Transient response in a dendritic neuron model for current injected at one branch

J. Rinzel, W. Rall

Research output: Contribution to journalArticle

Abstract

Mathematical expressions are obtained for the response function corresponding to an instantaneous pulse of current injected to a single dendritic branch in a branched dendritic neuron model. The theoretical model aasumes passive membrane properties and the equivalent cylinder constraint on branch diameters. The response function when used in a convolution formula enables one to compute the voltage transient at any specified point in the dendritic tree for an arbitary current injection at a given input location. A particular numerical example, for a brief current injection at a branch terminal, illustrates the attenuation and delay characteristics of the depolarization peak as it spreads throughout the neuron model. In contrast to the severe attenuation of voltage transients from branch input sites to the soma, the fraction of total input charge actually delivered to the soma and other trees is calculated to be about one half. This fraction is independent of the input time course. Other numerical examples, which compare a branch terminal input site with a soma input site, demonstrate that, for a given transient current injection, the peak depolarization is not proportional to the input resistance at the injection site and, for a given synaptic conductance transient, the effective synaptic driving potential can be significantly reduced, resulting in less synaptic current flow and charge, for a branch input site. Also, for the synaptic case, the 2 inputs are compared on the basis of excitatory postsynaptic potential seen at the soma and the total charge delivered to the soma.

Original languageEnglish (US)
Pages (from-to)759-790
Number of pages32
JournalBiophysical Journal
Volume14
Issue number10
StatePublished - 1974

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Carisoprodol
Neurons
Injections
Synaptic Potentials
Excitatory Postsynaptic Potentials
Theoretical Models
Membranes

ASJC Scopus subject areas

  • Biophysics

Cite this

Transient response in a dendritic neuron model for current injected at one branch. / Rinzel, J.; Rall, W.

In: Biophysical Journal, Vol. 14, No. 10, 1974, p. 759-790.

Research output: Contribution to journalArticle

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