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Biological Cybernetics

, Volume 107, Issue 6, pp 685–694 | Cite as

The Green’s function formalism as a bridge between single- and multi-compartmental modeling

  • Willem A. M. WyboEmail author
  • Klaus M. Stiefel
  • Benjamin Torben-Nielsen
Original Paper

Abstract

Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input location and the location of spike generation in the axon initial segment. However, many application such as simulations of brain networks use point-neurons—neurons without a morphological component—as computational units to keep the conceptual complexity and computational costs low. Inevitably, these applications thus omit a fundamental property of neuronal computation. In this work, we present an approach to model an artificial synapse that mimics dendritic processing without the need to explicitly simulate dendritic dynamics. The model synapse employs an analytic solution for the cable equation to compute the neuron’s membrane potential following dendritic inputs. Green’s function formalism is used to derive the closed version of the cable equation. We show that by using this synapse model, point-neurons can achieve results that were previously limited to the realms of multi-compartmental models. Moreover, a computational advantage is achieved when only a small number of simulated synapses impinge on a morphologically elaborate neuron. Opportunities and limitations are discussed.

Keywords

Morphological simplification Cable theory Interacting synapses Green’s function formalism  Transfer functions 

Notes

Acknowledgments

We thank Marc-Oliver Gewaltig for comments on the manuscript and Moritz Deger for helpful discussion. This work was supported by the BrainScaleS EU FET-proactive FP7 grant.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Willem A. M. Wybo
    • 1
    Email author
  • Klaus M. Stiefel
    • 2
  • Benjamin Torben-Nielsen
    • 1
  1. 1.Blue Brain Project, Brain Mind InstituteEPFLLausanneSwitzerland
  2. 2.MARCS InstituteUniversity of Western SydneySydneyAustralia

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