (HH) neuronal networks. Our study relies on a coarse-grained projection to event trees and to the event chains that comprise these trees by using a statistical collection of spatial-temporal sequences of relevant physiological observables (such as sequences of spiking multiple neurons). This projection can retain information about network dynamics that covers multiple features, swiftly and robustly. We demonstrate that for even small differences in inputs, some dynamical regimes of HH networks contain sufficiently higher order statistics as reflected in event chains within the event tree analysis. Therefore, this analysis is effective in discriminating small differences in inputs. Moreover, we use event trees to analyze the results computed from an efficient library-based numerical method proposed in our previous work, where a pre-computed high resolution data library of typical neuronal trajectories during the interval of an action potential (spike) allows us to avoid resolving the spikes in detail. In this way, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable statistical accuracy in terms of average firing rate and power spectra of voltage traces. Our numerical simulation results show that the library method is efficient in the sense that the results generated by using this numerical method with much larger time steps contain sufficiently high order statistical structure of firing events that are similar to the ones obtained using a regular HH solver. We use our event tree analysis to demonstrate these statistical similarities.
KW - Event tree analysis
KW - Hodgkin-Huxley neuronal network
KW - Information transmission
KW - Library method
KW - Neuronal coding
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U2 - 10.1007/s10827-011-0339-7
DO - 10.1007/s10827-011-0339-7
M3 - Article
C2 - 21597895
AN - SCOPUS:84858794944
SN - 0929-5313
VL - 32
SP - 55
EP - 72
JO - Journal of Computational Neuroscience
JF - Journal of Computational Neuroscience
IS - 1
ER -