### Abstract

An analytical method is outlined for calculating the passive voltage transient at each point in an extensively branched neuron model, for arbitrary current injection at a single branch. The method is based on a convolution formula that employs the transient response function, the voltage response to an instantaneous pulse of current. For branching that satisfies Rall's equivalent cylinder constraint, the response function is determined explicitly. Voltage transients for a brief current injected at a branch terminal, are evaluated at several locations to illustrate the attenuation and delay characteristics of passive spread. A comparison with the same transient input applied to the soma shows that the ratio voltage peaks at 2 different input sites is, in general, not equal to the ratio of the input resistances. Also for a branch terminal input, the fraction of input charge dissipated by various branches in the neuron model is illustrated. These fractions are independent of the input time course. For transient synaptic conductance change at a single branch terminal, a numerical example demonstrates the nonlinear effect of reduced synaptic driving potential. The branch terminal synaptic input is compared with the same synaptic conductance input applied to the soma, on the basis of excitatory postsynaptic potential amplitude at the soma and charge delivered to the soma.

Original language | English (US) |
---|---|

Pages (from-to) | 1350-1356 |

Number of pages | 7 |

Journal | Federation Proceedings |

Volume | 34 |

Issue number | 5 |

State | Published - 1975 |

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### ASJC Scopus subject areas

- Medicine(all)

### Cite this

*Federation Proceedings*,

*34*(5), 1350-1356.

**Voltage transients in neuronal dendritic trees.** / Rinzel, J.

Research output: Contribution to journal › Article

*Federation Proceedings*, vol. 34, no. 5, pp. 1350-1356.

}

TY - JOUR

T1 - Voltage transients in neuronal dendritic trees

AU - Rinzel, J.

PY - 1975

Y1 - 1975

N2 - An analytical method is outlined for calculating the passive voltage transient at each point in an extensively branched neuron model, for arbitrary current injection at a single branch. The method is based on a convolution formula that employs the transient response function, the voltage response to an instantaneous pulse of current. For branching that satisfies Rall's equivalent cylinder constraint, the response function is determined explicitly. Voltage transients for a brief current injected at a branch terminal, are evaluated at several locations to illustrate the attenuation and delay characteristics of passive spread. A comparison with the same transient input applied to the soma shows that the ratio voltage peaks at 2 different input sites is, in general, not equal to the ratio of the input resistances. Also for a branch terminal input, the fraction of input charge dissipated by various branches in the neuron model is illustrated. These fractions are independent of the input time course. For transient synaptic conductance change at a single branch terminal, a numerical example demonstrates the nonlinear effect of reduced synaptic driving potential. The branch terminal synaptic input is compared with the same synaptic conductance input applied to the soma, on the basis of excitatory postsynaptic potential amplitude at the soma and charge delivered to the soma.

AB - An analytical method is outlined for calculating the passive voltage transient at each point in an extensively branched neuron model, for arbitrary current injection at a single branch. The method is based on a convolution formula that employs the transient response function, the voltage response to an instantaneous pulse of current. For branching that satisfies Rall's equivalent cylinder constraint, the response function is determined explicitly. Voltage transients for a brief current injected at a branch terminal, are evaluated at several locations to illustrate the attenuation and delay characteristics of passive spread. A comparison with the same transient input applied to the soma shows that the ratio voltage peaks at 2 different input sites is, in general, not equal to the ratio of the input resistances. Also for a branch terminal input, the fraction of input charge dissipated by various branches in the neuron model is illustrated. These fractions are independent of the input time course. For transient synaptic conductance change at a single branch terminal, a numerical example demonstrates the nonlinear effect of reduced synaptic driving potential. The branch terminal synaptic input is compared with the same synaptic conductance input applied to the soma, on the basis of excitatory postsynaptic potential amplitude at the soma and charge delivered to the soma.

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M3 - Article

VL - 34

SP - 1350

EP - 1356

JO - Federation Proceedings

JF - Federation Proceedings

SN - 0014-9446

IS - 5

ER -