Biological Cybernetics

, Volume 97, Issue 2, pp 137–149

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


    • Department of Mathematical SciencesUniversity of Nottingham
  • Y. Timofeeva
    • Department of Mathematical SciencesUniversity of Nottingham
  • C. -M. Svensson
    • Department of Mathematical SciencesUniversity of Nottingham
  • G. J. Lord
    • Department of MathematicsHeriot-Watt University
  • K. Josić
    • Department of MathematicsUniversity of Houston
  • S. J. Cox
    • Computational and Applied MathematicsRice University
  • C. M. Colbert
    • Biology and BiochemistryUniversity of Houston
Original Paper

DOI: 10.1007/s00422-007-0161-5

Cite this article as:
Coombes, S., Timofeeva, Y., Svensson, C.-. et al. Biol Cybern (2007) 97: 137. doi:10.1007/s00422-007-0161-5


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.


DendritesQuasi-active membrane“Sum-over-trips”Cable theory

Copyright information

© Springer-Verlag 2007