Skip to main content
SpringerLink
Log in

Compartmental-model response function for dendritic trees

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

The membrane-potential response function of a dendritic tree is constructed using a compartmental model. It is shown that if certain conditions are imposed on the compartments at branching nodes and terminals of an arbitrary tree, then the response function has a simple matrix solution that may be evaluated explicitly. Moreover, it reduces to the corresponding path-integral expression of cable theory in the continuum limit. The response function in the presence of synaptic inputs with shunting is also constructed. The compartmental approach presented here provides a particularly simple method for exploring the effects of complex geometries on spatio-temporal pattern processing in neurons.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abbott LF, Farhi E, Gutmann S (1991) The path integral for dendritic trees. Biol Cybern 66:61–70

    Google Scholar 

  • Bressloff PC, Taylor JG (1991) Discrete time leaky-integrator networks with synaptic noise. Neural Networks 4:789–801

    Google Scholar 

  • Bressloff PC, Taylor JG (1993) Spatio-temporal pattern processing in a compartmental model neuron. Phys Rev E 47:2899–2910

    Google Scholar 

  • Grimmett G, Stirzaker D (1982) Probability and random processes. Clarendon Press, Oxford

    Google Scholar 

  • Koch C, Segev I (1989) Methods in neural modeling. MIT Press, Cambridge, Mass

    Google Scholar 

  • Perkel DH, Mulloney B, Budelli RW (1981) Quantitative methods for predicting neuronal behaviour. Neuroscience 6:823–837

    Google Scholar 

  • Rall W (1959) Branching dendritic trees and motoneuron membrane resistivity. Exp Neurol 2:503–532

    Google Scholar 

  • Rall W (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: Reiss RF (eds) Neural theory and modeling. Stanford University Press, Stanford, pp 73–97

    Google Scholar 

  • Shepherd GM (1992) The synaptic organisation of the brain. Oxford University Press, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University of Technology, LE11 3TU, Loughborough, Leicestershire, UK

    Paul C. Bressloff

  2. Department of Mathematics, King's College, Strand, WC2R 2LS, London, UK

    John G. Taylor

Authors
  1. Paul C. Bressloff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John G. Taylor
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bressloff, P.C., Taylor, J.G. Compartmental-model response function for dendritic trees. Biol. Cybern. 70, 199–207 (1993). https://doi.org/10.1007/BF00200833

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00200833

Keywords

Search

Navigation