Original Paper

Biological Cybernetics

, Volume 97, Issue 2, pp 137-149

First online:

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

  • S. CoombesAffiliated withDepartment of Mathematical Sciences, University of Nottingham Email author 
  • , Y. TimofeevaAffiliated withDepartment of Mathematical Sciences, University of Nottingham
  • , C. -M. SvenssonAffiliated withDepartment of Mathematical Sciences, University of Nottingham
  • , G. J. LordAffiliated withDepartment of Mathematics, Heriot-Watt University
  • , K. JosićAffiliated withDepartment of Mathematics, University of Houston
  • , S. J. CoxAffiliated withComputational and Applied Mathematics, Rice University
  • , C. M. ColbertAffiliated withBiology and Biochemistry, University of Houston

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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 I h current contributes to a voltage overshoot at the soma.


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