Biological Cybernetics

, Volume 97, Issue 2, pp 137–149 | Cite as

Branching dendrites with resonant membrane: a “sum-over-trips” approach

  • S. Coombes
  • Y. Timofeeva
  • C. -M. Svensson
  • G. J. Lord
  • K. Josić
  • S. J. Cox
  • C. M. Colbert
Original Paper


Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dendrites. Another important contribution to the response characteristics of a single neuron comes from the intrinsic resonant properties of dendritic membrane. In this paper we combine the effects of dendritic branching and resonant membrane dynamics by generalising the “sum-over-trips” approach (Abbott et al. in Biol Cybernetics 66, 49–60 1991). To illustrate how this formalism can shed light on the role of architecture and resonances in determining neuronal output we consider dual recording and reconstruction data from a rat CA1 hippocampal pyramidal cell. Specifically we explore the way in which an Ih current contributes to a voltage overshoot at the soma.


Dendrites Quasi-active membrane “Sum-over-trips” Cable theory 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • S. Coombes
    • 1
  • Y. Timofeeva
    • 1
  • C. -M. Svensson
    • 1
  • G. J. Lord
    • 2
  • K. Josić
    • 3
  • S. J. Cox
    • 4
  • C. M. Colbert
    • 5
  1. 1.Department of Mathematical SciencesUniversity of NottinghamNottinghamUK
  2. 2.Department of MathematicsHeriot-Watt UniversityEdinburghUK
  3. 3.Department of MathematicsUniversity of HoustonHoustonUSA
  4. 4.Computational and Applied MathematicsRice UniversityHoustonUSA
  5. 5.Biology and BiochemistryUniversity of HoustonHoustonUSA

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