Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model

W. Rall, J. Rinzel

Research output: Contribution to journalArticle

Abstract

Mathematical solutions and numerical illustrations are presented for the steady state distribution of membrane potential in an extensively branched neuron model, when steady electric current is injected into only one dendritic branch. Explicit expressions are obtained for input resistance at the branch input site and for voltage attenuation from the input site to the soma; expressions for AC steady state input impedance and attenuation are also presented. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. Numerical examples illustrate how branch input resistance and steady attenuation depend upon the following: the number of dendritic trees, the orders of dendritic branching, the electronic length of the dendritic trees, the location of the dendritic input site, and the input resistance at the soma. The application to cat spinal motoneurons, and to other neuron types, is discussed. The effect of a large dendritic input resistance upon the amount of local membrane depolarization at the synaptic site, and upon the amount of depolarization reaching the soma, is illustrated and discussed; simple proportionality with input resistance does not hold, in general. Also, branch input resistance is shown to exceed the input resistance at the soma by an amount that is always less than the sum of core resistances along the path from the input site to the soma.

Original languageEnglish (US)
Pages (from-to)648-688
Number of pages41
JournalBiophysical Journal
Volume13
Issue number7
StatePublished - 1973

Fingerprint

Carisoprodol
Neurons
Membranes
Motor Neurons
Electric Impedance
Membrane Potentials
Cats
Theoretical Models

ASJC Scopus subject areas

  • Biophysics

Cite this

Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. / Rall, W.; Rinzel, J.

In: Biophysical Journal, Vol. 13, No. 7, 1973, p. 648-688.

Research output: Contribution to journalArticle

@article{48c31cf811064c899563d1e58b9f0692,
title = "Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model",
abstract = "Mathematical solutions and numerical illustrations are presented for the steady state distribution of membrane potential in an extensively branched neuron model, when steady electric current is injected into only one dendritic branch. Explicit expressions are obtained for input resistance at the branch input site and for voltage attenuation from the input site to the soma; expressions for AC steady state input impedance and attenuation are also presented. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. Numerical examples illustrate how branch input resistance and steady attenuation depend upon the following: the number of dendritic trees, the orders of dendritic branching, the electronic length of the dendritic trees, the location of the dendritic input site, and the input resistance at the soma. The application to cat spinal motoneurons, and to other neuron types, is discussed. The effect of a large dendritic input resistance upon the amount of local membrane depolarization at the synaptic site, and upon the amount of depolarization reaching the soma, is illustrated and discussed; simple proportionality with input resistance does not hold, in general. Also, branch input resistance is shown to exceed the input resistance at the soma by an amount that is always less than the sum of core resistances along the path from the input site to the soma.",
author = "W. Rall and J. Rinzel",
year = "1973",
language = "English (US)",
volume = "13",
pages = "648--688",
journal = "Biophysical Journal",
issn = "0006-3495",
publisher = "Biophysical Society",
number = "7",

}

TY - JOUR

T1 - Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model

AU - Rall, W.

AU - Rinzel, J.

PY - 1973

Y1 - 1973

N2 - Mathematical solutions and numerical illustrations are presented for the steady state distribution of membrane potential in an extensively branched neuron model, when steady electric current is injected into only one dendritic branch. Explicit expressions are obtained for input resistance at the branch input site and for voltage attenuation from the input site to the soma; expressions for AC steady state input impedance and attenuation are also presented. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. Numerical examples illustrate how branch input resistance and steady attenuation depend upon the following: the number of dendritic trees, the orders of dendritic branching, the electronic length of the dendritic trees, the location of the dendritic input site, and the input resistance at the soma. The application to cat spinal motoneurons, and to other neuron types, is discussed. The effect of a large dendritic input resistance upon the amount of local membrane depolarization at the synaptic site, and upon the amount of depolarization reaching the soma, is illustrated and discussed; simple proportionality with input resistance does not hold, in general. Also, branch input resistance is shown to exceed the input resistance at the soma by an amount that is always less than the sum of core resistances along the path from the input site to the soma.

AB - Mathematical solutions and numerical illustrations are presented for the steady state distribution of membrane potential in an extensively branched neuron model, when steady electric current is injected into only one dendritic branch. Explicit expressions are obtained for input resistance at the branch input site and for voltage attenuation from the input site to the soma; expressions for AC steady state input impedance and attenuation are also presented. The theoretical model assumes passive membrane properties and the equivalent cylinder constraint on branch diameters. Numerical examples illustrate how branch input resistance and steady attenuation depend upon the following: the number of dendritic trees, the orders of dendritic branching, the electronic length of the dendritic trees, the location of the dendritic input site, and the input resistance at the soma. The application to cat spinal motoneurons, and to other neuron types, is discussed. The effect of a large dendritic input resistance upon the amount of local membrane depolarization at the synaptic site, and upon the amount of depolarization reaching the soma, is illustrated and discussed; simple proportionality with input resistance does not hold, in general. Also, branch input resistance is shown to exceed the input resistance at the soma by an amount that is always less than the sum of core resistances along the path from the input site to the soma.

UR - http://www.scopus.com/inward/record.url?scp=0015788083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0015788083&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 648

EP - 688

JO - Biophysical Journal

JF - Biophysical Journal

SN - 0006-3495

IS - 7

ER -